It seems that the problem of automatic integration of typical functions
is raised very often. Here is another integral (sorry if I have
missed some older posts):
(%i1) integrate(ln(x)/x^3, x);
(%i2) integrate(ln(x)/x^3, x, 1, %e);
Substitution t = ln(x) leads to readily evaluated integrals:
(%i3) integrate(t*exp(-2*t), t);
(%o3) -((2*t+1)*%e^(-2*t))/4
(%i4) integrate(t*exp(-2*t), t, 0, 1);
(%o4) 1/4-(3*%e^(-2))/4
Probably someone eager for integration who knows lisp will finally
update the .mac files. Unfortunately I don't know lisp :(
Best regards, Krzysztof Le?niak