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

Integrate : $\int \large\frac{\sec^4 x }{\sqrt {\tan x}}$$dx$

$(a)\;2 \sqrt {\tan x}+\frac{2}{5}(\tan x )^{5/2} +c \qquad(b)\;2 {\tan x}+\frac{2}{5}(\tan x )^{5/2} +c \qquad(c)\;2 \sqrt {\tan x}+\frac{2}{5}(\tan x )^{3/2} +c \qquad (d)\;2 \sqrt {\tan x}+\frac{2}{5}(\tan x )^{7/2} +c$

1 Answer

$\tan x =t$
$\sec^2 x dx =dt$
$\qquad= \int \large\frac{(1+t^2)}{\sqrt t}$$.dt$
$\qquad= \int t^{-1/2}+t^{3/2} dt$
$\qquad= 2 \sqrt t +\large\frac{2}{5} t^{5/2} +c$
$2 \sqrt {\tan x}+\frac{2}{5}(\tan x )^{5/2} +c$
Hence a is the correct answer.
answered Dec 24, 2013 by meena.p
 
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