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 ,

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.