令lnx=sint(t在-π/2到π/2),则x=e^sint,t=arcsinlnx
原式=∫1/(e^sint)*cost*e^sint*costdt=∫cos^2(t)dt=1/2∫cos(2t)dt+1/2∫dt=-1/4sin(2t)+1/2t+C=-1/2sintcost+1/2t+C=1/2lnx*[1-ln^2(x)]^(1/2)+1/2arcsinlnx+C
令lnx=sint(t在-π/2到π/2),则x=e^sint,t=arcsinlnx
原式=∫1/(e^sint)*cost*e^sint*costdt=∫cos^2(t)dt=1/2∫cos(2t)dt+1/2∫dt=-1/4sin(2t)+1/2t+C=-1/2sintcost+1/2t+C=1/2lnx*[1-ln^2(x)]^(1/2)+1/2arcsinlnx+C