I occasionally found an interesting trick about integration in Quora. It worth to be recorded.

Suppose you have a definite integral to calculate: , which is really hard to do.

Why not thinking about this function: and we can differentiate with respect to p.

Then, one could get:

So, one can easily integrate to get .

Moreover, since , we can pin down $ and finally got: .

And the original integral is just:

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