Question

How do you integrate `f(x)=(2-3x-x^2+x^3)(-1+2x^2+3x^3)` using the product rule?

Answer 1

There is no product rule for integrating.

Explanation:

We'll need to expand the product to integrate.

`int (2-3x-x^2+x^3)(-1+2x^2+3x^3) dx = int (3x^6-x^5-11x^4-x^3+5x^2+3x-2) dx`

`= 3/7x^7-1/6x^6-11/5x^5-1/4x^4+5/3x^3+3/2x^2-2x+C`