Optimal. Leaf size=87 \[ \frac{1}{5} a^6 c^5 x^5-\frac{2}{3} a^5 b c^5 x^6+\frac{5}{7} a^4 b^2 c^5 x^7-\frac{5}{9} a^2 b^4 c^5 x^9+\frac{2}{5} a b^5 c^5 x^{10}-\frac{1}{11} b^6 c^5 x^{11} \]
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Rubi [A] time = 0.141228, antiderivative size = 87, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ \frac{1}{5} a^6 c^5 x^5-\frac{2}{3} a^5 b c^5 x^6+\frac{5}{7} a^4 b^2 c^5 x^7-\frac{5}{9} a^2 b^4 c^5 x^9+\frac{2}{5} a b^5 c^5 x^{10}-\frac{1}{11} b^6 c^5 x^{11} \]
Antiderivative was successfully verified.
[In] Int[x^4*(a + b*x)*(a*c - b*c*x)^5,x]
[Out]
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Rubi in Sympy [A] time = 36.3125, size = 87, normalized size = 1. \[ \frac{a^{6} c^{5} x^{5}}{5} - \frac{2 a^{5} b c^{5} x^{6}}{3} + \frac{5 a^{4} b^{2} c^{5} x^{7}}{7} - \frac{5 a^{2} b^{4} c^{5} x^{9}}{9} + \frac{2 a b^{5} c^{5} x^{10}}{5} - \frac{b^{6} c^{5} x^{11}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**4*(b*x+a)*(-b*c*x+a*c)**5,x)
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Mathematica [A] time = 0.0063107, size = 73, normalized size = 0.84 \[ c^5 \left (\frac{a^6 x^5}{5}-\frac{2}{3} a^5 b x^6+\frac{5}{7} a^4 b^2 x^7-\frac{5}{9} a^2 b^4 x^9+\frac{2}{5} a b^5 x^{10}-\frac{1}{11} b^6 x^{11}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^4*(a + b*x)*(a*c - b*c*x)^5,x]
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Maple [A] time = 0.004, size = 76, normalized size = 0.9 \[{\frac{{a}^{6}{c}^{5}{x}^{5}}{5}}-{\frac{2\,{a}^{5}b{c}^{5}{x}^{6}}{3}}+{\frac{5\,{a}^{4}{b}^{2}{c}^{5}{x}^{7}}{7}}-{\frac{5\,{a}^{2}{b}^{4}{c}^{5}{x}^{9}}{9}}+{\frac{2\,a{b}^{5}{c}^{5}{x}^{10}}{5}}-{\frac{{b}^{6}{c}^{5}{x}^{11}}{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^4*(b*x+a)*(-b*c*x+a*c)^5,x)
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Maxima [A] time = 1.3831, size = 101, normalized size = 1.16 \[ -\frac{1}{11} \, b^{6} c^{5} x^{11} + \frac{2}{5} \, a b^{5} c^{5} x^{10} - \frac{5}{9} \, a^{2} b^{4} c^{5} x^{9} + \frac{5}{7} \, a^{4} b^{2} c^{5} x^{7} - \frac{2}{3} \, a^{5} b c^{5} x^{6} + \frac{1}{5} \, a^{6} c^{5} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^5*(b*x + a)*x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.179747, size = 1, normalized size = 0.01 \[ -\frac{1}{11} x^{11} c^{5} b^{6} + \frac{2}{5} x^{10} c^{5} b^{5} a - \frac{5}{9} x^{9} c^{5} b^{4} a^{2} + \frac{5}{7} x^{7} c^{5} b^{2} a^{4} - \frac{2}{3} x^{6} c^{5} b a^{5} + \frac{1}{5} x^{5} c^{5} a^{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^5*(b*x + a)*x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.157269, size = 87, normalized size = 1. \[ \frac{a^{6} c^{5} x^{5}}{5} - \frac{2 a^{5} b c^{5} x^{6}}{3} + \frac{5 a^{4} b^{2} c^{5} x^{7}}{7} - \frac{5 a^{2} b^{4} c^{5} x^{9}}{9} + \frac{2 a b^{5} c^{5} x^{10}}{5} - \frac{b^{6} c^{5} x^{11}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**4*(b*x+a)*(-b*c*x+a*c)**5,x)
[Out]
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GIAC/XCAS [A] time = 0.261511, size = 101, normalized size = 1.16 \[ -\frac{1}{11} \, b^{6} c^{5} x^{11} + \frac{2}{5} \, a b^{5} c^{5} x^{10} - \frac{5}{9} \, a^{2} b^{4} c^{5} x^{9} + \frac{5}{7} \, a^{4} b^{2} c^{5} x^{7} - \frac{2}{3} \, a^{5} b c^{5} x^{6} + \frac{1}{5} \, a^{6} c^{5} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^5*(b*x + a)*x^4,x, algorithm="giac")
[Out]