$\smallint \,\,\frac{{dx}}{{{{\cos }^3}\,\,\sqrt {2\,\,\sin \,\,2x} }}$ is equal to

$\sqrt {\tan \,\,x} \,\,\, + \,\,\frac{2}{5}\,\,{\tan ^{5/2}}x\,\, + \,\,c$

$2\,\sqrt {\tan \,\,x} \,\, + \,\,\frac{2}{5}\,\,{\tan ^{5/2}}x\,\, + \,\,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Analyzing +4 | -1

\int \,\,\frac{{dx}}{{{{\cos }^3}\,\,\sqrt {2\,\,\sin \,\,2x} }}

is equal to

View answer and explanation

Correct option: A

\sqrt {\tan \,\,x} \,\,\, + \,\,\frac{{{{\tan }^{5/2}}x}}{5}\,\, + \,\,c

Option A (

\sqrt {\tan \\,\\,x} \\,\\,\\ + \\,\frac{{{{\tan }^{5/2}}x}}{5}\\,\\ + \\,\\,c

) is correct because it is the result of the integration after appropriate trigonometric manipulation and substitution.