Optimal. Leaf size=24 \[ \frac {1}{2} b^5 f^a \log ^5(f) \Gamma \left (-5,-b x^2 \log (f)\right ) \]
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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} \[ \frac {1}{2} b^5 f^a \log ^5(f) \text {Gamma}\left (-5,-b x^2 \log (f)\right ) \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin {align*} \int \frac {f^{a+b x^2}}{x^{11}} \, dx &=\frac {1}{2} b^5 f^a \Gamma \left (-5,-b x^2 \log (f)\right ) \log ^5(f)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 24, normalized size = 1.00 \[ \frac {1}{2} b^5 f^a \log ^5(f) \Gamma \left (-5,-b x^2 \log (f)\right ) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.41, size = 83, normalized size = 3.46 \[ \frac {b^{5} f^{a} x^{10} {\rm Ei}\left (b x^{2} \log \relax (f)\right ) \log \relax (f)^{5} - {\left (b^{4} x^{8} \log \relax (f)^{4} + b^{3} x^{6} \log \relax (f)^{3} + 2 \, b^{2} x^{4} \log \relax (f)^{2} + 6 \, b x^{2} \log \relax (f) + 24\right )} f^{b x^{2} + a}}{240 \, x^{10}} \]
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 \[ \int \frac {f^{b x^{2} + a}}{x^{11}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.09, size = 123, normalized size = 5.12 \[ -\frac {b^{5} f^{a} \Ei \left (1, -b \,x^{2} \ln \relax (f )\right ) \ln \relax (f )^{5}}{240}-\frac {b^{4} f^{a} f^{b \,x^{2}} \ln \relax (f )^{4}}{240 x^{2}}-\frac {b^{3} f^{a} f^{b \,x^{2}} \ln \relax (f )^{3}}{240 x^{4}}-\frac {b^{2} f^{a} f^{b \,x^{2}} \ln \relax (f )^{2}}{120 x^{6}}-\frac {b \,f^{a} f^{b \,x^{2}} \ln \relax (f )}{40 x^{8}}-\frac {f^{a} f^{b \,x^{2}}}{10 x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.93, size = 22, normalized size = 0.92 \[ \frac {1}{2} \, b^{5} f^{a} \Gamma \left (-5, -b x^{2} \log \relax (f)\right ) \log \relax (f)^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.51, size = 102, normalized size = 4.25 \[ -\frac {b^5\,f^a\,{\ln \relax (f)}^5\,\mathrm {expint}\left (-b\,x^2\,\ln \relax (f)\right )}{240}-\frac {b^5\,f^a\,f^{b\,x^2}\,{\ln \relax (f)}^5\,\left (\frac {1}{120\,b\,x^2\,\ln \relax (f)}+\frac {1}{120\,b^2\,x^4\,{\ln \relax (f)}^2}+\frac {1}{60\,b^3\,x^6\,{\ln \relax (f)}^3}+\frac {1}{20\,b^4\,x^8\,{\ln \relax (f)}^4}+\frac {1}{5\,b^5\,x^{10}\,{\ln \relax (f)}^5}\right )}{2} \]
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 \[ \int \frac {f^{a + b x^{2}}}{x^{11}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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