here has a form identical to your second integral.
It's recursive though. You'll need to write a small program to evaluate it.
For your first integral there's nothing fundamentally tricky about it. You can use binomial expansion to deal with the second term and then just multiply by the first. Each of the summands is easily integrated. Again a short program will take care of keeping track of all the terms.
There may be some super clever trick here I don't know about.