Optimal. Leaf size=87 \[ \frac{1}{5} a^5 c^4 x^5-\frac{1}{2} a^4 b c^4 x^6+\frac{2}{7} a^3 b^2 c^4 x^7+\frac{1}{4} a^2 b^3 c^4 x^8-\frac{1}{3} a b^4 c^4 x^9+\frac{1}{10} b^5 c^4 x^{10} \]
[Out]
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Rubi [A] time = 0.140707, 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 \[ \frac{1}{5} a^5 c^4 x^5-\frac{1}{2} a^4 b c^4 x^6+\frac{2}{7} a^3 b^2 c^4 x^7+\frac{1}{4} a^2 b^3 c^4 x^8-\frac{1}{3} a b^4 c^4 x^9+\frac{1}{10} b^5 c^4 x^{10} \]
Antiderivative was successfully verified.
[In] Int[x^4*(a + b*x)*(a*c - b*c*x)^4,x]
[Out]
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Rubi in Sympy [A] time = 35.1911, size = 82, normalized size = 0.94 \[ \frac{a^{5} c^{4} x^{5}}{5} - \frac{a^{4} b c^{4} x^{6}}{2} + \frac{2 a^{3} b^{2} c^{4} x^{7}}{7} + \frac{a^{2} b^{3} c^{4} x^{8}}{4} - \frac{a b^{4} c^{4} x^{9}}{3} + \frac{b^{5} c^{4} x^{10}}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**4*(b*x+a)*(-b*c*x+a*c)**4,x)
[Out]
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Mathematica [A] time = 0.00722586, size = 87, normalized size = 1. \[ \frac{1}{5} a^5 c^4 x^5-\frac{1}{2} a^4 b c^4 x^6+\frac{2}{7} a^3 b^2 c^4 x^7+\frac{1}{4} a^2 b^3 c^4 x^8-\frac{1}{3} a b^4 c^4 x^9+\frac{1}{10} b^5 c^4 x^{10} \]
Antiderivative was successfully verified.
[In] Integrate[x^4*(a + b*x)*(a*c - b*c*x)^4,x]
[Out]
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Maple [A] time = 0.002, size = 76, normalized size = 0.9 \[{\frac{{a}^{5}{c}^{4}{x}^{5}}{5}}-{\frac{{a}^{4}b{c}^{4}{x}^{6}}{2}}+{\frac{2\,{a}^{3}{b}^{2}{c}^{4}{x}^{7}}{7}}+{\frac{{a}^{2}{b}^{3}{c}^{4}{x}^{8}}{4}}-{\frac{a{b}^{4}{c}^{4}{x}^{9}}{3}}+{\frac{{b}^{5}{c}^{4}{x}^{10}}{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^4*(b*x+a)*(-b*c*x+a*c)^4,x)
[Out]
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Maxima [A] time = 1.34917, size = 101, normalized size = 1.16 \[ \frac{1}{10} \, b^{5} c^{4} x^{10} - \frac{1}{3} \, a b^{4} c^{4} x^{9} + \frac{1}{4} \, a^{2} b^{3} c^{4} x^{8} + \frac{2}{7} \, a^{3} b^{2} c^{4} x^{7} - \frac{1}{2} \, a^{4} b c^{4} x^{6} + \frac{1}{5} \, a^{5} c^{4} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*c*x - a*c)^4*(b*x + a)*x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.186274, size = 1, normalized size = 0.01 \[ \frac{1}{10} x^{10} c^{4} b^{5} - \frac{1}{3} x^{9} c^{4} b^{4} a + \frac{1}{4} x^{8} c^{4} b^{3} a^{2} + \frac{2}{7} x^{7} c^{4} b^{2} a^{3} - \frac{1}{2} x^{6} c^{4} b a^{4} + \frac{1}{5} x^{5} c^{4} a^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*c*x - a*c)^4*(b*x + a)*x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.075412, size = 82, normalized size = 0.94 \[ \frac{a^{5} c^{4} x^{5}}{5} - \frac{a^{4} b c^{4} x^{6}}{2} + \frac{2 a^{3} b^{2} c^{4} x^{7}}{7} + \frac{a^{2} b^{3} c^{4} x^{8}}{4} - \frac{a b^{4} c^{4} x^{9}}{3} + \frac{b^{5} c^{4} x^{10}}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**4*(b*x+a)*(-b*c*x+a*c)**4,x)
[Out]
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GIAC/XCAS [A] time = 0.245858, size = 101, normalized size = 1.16 \[ \frac{1}{10} \, b^{5} c^{4} x^{10} - \frac{1}{3} \, a b^{4} c^{4} x^{9} + \frac{1}{4} \, a^{2} b^{3} c^{4} x^{8} + \frac{2}{7} \, a^{3} b^{2} c^{4} x^{7} - \frac{1}{2} \, a^{4} b c^{4} x^{6} + \frac{1}{5} \, a^{5} c^{4} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*c*x - a*c)^4*(b*x + a)*x^4,x, algorithm="giac")
[Out]