Verify the formula using any method.
for .
Proof. To accomplish this, we start with a slightly different integral and (eventually) recover a formula for the integral we want,
and integrate by parts, letting
This gives us,
Now, we solve for the integral ,
How did you know that solving for x^(n-1) in the first place would lead to the solution?
I alread know why, sorry for not being more attentive.