对1/(t³+t²）求积分,怎么求?过程……

对1/(t³+t²）求积分,怎么求?过程……
对1/(t³+t²）求积分,怎么求?过程……

对1/(t³+t²）求积分,怎么求?过程……
∫ 1/(t³+t²) dt
=∫ 1/[t²(t+1)] dt
=∫ (1+t-t)/[t²(t+1)] dt
=∫ (1+t)/[t²(t+1)] dt - ∫ t/[t²(t+1)] dt
=∫ 1/t² dt - ∫ 1/[t(t+1)] dt
=∫ 1/t² dt - ∫ 1/t dt + ∫ 1/(t+1) dt
=-1/t - ln|t| + ln|t+1| + C

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∫[1/(t³+t²)]dt
=∫dt/[t²(t+1)]
=∫[1/t²-1/t+1/(t+1)]dt
=∫dt/t²-∫dt/t+∫dt/(t+1)
=∫dt/t²-∫dt/t+∫dt/(t+1)
=-1/t²-ln(t)+ln(t+1)+C