Optimal. Leaf size=34 \[ \frac{x^{10}}{10 b}-\frac{2 x^5}{5 b}+\frac{4 \log \left (x^5+2\right )}{5 b} \]
[Out]
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Rubi [A] time = 0.0497654, antiderivative size = 34, 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 \[ \frac{x^{10}}{10 b}-\frac{2 x^5}{5 b}+\frac{4 \log \left (x^5+2\right )}{5 b} \]
Antiderivative was successfully verified.
[In] Int[x^14/(2*b + b*x^5),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{2 x^{5}}{5 b} + \frac{4 \log{\left (x^{5} + 2 \right )}}{5 b} + \frac{\int ^{x^{5}} x\, dx}{5 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**14/(b*x**5+2*b),x)
[Out]
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Mathematica [A] time = 0.0123581, size = 25, normalized size = 0.74 \[ \frac{x^{10}-4 x^5+8 \log \left (x^5+2\right )-12}{10 b} \]
Antiderivative was successfully verified.
[In] Integrate[x^14/(2*b + b*x^5),x]
[Out]
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Maple [A] time = 0.004, size = 29, normalized size = 0.9 \[ -{\frac{2\,{x}^{5}}{5\,b}}+{\frac{{x}^{10}}{10\,b}}+{\frac{4\,\ln \left ({x}^{5}+2 \right ) }{5\,b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^14/(b*x^5+2*b),x)
[Out]
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Maxima [A] time = 1.44392, size = 35, normalized size = 1.03 \[ \frac{x^{10} - 4 \, x^{5}}{10 \, b} + \frac{4 \, \log \left (x^{5} + 2\right )}{5 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^14/(b*x^5 + 2*b),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.215766, size = 30, normalized size = 0.88 \[ \frac{x^{10} - 4 \, x^{5} + 8 \, \log \left (x^{5} + 2\right )}{10 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^14/(b*x^5 + 2*b),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.500774, size = 26, normalized size = 0.76 \[ \frac{x^{10}}{10 b} - \frac{2 x^{5}}{5 b} + \frac{4 \log{\left (x^{5} + 2 \right )}}{5 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**14/(b*x**5+2*b),x)
[Out]
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GIAC/XCAS [A] time = 0.233317, size = 41, normalized size = 1.21 \[ \frac{4 \,{\rm ln}\left ({\left | x^{5} + 2 \right |}\right )}{5 \, b} + \frac{b x^{10} - 4 \, b x^{5}}{10 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^14/(b*x^5 + 2*b),x, algorithm="giac")
[Out]