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Home  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus

Integrate : $\int \large\frac{\sec^2 x }{\sqrt {\tan x} }$$dx$

\[\begin {array} {1 1} (a)\;2 \sqrt {\sec x }+c \\ (b)\;2 \sec x +c \\ (c)\;2 \tan x +c \\ (d)\;2 \sqrt {\tan x }+c \end {array}\]
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1 Answer

$\tan x =t$
$\sec ^2 x. dx=dt$
$\int \large\frac{dt}{\sqrt {t}}$
=> $ 2(t)^{1/2}+c$
=> $2 \sqrt t+c$
=>$2 \sqrt {\tan x }+c $
Hence d is the correct answer.
answered Dec 19, 2013 by meena.p
 
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