Optimal. Leaf size=24 \[ -\frac {1}{2} b^5 f^a \log ^5(f) \Gamma \left (-5,-\frac {b \log (f)}{x^2}\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 24, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {2218} \[ -\frac {1}{2} b^5 f^a \log ^5(f) \text {Gamma}\left (-5,-\frac {b \log (f)}{x^2}\right ) \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin {align*} \int f^{a+\frac {b}{x^2}} x^9 \, dx &=-\frac {1}{2} b^5 f^a \Gamma \left (-5,-\frac {b \log (f)}{x^2}\right ) \log ^5(f)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 24, normalized size = 1.00 \[ -\frac {1}{2} b^5 f^a \log ^5(f) \Gamma \left (-5,-\frac {b \log (f)}{x^2}\right ) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.42, size = 84, normalized size = 3.50 \[ -\frac {1}{240} \, b^{5} f^{a} {\rm Ei}\left (\frac {b \log \relax (f)}{x^{2}}\right ) \log \relax (f)^{5} + \frac {1}{240} \, {\left (24 \, x^{10} + 6 \, b x^{8} \log \relax (f) + 2 \, b^{2} x^{6} \log \relax (f)^{2} + b^{3} x^{4} \log \relax (f)^{3} + b^{4} x^{2} \log \relax (f)^{4}\right )} f^{\frac {a x^{2} + b}{x^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int f^{a + \frac {b}{x^{2}}} x^{9}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.08, size = 123, normalized size = 5.12 \[ \frac {b^{5} f^{a} \Ei \left (1, -\frac {b \ln \relax (f )}{x^{2}}\right ) \ln \relax (f )^{5}}{240}+\frac {b^{4} x^{2} f^{a} f^{\frac {b}{x^{2}}} \ln \relax (f )^{4}}{240}+\frac {b^{3} x^{4} f^{a} f^{\frac {b}{x^{2}}} \ln \relax (f )^{3}}{240}+\frac {b^{2} x^{6} f^{a} f^{\frac {b}{x^{2}}} \ln \relax (f )^{2}}{120}+\frac {b \,x^{8} f^{a} f^{\frac {b}{x^{2}}} \ln \relax (f )}{40}+\frac {x^{10} f^{a} f^{\frac {b}{x^{2}}}}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.32, size = 22, normalized size = 0.92 \[ -\frac {1}{2} \, b^{5} f^{a} \Gamma \left (-5, -\frac {b \log \relax (f)}{x^{2}}\right ) \log \relax (f)^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.79, size = 102, normalized size = 4.25 \[ \frac {b^5\,f^a\,{\ln \relax (f)}^5\,\mathrm {expint}\left (-\frac {b\,\ln \relax (f)}{x^2}\right )}{240}+\frac {b^5\,f^a\,f^{\frac {b}{x^2}}\,{\ln \relax (f)}^5\,\left (\frac {x^2}{120\,b\,\ln \relax (f)}+\frac {x^4}{120\,b^2\,{\ln \relax (f)}^2}+\frac {x^6}{60\,b^3\,{\ln \relax (f)}^3}+\frac {x^8}{20\,b^4\,{\ln \relax (f)}^4}+\frac {x^{10}}{5\,b^5\,{\ln \relax (f)}^5}\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int f^{a + \frac {b}{x^{2}}} x^{9}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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