Question

Please help me to solve this ∫ 1/(x + √x) dx

Answer 1

Answer:

$\boxed{2ln (\sqrt{x} + 1 ) + c}$

Step-by-step explanation:

$\int\limits {\frac{1}{x + \sqrt{x} } } \, dx$

$= \int\limits {\frac{1}{\sqrt{x} (\sqrt{x} + 1 )} } \, dx$

$= \int\limits {\frac{2}{(\sqrt{x} + 1 )} } \, d(\sqrt{x} + 1 )$

$= 2ln (\sqrt{x} + 1 ) + c$