Optimal. Leaf size=28 \[ a x+\frac{b x^2}{2}+\frac{c x^3}{3}+\frac{d x^4}{4} \]
[Out]
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Rubi [A] time = 0.0129856, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ a x+\frac{b x^2}{2}+\frac{c x^3}{3}+\frac{d x^4}{4} \]
Antiderivative was successfully verified.
[In] Int[a + b*x + c*x^2 + d*x^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ b \int x\, dx + \frac{c x^{3}}{3} + \frac{d x^{4}}{4} + \int a\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(d*x**3+c*x**2+b*x+a,x)
[Out]
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Mathematica [A] time = 0.0000611168, size = 28, normalized size = 1. \[ a x+\frac{b x^2}{2}+\frac{c x^3}{3}+\frac{d x^4}{4} \]
Antiderivative was successfully verified.
[In] Integrate[a + b*x + c*x^2 + d*x^3,x]
[Out]
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Maple [A] time = 0.001, size = 23, normalized size = 0.8 \[ ax+{\frac{b{x}^{2}}{2}}+{\frac{c{x}^{3}}{3}}+{\frac{d{x}^{4}}{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(d*x^3+c*x^2+b*x+a,x)
[Out]
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Maxima [A] time = 1.32398, size = 30, normalized size = 1.07 \[ \frac{1}{4} \, d x^{4} + \frac{1}{3} \, c x^{3} + \frac{1}{2} \, b x^{2} + a x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(d*x^3 + c*x^2 + b*x + a,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.179296, size = 1, normalized size = 0.04 \[ \frac{1}{4} x^{4} d + \frac{1}{3} x^{3} c + \frac{1}{2} x^{2} b + x a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(d*x^3 + c*x^2 + b*x + a,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.037245, size = 22, normalized size = 0.79 \[ a x + \frac{b x^{2}}{2} + \frac{c x^{3}}{3} + \frac{d x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(d*x**3+c*x**2+b*x+a,x)
[Out]
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GIAC/XCAS [A] time = 0.232431, size = 30, normalized size = 1.07 \[ \frac{1}{4} \, d x^{4} + \frac{1}{3} \, c x^{3} + \frac{1}{2} \, b x^{2} + a x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(d*x^3 + c*x^2 + b*x + a,x, algorithm="giac")
[Out]