Optimal. Leaf size=87 \[ \frac{1}{4} a^5 c^4 x^4-\frac{3}{5} a^4 b c^4 x^5+\frac{1}{3} a^3 b^2 c^4 x^6+\frac{2}{7} a^2 b^3 c^4 x^7-\frac{3}{8} a b^4 c^4 x^8+\frac{1}{9} b^5 c^4 x^9 \]
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Rubi [A] time = 0.129145, 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 \[ \frac{1}{4} a^5 c^4 x^4-\frac{3}{5} a^4 b c^4 x^5+\frac{1}{3} a^3 b^2 c^4 x^6+\frac{2}{7} a^2 b^3 c^4 x^7-\frac{3}{8} a b^4 c^4 x^8+\frac{1}{9} b^5 c^4 x^9 \]
Antiderivative was successfully verified.
[In] Int[x^3*(a + b*x)*(a*c - b*c*x)^4,x]
[Out]
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Rubi in Sympy [A] time = 34.3876, size = 85, normalized size = 0.98 \[ \frac{a^{5} c^{4} x^{4}}{4} - \frac{3 a^{4} b c^{4} x^{5}}{5} + \frac{a^{3} b^{2} c^{4} x^{6}}{3} + \frac{2 a^{2} b^{3} c^{4} x^{7}}{7} - \frac{3 a b^{4} c^{4} x^{8}}{8} + \frac{b^{5} c^{4} x^{9}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3*(b*x+a)*(-b*c*x+a*c)**4,x)
[Out]
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Mathematica [A] time = 0.00489126, size = 87, normalized size = 1. \[ \frac{1}{4} a^5 c^4 x^4-\frac{3}{5} a^4 b c^4 x^5+\frac{1}{3} a^3 b^2 c^4 x^6+\frac{2}{7} a^2 b^3 c^4 x^7-\frac{3}{8} a b^4 c^4 x^8+\frac{1}{9} b^5 c^4 x^9 \]
Antiderivative was successfully verified.
[In] Integrate[x^3*(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 \[{\frac{{a}^{5}{c}^{4}{x}^{4}}{4}}-{\frac{3\,{a}^{4}b{c}^{4}{x}^{5}}{5}}+{\frac{{a}^{3}{b}^{2}{c}^{4}{x}^{6}}{3}}+{\frac{2\,{a}^{2}{b}^{3}{c}^{4}{x}^{7}}{7}}-{\frac{3\,a{b}^{4}{c}^{4}{x}^{8}}{8}}+{\frac{{b}^{5}{c}^{4}{x}^{9}}{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3*(b*x+a)*(-b*c*x+a*c)^4,x)
[Out]
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Maxima [A] time = 1.34337, size = 101, normalized size = 1.16 \[ \frac{1}{9} \, b^{5} c^{4} x^{9} - \frac{3}{8} \, a b^{4} c^{4} x^{8} + \frac{2}{7} \, a^{2} b^{3} c^{4} x^{7} + \frac{1}{3} \, a^{3} b^{2} c^{4} x^{6} - \frac{3}{5} \, a^{4} b c^{4} x^{5} + \frac{1}{4} \, a^{5} c^{4} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*c*x - a*c)^4*(b*x + a)*x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.17796, size = 1, normalized size = 0.01 \[ \frac{1}{9} x^{9} c^{4} b^{5} - \frac{3}{8} x^{8} c^{4} b^{4} a + \frac{2}{7} x^{7} c^{4} b^{3} a^{2} + \frac{1}{3} x^{6} c^{4} b^{2} a^{3} - \frac{3}{5} x^{5} c^{4} b a^{4} + \frac{1}{4} x^{4} c^{4} a^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*c*x - a*c)^4*(b*x + a)*x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.075467, size = 85, normalized size = 0.98 \[ \frac{a^{5} c^{4} x^{4}}{4} - \frac{3 a^{4} b c^{4} x^{5}}{5} + \frac{a^{3} b^{2} c^{4} x^{6}}{3} + \frac{2 a^{2} b^{3} c^{4} x^{7}}{7} - \frac{3 a b^{4} c^{4} x^{8}}{8} + \frac{b^{5} c^{4} x^{9}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3*(b*x+a)*(-b*c*x+a*c)**4,x)
[Out]
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GIAC/XCAS [A] time = 0.241223, size = 101, normalized size = 1.16 \[ \frac{1}{9} \, b^{5} c^{4} x^{9} - \frac{3}{8} \, a b^{4} c^{4} x^{8} + \frac{2}{7} \, a^{2} b^{3} c^{4} x^{7} + \frac{1}{3} \, a^{3} b^{2} c^{4} x^{6} - \frac{3}{5} \, a^{4} b c^{4} x^{5} + \frac{1}{4} \, a^{5} c^{4} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*c*x - a*c)^4*(b*x + a)*x^3,x, algorithm="giac")
[Out]