Optimal. Leaf size=24 \[ -\frac{1}{2} b^5 f^a \log ^5(f) \text{Gamma}\left (-5,-\frac{b \log (f)}{x^2}\right ) \]
[Out]
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Rubi [A] time = 0.039484, antiderivative size = 24, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{1}{2} b^5 f^a \log ^5(f) \text{Gamma}\left (-5,-\frac{b \log (f)}{x^2}\right ) \]
Antiderivative was successfully verified.
[In] Int[f^(a + b/x^2)*x^9,x]
[Out]
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Rubi in Sympy [A] time = 3.62792, size = 27, normalized size = 1.12 \[ - \frac{b^{5} f^{a} \Gamma{\left (-5,- \frac{b \log{\left (f \right )}}{x^{2}} \right )} \log{\left (f \right )}^{5}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(f**(a+b/x**2)*x**9,x)
[Out]
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Mathematica [B] time = 0.0439682, size = 81, normalized size = 3.38 \[ \frac{1}{240} f^a \left (x^2 f^{\frac{b}{x^2}} \left (b^4 \log ^4(f)+b^3 x^2 \log ^3(f)+2 b^2 x^4 \log ^2(f)+6 b x^6 \log (f)+24 x^8\right )-b^5 \log ^5(f) \text{ExpIntegralEi}\left (\frac{b \log (f)}{x^2}\right )\right ) \]
Antiderivative was successfully verified.
[In] Integrate[f^(a + b/x^2)*x^9,x]
[Out]
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Maple [B] time = 0.039, size = 123, normalized size = 5.1 \[{\frac{{f}^{a}{x}^{10}}{10}{f}^{{\frac{b}{{x}^{2}}}}}+{\frac{{f}^{a}\ln \left ( f \right ) b{x}^{8}}{40}{f}^{{\frac{b}{{x}^{2}}}}}+{\frac{{f}^{a} \left ( \ln \left ( f \right ) \right ) ^{2}{b}^{2}{x}^{6}}{120}{f}^{{\frac{b}{{x}^{2}}}}}+{\frac{{f}^{a} \left ( \ln \left ( f \right ) \right ) ^{3}{b}^{3}{x}^{4}}{240}{f}^{{\frac{b}{{x}^{2}}}}}+{\frac{{f}^{a} \left ( \ln \left ( f \right ) \right ) ^{4}{b}^{4}{x}^{2}}{240}{f}^{{\frac{b}{{x}^{2}}}}}+{\frac{{f}^{a} \left ( \ln \left ( f \right ) \right ) ^{5}{b}^{5}}{240}{\it Ei} \left ( 1,-{\frac{b\ln \left ( f \right ) }{{x}^{2}}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(f^(a+b/x^2)*x^9,x)
[Out]
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Maxima [A] time = 0.802582, size = 126, normalized size = 5.25 \[ -\frac{1}{240} \, b^{5} f^{a}{\rm Ei}\left (\frac{b \log \left (f\right )}{x^{2}}\right ) \log \left (f\right )^{5} + \frac{1}{240} \,{\left (24 \, f^{a} x^{10} + 6 \, b f^{a} x^{8} \log \left (f\right ) + 2 \, b^{2} f^{a} x^{6} \log \left (f\right )^{2} + b^{3} f^{a} x^{4} \log \left (f\right )^{3} + b^{4} f^{a} x^{2} \log \left (f\right )^{4}\right )} f^{\frac{b}{x^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(a + b/x^2)*x^9,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.263752, size = 113, normalized size = 4.71 \[ -\frac{1}{240} \, b^{5} f^{a}{\rm Ei}\left (\frac{b \log \left (f\right )}{x^{2}}\right ) \log \left (f\right )^{5} + \frac{1}{240} \,{\left (24 \, x^{10} + 6 \, b x^{8} \log \left (f\right ) + 2 \, b^{2} x^{6} \log \left (f\right )^{2} + b^{3} x^{4} \log \left (f\right )^{3} + b^{4} x^{2} \log \left (f\right )^{4}\right )} f^{\frac{a x^{2} + b}{x^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(a + b/x^2)*x^9,x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f**(a+b/x**2)*x**9,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int f^{a + \frac{b}{x^{2}}} x^{9}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(a + b/x^2)*x^9,x, algorithm="giac")
[Out]