Optimal. Leaf size=34 \[ -\frac{f^a \left (-b x^2 \log (f)\right )^{11/2} \text{Gamma}\left (-\frac{11}{2},-b x^2 \log (f)\right )}{2 x^{11}} \]
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Rubi [A] time = 0.0208784, antiderivative size = 34, 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, Rules used = {2218} \[ -\frac{f^a \left (-b x^2 \log (f)\right )^{11/2} \text{Gamma}\left (-\frac{11}{2},-b x^2 \log (f)\right )}{2 x^{11}} \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin{align*} \int \frac{f^{a+b x^2}}{x^{12}} \, dx &=-\frac{f^a \Gamma \left (-\frac{11}{2},-b x^2 \log (f)\right ) \left (-b x^2 \log (f)\right )^{11/2}}{2 x^{11}}\\ \end{align*}
Mathematica [A] time = 0.0054607, size = 34, normalized size = 1. \[ -\frac{f^a \left (-b x^2 \log (f)\right )^{11/2} \text{Gamma}\left (-\frac{11}{2},-b x^2 \log (f)\right )}{2 x^{11}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.091, size = 155, normalized size = 4.6 \begin{align*} -{\frac{{f}^{a}{f}^{b{x}^{2}}}{11\,{x}^{11}}}-{\frac{2\,{f}^{a}\ln \left ( f \right ) b{f}^{b{x}^{2}}}{99\,{x}^{9}}}-{\frac{4\,{f}^{a} \left ( \ln \left ( f \right ) \right ) ^{2}{b}^{2}{f}^{b{x}^{2}}}{693\,{x}^{7}}}-{\frac{8\,{f}^{a} \left ( \ln \left ( f \right ) \right ) ^{3}{b}^{3}{f}^{b{x}^{2}}}{3465\,{x}^{5}}}-{\frac{16\,{f}^{a} \left ( \ln \left ( f \right ) \right ) ^{4}{b}^{4}{f}^{b{x}^{2}}}{10395\,{x}^{3}}}-{\frac{32\,{f}^{a} \left ( \ln \left ( f \right ) \right ) ^{5}{b}^{5}{f}^{b{x}^{2}}}{10395\,x}}+{\frac{32\,{f}^{a} \left ( \ln \left ( f \right ) \right ) ^{6}{b}^{6}\sqrt{\pi }}{10395}{\it Erf} \left ( \sqrt{-b\ln \left ( f \right ) }x \right ){\frac{1}{\sqrt{-b\ln \left ( f \right ) }}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.30194, size = 38, normalized size = 1.12 \begin{align*} -\frac{\left (-b x^{2} \log \left (f\right )\right )^{\frac{11}{2}} f^{a} \Gamma \left (-\frac{11}{2}, -b x^{2} \log \left (f\right )\right )}{2 \, x^{11}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.82728, size = 297, normalized size = 8.74 \begin{align*} -\frac{32 \, \sqrt{\pi } \sqrt{-b \log \left (f\right )} b^{5} f^{a} x^{11} \operatorname{erf}\left (\sqrt{-b \log \left (f\right )} x\right ) \log \left (f\right )^{5} +{\left (32 \, b^{5} x^{10} \log \left (f\right )^{5} + 16 \, b^{4} x^{8} \log \left (f\right )^{4} + 24 \, b^{3} x^{6} \log \left (f\right )^{3} + 60 \, b^{2} x^{4} \log \left (f\right )^{2} + 210 \, b x^{2} \log \left (f\right ) + 945\right )} f^{b x^{2} + a}}{10395 \, x^{11}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{f^{b x^{2} + a}}{x^{12}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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