Anti-derivative question - I want to verify I'm doing this right

[irishpump]

f'(x)= (x^2)/(Sqrt[(x^3)-1]

What I did so far was let U=(x^3) - 1 --> (1/3)(x^3)/u^(1/2) --> From here I'm not sure what to do, or if I'm necessarily doing it right. Any help or direction offered is much appreciated!

 

[galactus]

You chose a good sub. The thing is, after you make the sub, there can be no more x's in the integrand.

If you let \(\displaystyle u=x^{3}-1, \;\ du=3x^{2}dx, \;\ \frac{du}{3}=x^{2}dx\)

Then it becomes:

\(\displaystyle \frac{1}{3}\int \frac{1}{\sqrt{u}}du=\frac{1}{3}\int u^{\frac{-1}{2}}du\)

Now, integrate and resub \(\displaystyle u=x^{3}-1\)

 

[irishpump]

Thank you so much! So, 1/3u^(-1/2) gives me 2u/3 --> 2Sqrt[x^3 - 1] / 3 Thank you very much!