Recent content by mllamontagne

SammyS, you are the best. That was exactly what I needed to do. I promise I will never forget how to do that integration again.

As you suggest, Partial fractions can be used to break up 3∫\frac{u}{(u-1)(u^{2}+u+1)}du with u=\sqrt[3]{x+1} to ∫\frac{1}{u-1}du +∫\frac{1}{u^{2}+u+1} du -∫\frac{u}{u^{2}+u+1} du the first integral is a simple natural log, the second is and arctan, but now the third one gives me...

Thanks for the welcome and the advice. If I u substitute with u=\sqrt[3]{x+1}, I get 3∫\frac{u}{u^{3}-1}du which admittedly looks better, but which I still can't figure out how to solve.

Homework Statement \int\frac{1}{x\sqrt[3]{x+1}}dx (That's a cubic root in the denominator, by the way. Not an x cubed.) The Attempt at a Solution I thought possibly partial fractions, but I've never seen it done with a root in the denominator. Integration by parts was...