Optimal. Leaf size=17 \[ -\frac{1}{3 c^3 e (d+e x)^3} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0168868, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 30, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ -\frac{1}{3 c^3 e (d+e x)^3} \]
Antiderivative was successfully verified.
[In] Int[(d + e*x)^2/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^3,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 18.1522, size = 15, normalized size = 0.88 \[ - \frac{1}{3 c^{3} e \left (d + e x\right )^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e*x+d)**2/(c*e**2*x**2+2*c*d*e*x+c*d**2)**3,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.006799, size = 17, normalized size = 1. \[ -\frac{1}{3 c^3 e (d+e x)^3} \]
Antiderivative was successfully verified.
[In] Integrate[(d + e*x)^2/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^3,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.005, size = 16, normalized size = 0.9 \[ -{\frac{1}{3\,{c}^{3}e \left ( ex+d \right ) ^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.698933, size = 63, normalized size = 3.71 \[ -\frac{1}{3 \,{\left (c^{3} e^{4} x^{3} + 3 \, c^{3} d e^{3} x^{2} + 3 \, c^{3} d^{2} e^{2} x + c^{3} d^{3} e\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)^2/(c*e^2*x^2 + 2*c*d*e*x + c*d^2)^3,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.202565, size = 63, normalized size = 3.71 \[ -\frac{1}{3 \,{\left (c^{3} e^{4} x^{3} + 3 \, c^{3} d e^{3} x^{2} + 3 \, c^{3} d^{2} e^{2} x + c^{3} d^{3} e\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)^2/(c*e^2*x^2 + 2*c*d*e*x + c*d^2)^3,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.64675, size = 51, normalized size = 3. \[ - \frac{1}{3 c^{3} d^{3} e + 9 c^{3} d^{2} e^{2} x + 9 c^{3} d e^{3} x^{2} + 3 c^{3} e^{4} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x+d)**2/(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)^2/(c*e^2*x^2 + 2*c*d*e*x + c*d^2)^3,x, algorithm="giac")
[Out]