$\smallint \,\,\frac{{dx}}{{2\,\sqrt x \,\,\left( {1 + x} \right)}}$ is equal to

$\frac{1}{2}\,\,{\tan ^{ - 1}}\,\,\left( {\sqrt x } \right) + c$

$2\,\,{\tan ^{ - 1}}\,\,\left( {\sqrt x } \right) + c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \,\,\frac{{dx}}{{2\,\sqrt x \,\,\left( {1 + x} \right)}}

is equal to

View answer and explanation

Correct option: B

{\tan ^{ - 1}}\,\,\left( {\sqrt x } \right) + c

Option B (

{\tan ^{ - 1}}\,\,\left( {\sqrt x } \right) + c

) is correct because it is obtained by using a simple u-substitution with

u = \sqrt{x}