Optimal. Leaf size=20 \[ \frac{(a e+c d x)^4}{4 c d} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0298317, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 35, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.057 \[ \frac{(a e+c d x)^4}{4 c d} \]
Antiderivative was successfully verified.
[In] Int[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3/(d + e*x)^3,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 10.4509, size = 14, normalized size = 0.7 \[ \frac{\left (a e + c d x\right )^{4}}{4 c d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3/(e*x+d)**3,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0041265, size = 20, normalized size = 1. \[ \frac{(a e+c d x)^4}{4 c d} \]
Antiderivative was successfully verified.
[In] Integrate[(a*d*e + (c*d^2 + a*e^2)*x + c*d*e*x^2)^3/(d + e*x)^3,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.001, size = 19, normalized size = 1. \[{\frac{ \left ( cdx+ae \right ) ^{4}}{4\,cd}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a*e*d+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^3,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.71604, size = 61, normalized size = 3.05 \[ \frac{1}{4} \, c^{3} d^{3} x^{4} + a c^{2} d^{2} e x^{3} + \frac{3}{2} \, a^{2} c d e^{2} x^{2} + a^{3} e^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^3/(e*x + d)^3,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.20611, size = 61, normalized size = 3.05 \[ \frac{1}{4} \, c^{3} d^{3} x^{4} + a c^{2} d^{2} e x^{3} + \frac{3}{2} \, a^{2} c d e^{2} x^{2} + a^{3} e^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^3/(e*x + d)^3,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.345598, size = 49, normalized size = 2.45 \[ a^{3} e^{3} x + \frac{3 a^{2} c d e^{2} x^{2}}{2} + a c^{2} d^{2} e x^{3} + \frac{c^{3} d^{3} x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**3/(e*x+d)**3,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.213708, size = 69, normalized size = 3.45 \[ \frac{1}{4} \,{\left (c^{3} d^{3} x^{4} e^{12} + 4 \, a c^{2} d^{2} x^{3} e^{13} + 6 \, a^{2} c d x^{2} e^{14} + 4 \, a^{3} x e^{15}\right )} e^{\left (-12\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^3/(e*x + d)^3,x, algorithm="giac")
[Out]