$\smallint {\cos ^3}\,\,x{e^{\log \left( {\sin x} \right)}}\,\,dx$ is equal to

$ - \,\,\frac{{{{\sin }^4}\,\,x}}{4}\,\, + \,\,C$

$\frac{{{e^{\sin x}}}}{4}\,\, + \,\,C$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int {\cos ^3}\,\,x{e^{\log \left( {\sin x} \right)}}\,\,dx

is equal to

View answer and explanation

Correct option: B

- \,\,\frac{{{{\cos }^4}\,\,x}}{4}\,\, + \,\,C

Option B (

\ - \,\,\frac{{{{\cos }^4}\,x}}{4}\, + \,C

) is correct. Simplifying the integral using properties of logarithms and then integrating leads to the correct result.