Question

How do you integrate `int12x^3(3x^4+4)^4` using substitution?

Answer 1

Please see the explanation

Explanation:

Given

`int12x^3(3x^4 + 4)^4dx`

let `u = 3x^4 + 4`, then `du = 12x^3dx`

`int12x^3(3x^4 + 4)^4dx = intu^4du = (1/5)u^5 + C`

Reverse the substitution:

`int12x^3(3x^4 + 4)^4dx = (1/5)(3x^4 + 4)^5 + C`