Optimal. Leaf size=82 \[ \frac {f^{a+\frac {b}{x^2}} \left (-b^5 \log ^5(f)+5 b^4 x^2 \log ^4(f)-20 b^3 x^4 \log ^3(f)+60 b^2 x^6 \log ^2(f)-120 b x^8 \log (f)+120 x^{10}\right )}{2 b^6 x^{10} \log ^6(f)} \]
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Rubi [C] time = 0.02, antiderivative size = 24, normalized size of antiderivative = 0.29, 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} \[ \frac {f^a \text {Gamma}\left (6,-\frac {b \log (f)}{x^2}\right )}{2 b^6 \log ^6(f)} \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin {align*} \int \frac {f^{a+\frac {b}{x^2}}}{x^{13}} \, dx &=\frac {f^a \Gamma \left (6,-\frac {b \log (f)}{x^2}\right )}{2 b^6 \log ^6(f)}\\ \end {align*}
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Mathematica [C] time = 0.00, size = 24, normalized size = 0.29 \[ \frac {f^a \Gamma \left (6,-\frac {b \log (f)}{x^2}\right )}{2 b^6 \log ^6(f)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 84, normalized size = 1.02 \[ \frac {{\left (120 \, x^{10} - 120 \, b x^{8} \log \relax (f) + 60 \, b^{2} x^{6} \log \relax (f)^{2} - 20 \, b^{3} x^{4} \log \relax (f)^{3} + 5 \, b^{4} x^{2} \log \relax (f)^{4} - b^{5} \log \relax (f)^{5}\right )} f^{\frac {a x^{2} + b}{x^{2}}}}{2 \, b^{6} x^{10} \log \relax (f)^{6}} \]
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 \[ \int \frac {f^{a + \frac {b}{x^{2}}}}{x^{13}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 144, normalized size = 1.76 \[ \frac {-\frac {x^{2} {\mathrm e}^{\left (a +\frac {b}{x^{2}}\right ) \ln \relax (f )}}{2 b \ln \relax (f )}+\frac {5 x^{4} {\mathrm e}^{\left (a +\frac {b}{x^{2}}\right ) \ln \relax (f )}}{2 b^{2} \ln \relax (f )^{2}}-\frac {10 x^{6} {\mathrm e}^{\left (a +\frac {b}{x^{2}}\right ) \ln \relax (f )}}{b^{3} \ln \relax (f )^{3}}+\frac {30 x^{8} {\mathrm e}^{\left (a +\frac {b}{x^{2}}\right ) \ln \relax (f )}}{b^{4} \ln \relax (f )^{4}}-\frac {60 x^{10} {\mathrm e}^{\left (a +\frac {b}{x^{2}}\right ) \ln \relax (f )}}{b^{5} \ln \relax (f )^{5}}+\frac {60 x^{12} {\mathrm e}^{\left (a +\frac {b}{x^{2}}\right ) \ln \relax (f )}}{b^{6} \ln \relax (f )^{6}}}{x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 1.28, size = 22, normalized size = 0.27 \[ \frac {f^{a} \Gamma \left (6, -\frac {b \log \relax (f)}{x^{2}}\right )}{2 \, b^{6} \log \relax (f)^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.61, size = 84, normalized size = 1.02 \[ -\frac {f^{a+\frac {b}{x^2}}\,\left (\frac {1}{2\,b\,\ln \relax (f)}-\frac {5\,x^2}{2\,b^2\,{\ln \relax (f)}^2}+\frac {10\,x^4}{b^3\,{\ln \relax (f)}^3}-\frac {30\,x^6}{b^4\,{\ln \relax (f)}^4}+\frac {60\,x^8}{b^5\,{\ln \relax (f)}^5}-\frac {60\,x^{10}}{b^6\,{\ln \relax (f)}^6}\right )}{x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 85, normalized size = 1.04 \[ \frac {f^{a + \frac {b}{x^{2}}} \left (- b^{5} \log {\relax (f )}^{5} + 5 b^{4} x^{2} \log {\relax (f )}^{4} - 20 b^{3} x^{4} \log {\relax (f )}^{3} + 60 b^{2} x^{6} \log {\relax (f )}^{2} - 120 b x^{8} \log {\relax (f )} + 120 x^{10}\right )}{2 b^{6} x^{10} \log {\relax (f )}^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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