Optimal. Leaf size=34 \[ -\frac{f^a \left (-b x^2 \log (f)\right )^{9/2} \text{Gamma}\left (-\frac{9}{2},-b x^2 \log (f)\right )}{2 x^9} \]
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Rubi [A] time = 0.0206185, 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} \[ -\frac{f^a \left (-b x^2 \log (f)\right )^{9/2} \text{Gamma}\left (-\frac{9}{2},-b x^2 \log (f)\right )}{2 x^9} \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin{align*} \int \frac{f^{a+b x^2}}{x^{10}} \, dx &=-\frac{f^a \Gamma \left (-\frac{9}{2},-b x^2 \log (f)\right ) \left (-b x^2 \log (f)\right )^{9/2}}{2 x^9}\\ \end{align*}
Mathematica [A] time = 0.0056244, size = 34, normalized size = 1. \[ -\frac{f^a \left (-b x^2 \log (f)\right )^{9/2} \text{Gamma}\left (-\frac{9}{2},-b x^2 \log (f)\right )}{2 x^9} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.058, size = 133, normalized size = 3.9 \begin{align*} -{\frac{{f}^{a}{f}^{b{x}^{2}}}{9\,{x}^{9}}}-{\frac{2\,{f}^{a}\ln \left ( f \right ) b{f}^{b{x}^{2}}}{63\,{x}^{7}}}-{\frac{4\,{f}^{a} \left ( \ln \left ( f \right ) \right ) ^{2}{b}^{2}{f}^{b{x}^{2}}}{315\,{x}^{5}}}-{\frac{8\,{f}^{a} \left ( \ln \left ( f \right ) \right ) ^{3}{b}^{3}{f}^{b{x}^{2}}}{945\,{x}^{3}}}-{\frac{16\,{f}^{a} \left ( \ln \left ( f \right ) \right ) ^{4}{b}^{4}{f}^{b{x}^{2}}}{945\,x}}+{\frac{16\,{f}^{a} \left ( \ln \left ( f \right ) \right ) ^{5}{b}^{5}\sqrt{\pi }}{945}{\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 = 1.19433, size = 38, normalized size = 1.12 \begin{align*} -\frac{\left (-b x^{2} \log \left (f\right )\right )^{\frac{9}{2}} f^{a} \Gamma \left (-\frac{9}{2}, -b x^{2} \log \left (f\right )\right )}{2 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.74763, size = 258, normalized size = 7.59 \begin{align*} -\frac{16 \, \sqrt{\pi } \sqrt{-b \log \left (f\right )} b^{4} f^{a} x^{9} \operatorname{erf}\left (\sqrt{-b \log \left (f\right )} x\right ) \log \left (f\right )^{4} +{\left (16 \, b^{4} x^{8} \log \left (f\right )^{4} + 8 \, b^{3} x^{6} \log \left (f\right )^{3} + 12 \, b^{2} x^{4} \log \left (f\right )^{2} + 30 \, b x^{2} \log \left (f\right ) + 105\right )} f^{b x^{2} + a}}{945 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{f^{a + b x^{2}}}{x^{10}}\, dx \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^{10}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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