Optimal. Leaf size=87 \[ \frac{1}{4} a^6 c^5 x^4-\frac{4}{5} a^5 b c^5 x^5+\frac{5}{6} a^4 b^2 c^5 x^6-\frac{5}{8} a^2 b^4 c^5 x^8+\frac{4}{9} a b^5 c^5 x^9-\frac{1}{10} b^6 c^5 x^{10} \]
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Rubi [A] time = 0.135238, 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 \[ \frac{1}{4} a^6 c^5 x^4-\frac{4}{5} a^5 b c^5 x^5+\frac{5}{6} a^4 b^2 c^5 x^6-\frac{5}{8} a^2 b^4 c^5 x^8+\frac{4}{9} a b^5 c^5 x^9-\frac{1}{10} b^6 c^5 x^{10} \]
Antiderivative was successfully verified.
[In] Int[x^3*(a + b*x)*(a*c - b*c*x)^5,x]
[Out]
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Rubi in Sympy [A] time = 35.0023, size = 87, normalized size = 1. \[ \frac{a^{6} c^{5} x^{4}}{4} - \frac{4 a^{5} b c^{5} x^{5}}{5} + \frac{5 a^{4} b^{2} c^{5} x^{6}}{6} - \frac{5 a^{2} b^{4} c^{5} x^{8}}{8} + \frac{4 a b^{5} c^{5} x^{9}}{9} - \frac{b^{6} c^{5} x^{10}}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3*(b*x+a)*(-b*c*x+a*c)**5,x)
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Mathematica [A] time = 0.00495686, size = 73, normalized size = 0.84 \[ c^5 \left (\frac{a^6 x^4}{4}-\frac{4}{5} a^5 b x^5+\frac{5}{6} a^4 b^2 x^6-\frac{5}{8} a^2 b^4 x^8+\frac{4}{9} a b^5 x^9-\frac{1}{10} b^6 x^{10}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^3*(a + b*x)*(a*c - b*c*x)^5,x]
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Maple [A] time = 0.001, size = 76, normalized size = 0.9 \[{\frac{{a}^{6}{c}^{5}{x}^{4}}{4}}-{\frac{4\,{a}^{5}b{c}^{5}{x}^{5}}{5}}+{\frac{5\,{a}^{4}{b}^{2}{c}^{5}{x}^{6}}{6}}-{\frac{5\,{a}^{2}{b}^{4}{c}^{5}{x}^{8}}{8}}+{\frac{4\,a{b}^{5}{c}^{5}{x}^{9}}{9}}-{\frac{{b}^{6}{c}^{5}{x}^{10}}{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3*(b*x+a)*(-b*c*x+a*c)^5,x)
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Maxima [A] time = 1.39324, size = 101, normalized size = 1.16 \[ -\frac{1}{10} \, b^{6} c^{5} x^{10} + \frac{4}{9} \, a b^{5} c^{5} x^{9} - \frac{5}{8} \, a^{2} b^{4} c^{5} x^{8} + \frac{5}{6} \, a^{4} b^{2} c^{5} x^{6} - \frac{4}{5} \, a^{5} b c^{5} x^{5} + \frac{1}{4} \, a^{6} c^{5} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^5*(b*x + a)*x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.182011, size = 1, normalized size = 0.01 \[ -\frac{1}{10} x^{10} c^{5} b^{6} + \frac{4}{9} x^{9} c^{5} b^{5} a - \frac{5}{8} x^{8} c^{5} b^{4} a^{2} + \frac{5}{6} x^{6} c^{5} b^{2} a^{4} - \frac{4}{5} x^{5} c^{5} b a^{5} + \frac{1}{4} x^{4} c^{5} a^{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^5*(b*x + a)*x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.151745, size = 87, normalized size = 1. \[ \frac{a^{6} c^{5} x^{4}}{4} - \frac{4 a^{5} b c^{5} x^{5}}{5} + \frac{5 a^{4} b^{2} c^{5} x^{6}}{6} - \frac{5 a^{2} b^{4} c^{5} x^{8}}{8} + \frac{4 a b^{5} c^{5} x^{9}}{9} - \frac{b^{6} c^{5} x^{10}}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3*(b*x+a)*(-b*c*x+a*c)**5,x)
[Out]
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GIAC/XCAS [A] time = 0.242206, size = 101, normalized size = 1.16 \[ -\frac{1}{10} \, b^{6} c^{5} x^{10} + \frac{4}{9} \, a b^{5} c^{5} x^{9} - \frac{5}{8} \, a^{2} b^{4} c^{5} x^{8} + \frac{5}{6} \, a^{4} b^{2} c^{5} x^{6} - \frac{4}{5} \, a^{5} b c^{5} x^{5} + \frac{1}{4} \, a^{6} c^{5} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^5*(b*x + a)*x^3,x, algorithm="giac")
[Out]