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∫a+bx2+cx4x2d−exd+exdx
Optimal antiderivative −(2be2+cd2)arctan(−ex+dex+d)e3+cx(ex−d)ex+d2e2−ex+d−a−ex+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|d2e−2iπe2x2)4π32d2−ibG6,66,2(14,3412,12,1,10,14,12,34,1,0|d2e2x2)4π32e+bG6,62,6(−12,−14,0,14,12,1−14,14−12,0,0,0|d2e−2iπe2x2)4π32e−icd2G6,66,2(−34,−14−12,−12,0,1−1,−34,−12,−14,0,0|d2e2x2)4π32e3+cd2G6,62,6(−32,−54,−1,−34,−12,1−54,−34−32,−1,−1,0|d2e−2iπe2x2)4π32e3
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