Optimal. Leaf size=22 \[ a^2 x+a b x^2+\frac{b^2 x^3}{3} \]
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Rubi [A] time = 0.0169338, antiderivative size = 22, 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. \[ a^2 x+a b x^2+\frac{b^2 x^3}{3} \]
Antiderivative was successfully verified.
[In] Int[a^2 + 2*a*b*x + b^2*x^2,x]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ 2 a b \int x\, dx + \frac{b^{2} x^{3}}{3} + \int a^{2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(b**2*x**2+2*a*b*x+a**2,x)
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Mathematica [A] time = 0.0000867154, size = 22, normalized size = 1. \[ a^2 x+a b x^2+\frac{b^2 x^3}{3} \]
Antiderivative was successfully verified.
[In] Integrate[a^2 + 2*a*b*x + b^2*x^2,x]
[Out]
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Maple [A] time = 0.001, size = 21, normalized size = 1. \[{a}^{2}x+ab{x}^{2}+{\frac{{b}^{2}{x}^{3}}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(b^2*x^2+2*a*b*x+a^2,x)
[Out]
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Maxima [A] time = 0.682515, size = 27, normalized size = 1.23 \[ \frac{1}{3} \, b^{2} x^{3} + a b x^{2} + a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(b^2*x^2 + 2*a*b*x + a^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.177512, size = 1, normalized size = 0.05 \[ \frac{1}{3} x^{3} b^{2} + x^{2} b a + x a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(b^2*x^2 + 2*a*b*x + a^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.076543, size = 19, normalized size = 0.86 \[ a^{2} x + a b x^{2} + \frac{b^{2} x^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(b**2*x**2+2*a*b*x+a**2,x)
[Out]
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GIAC/XCAS [A] time = 0.209654, size = 27, normalized size = 1.23 \[ \frac{1}{3} \, b^{2} x^{3} + a b x^{2} + a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(b^2*x^2 + 2*a*b*x + a^2,x, algorithm="giac")
[Out]