format long g
H = 1017789684612629
eps(H)
Risky, but 1017789684612629 exactly can be converted to symbolic. But it is such an arbitrary number, that we have to wonder whether the real value is 1017789684612628.93158 (for example)
Integrating a very long expression containing symbolic values
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clc
clear all
close all
syms x y m k
A(x,y)=(10000*m^4*pi^4*sin(m*x*pi))/77 - m^3*pi^3*cos(m*x*pi)*(- (1017789684612629*((10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/27 - (200*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/81 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27)^3*(- (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2)/27 - (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 13/20)^2)/27 - (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(2*x - 13/10))/27 + (2000*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/243 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/81 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/81 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)^2*(x - 7/20)^2*(x - 13/20)^2)/27 + (4000*pi^2*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/243 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*((200*x)/9 - 100/9)*(x - 13/20)^2)/27 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*((200*x)/9 - 100/9)*(x - 7/20)^2)/27 - (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/81))/(1099511627776*(((10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 13/10)*(x - 7/20)^2)/27 - (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27 - (200*pi*sin((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(x - 7/20)^2*(x - 13/20)^2)/81)^2 + 1)^2) + (112000*((10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/27 - (200*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/81 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27)^3*(- (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2)/27 - (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 13/20)^2)/27 - (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(2*x - 13/10))/27 + (2000*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/243 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/81 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/81 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)^2*(x - 7/20)^2*(x - 13/20)^2)/27 + (4000*pi^2*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/243 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*((200*x)/9 - 100/9)*(x - 13/20)^2)/27 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*((200*x)/9 - 100/9)*(x - 7/20)^2)/27 - (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/81))/(143*(((10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 13/10)*(x - 7/20)^2)/27 - (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27 - (200*pi*sin((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(x - 7/20)^2*(x - 13/20)^2)/81)^2 + 1)^3) + (1017789684612629*((10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/27 - (200*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/81 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27)^5*(- (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2)/27 - (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 13/20)^2)/27 - (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(2*x - 13/10))/27 + (2000*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/243 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/81 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/81 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)^2*(x - 7/20)^2*(x - 13/20)^2)/27 + (4000*pi^2*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/243 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*((200*x)/9 - 100/9)*(x - 13/20)^2)/27 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*((200*x)/9 - 100/9)*(x - 7/20)^2)/27 - (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/81))/(1099511627776*(((10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 13/10)*(x - 7/20)^2)/27 - (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27 - (200*pi*sin((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(x - 7/20)^2*(x - 13/20)^2)/81)^2 + 1)^3) - (56000*((10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/27 - (200*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/81 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27)*(- (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2)/27 - (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 13/20)^2)/27 - (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(2*x - 13/10))/27 + (2000*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/243 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/81 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/81 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)^2*(x - 7/20)^2*(x - 13/20)^2)/27 + (4000*pi^2*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/243 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*((200*x)/9 - 100/9)*(x - 13/20)^2)/27 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*((200*x)/9 - 100/9)*(x - 7/20)^2)/27 - (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/81))/(143*(((10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 13/10)*(x - 7/20)^2)/27 - (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27 - (200*pi*sin((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(x - 7/20)^2*(x - 13/20)^2)/81)^2 + 1)^2) + (80000*((10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/27 - (200*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/81 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27)*(- (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2)/27 - (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 13/20)^2)/27 - (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(2*x - 13/10))/27 + (2000*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/243 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/81 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/81 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)^2*(x - 7/20)^2*(x - 13/20)^2)/27 + (4000*pi^2*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/243 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*((200*x)/9 - 100/9)*(x - 13/20)^2)/27 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*((200*x)/9 - 100/9)*(x - 7/20)^2)/27 - (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/81))/(77*(((10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 13/10)*(x - 7/20)^2)/27 - (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27 - (200*pi*sin((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(x - 7/20)^2*(x - 13/20)^2)/81)^2 + 1)^3)) - m^2*pi^2*sin(m*x*pi)*((28000*(- (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2)/27 - (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 13/20)^2)/27 - (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(2*x - 13/10))/27 + (2000*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/243 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/81 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/81 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)^2*(x - 7/20)^2*(x - 13/20)^2)/27 + (4000*pi^2*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/243 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*((200*x)/9 - 100/9)*(x - 13/20)^2)/27 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*((200*x)/9 - 100/9)*(x - 7/20)^2)/27 - (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/81)^2)/(143*(((10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 13/10)*(x - 7/20)^2)/27 - (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27 - (200*pi*sin((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(x - 7/20)^2*(x - 13/20)^2)/81)^2 + 1)^2) - (40000*(- (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2)/27 - (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 13/20)^2)/27 - (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(2*x - 13/10))/27 + (2000*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/243 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/81 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/81 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)^2*(x - 7/20)^2*(x - 13/20)^2)/27 + (4000*pi^2*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/243 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*((200*x)/9 - 100/9)*(x - 13/20)^2)/27 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*((200*x)/9 - 100/9)*(x - 7/20)^2)/27 - (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/81)^2)/(77*(((10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 13/10)*(x - 7/20)^2)/27 - (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27 - (200*pi*sin((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(x - 7/20)^2*(x - 13/20)^2)/81)^2 + 1)^3) - (1017789684612629*((10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/27 - (200*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/81 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27)^3*(- (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10))/9 - (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10))/9 + (2000*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/81 + (2000*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/81 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2)/9 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 13/20)^2)/9 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 7/20)^2)/27 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 13/20)^2)/27 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(2*x - 13/10))/27 - (40000*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/243 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*((200*x)/9 - 100/9)^2*(x - 13/20)^2)/9 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*((200*x)/9 - 100/9)^2*(x - 7/20)^2)/9 + (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)^3*(x - 7/20)^2*(x - 13/20)^2)/27 + (4000*pi^2*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/81 + (4000*pi^2*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/81 - (80000*pi^3*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/729 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(2*x - 13/10)*((200*x)/9 - 100/9))/9 - (2000*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/243 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((80000*x)/81 - 40000/81)*(x - 7/20)^2*(x - 13/20)^2)/27 - (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 7/10)*((200*x)/9 - 100/9)*(x - 13/20)^2)/27 - (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 13/10)*((200*x)/9 - 100/9)*(x - 7/20)^2)/27 - (4000*pi^2*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/81 + (200*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)^2*(x - 7/20)^2*(x - 13/20)^2)/27))/(2199023255552*(((10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 13/10)*(x - 7/20)^2)/27 - (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27 - (200*pi*sin((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(x - 7/20)^2*(x - 13/20)^2)/81)^2 + 1)^2) + (56000*((10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/27 - (200*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/81 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27)^3*(- (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10))/9 - (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10))/9 + (2000*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/81 + (2000*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/81 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2)/9 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 13/20)^2)/9 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 7/20)^2)/27 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 13/20)^2)/27 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(2*x - 13/10))/27 - (40000*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/243 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*((200*x)/9 - 100/9)^2*(x - 13/20)^2)/9 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*((200*x)/9 - 100/9)^2*(x - 7/20)^2)/9 + (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)^3*(x - 7/20)^2*(x - 13/20)^2)/27 + (4000*pi^2*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/81 + (4000*pi^2*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/81 - (80000*pi^3*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/729 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(2*x - 13/10)*((200*x)/9 - 100/9))/9 - (2000*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/243 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((80000*x)/81 - 40000/81)*(x - 7/20)^2*(x - 13/20)^2)/27 - (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 7/10)*((200*x)/9 - 100/9)*(x - 13/20)^2)/27 - (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 13/10)*((200*x)/9 - 100/9)*(x - 7/20)^2)/27 - (4000*pi^2*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/81 + (200*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)^2*(x - 7/20)^2*(x - 13/20)^2)/27))/(143*(((10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 13/10)*(x - 7/20)^2)/27 - (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27 - (200*pi*sin((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(x - 7/20)^2*(x - 13/20)^2)/81)^2 + 1)^3) + (1017789684612629*((10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/27 - (200*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/81 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27)^5*(- (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10))/9 - (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10))/9 + (2000*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/81 + (2000*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/81 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2)/9 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 13/20)^2)/9 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 7/20)^2)/27 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 13/20)^2)/27 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(2*x - 13/10))/27 - (40000*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/243 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*((200*x)/9 - 100/9)^2*(x - 13/20)^2)/9 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*((200*x)/9 - 100/9)^2*(x - 7/20)^2)/9 + (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)^3*(x - 7/20)^2*(x - 13/20)^2)/27 + (4000*pi^2*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/81 + (4000*pi^2*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/81 - (80000*pi^3*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/729 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(2*x - 13/10)*((200*x)/9 - 100/9))/9 - (2000*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/243 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((80000*x)/81 - 40000/81)*(x - 7/20)^2*(x - 13/20)^2)/27 - (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 7/10)*((200*x)/9 - 100/9)*(x - 13/20)^2)/27 - (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 13/10)*((200*x)/9 - 100/9)*(x - 7/20)^2)/27 - (4000*pi^2*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/81 + (200*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)^2*(x - 7/20)^2*(x - 13/20)^2)/27))/(2199023255552*(((10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 13/10)*(x - 7/20)^2)/27 - (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27 - (200*pi*sin((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(x - 7/20)^2*(x - 13/20)^2)/81)^2 + 1)^3) + (3053369053837887*((10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/27 - (200*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/81 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27)^2*(- (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2)/27 - (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 13/20)^2)/27 - (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(2*x - 13/10))/27 + (2000*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/243 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/81 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/81 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)^2*(x - 7/20)^2*(x - 13/20)^2)/27 + (4000*pi^2*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/243 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*((200*x)/9 - 100/9)*(x - 13/20)^2)/27 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*((200*x)/9 - 100/9)*(x - 7/20)^2)/27 - (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/81)^2)/(2199023255552*(((10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 13/10)*(x - 7/20)^2)/27 - (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27 - (200*pi*sin((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(x - 7/20)^2*(x - 13/20)^2)/81)^2 + 1)^2) - (280000*((10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/27 - (200*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/81 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27)^2*(- (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2)/27 - (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 13/20)^2)/27 - (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(2*x - 13/10))/27 + (2000*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/243 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/81 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/81 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)^2*(x - 7/20)^2*(x - 13/20)^2)/27 + (4000*pi^2*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/243 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*((200*x)/9 - 100/9)*(x - 13/20)^2)/27 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*((200*x)/9 - 100/9)*(x - 7/20)^2)/27 - (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/81)^2)/(143*(((10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 13/10)*(x - 7/20)^2)/27 - (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27 - (200*pi*sin((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(x - 7/20)^2*(x - 13/20)^2)/81)^2 + 1)^3) + (240000*((10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/27 - (200*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/81 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27)^2*(- (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2)/27 - (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 13/20)^2)/27 - (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(2*x - 13/10))/27 + (2000*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/243 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/81 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/81 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)^2*(x - 7/20)^2*(x - 13/20)^2)/27 + (4000*pi^2*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/243 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*((200*x)/9 - 100/9)*(x - 13/20)^2)/27 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*((200*x)/9 - 100/9)*(x - 7/20)^2)/27 - (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/81)^2)/(77*(((10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 13/10)*(x - 7/20)^2)/27 - (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27 - (200*pi*sin((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(x - 7/20)^2*(x - 13/20)^2)/81)^2 + 1)^4) - (9160107161513661*((10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/27 - (200*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/81 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27)^4*(- (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2)/27 - (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 13/20)^2)/27 - (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(2*x - 13/10))/27 + (2000*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/243 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/81 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/81 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)^2*(x - 7/20)^2*(x - 13/20)^2)/27 + (4000*pi^2*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/243 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*((200*x)/9 - 100/9)*(x - 13/20)^2)/27 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*((200*x)/9 - 100/9)*(x - 7/20)^2)/27 - (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/81)^2)/(2199023255552*(((10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 13/10)*(x - 7/20)^2)/27 - (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27 - (200*pi*sin((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(x - 7/20)^2*(x - 13/20)^2)/81)^2 + 1)^3) + (336000*((10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/27 - (200*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/81 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27)^4*(- (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2)/27 - (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 13/20)^2)/27 - (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(2*x - 13/10))/27 + (2000*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/243 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/81 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/81 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)^2*(x - 7/20)^2*(x - 13/20)^2)/27 + (4000*pi^2*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/243 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*((200*x)/9 - 100/9)*(x - 13/20)^2)/27 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*((200*x)/9 - 100/9)*(x - 7/20)^2)/27 - (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/81)^2)/(143*(((10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 13/10)*(x - 7/20)^2)/27 - (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27 - (200*pi*sin((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(x - 7/20)^2*(x - 13/20)^2)/81)^2 + 1)^4) + (3053369053837887*((10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/27 - (200*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/81 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27)^6*(- (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2)/27 - (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 13/20)^2)/27 - (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(2*x - 13/10))/27 + (2000*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/243 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/81 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/81 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)^2*(x - 7/20)^2*(x - 13/20)^2)/27 + (4000*pi^2*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/243 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*((200*x)/9 - 100/9)*(x - 13/20)^2)/27 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*((200*x)/9 - 100/9)*(x - 7/20)^2)/27 - (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/81)^2)/(1099511627776*(((10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 13/10)*(x - 7/20)^2)/27 - (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27 - (200*pi*sin((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(x - 7/20)^2*(x - 13/20)^2)/81)^2 + 1)^4) - (28000*((10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/27 - (200*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/81 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27)*(- (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10))/9 - (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10))/9 + (2000*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/81 + (2000*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/81 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2)/9 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 13/20)^2)/9 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 7/20)^2)/27 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 13/20)^2)/27 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(2*x - 13/10))/27 - (40000*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/243 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*((200*x)/9 - 100/9)^2*(x - 13/20)^2)/9 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*((200*x)/9 - 100/9)^2*(x - 7/20)^2)/9 + (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)^3*(x - 7/20)^2*(x - 13/20)^2)/27 + (4000*pi^2*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/81 + (4000*pi^2*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/81 - (80000*pi^3*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/729 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(2*x - 13/10)*((200*x)/9 - 100/9))/9 - (2000*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/243 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((80000*x)/81 - 40000/81)*(x - 7/20)^2*(x - 13/20)^2)/27 - (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 7/10)*((200*x)/9 - 100/9)*(x - 13/20)^2)/27 - (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 13/10)*((200*x)/9 - 100/9)*(x - 7/20)^2)/27 - (4000*pi^2*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/81 + (200*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)^2*(x - 7/20)^2*(x - 13/20)^2)/27))/(143*(((10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 13/10)*(x - 7/20)^2)/27 - (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27 - (200*pi*sin((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(x - 7/20)^2*(x - 13/20)^2)/81)^2 + 1)^2) + (40000*((10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/27 - (200*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/81 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27)*(- (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10))/9 - (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10))/9 + (2000*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/81 + (2000*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/81 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2)/9 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 13/20)^2)/9 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 7/20)^2)/27 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 13/20)^2)/27 + (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(2*x - 13/10))/27 - (40000*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/243 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*((200*x)/9 - 100/9)^2*(x - 13/20)^2)/9 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*((200*x)/9 - 100/9)^2*(x - 7/20)^2)/9 + (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)^3*(x - 7/20)^2*(x - 13/20)^2)/27 + (4000*pi^2*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(x - 13/20)^2)/81 + (4000*pi^2*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 13/10)*(x - 7/20)^2)/81 - (80000*pi^3*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(x - 7/20)^2*(x - 13/20)^2)/729 + (20*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*(2*x - 7/10)*(2*x - 13/10)*((200*x)/9 - 100/9))/9 - (2000*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/243 - (10*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((80000*x)/81 - 40000/81)*(x - 7/20)^2*(x - 13/20)^2)/27 - (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 7/10)*((200*x)/9 - 100/9)*(x - 13/20)^2)/27 - (400*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*(2*x - 13/10)*((200*x)/9 - 100/9)*(x - 7/20)^2)/27 - (4000*pi^2*exp(-(100*(x - 1/2)^2)/9)*cos((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/81 + (200*pi*exp(-(100*(x - 1/2)^2)/9)*sin((20*pi*(x - 1/2))/3)*((200*x)/9 - 100/9)^2*(x - 7/20)^2*(x - 13/20)^2)/27))/(77*(((10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 7/10)*(x - 13/20)^2)/27 + (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(2*x - 13/10)*(x - 7/20)^2)/27 - (10*cos((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*((200*x)/9 - 100/9)*(x - 7/20)^2*(x - 13/20)^2)/27 - (200*pi*sin((20*pi*(x - 1/2))/3)*exp(-(100*(x - 1/2)^2)/9)*(x - 7/20)^2*(x - 13/20)^2)/81)^2 + 1)^3));
AA(x,y)=A(x,y)*sin(k*pi*x);
integral_AA_sym = int(AA, x, 0, 1);
Unfortunately, the int command cannot take the integral. How can I integrate such an expression?
Kind regards.
回答（3 个）
John D'Errico
2025-2-22
Is there some law of mathematics that everything you can or will write down has a solution? (No.) That int did not find a solution implies this is one of those cases, though there is no simple way to prove that is impossible.
I'm sorry, but not everything you will want will prove to be possible.
What choices do you have? The presence of symbolic parameters in there prevents any numerical integration too.
Is there ANYTHING you might possibly do? One vague possibility might be to approximate this expression with some sort of Taylor series in x. If that series was convergent, then you could integrate the series. (I'm sorry, but that clearly will not happen on this expression.)
That expression is so lengthy that I cannot even look at it online, and trying to get MATLAB to manipulate at it at all seems to be, lets say, frustrating. Expressed as a character string, MATLAB counts 38450 charcters. If we wrap this into 70 character lines, I count roughly 550 lines of code. Sigh.
Worse, there are exponentials and trig functions with seriously large coefficients inside. And that will mean that literally anything you do will fail in terms of any numerical process you might try anyway.
I'd strongly recommend you step back, and try to reformulate your basic problem. Look for a different approach. This is a fundamental part of mathematics. If one approach fails, then look for another.
I'll wish you good luck, but you need to recognize what you are doing here is a dead end street.
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Walter Roberson
2025-2-22
The expression involves pi to various powers. The logic that automatically converts double precision numbers to symbolic numbers is fully able to convert "small" rational multiples of pi to rational multiples of symbolic π but the conversion algorithm does not work on double precision numbers formed by pi^N for N > 1. So the expressions such as pi^4 get replaced by rational approximations.
It would be better if instead of using pi to various powers, the user did something like
Pi = sym(pi);
and then wrote the expression in terms of Pi -- sym(pi)^N gets expressed fully symbolically.
Still, this change will not save all that much in the expression size... a few hundred characters at most.
Walter Roberson
2025-2-22
How can I integrate such an expression?
You can wait however many months it takes.
I would point out that you have not restricted y or m or k to be real-valued or integer valued or positive, so there is no way to reason about the range of sin(m*x*pi) or the like expression.
Your expression is just a large mass of symbols, and most components are unlikely to have explicit integrals. Integrating it is likely a waste of time.
The situation is potentially different if m and k are restricted to positive integers. Your y does not matter because it is not involved in the expression
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