Question

How do you integrate by substitution `int x^3(x^4+3)^2 dx`?

Answer 1

Please see the explanation.

Explanation:

Let `u = x^4 + 3`, then `du = 4x^3dx` or `x^3dx = (1/4)du`

`intx^3(x^4+3)^2dx = 1/4intu^2du`

Integrate using the power rule:

`intx^3(x^4+3)^2dx = (1/12)u^3 + C`

Reverse the substitution:

`intx^3(x^4+3)^2dx = (1/12)(x^4 + 3)^3 + C`