$\smallint \,\,\frac{1}{{{{\left( {{a^2} + {x^2}} \right)}^{3/2}}}}\,\,dx$ is equal to

$\frac{x}{{{{({a^2}\,\, + \,\,{x^2})}^{3/2}}}}\,\, + \,\,C$

$\frac{1}{{{a^2}\sqrt {{a^2}\,\, + \,\,{x^2}} }}\,\, + \,\,C$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \,\,\frac{1}{{{{\left( {{a^2} + {x^2}} \right)}^{3/2}}}}\,\,dx

is equal to

View answer and explanation

Correct option: A

\frac{x}{{{a^2}\,\sqrt {{a^2}\,\, + \,\,{x^2}} }}\,\, + \,\,C

Option A (

\frac{x}{{{a^2}\,\sqrt {{a^2}\, + \,{x^2}} }}\, + \,C

) is correct because it results from a trigonometric substitution, specifically

x = a \tan \theta

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