___ 2*\/ 3 / | | ________ | / 4 | \/ x + 4 | ----------- dx | 2 | x | / 2
Integral(sqrt(x^4 + 4)/x^2, (x, 2, 2*sqrt(3)))
/ / | | | ________ | _______________________________ | / 4 | / / 2 \ / 2 \ | \/ x + 4 | \/ \2 + x - 2*x/*\2 + x + 2*x/ | ----------- dx = C + | ---------------------------------- dx | 2 | 2 | x | x | | / /
_ _ |_ /-1/2, -1/4 | pi*I\ ___ |_ /-1/2, -1/4 | pi*I\ Gamma(-1/4)* | | | 4*e | \/ 3 *Gamma(-1/4)* | | | 36*e | 2 1 \ 3/4 | / 2 1 \ 3/4 | / - --------------------------------------- + ---------------------------------------------- 4*Gamma(3/4) 12*Gamma(3/4)
=
_ _ |_ /-1/2, -1/4 | pi*I\ ___ |_ /-1/2, -1/4 | pi*I\ Gamma(-1/4)* | | | 4*e | \/ 3 *Gamma(-1/4)* | | | 36*e | 2 1 \ 3/4 | / 2 1 \ 3/4 | / - --------------------------------------- + ---------------------------------------------- 4*Gamma(3/4) 12*Gamma(3/4)
-gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), 4*exp_polar(pi*i))/(4*gamma(3/4)) + sqrt(3)*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), 36*exp_polar(pi*i))/(12*gamma(3/4))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.