Question

How do you integrate `int (x^2(x^3 + 1)^3)dx`?

Answer 1

If we expand the product `x^2*(x^3+1)^3` we get

`x^11+3x^8+3x^5+x^2`

hence we have that

`int x^2(x^3+1)^3dx=int (x^11+3x^8+3x^5+x^2)dx=x^12/12+3*x^9/9+3*x^6/6+x^3/3=x^12/12+x^9/3+x^6/2+x^3/3+c`