Need help evaluating indefinate integral.

Printable View

December 16th 2010, 05:49 AM
saykhong

Need help evaluating indefinate integral.

int [x/(x+1)^(1/2)]
December 16th 2010, 05:59 AM
TheCoffeeMachine

Quote:

Originally Posted by saykhong

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

$\int\frac{x}{\sqrt{x+1}}\;{dx}$ . Letting $u = \sqrt{x+1}$ gives ${2}\int\frac{u(u^2-1)}{u}\;{du} = {2}\int\left(u^2-1\right)\;{du} = ...$
December 16th 2010, 06:10 AM
Danny

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

$\displaystyle \int \dfrac{(u-1)^2}{\sqrt{u}}du$ expand and integrate.
December 16th 2010, 03:06 PM
Krizalid

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

All times are GMT -8. The time now is 11:21 PM.