Question

∫[(x^2-x+6)/(x^3+3x)]dx

Answer 1

(x^2-x+6)/(x^3+3x)=2/x-(x+1)/(x^2+3).

原式=∫2/xdx-∫(x+1)/(x^2+3)dx

=2ln|x|-(1/2)ln(x^2+3)-(1/√3)arctan(x/√3)+C.