Optimal. Leaf size=5 \[ \frac{x}{c^3} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.00975084, antiderivative size = 5, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 30, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{x}{c^3} \]
Antiderivative was successfully verified.
[In] Int[(d + e*x)^6/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^3,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 16.625, size = 3, normalized size = 0.6 \[ \frac{x}{c^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e*x+d)**6/(c*e**2*x**2+2*c*d*e*x+c*d**2)**3,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.000768919, size = 5, normalized size = 1. \[ \frac{x}{c^3} \]
Antiderivative was successfully verified.
[In] Integrate[(d + e*x)^6/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^3,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0., size = 6, normalized size = 1.2 \[{\frac{x}{{c}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x+d)^6/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.694819, size = 7, normalized size = 1.4 \[ \frac{x}{c^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)^6/(c*e^2*x^2 + 2*c*d*e*x + c*d^2)^3,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.214832, size = 7, normalized size = 1.4 \[ \frac{x}{c^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)^6/(c*e^2*x^2 + 2*c*d*e*x + c*d^2)^3,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.230588, size = 3, normalized size = 0.6 \[ \frac{x}{c^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x+d)**6/(c*e**2*x**2+2*c*d*e*x+c*d**2)**3,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: NotImplementedError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)^6/(c*e^2*x^2 + 2*c*d*e*x + c*d^2)^3,x, algorithm="giac")
[Out]