Question

How do you find the integral of `(x^3)((x^2 + 4)^(1/2)) dx`?

Answer 1

Let `u=x^2+4`.

Explanation:

`int x^3(x^2 + 4)^(1/2) dx = intx^2(x^2+4)^(1/2)xdx`

Let `u=x^2+4`, so that `du=2xdx` and `x^2=u-4`.

After substitution, the integral becomes:

`1/2 int (u-4)u^(1/2)du`

Distribute the `u^(1/2)` and finish the integral.