The value of $\smallint {e^{\sec x}}\,\, \cdot \,\,{\sec ^3}\,\,x\,\,\left( {{{\sin }^2}\,\,x\,\, + \,\,\cos \,\,x\,\, + \,\,\sin \,\,x\,\, + \,\,\sin \,\,x\,\,\cos \,\,x} \right)dx$ is

${e^{\sec x}}\,\,\left( {{{\sec }^2}\,\,x\,\, + \,\,\sec \,\,x\,\,\tan \,\,x} \right) + C$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

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The value of

\int {e^{\sec x}}\,\, \cdot \,\,{\sec ^3}\,\,x\,\,\left( {{{\sin }^2}\,\,x\,\, + \,\,\cos \,\,x\,\, + \,\,\sin \,\,x\,\, + \,\,\sin \,\,x\,\,\cos \,\,x} \right)dx

View answer and explanation

Correct option: C

{e^{\sec x}}\,\,\left( {\sec \,\,x\,\, + \,\,\tan \,\,x} \right)\,\, + \,\,C

Option C (

{e^{\sec x}}\,\,\left( {\sec \,\,x\,\, + \,\,\tan \,\,x} \right)\,\, + \,\,C

) is correct because it results from integrating the given expression using integration by parts and simplification.