Hi people!
I can't solve these ones, they're tough!
Solve
Evaluate
Thanks!
The definition of "tough" always has eluded me.
Frequent Definition: I don't know how to do it.
Occasional Definition: I can do it, but it takes too long and requires too much effort.
Pratical Definition: It can be done, but who would want to?
Reasonable Definition: I could spend a lot of time on this, using some way that I have concocted, but even if it works, there simply MUST be an easier way.
This leads me to ask two things:
1) Why have you been given these integrals? Are you REALLY expected to solve them in a closed form? Without a very specific hint, and with your missing he Integration by Parts on the second, it seems to me that the first is not reasonable. Do you have a specific hint?
2) Does one get to use numerical methods? Numbers are not evil. It's okay if that's what we have.
Here's a specific calculation in this case.
So,
The rest is routine, and the answer is
Even I'd like to take a more general case:
Let
Define
Make substitution which can be written as the integral becomes
Define another substitution according to
--
As for the first integral, set