Optimal. Leaf size=35 \[ a^3 x+\frac{3}{2} a^2 b x^2+a b^2 x^3+\frac{b^3 x^4}{4} \]
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Rubi [A] time = 0.0181635, antiderivative size = 35, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 27, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ a^3 x+\frac{3}{2} a^2 b x^2+a b^2 x^3+\frac{b^3 x^4}{4} \]
Antiderivative was successfully verified.
[In] Int[a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3,x]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ 3 a^{2} b \int x\, dx + a b^{2} x^{3} + \frac{b^{3} x^{4}}{4} + \int a^{3}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(b**3*x**3+3*a*b**2*x**2+3*a**2*b*x+a**3,x)
[Out]
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Mathematica [A] time = 0.0000883153, size = 35, normalized size = 1. \[ a^3 x+\frac{3}{2} a^2 b x^2+a b^2 x^3+\frac{b^3 x^4}{4} \]
Antiderivative was successfully verified.
[In] Integrate[a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3,x]
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Maple [A] time = 0.001, size = 32, normalized size = 0.9 \[{a}^{3}x+{\frac{3\,{a}^{2}b{x}^{2}}{2}}+a{b}^{2}{x}^{3}+{\frac{{b}^{3}{x}^{4}}{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(b^3*x^3+3*a*b^2*x^2+3*a^2*b*x+a^3,x)
[Out]
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Maxima [A] time = 0.757947, size = 42, normalized size = 1.2 \[ \frac{1}{4} \, b^{3} x^{4} + a b^{2} x^{3} + \frac{3}{2} \, a^{2} b x^{2} + a^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.23837, size = 1, normalized size = 0.03 \[ \frac{1}{4} x^{4} b^{3} + x^{3} b^{2} a + \frac{3}{2} x^{2} b a^{2} + x a^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.084519, size = 32, normalized size = 0.91 \[ a^{3} x + \frac{3 a^{2} b x^{2}}{2} + a b^{2} x^{3} + \frac{b^{3} x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(b**3*x**3+3*a*b**2*x**2+3*a**2*b*x+a**3,x)
[Out]
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GIAC/XCAS [A] time = 0.259653, size = 42, normalized size = 1.2 \[ \frac{1}{4} \, b^{3} x^{4} + a b^{2} x^{3} + \frac{3}{2} \, a^{2} b x^{2} + a^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3,x, algorithm="giac")
[Out]