well, I have trouble with this problem! Where should I start?

You can use u-subsitution.

u = x^{3}

du = 3x^{2}dx

∫x^{2}/(x^{6}+3x^{3}+2) dx

= ∫(1/3)/(u^{2}+3u+2) du

= ∫(1/3)[1/(u+1) - 1/(u+2)] du

= (1/3)ln|(u+1)/(u+2)| + c

= (1/3)ln|(x^{3}+1)/(x^{3}+2)| + c

## Comments

Elaine, in the third step from the bottom, he's using integration by partial fractions. If you aren't sure how to do that, this may help: http://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/partialfracdirectory/PartialFrac.html ;

Good answer by the way, Robert.