关于微积分：怎样求有理分式积分中（Ax+B）/（X^2+px+q）的积分?

∫(ax+b)/(x?+px+q)dx
=∫ax/(x?+px+q)dx+∫b/(x?+px+q)dx
=(a/2)ln|x?+px+q|-(ap/2)∫1/(x?+px+q)dx+b∫1/(x?+px+q)dx
=(a/2)ln|x?+px+q|+(b-ap/2)∫1/(x?+px+q)dx
而∫1/(x?+px+q)dx
[2/√(4q-p?)]arctan[(2x+p)/√(4q-p?)]+C (p?4q)
所以
∫(ax+b)/(x?+px+q)dx
(a/2)ln|x?+px+q|+(b-ap/2)[2/√(4q-p?)]arctan[(2x+p)/√(4q-p?)]+C (p?4q)
计算量有点大,不知道对不

做变换t=x+p/2,便变成了at+N/(t^2+r^2)=at/(T^2+r^2)+N(t^2+r^2), 其中r^2=q+p^2/4, n=b-ap/2,后面直接带入计算