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求下列不定积分∫1/x(x²-1)^1/2∫1/x(x²-1)^1/2dx
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答案和解析
设x=1/sint
那么(x²-1)^1/2 = cost/sint
dx = -cost/sin^2t dt
∫ 1 / x(x²-1)^1/2 dx = ∫ sint * sint / cost * (-cost/sin^2t dt) = -∫ dt = -t + c = -arcsin1/x + c
那么(x²-1)^1/2 = cost/sint
dx = -cost/sin^2t dt
∫ 1 / x(x²-1)^1/2 dx = ∫ sint * sint / cost * (-cost/sin^2t dt) = -∫ dt = -t + c = -arcsin1/x + c
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