$\smallint \,\,\frac{{\sin \,\,x\,\,\cos \,\,x}}{{\sqrt {1\,\, - \,\,{{\sin }^4}\,\,x} }}\,\,dx$ is equal to

$\frac{1}{2}\,\,{\cos ^{ - 1}}\,\,({\sin ^2}\,\,x) + c$

${\tan ^{ - 1}}\,\,\left( {{{\sin }^2}\,\,x} \right) + c$

${\tan ^{ - 1}}\,\,\left( {2\,\,{{\sin }^2}\,\,x} \right) + c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \,\,\frac{{\sin \,\,x\,\,\cos \,\,x}}{{\sqrt {1\,\, - \,\,{{\sin }^4}\,\,x} }}\,\,dx

is equal to

View answer and explanation

Correct option: A

\frac{1}{2}\,\,{\sin ^{ - 1}}\,\,\left( {{{\sin }^2}\,\,x} \right) + c

Option A (

\frac{1}{2}\,{\sin ^{ - 1}}\,\,\left( {{{\sin }^2}\,\,x} \right) + c

) is correct because after substitution, the integral simplifies to a standard arcsin form.