`int (x^2 - x + 6)/(x^3 + 3x) dx` Evaluate the integral

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Integrate `int(x^2-x+6)/(x^3+3x)`

Rewrite the rational function using partial fractions.





Equate coefficients and solve for A, B, and C.













The first integral matches the form `int (du)/u=ln|u|+C`



Integrate the second integral using u-substitution.

Let `u=x^2+3`



` ` `-intx/(x^2+3)dx`





The third integral matches the form





The final answer is:




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