【紧急求助】请问（t^2+1)^0.5/t的积分怎 - 知识问答

【紧急求助】请问（t^2+1)^0.5/t的积分怎么求?实在不会算!

3个回答

∫√(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

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