JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \,\,\frac{1}{{\sqrt {{{\sin }^3}\,\,x\,\,\sin \,\,\left( {x + \alpha } \right)} }}\,\,dx

is equal to

View answer and explanation

Correct option: B

- \,2\,\,\mathrm{cosec}\,\,\alpha \,\,\sqrt {\cos \,\,\alpha + \sin \,\,\alpha \,\,\cot \,\,x} + C

Option B is correct because the integral simplifies to

-2 \,\,\mathrm{cosec}\,\,\alpha \,\,\sqrt {\cos \,\,\alpha + \sin \,\,\alpha \,\,\cot \,\,x} + C

after trigonometric manipulation and substitution.

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