Can I use integration method like fourier transform? How should I integral
$$ f(p)=\frac a {p^2+a^2}$$ to inverse it to $\sin(at)$ ?
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Yes, you basically apply the (inverse) Fourier transform with the axis shifted so the integral converges. But it is a lot slower than tables. – copper.hat Jan 22 '20 at 19:44
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Welcome to math SE. Have a look at mathjax to improve your mathematical expressions. – Alain Remillard Jan 22 '20 at 19:58