" 34."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

The series expansion of log[(1 + x)^((1 + x))(1-x)^(1-x)] is (1) 2[(x^(2))/(1.2) + (x^(4))/(3.4)+(x^(6))/(5.6)+...] (2) [(x^(2))/(1.2) + (x^(4))/(3.4)+(x^(6))/(5.6)+...] (3) 2[(x^(2))/(1.2) + (x^(4))/(2.3)+(x^(6))/(3.4)+...] (4) 2[(x^(2))/(1.2) -(x^(4))/(2.3)+(x^(6))/(3.4)-...]