Optimal. Leaf size=16 \[ \frac{\left (a+b x^2\right )^3}{6 b} \]
[Out]
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Rubi [A] time = 0.0122781, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{\left (a+b x^2\right )^3}{6 b} \]
Antiderivative was successfully verified.
[In] Int[x*(a + b*x^2)^2,x]
[Out]
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Rubi in Sympy [A] time = 2.16477, size = 10, normalized size = 0.62 \[ \frac{\left (a + b x^{2}\right )^{3}}{6 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(b*x**2+a)**2,x)
[Out]
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Mathematica [A] time = 0.0037182, size = 16, normalized size = 1. \[ \frac{\left (a+b x^2\right )^3}{6 b} \]
Antiderivative was successfully verified.
[In] Integrate[x*(a + b*x^2)^2,x]
[Out]
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Maple [A] time = 0., size = 25, normalized size = 1.6 \[{\frac{{b}^{2}{x}^{6}}{6}}+{\frac{ab{x}^{4}}{2}}+{\frac{{a}^{2}{x}^{2}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(b*x^2+a)^2,x)
[Out]
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Maxima [A] time = 1.32701, size = 19, normalized size = 1.19 \[ \frac{{\left (b x^{2} + a\right )}^{3}}{6 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^2*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.193589, size = 1, normalized size = 0.06 \[ \frac{1}{6} x^{6} b^{2} + \frac{1}{2} x^{4} b a + \frac{1}{2} x^{2} a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^2*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.085306, size = 24, normalized size = 1.5 \[ \frac{a^{2} x^{2}}{2} + \frac{a b x^{4}}{2} + \frac{b^{2} x^{6}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(b*x**2+a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.207605, size = 19, normalized size = 1.19 \[ \frac{{\left (b x^{2} + a\right )}^{3}}{6 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^2*x,x, algorithm="giac")
[Out]