Optimal. Leaf size=55 \[ \frac{1}{3} a^4 c^3 x^3-\frac{1}{2} a^3 b c^3 x^4+\frac{1}{3} a b^3 c^3 x^6-\frac{1}{7} b^4 c^3 x^7 \]
[Out]
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Rubi [A] time = 0.0969724, antiderivative size = 55, 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 \[ \frac{1}{3} a^4 c^3 x^3-\frac{1}{2} a^3 b c^3 x^4+\frac{1}{3} a b^3 c^3 x^6-\frac{1}{7} b^4 c^3 x^7 \]
Antiderivative was successfully verified.
[In] Int[x^2*(a + b*x)*(a*c - b*c*x)^3,x]
[Out]
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Rubi in Sympy [A] time = 22.3337, size = 49, normalized size = 0.89 \[ \frac{a^{4} c^{3} x^{3}}{3} - \frac{a^{3} b c^{3} x^{4}}{2} + \frac{a b^{3} c^{3} x^{6}}{3} - \frac{b^{4} c^{3} x^{7}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2*(b*x+a)*(-b*c*x+a*c)**3,x)
[Out]
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Mathematica [A] time = 0.00588609, size = 47, normalized size = 0.85 \[ c^3 \left (\frac{a^4 x^3}{3}-\frac{1}{2} a^3 b x^4+\frac{1}{3} a b^3 x^6-\frac{1}{7} b^4 x^7\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^2*(a + b*x)*(a*c - b*c*x)^3,x]
[Out]
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Maple [A] time = 0.001, size = 48, normalized size = 0.9 \[{\frac{{a}^{4}{c}^{3}{x}^{3}}{3}}-{\frac{{a}^{3}b{c}^{3}{x}^{4}}{2}}+{\frac{a{b}^{3}{c}^{3}{x}^{6}}{3}}-{\frac{{b}^{4}{c}^{3}{x}^{7}}{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2*(b*x+a)*(-b*c*x+a*c)^3,x)
[Out]
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Maxima [A] time = 1.35392, size = 63, normalized size = 1.15 \[ -\frac{1}{7} \, b^{4} c^{3} x^{7} + \frac{1}{3} \, a b^{3} c^{3} x^{6} - \frac{1}{2} \, a^{3} b c^{3} x^{4} + \frac{1}{3} \, a^{4} c^{3} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^3*(b*x + a)*x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.182293, size = 1, normalized size = 0.02 \[ -\frac{1}{7} x^{7} c^{3} b^{4} + \frac{1}{3} x^{6} c^{3} b^{3} a - \frac{1}{2} x^{4} c^{3} b a^{3} + \frac{1}{3} x^{3} c^{3} a^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^3*(b*x + a)*x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.063702, size = 49, normalized size = 0.89 \[ \frac{a^{4} c^{3} x^{3}}{3} - \frac{a^{3} b c^{3} x^{4}}{2} + \frac{a b^{3} c^{3} x^{6}}{3} - \frac{b^{4} c^{3} x^{7}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2*(b*x+a)*(-b*c*x+a*c)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.324206, size = 63, normalized size = 1.15 \[ -\frac{1}{7} \, b^{4} c^{3} x^{7} + \frac{1}{3} \, a b^{3} c^{3} x^{6} - \frac{1}{2} \, a^{3} b c^{3} x^{4} + \frac{1}{3} \, a^{4} c^{3} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^3*(b*x + a)*x^2,x, algorithm="giac")
[Out]