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

Published On :2021-01-27 12:06:00

[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}]