设x=tant,t=arctanx,dx=(sect)^2dt
cost=1/√(1+x^2),
sint=x/√(1+x^2)
原式=∫ tant*e^t*(sect)^2dt/([1+(tant)^2]^(3/2)
=∫ tant*e^t*(sect)^2dt/(sect)^3
=∫ sint*e^tdt
=e^t(sint-cost)/2+C
设x=tant,t=arctanx,dx=(sect)^2dt
cost=1/√(1+x^2),
sint=x/√(1+x^2)
原式=∫ tant*e^t*(sect)^2dt/([1+(tant)^2]^(3/2)
=∫ tant*e^t*(sect)^2dt/(sect)^3
=∫ sint*e^tdt
=e^t(sint-cost)/2+C