Optimal. Leaf size=30 \[ \frac{a^2 x^4}{4}+\frac{1}{3} a b x^6+\frac{b^2 x^8}{8} \]
[Out]
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Rubi [A] time = 0.0539066, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{a^2 x^4}{4}+\frac{1}{3} a b x^6+\frac{b^2 x^8}{8} \]
Antiderivative was successfully verified.
[In] Int[x^3*(a + b*x^2)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{a^{2} \int ^{x^{2}} x\, dx}{2} + \frac{a b x^{6}}{3} + \frac{b^{2} x^{8}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3*(b*x**2+a)**2,x)
[Out]
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Mathematica [A] time = 0.00134393, size = 30, normalized size = 1. \[ \frac{a^2 x^4}{4}+\frac{1}{3} a b x^6+\frac{b^2 x^8}{8} \]
Antiderivative was successfully verified.
[In] Integrate[x^3*(a + b*x^2)^2,x]
[Out]
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Maple [A] time = 0., size = 25, normalized size = 0.8 \[{\frac{{a}^{2}{x}^{4}}{4}}+{\frac{ab{x}^{6}}{3}}+{\frac{{b}^{2}{x}^{8}}{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3*(b*x^2+a)^2,x)
[Out]
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Maxima [A] time = 1.32923, size = 32, normalized size = 1.07 \[ \frac{1}{8} \, b^{2} x^{8} + \frac{1}{3} \, a b x^{6} + \frac{1}{4} \, a^{2} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^2*x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.18926, size = 1, normalized size = 0.03 \[ \frac{1}{8} x^{8} b^{2} + \frac{1}{3} x^{6} b a + \frac{1}{4} x^{4} a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^2*x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.084781, size = 24, normalized size = 0.8 \[ \frac{a^{2} x^{4}}{4} + \frac{a b x^{6}}{3} + \frac{b^{2} x^{8}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3*(b*x**2+a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.208328, size = 32, normalized size = 1.07 \[ \frac{1}{8} \, b^{2} x^{8} + \frac{1}{3} \, a b x^{6} + \frac{1}{4} \, a^{2} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^2*x^3,x, algorithm="giac")
[Out]