Integration by change of variable

• Feb 29th 2008, 05:47 PM
doctorgk
Integration by change of variable
$\int \frac{-x}{(x+1)-\sqrt (x+1)} dx$

Kind of lost, I tried letting u=x+1, then follow through, but my answer does not match up with the right answer

the square root goes over the entire quantity $x+1$

thanks
• Feb 29th 2008, 06:36 PM
TwistedOne151
make the u substitution $u=\sqrt{x+1}$. Then $x=u^2-1$, and $dx=2u\,du$. When you make this subtitution, factor the numerator and the denominator (they're both polynomials) and cancel common factors. The result is easily integrable.
--Kevin C.
• Feb 29th 2008, 06:40 PM
galactus

Let $u=x+1, \;\ du=dx, \;\ u-1=x$

Make the subs and you get:

$\frac{1-u}{u-\sqrt{u}}=\frac{-1}{\sqrt{u}}-1$

Now integrate that. Easier, huh?.
• Feb 29th 2008, 06:46 PM
polymerase
Quote:

Originally Posted by doctorgk
$\int \frac{-x}{(x+1)-\sqrt (x+1)} dx$

Kind of lost, I tried letting u=x+1, then follow through, but my answer does not match up with the right answer

the square root goes over the entire quantity $x+1$

thanks

You can also make the substitution $u^2=x+1$, you would end up integrating $-2\int u+1\:du$