求不定积分：∫ dt/(t-1)^2求过程._数学解答

求不定积分：∫ dt/(t-1)^2求过程.

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解答

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