Question

t^2+1/根号(1-t^4)的积分

【紧急求助】请问（t^2+1)^0.5/t的积分怎么求?实在不会算!
就是分子是根号下（t^2+1）,分母是t

Answer 1

∫√(t^2+1)dt/t
t=tanu dt=secu^2du sinu=tanucosu=t/√(1+t^2)
=∫secu^3du/tanu
=∫secu(tanu^2+1)du/tanu
=∫secutanudu+∫secudu/tanu
=secu+∫du/sinu
=secu+(-1/2)ln|1+cosu|/|1-cosu|
=secu-ln|1+cosu|/|sinu|
=secu-ln|1/sinu+cotu|
=√(t^2+1)-ln|t/√(1+t^2)+(1/t)|+C