$\smallint \frac{{\cos \,\,2x}}{{{{\left( {\sin \,\,x\,\, + \,\,\cos \,\,x} \right)}^2}}}\,\,dx$ is equal to

$\frac{{ - 1}}{{\sin \,\,x\,\, + \,\,\cos \,\,x}}\,\, + \,\,C$

$\log {\left( {\sin \,\,x\,\, + \,\,\cos \,\,x} \right)^2}\,\, + \,\,C$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \frac{{\cos \,\,2x}}{{{{\left( {\sin \,\,x\,\, + \,\,\cos \,\,x} \right)}^2}}}\,\,dx

is equal to

View answer and explanation

Correct option: B

\log \left( {\sin \,x\,\, + \,\,\cos \,\,x} \right)\,\, + \,\,C

Option B is correct because the integral simplifies to a logarithmic function after simplification.