$\smallint \frac{1}{{1\,\, + \,\,\cos \,\,x\,\, + \,\,\sin \,\,x}}\;dx$ is equal to

$\frac{1}{2}\,\,\log \,\,\left| {\,1 + \tan \,\,\frac{x}{2}\,} \right| + c$

$2\,\,\log \,\,\left| {\,1 + \tan \,\,\frac{x}{2}\,} \right| + c$

$\frac{1}{2}\,\,\log \,\,\left| {\,1 - \tan \,\,\frac{x}{2}\,} \right| + c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \frac{1}{{1\,\, + \,\,\cos \,\,x\,\, + \,\,\sin \,\,x}}\;dx

is equal to

View answer and explanation

Correct option: A

\log \,\,\left| {\,1 + \tan \,\,\frac{x}{2}\,} \right| + c

Option A (

\log \,\,\left| {\,1 + \tan \,\,\frac{x}{2}\} \right| + c

) is correct because it is the result of substituting

t = \tan \frac{x}{2}

and integrating the simplified expression.