How to integrate (1+sqrt(x))^4

 

$$\begin{array}{rl}& \int \frac{1}{(1+\sqrt{x}{)}^4}dx=\\ & \text{ By Substitution }\\ & z=1+\sqrt{x}\\ & dz=\frac{1}{2\sqrt{x}}dx\\ & \int \frac{2(z-1)}{z^4}dz=\\ & \int \frac{2z-2}{z^4}dz=\int \frac{2z}{z^4}-\int \frac{2}{z^4}=\\ & -z^{-2}+2\frac{z^{-3}}{3}+c\\ & -(1+\sqrt{x}{)}^{-2}+2\frac{(1+\sqrt{x}{)}^{-3}}{3}+c\end{array}$$