Optimal. Leaf size=24 \[ \frac{1}{2} b^4 f^a \log ^4(f) \text{Gamma}\left (-4,-\frac{b \log (f)}{x^2}\right ) \]
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Rubi [A] time = 0.0246971, antiderivative size = 24, 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} \[ \frac{1}{2} b^4 f^a \log ^4(f) \text{Gamma}\left (-4,-\frac{b \log (f)}{x^2}\right ) \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin{align*} \int f^{a+\frac{b}{x^2}} x^7 \, dx &=\frac{1}{2} b^4 f^a \Gamma \left (-4,-\frac{b \log (f)}{x^2}\right ) \log ^4(f)\\ \end{align*}
Mathematica [A] time = 0.0024848, size = 24, normalized size = 1. \[ \frac{1}{2} b^4 f^a \log ^4(f) \text{Gamma}\left (-4,-\frac{b \log (f)}{x^2}\right ) \]
Antiderivative was successfully verified.
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Maple [B] time = 0.042, size = 101, normalized size = 4.2 \begin{align*}{\frac{{f}^{a}{x}^{8}}{8}{f}^{{\frac{b}{{x}^{2}}}}}+{\frac{{f}^{a}\ln \left ( f \right ) b{x}^{6}}{24}{f}^{{\frac{b}{{x}^{2}}}}}+{\frac{{f}^{a} \left ( \ln \left ( f \right ) \right ) ^{2}{b}^{2}{x}^{4}}{48}{f}^{{\frac{b}{{x}^{2}}}}}+{\frac{{f}^{a} \left ( \ln \left ( f \right ) \right ) ^{3}{b}^{3}{x}^{2}}{48}{f}^{{\frac{b}{{x}^{2}}}}}+{\frac{{f}^{a} \left ( \ln \left ( f \right ) \right ) ^{4}{b}^{4}}{48}{\it Ei} \left ( 1,-{\frac{b\ln \left ( f \right ) }{{x}^{2}}} \right ) } \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: TypeError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: TypeError} \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 f^{a + \frac{b}{x^{2}}} x^{7}\, 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 f^{a + \frac{b}{x^{2}}} x^{7}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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