Question

How do you find the indefinite integral of `int (x^2+1)^3dx`?

Answer 1

Expand the integrand and integrate term-by-term.

Explanation:

`(x^2+1)^3 = x^6+3x^4+3x^2+1`

So

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

`= 1/7x^7+3/5x^5+x^3+x +C`