$\smallint \,\,\frac{{1\,\, + \,\,x\,\, + \,\,\sqrt {x\,\, + \,\,{x^2}} }}{{\sqrt x \,\, + \,\,\sqrt {1\,\, + \,\,x} }}\,\,dx$ is equal to

$\frac{1}{2}\,\,\sqrt {1\,\, + \,\,x} \,\, + \,\,c$

$\sqrt {1\,\, + \,\,x} + \,\,c$

$2\,\,{\left( {1\,\, + \,\,x} \right)^{3/2}} + \,\,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \,\,\frac{{1\,\, + \,\,x\,\, + \,\,\sqrt {x\,\, + \,\,{x^2}} }}{{\sqrt x \,\, + \,\,\sqrt {1\,\, + \,\,x} }}\,\,dx

is equal to

View answer and explanation

Correct option: B

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

Option B (

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

) is correct because the integral simplifies to

\int \sqrt{1+x} dx

, which integrates to the given expression.