# Integrate : $\int \large\frac{\tan^2 (\sqrt x)}{\sqrt x}$$.dx $\begin {array} {1 1} (a)\;2(\sqrt x +\tan^{-1} \sqrt x)+c \\ (b)\;2(\sqrt x -\tan^{-1} \sqrt x)+c \\ (c)\;2(-\sqrt {x}+\tan ^{-1}(\sqrt x)]+c \\ (d)\;None \end {array}$ ## 1 Answer \sqrt x =t => \large\frac{-1}{2}$$(x)^{-1/2}.dx=dt$
$\qquad= -2 dt$
$\qquad= (-2) \int \tan ^2 (t) .dt$
$\qquad= (-2) \int (\sec^2 t-1).dt$
=> $-2. \tan t +2t +c$
=> $-2 \tan \sqrt x+ 2 \sqrt x +c$
=> $2 (\sqrt x - \tan x )+c$
Hence b is the correct answer.