How can I effectively use substitution to evaluate this integral?

[htoor9]

Homework Statement

Evaluate the integral.

Int((x+5)(x-5)^(1/3)dx

Homework Equations

The Attempt at a Solution

I've attempted the problem but subsitution doesn't seem to do anything, as du = dx if u = x-5, which doesn't cancel anything.

 

[quantumdude]

That's exactly the substitution you want to go with. If u=x-5 then x=u+5, which you can use in the other factor in the integrand.

 

[htoor9]

That's exactly the substitution you want to go with. If u=x-5 then x=u+5, which you can use in the other factor in the integrand.

So then what? I have integral of (u+10)(u)^(1/3) du.

 

[Char. Limit]

So then what? I have integral of (u+10)(u)^(1/3) du.

Expand the u^(1/3) into both terms. It should be easy to integrate then.