" 23."sin((1+x^(2))/(1-x^(2)))

sin^(-1) ((2x)/(1 + x^(2)))

The derivative of sin^(-1) ((2x)/(1+x^(2))) w.r.t sin^(-1) ((1-x^(2))/(1+x^(2))) is

∫sin^-1 ((2x)/(1+x^2))

sin[cot^(-1)((2x)/(1-x^(2)))+cos^(-1)((1-x^(2))/(1+x^(2)))]=

solve : sin ^(-1) ""((x)/(sqrt(1+x^(2))))-sin ^(-1)((1)/(sqrt(1+x^(2))))= sin ^(-1) ((1+x)/(1+x^(2)))

sin{tan^(-1)[(1-x^(2))/(2x)]+cos^(-1)[(1-x^(2))/(1+x^(2))]}=

sin [ tan^(-1). (1 - x^(2))/(2x) + cos^(-1) . (1-x^(2))/(1 + x^(2))] is

sin [ tan^(-1). (1 - x^(2))/(2x) + cos^(-1) . (1-x^(2))/(1 + x^(2))] is

if x^(2) !=npi+1 , ninN then int x sqrt((2sin(x^(2)-1)-sin2(x^(2)-1))/(2sin(x^(2)-1)+sin2(x^(2)-1))) dx is equal to (a) In cos ((x^(2)-1)/(2))+c (b) (1)/(2)In cos ((x^(2)-1)/(2))+c (c) In sec ((x^(2)-1)/(2))+c (d) (1)/(2)In sec ((x^(2)-1)/(2))+c