Symbolic math integrals not solving at all

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Florian Rössing 2021-4-30

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评论： Taw Tha 2023-4-24

采纳的回答： Tanmay Das

在 MATLAB Online 中打开

Hi all, I am playing around with functions and the symbolic math toolbox.

I want to calculate an integral of a difficult function:

syms t t0 tau x;
syms l(t,t0,tau);
l(t,t0,tau)= exp(-1/2*exp(-(t-t0)/tau));
syms f(t,t0,tau);
f(t,t0,tau)= exp(-1/2*((t-t0)/tau));
syms p(t,t0,tau);
p(t,t0,tau)=l(t,t0,tau)*f(t,t0,tau);

It can not integrate p directly, which is not that difficult, wolfram alpha does is. But anyhow, I'll help a little and do the substitution:

p=tau*subs(p,(t-t0)/tau,x)
int(p,x,-inf,inf)

But it still just comes up with nothing. It just puts out a formated version of my input instead of calculating the integral.

The answer should be

sqrt(2*pi)*tau

Did I use the toolbox wrong or is it just not that powerfull?

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Florian Rössing 2021-4-30

Thanks for your reply.

Actually it does not matter if you integrate with respect to t or t-t0, t0 just shifts the function along the t axis, but has no influence on the shape. The integral is independent of t0. In the first integral I want it to integrate by t.

However, the second integral clearly states to integrate by x, which still doesnt work.

Walter Roberson 2021-7-29

When I take the expression over to Maple and convert the exp() into sinh cosh, then Maple is able to integrate the system. However, I do not seem to be able to do the same thing for MATLAB.

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采纳的回答

Tanmay Das 2021-7-29

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Your function has no obvious closed form integral. You need to switch to numeric integration, such as with integral() or vpaintegral() which will require you to have a numeric value for x. Similar question has already been answered here:

My int function is returning the function back instead of an integral - MATLAB Answers - MATLAB Central (mathworks.com)

Also, the same is mentioned in the Tips Section of the int documentation:

Definite and indefinite integrals - MATLAB int (mathworks.com)

You can go through the documentations on integral and vpaintegral to try integrate the same function:

Numerical integration - MATLAB integral (mathworks.com)

Numerical integration using variable precision - MATLAB vpaintegral (mathworks.com)

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Paul 2022-4-27

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Nope. Also doesn't work anymore in 2021B.

However, that code yields the closed form solution in 2020B.

In 2021B I had to change the expression for the integrand

int(simplify(expand(p(t,t0,tau),'IgnoreAnalyticConstraints',true),'IgnoreAnalyticConstraints',true),t,-inf,inf,'IgnoreAnalyticConstraints',true)

to get the same integrand as in in 2020B, at least by visual comparison. But even though the integrands were the same, 2021B int() still did not yield the closed form solution.