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

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)=

View answer and explanation

Correct option: C

\tan \frac{x}{2}

Option C (

\tan \frac{x}{2}

) is correct because when the integral is simplified, the function f(x) is identified as

\tan \frac{x}{2}

based on the form

\int e^x[f(x) + f'(x)] dx = e^x f(x) + c

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{C}

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