Optimal. Leaf size=25 \[ \frac{a x^3}{3}+\frac{b x^4}{4}+\frac{c x^5}{5} \]
[Out]
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Rubi [A] time = 0.0111658, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \frac{a x^3}{3}+\frac{b x^4}{4}+\frac{c x^5}{5} \]
Antiderivative was successfully verified.
[In] Int[a*x^2 + b*x^3 + c*x^4,x]
[Out]
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Rubi in Sympy [A] time = 1.90647, size = 19, normalized size = 0.76 \[ \frac{a x^{3}}{3} + \frac{b x^{4}}{4} + \frac{c x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(c*x**4+b*x**3+a*x**2,x)
[Out]
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Mathematica [A] time = 0.0000735961, size = 25, normalized size = 1. \[ \frac{a x^3}{3}+\frac{b x^4}{4}+\frac{c x^5}{5} \]
Antiderivative was successfully verified.
[In] Integrate[a*x^2 + b*x^3 + c*x^4,x]
[Out]
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Maple [A] time = 0.001, size = 20, normalized size = 0.8 \[{\frac{a{x}^{3}}{3}}+{\frac{b{x}^{4}}{4}}+{\frac{c{x}^{5}}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(c*x^4+b*x^3+a*x^2,x)
[Out]
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Maxima [A] time = 0.754257, size = 26, normalized size = 1.04 \[ \frac{1}{5} \, c x^{5} + \frac{1}{4} \, b x^{4} + \frac{1}{3} \, a x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(c*x^4 + b*x^3 + a*x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.240485, size = 1, normalized size = 0.04 \[ \frac{1}{5} x^{5} c + \frac{1}{4} x^{4} b + \frac{1}{3} x^{3} a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(c*x^4 + b*x^3 + a*x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.062307, size = 19, normalized size = 0.76 \[ \frac{a x^{3}}{3} + \frac{b x^{4}}{4} + \frac{c x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(c*x**4+b*x**3+a*x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.261066, size = 26, normalized size = 1.04 \[ \frac{1}{5} \, c x^{5} + \frac{1}{4} \, b x^{4} + \frac{1}{3} \, a x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(c*x^4 + b*x^3 + a*x^2,x, algorithm="giac")
[Out]