# Math Help - stuck with this integral

1. ## stuck with this integral

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

i need help for the du,u and dv,v

This is not a by-parts problem . . .

$\int \frac{\sqrt{x}}{1+x}\,dx$
Let $\sqrt{x} = u\quad\Rightarrow\quad x = u^2\quad\Rightarrow\quad dx = 2u\,du$

Substitute: . $\int\frac{u}{1+u^2}(2u\,du) \;=\;2\int\frac{u^2}{1+u^2}\,du \;=\;2\int\left(1 - \frac{1}{1+u^2}\right)du$

Got it?

3. thank you for the help