$\smallint \,\,\frac{{dx}}{{{{\left( {{a^2} + {x^2}} \right)}^{3/2}}}}$ is equal to

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

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

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \,\,\frac{{dx}}{{{{\left( {{a^2} + {x^2}} \right)}^{3/2}}}}

is equal to

View answer and explanation

Correct option: B

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

Option B is correct because after trigonometric substitution and simplification, the integral evaluates to

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