The value of the $\smallint \,\,\frac{{\sin \,\,x\,\, + \,\,\cos \,\,x}}{{3\,\, + \,\,\sin \,\,2x}}\,\,dx$ is

$\frac{1}{2}\,\,\log \,\,\left( {\frac{{2\,\, + \,\,\sin \,\,x}}{{2\,\, - \,\,\sin \,\,x}}} \right) + c$

$\frac{1}{4}\,\,\log \,\,\left( {\frac{{1\,\, + \,\,\sin \,\,x}}{{1\,\, - \,\,\sin \,\,x}}} \right) + c$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

The value of the

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

View answer and explanation

Correct option: A

\frac{1}{4}\,\,\log \,\,\left( {\frac{{2 - \sin \,\,x\,\, + \,\,\cos \,\,x}}{{2 + \sin \,\,x\,\, - \,\,\cos \,\,x}}} \right) + c

Option A (

\frac{1}{4}\log \left( {\frac{{2 - \sin \\,x\\, + \\,\cos \\,x}}{{2 + \sin \\,x\\, - \\,\cos \\,x}}} \right) + c

) is correct because it is the result of the integration after a suitable substitution.