JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Analyzing +4 | -1

\int \frac{{{{\sin }^3}\,\,x}}{{\left( {1\,\, + \,\,{{\cos }^2}\,\,x} \right)\sqrt {1\,\, + \,\,{{\cos }^2}\,\,x\,\, + \,\,{{\cos }^4}\,\,x} }}\,\,dx

is equal to

View answer and explanation

Correct option: A

{\sec ^{ - 1}}\,\,\left( {\sec \,\,x + \cos \,\,x} \right) + C

Option A (

{\sec ^{ - 1}}\,\,\left( {\sec \,x + \cos \,x} \right) + C

) is correct because after substitution and simplification, the integral evaluates to the given expression.

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