Optimal. Leaf size=25 \[ a^2 x+\frac{1}{2} a b x^4+\frac{b^2 x^7}{7} \]
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Rubi [A] time = 0.019294, antiderivative size = 25, 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 \[ a^2 x+\frac{1}{2} a b x^4+\frac{b^2 x^7}{7} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{a b x^{4}}{2} + \frac{b^{2} x^{7}}{7} + \int a^{2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**2,x)
[Out]
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Mathematica [A] time = 0.00138265, size = 25, normalized size = 1. \[ a^2 x+\frac{1}{2} a b x^4+\frac{b^2 x^7}{7} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^2,x]
[Out]
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Maple [A] time = 0.002, size = 22, normalized size = 0.9 \[ x{a}^{2}+{\frac{ab{x}^{4}}{2}}+{\frac{{b}^{2}{x}^{7}}{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^2,x)
[Out]
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Maxima [A] time = 1.43386, size = 28, normalized size = 1.12 \[ \frac{1}{7} \, b^{2} x^{7} + \frac{1}{2} \, a b x^{4} + a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.230754, size = 1, normalized size = 0.04 \[ \frac{1}{7} x^{7} b^{2} + \frac{1}{2} x^{4} b a + x a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.08248, size = 20, normalized size = 0.8 \[ a^{2} x + \frac{a b x^{4}}{2} + \frac{b^{2} x^{7}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.22073, size = 28, normalized size = 1.12 \[ \frac{1}{7} \, b^{2} x^{7} + \frac{1}{2} \, a b x^{4} + a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2,x, algorithm="giac")
[Out]