Optimal. Leaf size=40 \[ \frac{a^2 \log \left (a+b x^5\right )}{5 b^3}-\frac{a x^5}{5 b^2}+\frac{x^{10}}{10 b} \]
[Out]
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Rubi [A] time = 0.0598736, antiderivative size = 40, 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 \[ \frac{a^2 \log \left (a+b x^5\right )}{5 b^3}-\frac{a x^5}{5 b^2}+\frac{x^{10}}{10 b} \]
Antiderivative was successfully verified.
[In] Int[x^14/(a + b*x^5),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{a^{2} \log{\left (a + b x^{5} \right )}}{5 b^{3}} + \frac{\int ^{x^{5}} x\, dx}{5 b} - \frac{\int ^{x^{5}} a\, dx}{5 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**14/(b*x**5+a),x)
[Out]
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Mathematica [A] time = 0.010259, size = 40, normalized size = 1. \[ \frac{a^2 \log \left (a+b x^5\right )}{5 b^3}-\frac{a x^5}{5 b^2}+\frac{x^{10}}{10 b} \]
Antiderivative was successfully verified.
[In] Integrate[x^14/(a + b*x^5),x]
[Out]
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Maple [A] time = 0.003, size = 35, normalized size = 0.9 \[ -{\frac{a{x}^{5}}{5\,{b}^{2}}}+{\frac{{x}^{10}}{10\,b}}+{\frac{{a}^{2}\ln \left ( b{x}^{5}+a \right ) }{5\,{b}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^14/(b*x^5+a),x)
[Out]
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Maxima [A] time = 1.44261, size = 46, normalized size = 1.15 \[ \frac{a^{2} \log \left (b x^{5} + a\right )}{5 \, b^{3}} + \frac{b x^{10} - 2 \, a x^{5}}{10 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^14/(b*x^5 + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212382, size = 45, normalized size = 1.12 \[ \frac{b^{2} x^{10} - 2 \, a b x^{5} + 2 \, a^{2} \log \left (b x^{5} + a\right )}{10 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^14/(b*x^5 + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.51939, size = 32, normalized size = 0.8 \[ \frac{a^{2} \log{\left (a + b x^{5} \right )}}{5 b^{3}} - \frac{a x^{5}}{5 b^{2}} + \frac{x^{10}}{10 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**14/(b*x**5+a),x)
[Out]
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GIAC/XCAS [A] time = 0.222877, size = 47, normalized size = 1.18 \[ \frac{a^{2}{\rm ln}\left ({\left | b x^{5} + a \right |}\right )}{5 \, b^{3}} + \frac{b x^{10} - 2 \, a x^{5}}{10 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^14/(b*x^5 + a),x, algorithm="giac")
[Out]