2 2 / x \ x |1 + -----------| -1 + ------ | ________| 2 | / 2 | 1 + x \ \/ 1 + x / - ----------- - ------------------ ________ ________ / 2 / 2 \/ 1 + x x + \/ 1 + x ---------------------------------- ________ / 2 x + \/ 1 + x
(-(-1 + x^2/(1 + x^2))/sqrt(1 + x^2) - (1 + x/sqrt(1 + x^2))^2/(x + sqrt(1 + x^2)))/(x + sqrt(1 + x^2))
3/2 / ________\ 2 / 2\ | / 2 | 1 + x - \1 + x / *\x + \/ 1 + x / -------------------------------------- 5/2 / ________\ / 2\ | / 2 | \1 + x / *\x + \/ 1 + x /
(1 + x^2 - (1 + x^2)^(3/2)*(x + sqrt(1 + x^2)))/((1 + x^2)^(5/2)*(x + sqrt(1 + x^2)))
/ ________\ | 3 2 / 2 | -\x + 2*x + 2*x *\/ 1 + x / --------------------------------------------------------------------- ________ ________ ________ / 2 5 3 4 / 2 2 / 2 \/ 1 + x + 2*x + 2*x + 4*x + 2*x *\/ 1 + x + 3*x *\/ 1 + x
-(x + 2*x^3 + 2*x^2*sqrt(1 + x^2))/(sqrt(1 + x^2) + 2*x + 2*x^5 + 4*x^3 + 2*x^4*sqrt(1 + x^2) + 3*x^2*sqrt(1 + x^2))
2 2 / x \ x |1 + -----------| 1 - ------ | ________| 2 | / 2 | 1 + x \ \/ 1 + x / ----------- - ------------------ ________ ________ / 2 / 2 \/ 1 + x x + \/ 1 + x -------------------------------- ________ / 2 x + \/ 1 + x
((1 - x^2/(1 + x^2))/sqrt(1 + x^2) - (1 + x/sqrt(1 + x^2))^2/(x + sqrt(1 + x^2)))/(x + sqrt(1 + x^2))
2 / 2\ / ________\ | ________ ________ 2 / ________\ | | / 2 | | 4 2 / 2 3 / 2 / 2\ | / 2 | | \x - \/ 1 + x / *\1 + x + 2*x + x*\/ 1 + x + x *\/ 1 + x - \1 + x / *\x + \/ 1 + x / / -------------------------------------------------------------------------------------------------- 6 2 4 1 + x + 3*x + 3*x
(x - sqrt(1 + x^2))^2*(1 + x^4 + 2*x^2 + x*sqrt(1 + x^2) + x^3*sqrt(1 + x^2) - (1 + x^2)^2*(x + sqrt(1 + x^2))^2)/(1 + x^6 + 3*x^2 + 3*x^4)
(-(1.0 + x^2)^(-0.5)*(-1.0 + x^2/(1.0 + x^2)) - (1.0 + x*(1.0 + x^2)^(-0.5))^2/(x + (1.0 + x^2)^0.5))/(x + (1.0 + x^2)^0.5)
(-(1.0 + x^2)^(-0.5)*(-1.0 + x^2/(1.0 + x^2)) - (1.0 + x*(1.0 + x^2)^(-0.5))^2/(x + (1.0 + x^2)^0.5))/(x + (1.0 + x^2)^0.5)
3/2 / ________\ 2 / 2\ | / 2 | 1 + x - \1 + x / *\x + \/ 1 + x / -------------------------------------- 5/2 / ________\ / 2\ | / 2 | \1 + x / *\x + \/ 1 + x /
(1 + x^2 - (1 + x^2)^(3/2)*(x + sqrt(1 + x^2)))/((1 + x^2)^(5/2)*(x + sqrt(1 + x^2)))