Hello,

I just have a quick integral question in which I can not figure out how to get the right answer. Or, I know what I have to do to get it, I just don't know WHY I can do it...No answers please, just a tip in the right direction

$\displaystyle \int \frac {x^{1/2}}{x^{3/2} - 8}$

$\displaystyle Let u = x^{3/2}, du=\frac {3}{2} x^{1/2}$

$\displaystyle \frac {3}{2} \int \frac {1}{u^4} du$

Now, have I got this set up right? U-substitution still confuses me a little, and I'm not sure if I've done it properly. If I go ahead and finish this equation, I get.

$\displaystyle \frac {1}{-3(x^{3/2}-8)^3}$

I should be getting $\displaystyle \frac {2}{-9(x^{3/2} - 8}$

I can see how I should be getting that answer - by inverting the 3/2, to make it 2/3. But why is the 3/2 being inverted to 2/3 in the first place? The only reason I can think of is that it's in the denominator of a fraction, so it would be inverted, but I'm not sure...