\[\smallint \,\,\frac{{{a^{x/2}}}}{{\sqrt {{a^{ - x}} - \,\,{a^x}} }}\,\,dx\] is equal to

$\frac{1}{{\log \,\,a}}\,\,{\tan ^{ - 1}}\,\,\left( {{a^x}} \right)\,\, + \,\,c$

$2\,\,\sqrt {{a^{ - x}} - {a^x}} \,\, + \,\,c$

$\log \,\,\left( {{a^x} - 1} \right)\,\, + \,\,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \,\,\frac{{{a^{x/2}}}}{{\sqrt {{a^{ - x}} - \,\,{a^x}} }}\,\,dx

is equal to

View answer and explanation

Correct option: A

\frac{1}{{\log \,\,a}}\,\,{\sin ^{ - 1}}\,\,\left( {{a^x}} \right)\,\, + \,\,c

Option A (

\frac{1}{{\log \,a}}\,{\sin ^{ - 1}}\,\left( {{a^x}} \right)\, + \,c

) is correct because it is the result of integrating the given expression using substitution.