Robert J. answered • 12/12/12
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Certified High School AP Calculus and Physics Teacher
You can use u-subsitution.
u = x3
du = 3x2dx
∫x2/(x6+3x3+2) dx
= ∫(1/3)/(u2+3u+2) du
= ∫(1/3)[1/(u+1) - 1/(u+2)] du
= (1/3)ln|(u+1)/(u+2)| + c
= (1/3)ln|(x3+1)/(x3+2)| + c
Daniel O.
Good answer by the way, Robert.
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12/14/12
Daniel O.
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
12/14/12