$\int \frac{d x}{(2 x+1)(1+\sqrt{(2 x+1)}}$ is equal to :
Answer & explanation
Correct answer: option 2
$I=\int \frac{d x}{(2 x+1)(1+\sqrt{(2 x+1)}}$
so let $y=\sqrt{2x+1}$
$dy=\frac{1}{\sqrt{2x+1}}dx$
$⇒I=\int\frac{dy}{y(1+y)}=\int\frac{1}{y}-\frac{1}{1+y}dy$
$=\log y-\log 1+y+C$
$=\log\frac{y}{1+y}+C=\log\frac{\sqrt{2x+1}}{1+\sqrt{2x+1}}+C$