Answer
$\int\frac{4x}{(2-5x)^2}dx=$ $\frac{8}{50-125x}$ $+\frac{4}{25}\ln|2-5x|+c $
Work Step by Step
$\int\frac{4x}{(2-5x)^2}dx=4$$\int\frac{x}{(2-5x)^2}dx$
$Let$ $u=x$ $,$ $du=dx$ $, $ $b=-5$ $,$ $a=2$
$\int\frac{4x}{(2-5x)^2}dx$$=4$ $\int\frac{u}{(a+bu)^2}du$
$=$ $\frac{4}{b^2}$ $(\frac{a}{a+bu}+\ln|a+bu|)+c $
$=$ $\frac{4}{25}$ $(\frac{2}{2-5x}+\ln|2-5x|)+c $
$=\frac{8}{50-125x}$ $+\frac{4}{25}\ln|2-5x|+c $
