Verify the formula using any method.
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 ,
Integrands are all continuous, so it may be more straightforward to just use that any indefinite integral of a continuous f is also a primitive of f (page 211).
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.