Question

Evaluate integral: 1/(x+sqrt(x))

Answer 1

\[\int\frac{dx}{x+\sqrt{x}}=\int\frac{dx}{\sqrt{x}(\sqrt{x}+1)}\quad;\quad y=\sqrt{x}\quad,\quad dy=\frac{dx}{2\sqrt{x}}\]\[=2\int\frac{dy}{y+1}=2\ln{(y+1)}+C=2\ln{(\sqrt{x}+1)}+C\]