Optimal. Leaf size=11 \[ \frac{1}{18} \left (x^2+5\right )^9 \]
[Out]
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Rubi [A] time = 0.00692123, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \frac{1}{18} \left (x^2+5\right )^9 \]
Antiderivative was successfully verified.
[In] Int[x*(5 + x^2)^8,x]
[Out]
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Rubi in Sympy [A] time = 0.778112, size = 7, normalized size = 0.64 \[ \frac{\left (x^{2} + 5\right )^{9}}{18} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(x**2+5)**8,x)
[Out]
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Mathematica [A] time = 0.0026133, size = 11, normalized size = 1. \[ \frac{1}{18} \left (x^2+5\right )^9 \]
Antiderivative was successfully verified.
[In] Integrate[x*(5 + x^2)^8,x]
[Out]
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Maple [B] time = 0.003, size = 47, normalized size = 4.3 \[{\frac{{x}^{18}}{18}}+{\frac{5\,{x}^{16}}{2}}+50\,{x}^{14}+{\frac{1750\,{x}^{12}}{3}}+4375\,{x}^{10}+21875\,{x}^{8}+{\frac{218750\,{x}^{6}}{3}}+156250\,{x}^{4}+{\frac{390625\,{x}^{2}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(x^2+5)^8,x)
[Out]
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Maxima [A] time = 1.35063, size = 12, normalized size = 1.09 \[ \frac{1}{18} \,{\left (x^{2} + 5\right )}^{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 5)^8*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.167509, size = 1, normalized size = 0.09 \[ \frac{1}{18} x^{18} + \frac{5}{2} x^{16} + 50 x^{14} + \frac{1750}{3} x^{12} + 4375 x^{10} + 21875 x^{8} + \frac{218750}{3} x^{6} + 156250 x^{4} + \frac{390625}{2} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 5)^8*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.038304, size = 51, normalized size = 4.64 \[ \frac{x^{18}}{18} + \frac{5 x^{16}}{2} + 50 x^{14} + \frac{1750 x^{12}}{3} + 4375 x^{10} + 21875 x^{8} + \frac{218750 x^{6}}{3} + 156250 x^{4} + \frac{390625 x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(x**2+5)**8,x)
[Out]
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GIAC/XCAS [A] time = 0.209293, size = 12, normalized size = 1.09 \[ \frac{1}{18} \,{\left (x^{2} + 5\right )}^{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 5)^8*x,x, algorithm="giac")
[Out]