Question

How do you integrate `int (x^3-x^2)/ (x+3)^4` using partial fractions?

Answer 1

`ln|x+3| +10/(x+3)-33/(2(x+3)^2)+12/(x+3)^3+c`

Explanation:

Let `u=x+3`, `(du)/(dx)=1`.
`int((u-3)^3-(u-3)^2)/u^4 du`
`=int(u^3-10u^2+33u-36)/u^4du`
`=int u^-1-10u^-2+33u^-3-36u^-4dx`
`=ln|u|+10/u-33/(2u^2)+12/u^3+c`