If $\int \frac{e^x(1+\sin x) d x}{1+\cos x}=e^x f(x)+C$, then $f(x)$ is equal to

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \frac{e^x(1+\sin x) d x}{1+\cos x}=e^x f(x)+C

, then

f(x)

is equal to

View answer and explanation

Correct option: C

\tan \frac{x}{2}

Option C (

\tan \frac{x}{2}

) is correct because it is the function that satisfies the given integral equation after simplification and integration.

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