trying to Integrate (x^2-1)/(2x-1)^.5 with substitution

[eiei0]

Hello,

I am trying to integrate (x^2-1)/(2x-1)^.5 (sorry if it looks bad on a computer screen)

im having problems dealing with the 1 that is being subtracted from the 2x under the square root (the last half that's to that .5 power) if i set u=x^2-1, should i be setting u to something else?

 

[skeeter]

Re: trying to Integrating with substitution

\(\displaystyle u^2 = 2x-1\)

\(\displaystyle u \, du = dx\)

\(\displaystyle x = \frac{u^2 + 1}{2}\)

\(\displaystyle x^2 - 1 = \frac{u^4 + 2u^2 + 1}{4} - 1 = \frac{u^4 + 2u^2 - 3}{4}\)

\(\displaystyle \int \frac{x^2 - 1}{\sqrt{2x-1}} \, dx\)

\(\displaystyle \int \frac{u^4 + 2u^2 - 3}{4u} \cdot u \, du\)

\(\displaystyle \frac{1}{4} \int u^4 + 2u^2 - 3 \, du\)

 

[eiei0]

ty that helped a lot