Optimal. Leaf size=16 \[ \frac{\left (a+b x^3\right )^3}{9 b} \]
[Out]
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Rubi [A] time = 0.0110733, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{\left (a+b x^3\right )^3}{9 b} \]
Antiderivative was successfully verified.
[In] Int[x^2*(a + b*x^3)^2,x]
[Out]
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Rubi in Sympy [A] time = 2.1535, size = 10, normalized size = 0.62 \[ \frac{\left (a + b x^{3}\right )^{3}}{9 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2*(b*x**3+a)**2,x)
[Out]
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Mathematica [A] time = 0.00129401, size = 30, normalized size = 1.88 \[ \frac{a^2 x^3}{3}+\frac{1}{3} a b x^6+\frac{b^2 x^9}{9} \]
Antiderivative was successfully verified.
[In] Integrate[x^2*(a + b*x^3)^2,x]
[Out]
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Maple [A] time = 0.001, size = 25, normalized size = 1.6 \[{\frac{{b}^{2}{x}^{9}}{9}}+{\frac{ab{x}^{6}}{3}}+{\frac{{x}^{3}{a}^{2}}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2*(b*x^3+a)^2,x)
[Out]
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Maxima [A] time = 1.42649, size = 19, normalized size = 1.19 \[ \frac{{\left (b x^{3} + a\right )}^{3}}{9 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2*x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.201224, size = 1, normalized size = 0.06 \[ \frac{1}{9} x^{9} b^{2} + \frac{1}{3} x^{6} b a + \frac{1}{3} x^{3} a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2*x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.089508, size = 24, normalized size = 1.5 \[ \frac{a^{2} x^{3}}{3} + \frac{a b x^{6}}{3} + \frac{b^{2} x^{9}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2*(b*x**3+a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.213153, size = 19, normalized size = 1.19 \[ \frac{{\left (b x^{3} + a\right )}^{3}}{9 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2*x^2,x, algorithm="giac")
[Out]