$\smallint \,\,\frac{{1\,\, + \,\,x\,\, + \,\,\sqrt {x\,\, + \,\,{x^2}} }}{{\sqrt x \,\, + \,\,\sqrt {1\,\, + \,\,x} }}\,\,dx = $

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

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

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

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Analyzing +4 | -1

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

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.