$\mathop \smallint \limits_0^\infty \,\,\frac{{dx}}{{{{\left[ {x\,\, + \,\,\sqrt {{x^2}\,\, + \,\,1} } \right]}^3}}} = $

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

\int \limits_0^\infty \,\,\frac{{dx}}{{{{\left[ {x\,\, + \,\,\sqrt {{x^2}\,\, + \,\,1} } \right]}^3}}} =

View answer and explanation

Correct option: A

\frac{3}{8}

Option A (

\frac{3}{8}

) is correct because the definite integral evaluates to 3/8 after using a trigonometric substitution.

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