Optimal. Leaf size=26 \[ -\frac{e^2}{6 b d \left (a+b (c+d x)^3\right )^2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0205499, antiderivative size = 26, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.042 \[ -\frac{e^2}{6 b d \left (a+b (c+d x)^3\right )^2} \]
Antiderivative was successfully verified.
[In] Int[(c*e + d*e*x)^2/(a + b*(c + d*x)^3)^3,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 5.45966, size = 20, normalized size = 0.77 \[ - \frac{e^{2}}{6 b d \left (a + b \left (c + d x\right )^{3}\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((d*e*x+c*e)**2/(a+b*(d*x+c)**3)**3,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0310425, size = 26, normalized size = 1. \[ -\frac{e^2}{6 b d \left (a+b (c+d x)^3\right )^2} \]
Antiderivative was successfully verified.
[In] Integrate[(c*e + d*e*x)^2/(a + b*(c + d*x)^3)^3,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.002, size = 47, normalized size = 1.8 \[ -{\frac{{e}^{2}}{6\,bd \left ( b{d}^{3}{x}^{3}+3\,bc{d}^{2}{x}^{2}+3\,b{c}^{2}dx+b{c}^{3}+a \right ) ^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((d*e*x+c*e)^2/(a+b*(d*x+c)^3)^3,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.43231, size = 184, normalized size = 7.08 \[ -\frac{e^{2}}{6 \,{\left (b^{3} d^{7} x^{6} + 6 \, b^{3} c d^{6} x^{5} + 15 \, b^{3} c^{2} d^{5} x^{4} + 2 \,{\left (10 \, b^{3} c^{3} + a b^{2}\right )} d^{4} x^{3} + 3 \,{\left (5 \, b^{3} c^{4} + 2 \, a b^{2} c\right )} d^{3} x^{2} + 6 \,{\left (b^{3} c^{5} + a b^{2} c^{2}\right )} d^{2} x +{\left (b^{3} c^{6} + 2 \, a b^{2} c^{3} + a^{2} b\right )} d\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*e*x + c*e)^2/((d*x + c)^3*b + a)^3,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.226822, size = 184, normalized size = 7.08 \[ -\frac{e^{2}}{6 \,{\left (b^{3} d^{7} x^{6} + 6 \, b^{3} c d^{6} x^{5} + 15 \, b^{3} c^{2} d^{5} x^{4} + 2 \,{\left (10 \, b^{3} c^{3} + a b^{2}\right )} d^{4} x^{3} + 3 \,{\left (5 \, b^{3} c^{4} + 2 \, a b^{2} c\right )} d^{3} x^{2} + 6 \,{\left (b^{3} c^{5} + a b^{2} c^{2}\right )} d^{2} x +{\left (b^{3} c^{6} + 2 \, a b^{2} c^{3} + a^{2} b\right )} d\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*e*x + c*e)^2/((d*x + c)^3*b + a)^3,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 83.7215, size = 155, normalized size = 5.96 \[ - \frac{e^{2}}{6 a^{2} b d + 12 a b^{2} c^{3} d + 6 b^{3} c^{6} d + 90 b^{3} c^{2} d^{5} x^{4} + 36 b^{3} c d^{6} x^{5} + 6 b^{3} d^{7} x^{6} + x^{3} \left (12 a b^{2} d^{4} + 120 b^{3} c^{3} d^{4}\right ) + x^{2} \left (36 a b^{2} c d^{3} + 90 b^{3} c^{4} d^{3}\right ) + x \left (36 a b^{2} c^{2} d^{2} + 36 b^{3} c^{5} d^{2}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*e*x+c*e)**2/(a+b*(d*x+c)**3)**3,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.217033, size = 61, normalized size = 2.35 \[ -\frac{e^{2}}{6 \,{\left (b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right )}^{2} b d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*e*x + c*e)^2/((d*x + c)^3*b + a)^3,x, algorithm="giac")
[Out]