Optimal. Leaf size=24 \[ \frac{x^5}{5 b}-\frac{2 \log \left (x^5+2\right )}{5 b} \]
[Out]
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Rubi [A] time = 0.0372038, antiderivative size = 24, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{x^5}{5 b}-\frac{2 \log \left (x^5+2\right )}{5 b} \]
Antiderivative was successfully verified.
[In] Int[x^9/(2*b + b*x^5),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{\int ^{x^{5}} \frac{1}{b}\, dx}{5} - \frac{2 \log{\left (x^{5} + 2 \right )}}{5 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**9/(b*x**5+2*b),x)
[Out]
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Mathematica [A] time = 0.00584097, size = 24, normalized size = 1. \[ \frac{x^5}{5 b}-\frac{2 \log \left (x^5+2\right )}{5 b} \]
Antiderivative was successfully verified.
[In] Integrate[x^9/(2*b + b*x^5),x]
[Out]
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Maple [A] time = 0.002, size = 21, normalized size = 0.9 \[{\frac{{x}^{5}}{5\,b}}-{\frac{2\,\ln \left ({x}^{5}+2 \right ) }{5\,b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^9/(b*x^5+2*b),x)
[Out]
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Maxima [A] time = 1.43104, size = 27, normalized size = 1.12 \[ \frac{x^{5}}{5 \, b} - \frac{2 \, \log \left (x^{5} + 2\right )}{5 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^9/(b*x^5 + 2*b),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214822, size = 23, normalized size = 0.96 \[ \frac{x^{5} - 2 \, \log \left (x^{5} + 2\right )}{5 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^9/(b*x^5 + 2*b),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.482312, size = 17, normalized size = 0.71 \[ \frac{x^{5}}{5 b} - \frac{2 \log{\left (x^{5} + 2 \right )}}{5 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**9/(b*x**5+2*b),x)
[Out]
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GIAC/XCAS [A] time = 0.232032, size = 28, normalized size = 1.17 \[ \frac{x^{5}}{5 \, b} - \frac{2 \,{\rm ln}\left ({\left | x^{5} + 2 \right |}\right )}{5 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^9/(b*x^5 + 2*b),x, algorithm="giac")
[Out]