Optimal. Leaf size=32 \[ 3 a b x+\frac{3 b^2 x^2}{2}+b c x^3+\frac{c^2 x^4}{4} \]
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Rubi [A] time = 0.0170615, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ 3 a b x+\frac{3 b^2 x^2}{2}+b c x^3+\frac{c^2 x^4}{4} \]
Antiderivative was successfully verified.
[In] Int[3*a*b + 3*b^2*x + 3*b*c*x^2 + c^2*x^3,x]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ 3 a b x + 3 b^{2} \int x\, dx + b c x^{3} + \frac{c^{2} x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(c**2*x**3+3*b*c*x**2+3*b**2*x+3*a*b,x)
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Mathematica [A] time = 0.0000655965, size = 32, normalized size = 1. \[ 3 a b x+\frac{3 b^2 x^2}{2}+b c x^3+\frac{c^2 x^4}{4} \]
Antiderivative was successfully verified.
[In] Integrate[3*a*b + 3*b^2*x + 3*b*c*x^2 + c^2*x^3,x]
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Maple [A] time = 0.001, size = 29, normalized size = 0.9 \[ 3\,abx+{\frac{3\,{b}^{2}{x}^{2}}{2}}+bc{x}^{3}+{\frac{{c}^{2}{x}^{4}}{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(c^2*x^3+3*b*c*x^2+3*b^2*x+3*a*b,x)
[Out]
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Maxima [A] time = 0.77087, size = 38, normalized size = 1.19 \[ \frac{1}{4} \, c^{2} x^{4} + b c x^{3} + \frac{3}{2} \, b^{2} x^{2} + 3 \, a b x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(c^2*x^3 + 3*b*c*x^2 + 3*b^2*x + 3*a*b,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.2788, size = 1, normalized size = 0.03 \[ \frac{1}{4} x^{4} c^{2} + x^{3} c b + \frac{3}{2} x^{2} b^{2} + 3 x b a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(c^2*x^3 + 3*b*c*x^2 + 3*b^2*x + 3*a*b,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.090594, size = 31, normalized size = 0.97 \[ 3 a b x + \frac{3 b^{2} x^{2}}{2} + b c x^{3} + \frac{c^{2} x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(c**2*x**3+3*b*c*x**2+3*b**2*x+3*a*b,x)
[Out]
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GIAC/XCAS [A] time = 0.25942, size = 38, normalized size = 1.19 \[ \frac{1}{4} \, c^{2} x^{4} + b c x^{3} + \frac{3}{2} \, b^{2} x^{2} + 3 \, a b x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(c^2*x^3 + 3*b*c*x^2 + 3*b^2*x + 3*a*b,x, algorithm="giac")
[Out]