Math Help - Need help evaluating indefinate integral.

1. Need help evaluating indefinate integral.

int [x/(x+1)^(1/2)]

2. Originally Posted by saykhong
int [x/(x+1)^(1/2)]
$\int\frac{x}{\sqrt{x+1}}\;{dx}$. Letting $u = \sqrt{x+1}$ gives ${2}\int\frac{u(u^2-1)}{u}\;{du} = {2}\int\left(u^2-1\right)\;{du} = ...$

3. You could also let $u = x + 1$ then

$\displaystyle \int \dfrac{(u-1)^2}{\sqrt{u}}du$ expand and integrate.

4. $\displaystyle\int{\frac{x}{\sqrt{x+1}}\,dx}=\int{\ sqrt{x+1}\,dx}-\int{\frac{dx}{\sqrt{x+1}}}=\frac{2}{3}{{(x+1)}^{\ frac{3}{2}}}-2\sqrt{x+1}+k.$