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。

设t = x ^ 2，

原公式=∫(t-2)dt/(t3-t)

=∫dt/(t2-1)-2∫dt/(t3-t)

=(1/2)ln[(t-1)/(t 1)]-∫dt2/[T2(T2-1)]

=(1/2)ln[(x 1)/(x 3)]-∫d(T2-1/2)/[(T2-1/2)1/2)(T2-1/2-1/2)]

=(1/2)ln[(x 1)/(x 3)]-ln[(T2-1/2-1/2)/(T2-1/2 1/2)]C

=[ln(x 1)]/2-[ln(x 3)]/2-ln(x2 4x 3)2ln(x2)C