Optimal. Leaf size=36 \[ \frac{9 \log \left (b x^5+3\right )}{5 b^3}-\frac{3 x^5}{5 b^2}+\frac{x^{10}}{10 b} \]
[Out]
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Rubi [A] time = 0.056229, antiderivative size = 36, 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 \[ \frac{9 \log \left (b x^5+3\right )}{5 b^3}-\frac{3 x^5}{5 b^2}+\frac{x^{10}}{10 b} \]
Antiderivative was successfully verified.
[In] Int[x^14/(3 + b*x^5),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{\int ^{x^{5}} x\, dx}{5 b} - \frac{3 x^{5}}{5 b^{2}} + \frac{9 \log{\left (b x^{5} + 3 \right )}}{5 b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**14/(b*x**5+3),x)
[Out]
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Mathematica [A] time = 0.00954957, size = 36, normalized size = 1. \[ \frac{9 \log \left (b x^5+3\right )}{5 b^3}-\frac{3 x^5}{5 b^2}+\frac{x^{10}}{10 b} \]
Antiderivative was successfully verified.
[In] Integrate[x^14/(3 + b*x^5),x]
[Out]
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Maple [A] time = 0.005, size = 31, normalized size = 0.9 \[ -{\frac{3\,{x}^{5}}{5\,{b}^{2}}}+{\frac{{x}^{10}}{10\,b}}+{\frac{9\,\ln \left ( b{x}^{5}+3 \right ) }{5\,{b}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^14/(b*x^5+3),x)
[Out]
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Maxima [A] time = 1.43529, size = 41, normalized size = 1.14 \[ \frac{b x^{10} - 6 \, x^{5}}{10 \, b^{2}} + \frac{9 \, \log \left (b x^{5} + 3\right )}{5 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^14/(b*x^5 + 3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214471, size = 39, normalized size = 1.08 \[ \frac{b^{2} x^{10} - 6 \, b x^{5} + 18 \, \log \left (b x^{5} + 3\right )}{10 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^14/(b*x^5 + 3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.34325, size = 31, normalized size = 0.86 \[ \frac{x^{10}}{10 b} - \frac{3 x^{5}}{5 b^{2}} + \frac{9 \log{\left (b x^{5} + 3 \right )}}{5 b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**14/(b*x**5+3),x)
[Out]
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GIAC/XCAS [A] time = 0.289198, size = 42, normalized size = 1.17 \[ \frac{b x^{10} - 6 \, x^{5}}{10 \, b^{2}} + \frac{9 \,{\rm ln}\left ({\left | b x^{5} + 3 \right |}\right )}{5 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^14/(b*x^5 + 3),x, algorithm="giac")
[Out]