x^2-2 x^3 x^2-1 d x=

Step-by-step solution

u= x^2-1 d u= 1 z (x^2-1 )^ 1 / 2-1 2 xd_x= x x^2-1 d xd x= x^2-1 x d u aligned & u= x^2-1 & x^2-1=u^2 aligned aligned & x^2=u^2+1 & x^4= (u^2+1 )^2 aligned x^2-1-1 x^3 y x-1 x d u x^2-1-1 x^4 d u u^2-1 (u^2+1 )^2 d u u^2+1-2 (u^2+1 )^2 d u u^2+1 (u^2+1 )^2 d u- 2 (u^2+1 )^2 d u d u u^2+1 -2 1 (u^2+1 )^2 1 (a x^2+b )^n 2 n-3 2 b(n-1) 1 (a x^2+b )^ n-1 d x+ x 2 b(n-1) (a x^2+b )^ n-1 1 (u^2+1 )^2 = 1 2(2-1) 1 (u^2+1 ) d u+ u 2(2-1) (u^2+1 ) = 1 2 ⁻¹(u)+ u 2 (v^2+1 ) d u u^2+1 -2 1 (u^2+1 )^2 ⁻¹ u-2 ( 1 2 ⁻¹ u+ v 2 (