Question

`int(x^3/(x + 2))` equals ??

Answer 1

`x^3/3-x^2+4x-8ln|x+2|+C`

Explanation:

We can divide out the integrand using

`x^3/(x+2) = (x^3+2^3-2^3)/(x+2) = x^2-2x+4-2^3/(x+2)`

Thus

`int x^3/(x+2)dx = int\ [x^2-2x+4-8/(x+2)]dx`
`qquad qquad qquad qquad quad = x^3/3-x^2+4x-8ln|x+2|+C`