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Let t = x 2,

Original formula =∫(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