Optimal. Leaf size=30 \[ \frac{a^2 x^2}{2}+\frac{2}{5} a b x^5+\frac{b^2 x^8}{8} \]
[Out]
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Rubi [A] time = 0.0300272, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{a^2 x^2}{2}+\frac{2}{5} a b x^5+\frac{b^2 x^8}{8} \]
Antiderivative was successfully verified.
[In] Int[x*(a + b*x^3)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ a^{2} \int x\, dx + \frac{2 a b x^{5}}{5} + \frac{b^{2} x^{8}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(b*x**3+a)**2,x)
[Out]
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Mathematica [A] time = 0.00237939, size = 30, normalized size = 1. \[ \frac{a^2 x^2}{2}+\frac{2}{5} a b x^5+\frac{b^2 x^8}{8} \]
Antiderivative was successfully verified.
[In] Integrate[x*(a + b*x^3)^2,x]
[Out]
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Maple [A] time = 0., size = 25, normalized size = 0.8 \[{\frac{{a}^{2}{x}^{2}}{2}}+{\frac{2\,{x}^{5}ab}{5}}+{\frac{{b}^{2}{x}^{8}}{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(b*x^3+a)^2,x)
[Out]
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Maxima [A] time = 1.4479, size = 32, normalized size = 1.07 \[ \frac{1}{8} \, b^{2} x^{8} + \frac{2}{5} \, a b x^{5} + \frac{1}{2} \, a^{2} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.213689, size = 1, normalized size = 0.03 \[ \frac{1}{8} x^{8} b^{2} + \frac{2}{5} x^{5} b a + \frac{1}{2} x^{2} a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.083848, size = 26, normalized size = 0.87 \[ \frac{a^{2} x^{2}}{2} + \frac{2 a b x^{5}}{5} + \frac{b^{2} x^{8}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(b*x**3+a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.217683, size = 32, normalized size = 1.07 \[ \frac{1}{8} \, b^{2} x^{8} + \frac{2}{5} \, a b x^{5} + \frac{1}{2} \, a^{2} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2*x,x, algorithm="giac")
[Out]