Optimal. Leaf size=20 \[ a x+\frac{b x^2}{2}+\frac{c x^3}{3} \]
[Out]
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Rubi [A] time = 0.0130694, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ a x+\frac{b x^2}{2}+\frac{c x^3}{3} \]
Antiderivative was successfully verified.
[In] Int[a + b*x + c*x^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ b \int x\, dx + \frac{c x^{3}}{3} + \int a\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(c*x**2+b*x+a,x)
[Out]
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Mathematica [A] time = 0.0000812757, size = 20, normalized size = 1. \[ a x+\frac{b x^2}{2}+\frac{c x^3}{3} \]
Antiderivative was successfully verified.
[In] Integrate[a + b*x + c*x^2,x]
[Out]
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Maple [A] time = 0.001, size = 17, normalized size = 0.9 \[ ax+{\frac{b{x}^{2}}{2}}+{\frac{c{x}^{3}}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(c*x^2+b*x+a,x)
[Out]
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Maxima [A] time = 0.817472, size = 22, normalized size = 1.1 \[ \frac{1}{3} \, c x^{3} + \frac{1}{2} \, b x^{2} + a x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(c*x^2 + b*x + a,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.180951, size = 1, normalized size = 0.05 \[ \frac{1}{3} x^{3} c + \frac{1}{2} x^{2} b + x a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(c*x^2 + b*x + a,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.06902, size = 15, normalized size = 0.75 \[ a x + \frac{b x^{2}}{2} + \frac{c x^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(c*x**2+b*x+a,x)
[Out]
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GIAC/XCAS [A] time = 0.201113, size = 22, normalized size = 1.1 \[ \frac{1}{3} \, c x^{3} + \frac{1}{2} \, b x^{2} + a x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(c*x^2 + b*x + a,x, algorithm="giac")
[Out]