Optimal. Leaf size=55 \[ \frac{1}{2} a^4 c^3 x^2-\frac{2}{3} a^3 b c^3 x^3+\frac{2}{5} a b^3 c^3 x^5-\frac{1}{6} b^4 c^3 x^6 \]
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Rubi [A] time = 0.0799337, antiderivative size = 55, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056 \[ \frac{1}{2} a^4 c^3 x^2-\frac{2}{3} a^3 b c^3 x^3+\frac{2}{5} a b^3 c^3 x^5-\frac{1}{6} b^4 c^3 x^6 \]
Antiderivative was successfully verified.
[In] Int[x*(a + b*x)*(a*c - b*c*x)^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ a^{4} c^{3} \int x\, dx - \frac{2 a^{3} b c^{3} x^{3}}{3} + \frac{2 a b^{3} c^{3} x^{5}}{5} - \frac{b^{4} c^{3} x^{6}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(b*x+a)*(-b*c*x+a*c)**3,x)
[Out]
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Mathematica [A] time = 0.00362285, size = 47, normalized size = 0.85 \[ c^3 \left (\frac{a^4 x^2}{2}-\frac{2}{3} a^3 b x^3+\frac{2}{5} a b^3 x^5-\frac{1}{6} b^4 x^6\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x*(a + b*x)*(a*c - b*c*x)^3,x]
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Maple [A] time = 0.001, size = 48, normalized size = 0.9 \[{\frac{{a}^{4}{c}^{3}{x}^{2}}{2}}-{\frac{2\,{a}^{3}b{c}^{3}{x}^{3}}{3}}+{\frac{2\,a{b}^{3}{c}^{3}{x}^{5}}{5}}-{\frac{{b}^{4}{c}^{3}{x}^{6}}{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(b*x+a)*(-b*c*x+a*c)^3,x)
[Out]
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Maxima [A] time = 1.3479, size = 63, normalized size = 1.15 \[ -\frac{1}{6} \, b^{4} c^{3} x^{6} + \frac{2}{5} \, a b^{3} c^{3} x^{5} - \frac{2}{3} \, a^{3} b c^{3} x^{3} + \frac{1}{2} \, a^{4} c^{3} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^3*(b*x + a)*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.179631, size = 1, normalized size = 0.02 \[ -\frac{1}{6} x^{6} c^{3} b^{4} + \frac{2}{5} x^{5} c^{3} b^{3} a - \frac{2}{3} x^{3} c^{3} b a^{3} + \frac{1}{2} x^{2} c^{3} a^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^3*(b*x + a)*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.070649, size = 53, normalized size = 0.96 \[ \frac{a^{4} c^{3} x^{2}}{2} - \frac{2 a^{3} b c^{3} x^{3}}{3} + \frac{2 a b^{3} c^{3} x^{5}}{5} - \frac{b^{4} c^{3} x^{6}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(b*x+a)*(-b*c*x+a*c)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.244508, size = 63, normalized size = 1.15 \[ -\frac{1}{6} \, b^{4} c^{3} x^{6} + \frac{2}{5} \, a b^{3} c^{3} x^{5} - \frac{2}{3} \, a^{3} b c^{3} x^{3} + \frac{1}{2} \, a^{4} c^{3} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^3*(b*x + a)*x,x, algorithm="giac")
[Out]