Question

How solve it ? PLEASE use Integration by Change of Variable U Substitution

Answer 1

Let `u = x^3-3x+16` (the argument of the radical).

Explanation:

Then `du = (3x^2-3)dx = 3(x^2-1)dx`

`int (x^2-1)/root(3)(x^3-3x+16) dx = 1/3 int (x^3-3x+16)^(-1/3) * 3(x^2-1)dx`

`= 1/3 int u^(-1/3) du = 1/3(3/2 u^(2/3))+C`

`=1/2 root(3)((x^3-3x+16)^2) + C`