Question

这个不定积分怎么求？

Answer 1

∫（t-1）／（t＾2+1）dt
＝∫t/（t＾2-1）dt-∫1/（t＾2+1）dt
＝（1/2）*∫d（t＾2-1）／（t＾2-1）-∫1／（t＾2+1）dt
＝（1/2）*ln（t＾2+1）-arctant＋C

Answer 2

∫(t-1)/(t^2+1) dt
=∫t/(t^2+1) dt -∫dt/(t^2+1)
=(1/2)∫d(t^2+1)/(t^2+1) -∫dt/(t^2+1)
=(1/2)ln|t^2+1| -arctant + C