calculus - Integral of $4x(1+x)^{-5}$ without partial fractions

The question is asking me to do $\int_{0}^{\infty}{4x\over(1+x)^5}dx$

My question is, is there any way to do this without partial fractions. If there is a formula for equations of this type, I will gladly memorize it, I just don't think I'll have time to partial fraction expand a question like this on the P exam.

Answer

Let $u=1+x,$ then $du=dx$ and so your integral is now

$$\int_{u=1}^{\infty}4(u-1)u^{-5}du=4\int_{1}^{\infty}(u^{-4}-u^{-5})du=\frac{1}{3}$$