Optimal. Leaf size=49 \[ -\frac{b^2 \log \left (a+b x^5\right )}{5 a^3}+\frac{b^2 \log (x)}{a^3}+\frac{b}{5 a^2 x^5}-\frac{1}{10 a x^{10}} \]
[Out]
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Rubi [A] time = 0.0654487, antiderivative size = 49, 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 \[ -\frac{b^2 \log \left (a+b x^5\right )}{5 a^3}+\frac{b^2 \log (x)}{a^3}+\frac{b}{5 a^2 x^5}-\frac{1}{10 a x^{10}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^11*(a + b*x^5)),x]
[Out]
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Rubi in Sympy [A] time = 10.5353, size = 48, normalized size = 0.98 \[ - \frac{1}{10 a x^{10}} + \frac{b}{5 a^{2} x^{5}} + \frac{b^{2} \log{\left (x^{5} \right )}}{5 a^{3}} - \frac{b^{2} \log{\left (a + b x^{5} \right )}}{5 a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**11/(b*x**5+a),x)
[Out]
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Mathematica [A] time = 0.0119805, size = 49, normalized size = 1. \[ -\frac{b^2 \log \left (a+b x^5\right )}{5 a^3}+\frac{b^2 \log (x)}{a^3}+\frac{b}{5 a^2 x^5}-\frac{1}{10 a x^{10}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^11*(a + b*x^5)),x]
[Out]
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Maple [A] time = 0.011, size = 44, normalized size = 0.9 \[ -{\frac{1}{10\,a{x}^{10}}}+{\frac{b}{5\,{x}^{5}{a}^{2}}}+{\frac{{b}^{2}\ln \left ( x \right ) }{{a}^{3}}}-{\frac{{b}^{2}\ln \left ( b{x}^{5}+a \right ) }{5\,{a}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^11/(b*x^5+a),x)
[Out]
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Maxima [A] time = 1.44414, size = 63, normalized size = 1.29 \[ -\frac{b^{2} \log \left (b x^{5} + a\right )}{5 \, a^{3}} + \frac{b^{2} \log \left (x^{5}\right )}{5 \, a^{3}} + \frac{2 \, b x^{5} - a}{10 \, a^{2} x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^5 + a)*x^11),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.22277, size = 61, normalized size = 1.24 \[ -\frac{2 \, b^{2} x^{10} \log \left (b x^{5} + a\right ) - 10 \, b^{2} x^{10} \log \left (x\right ) - 2 \, a b x^{5} + a^{2}}{10 \, a^{3} x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^5 + a)*x^11),x, algorithm="fricas")
[Out]
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Sympy [A] time = 18.8188, size = 42, normalized size = 0.86 \[ \frac{- a + 2 b x^{5}}{10 a^{2} x^{10}} + \frac{b^{2} \log{\left (x \right )}}{a^{3}} - \frac{b^{2} \log{\left (\frac{a}{b} + x^{5} \right )}}{5 a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**11/(b*x**5+a),x)
[Out]
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GIAC/XCAS [A] time = 0.238084, size = 74, normalized size = 1.51 \[ -\frac{b^{2}{\rm ln}\left ({\left | b x^{5} + a \right |}\right )}{5 \, a^{3}} + \frac{b^{2}{\rm ln}\left ({\left | x \right |}\right )}{a^{3}} - \frac{3 \, b^{2} x^{10} - 2 \, a b x^{5} + a^{2}}{10 \, a^{3} x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^5 + a)*x^11),x, algorithm="giac")
[Out]