$\smallint \,\,{\left( {x + 1} \right)^{3/2}}\,\,[{\sin ^{ - 1}}\,\,(\log \,\,x)\,\, + \,\,{\cos ^{ - 1}}\,\,(\log \,\,x)]\,\,dx$ is equal to

$\frac{{2\,\pi }}{2}\,\,{\left( {x + 1} \right)^{5/2}}\,\, + \,\,c$

$\frac{\pi }{5}\,\,{\left( {x + 1} \right)^{5/2}}\,\, + \,\,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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\int \,\,{\left( {x + 1} \right)^{3/2}}\,\,[{\sin ^{ - 1}}\,\,(\log \,\,x)\,\, + \,\,{\cos ^{ - 1}}\,\,(\log \,\,x)]\,\,dx

is equal to

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Correct option: C

Does not exist

Option C (Does not exist) is correct because the domain of the inverse trigonometric functions requires the argument to be within [-1, 1], which is not satisfied for all x in the integral.

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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