26.3 Problem number 141

a+bx2+cx4x2dexd+exdx

Optimal antiderivative (2be2+cd2)arctan(ex+dex+d)e3+cx(exd)ex+d2e2ex+daex+dex+dd2x

command

integrate((c*x**4+b*x**2+a)/x**2/(-e*x+d)**(1/2)/(e*x+d)**(1/2),x)

Sympy 1.10.1 under Python 3.10.4 output

Timed out

Sympy 1.8 under Python 3.8.8 output

iaeG6,65,3(54,74,132,32,21,54,32,74,20|d2e2x2)4π32d2+aeG6,62,6(12,34,1,54,32,134,5412,1,1,0|d2e2iπe2x2)4π32d2ibG6,66,2(14,3412,12,1,10,14,12,34,1,0|d2e2x2)4π32e+bG6,62,6(12,14,0,14,12,114,1412,0,0,0|d2e2iπe2x2)4π32eicd2G6,66,2(34,1412,12,0,11,34,12,14,0,0|d2e2x2)4π32e3+cd2G6,62,6(32,54,1,34,12,154,3432,1,1,0|d2e2iπe2x2)4π32e3