Integral from a function that has a singularity

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Kurt Hakan
Kurt Hakan 2017-1-29
评论： Star Strider 2017-1-29
Hello I want to take an integral from the function that has a singularity(pole), by quadgk but this common don't give a right answer .for instance an integral of the function 1/(x-1) from(-2,2) anyone can guide me thanks

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Star Strider
Star Strider 2017-1-29
The best I can do is to rely on the Symbolic Math Toolbox, that came up with a piecewise result. Perhaps you can use this in your code:
syms x L U
f(x) = 1/(x-1);
intf = int(f,x, L, U)
intf =
piecewise(L <= 1 & 1 <= U, int(1/(x - 1), x, L, U), 1 < L | U < 1, log(U - 1) - log(L - 1))
The ‘L’ and ‘U’ variables are the lower and upper limits of integration, respectively.
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Star Strider
Star Strider 2017-1-29
As always, my pleasure.
Wolfram Alpha evaluates it using the Cauchy principal value

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