\[\begin{equation} \begin{aligned} &\int \frac{1}{(1+\sqrt{x})^{4}} d x=\\ &\text { By Substitution }\\ &z=1+\sqrt{x}\\ &d z=\frac{1}{2 \sqrt{x}} d x\\ &\int \frac{2(z-1)}{z^{4}} d z=\\ &\int \frac{2 z-2}{z^{4}} d z=\int \frac{2 z}{z^{4}}-\int \frac{2}{z^{4}}=\\ &-z^{-2}+2 \frac{z^{-3}}{3}+c\\ &-(1+\sqrt{x})^{-2}+2 \frac{(1+\sqrt{x})^{-3}}{3}+c \end{aligned} \end{equation}\]
Tags:
integration