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how to solve integral of x^2 dx/x^6+3x^3+2

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

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1 Answer

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


Good answer by the way, Robert.