If $\smallint \,\,{e^x}\,\,\left( {\frac{{1 - \,\,\sin \,\,x}}{{1\,\, - \,\,\cos \,\,x}}} \right)\,\,dx = f\left( x \right)\,\, + \,\,{\rm{constant}}$, then $f\left( x \right)$ is equal to

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \,\,{e^x}\,\,\left( {\frac{{1 - \,\,\sin \,\,x}}{{1\,\, - \,\,\cos \,\,x}}} \right)\,\,dx = f\left( x \right)\,\, + \,\,\mathrm{constant}

, then

f\left( x \right)

is equal to

View answer and explanation

Correct option: C

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

Option C (

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

) is correct because the integral is solved by using trigonometric identities to simplify the integrand and then recognizing a pattern for integration.

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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