What is an example of an integral that CANNOT be done without contour integration ? If that exist.

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What is an example of an indefinite integral that CANNOT be done without contour integration ? If that exist.

Im talking about closed forms for integrals, not numerical methods.

Note that there are many tricks to do an integral. As a reference to some less common techniques, I give a link

http://ocw.mit.edu/courses/mathematics/18-304-undergraduate-seminar-in-discrete-mathematics-spring-2006/projects/integratnfeynman.pdf

Note however that this link talks about definite integrals mainly, where my question is about indefinite integrals.