Question

How do you use substitution to integrate `x^3sqrt(x-3)`?

Answer 1

See the explanation.

Explanation:

Let `u = x-3` so `du=dx` and `x = u+3`

Then `intx^3sqrt(x-3) dx = int (u+3)^3u^(1/2) du`

Now expand `(u+3)^3`, distribute `u^(1/2)` and finish by integrating term by term.