Difficult definite integrals.
I'm trying to get the exact value of following definite integrals without using a CAS or tables. Any help would be appreciated:
I can get answers using the Wolframalpha website and also from a table of integrals. But I'd really like a calculus approach. I can't see what contour to use using contour integration. I can't see how to 'differentiate under the integral'. I can't see any substitution that will help. I know they can be done otherwise there would be no answer in the tables. I'm stuck.
I've seen a few members who are absolutely amazing in the sorts of integrals they have solved. Hopefully someone can help me with these ones.