Need Calculus Help!!!?

Question

I need to come up with my own math problem.
Requirements are:
-use "ln" or "e"
-has to be with integration ( ∫)
-have three steps to it, all relating to eachother. (A) (B) (C)

So something like...

∫(e^xn + x^n) dx

So something like that but with two other parts relating to the main problem.

Sorry this is a long question but if you help your the best!!!

Answer 1

Integrate x ln (x)

It requires integration by parts.

(A) Denote u and dv and find du and v
(B) Write uv - ∫v*du
(C) Integrate vdu
(I hope you picked your u and dv wisely!)

1/(x(lnx)) could be quite interesting.