$\smallint \,\,\frac{{{e^x}\left( {1 + \,\sin \,\,x} \right)}}{{1 + \cos \,\,x}}\,\,dx$ is equal to

${e^x}\,\,\left( {\frac{{1 + \sin \,\,x}}{{1 - \cos \,\,x}}} \right)\,\, + \,\,c$

$c\,\, - \,\,{e^x}\,\,\cot \left( {\frac{x}{2}} \right)$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \,\,\frac{{{e^x}\left( {1 + \,\sin \,\,x} \right)}}{{1 + \cos \,\,x}}\,\,dx

is equal to

View answer and explanation

Correct option: A

{e^x}\,\,\tan \,\,\left( {\frac{x}{2}} \right) + c

Option A is correct because the integral can be simplified and solved using the properties of exponential functions and trigonometric identities.