I got a nice "Alternative Method" from the comments
5:17
Every integral I see has a sine in it
13:47
Hardy's Integral
12:13
Feynman's technique is the greatest integration method of all time
20:37
Integrate x^-x dx
8:42
The Intuition behind Hilbert Spaces and Fourier Series
11:18
So much TRIG!!!
17:39
the integral that Feynman('s trick) couldn't solve
22:40