Optimal. Leaf size=30 \[ \frac{a^2 x^2}{2}+\frac{2}{3} a b x^3+\frac{b^2 x^4}{4} \]
[Out]
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Rubi [A] time = 0.0255135, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \frac{a^2 x^2}{2}+\frac{2}{3} a b x^3+\frac{b^2 x^4}{4} \]
Antiderivative was successfully verified.
[In] Int[x*(a + b*x)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ a^{2} \int x\, dx + \frac{2 a b x^{3}}{3} + \frac{b^{2} x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(b*x+a)**2,x)
[Out]
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Mathematica [A] time = 0.00187126, size = 30, normalized size = 1. \[ \frac{a^2 x^2}{2}+\frac{2}{3} a b x^3+\frac{b^2 x^4}{4} \]
Antiderivative was successfully verified.
[In] Integrate[x*(a + b*x)^2,x]
[Out]
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Maple [A] time = 0., size = 25, normalized size = 0.8 \[{\frac{{a}^{2}{x}^{2}}{2}}+{\frac{2\,ab{x}^{3}}{3}}+{\frac{{b}^{2}{x}^{4}}{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(b*x+a)^2,x)
[Out]
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Maxima [A] time = 1.33277, size = 32, normalized size = 1.07 \[ \frac{1}{4} \, b^{2} x^{4} + \frac{2}{3} \, a b x^{3} + \frac{1}{2} \, a^{2} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^2*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.177388, size = 1, normalized size = 0.03 \[ \frac{1}{4} x^{4} b^{2} + \frac{2}{3} x^{3} b a + \frac{1}{2} x^{2} a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^2*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.080362, size = 26, normalized size = 0.87 \[ \frac{a^{2} x^{2}}{2} + \frac{2 a b x^{3}}{3} + \frac{b^{2} x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(b*x+a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.208858, size = 32, normalized size = 1.07 \[ \frac{1}{4} \, b^{2} x^{4} + \frac{2}{3} \, a b x^{3} + \frac{1}{2} \, a^{2} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^2*x,x, algorithm="giac")
[Out]