Optimal. Leaf size=69 \[ -\frac {f^{a+\frac {b}{x^2}} \left (b^4 \log ^4(f)-4 b^3 x^2 \log ^3(f)+12 b^2 x^4 \log ^2(f)-24 b x^6 \log (f)+24 x^8\right )}{2 b^5 x^8 \log ^5(f)} \]
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Rubi [C] time = 0.02, antiderivative size = 24, normalized size of antiderivative = 0.35, 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} \[ -\frac {f^a \text {Gamma}\left (5,-\frac {b \log (f)}{x^2}\right )}{2 b^5 \log ^5(f)} \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin {align*} \int \frac {f^{a+\frac {b}{x^2}}}{x^{11}} \, dx &=-\frac {f^a \Gamma \left (5,-\frac {b \log (f)}{x^2}\right )}{2 b^5 \log ^5(f)}\\ \end {align*}
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Mathematica [C] time = 0.00, size = 24, normalized size = 0.35 \[ -\frac {f^a \Gamma \left (5,-\frac {b \log (f)}{x^2}\right )}{2 b^5 \log ^5(f)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 71, normalized size = 1.03 \[ -\frac {{\left (24 \, x^{8} - 24 \, b x^{6} \log \relax (f) + 12 \, b^{2} x^{4} \log \relax (f)^{2} - 4 \, b^{3} x^{2} \log \relax (f)^{3} + b^{4} \log \relax (f)^{4}\right )} f^{\frac {a x^{2} + b}{x^{2}}}}{2 \, b^{5} x^{8} \log \relax (f)^{5}} \]
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 \[ \int \frac {f^{a + \frac {b}{x^{2}}}}{x^{11}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 121, normalized size = 1.75 \[ \frac {-\frac {x^{2} {\mathrm e}^{\left (a +\frac {b}{x^{2}}\right ) \ln \relax (f )}}{2 b \ln \relax (f )}+\frac {2 x^{4} {\mathrm e}^{\left (a +\frac {b}{x^{2}}\right ) \ln \relax (f )}}{b^{2} \ln \relax (f )^{2}}-\frac {6 x^{6} {\mathrm e}^{\left (a +\frac {b}{x^{2}}\right ) \ln \relax (f )}}{b^{3} \ln \relax (f )^{3}}+\frac {12 x^{8} {\mathrm e}^{\left (a +\frac {b}{x^{2}}\right ) \ln \relax (f )}}{b^{4} \ln \relax (f )^{4}}-\frac {12 x^{10} {\mathrm e}^{\left (a +\frac {b}{x^{2}}\right ) \ln \relax (f )}}{b^{5} \ln \relax (f )^{5}}}{x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 1.27, size = 22, normalized size = 0.32 \[ -\frac {f^{a} \Gamma \left (5, -\frac {b \log \relax (f)}{x^{2}}\right )}{2 \, b^{5} \log \relax (f)^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.60, size = 72, normalized size = 1.04 \[ -\frac {f^{a+\frac {b}{x^2}}\,\left (\frac {1}{2\,b\,\ln \relax (f)}-\frac {2\,x^2}{b^2\,{\ln \relax (f)}^2}+\frac {6\,x^4}{b^3\,{\ln \relax (f)}^3}-\frac {12\,x^6}{b^4\,{\ln \relax (f)}^4}+\frac {12\,x^8}{b^5\,{\ln \relax (f)}^5}\right )}{x^8} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 71, normalized size = 1.03 \[ \frac {f^{a + \frac {b}{x^{2}}} \left (- b^{4} \log {\relax (f )}^{4} + 4 b^{3} x^{2} \log {\relax (f )}^{3} - 12 b^{2} x^{4} \log {\relax (f )}^{2} + 24 b x^{6} \log {\relax (f )} - 24 x^{8}\right )}{2 b^{5} x^{8} \log {\relax (f )}^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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