Question

How do you integrate `int ((4-x)^2)^(3/2)dx` using trigonometric substitution?

Answer 1

The answer `-[1/4*(4-x)^4]+c`

Explanation:

Show the steps

`int ((4-x)^2)^(3/2)dx=int(4-x)^(3/2*2)*dx=int(4-x)^3*dx`

`-[1/4*(4-x)^4]+c`

Note that

`((x)^n)^m=x^(n*m)`