$\smallint \,\,{e^x}\left( {\log \,\,\sin \,\,x\,\, + \,\,\cot \,\,x} \right)\,\,dx$ is equal to

${e^x}\,\,\log \,\,\sin \,\,x + \,\,\tan \,\,x + \,\,c$

${e^x} + \,\,\sin \,\,x\,\, + \,\,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \,\,{e^x}\left( {\log \,\,\sin \,\,x\,\, + \,\,\cot \,\,x} \right)\,\,dx

is equal to

View answer and explanation

Correct option: B

{e^x}\,\,\log \,\,\sin \,\,x\,\, + \,\,c

Option B (

{e^x}\,\,\log \,\,\sin \,\,x\,\, + \,\,c

) is correct because the integral matches the form

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

, where

f(x) = \log(\sin x)