求不定积分√(x-1)/x dx

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求不定积分√(x-1)/x dx
求不定积分√(x-1)/x dx

求不定积分√(x-1)/x dx
∫ [√(x-1) /x] dx
let
x = (secy)^2
dx = 2secytany dy
∫ [√(x-1) /x] dx
= ∫ 2(tany)^2 /(secy) dy
=2∫ (siny)^2/ cosy dy
=2∫ (1- (cosy)^2)/ cosy dy
=2∫ (secy- cosy) dy
=2[ln|secy+tany| - siny] + C