Optimal. Leaf size=24 \[ -\frac {1}{2} b^4 f^a \log ^4(f) \Gamma \left (-4,-b x^2 \log (f)\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 24, normalized size of antiderivative = 1.00, 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} \[ -\frac {1}{2} b^4 f^a \log ^4(f) \text {Gamma}\left (-4,-b x^2 \log (f)\right ) \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin {align*} \int \frac {f^{a+b x^2}}{x^9} \, dx &=-\frac {1}{2} b^4 f^a \Gamma \left (-4,-b x^2 \log (f)\right ) \log ^4(f)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 24, normalized size = 1.00 \[ -\frac {1}{2} b^4 f^a \log ^4(f) \Gamma \left (-4,-b x^2 \log (f)\right ) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.41, size = 71, normalized size = 2.96 \[ \frac {b^{4} f^{a} x^{8} {\rm Ei}\left (b x^{2} \log \relax (f)\right ) \log \relax (f)^{4} - {\left (b^{3} x^{6} \log \relax (f)^{3} + b^{2} x^{4} \log \relax (f)^{2} + 2 \, b x^{2} \log \relax (f) + 6\right )} f^{b x^{2} + a}}{48 \, x^{8}} \]
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 \[ \int \frac {f^{b x^{2} + a}}{x^{9}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.07, size = 101, normalized size = 4.21 \[ -\frac {b^{4} f^{a} \Ei \left (1, -b \,x^{2} \ln \relax (f )\right ) \ln \relax (f )^{4}}{48}-\frac {b^{3} f^{a} f^{b \,x^{2}} \ln \relax (f )^{3}}{48 x^{2}}-\frac {b^{2} f^{a} f^{b \,x^{2}} \ln \relax (f )^{2}}{48 x^{4}}-\frac {b \,f^{a} f^{b \,x^{2}} \ln \relax (f )}{24 x^{6}}-\frac {f^{a} f^{b \,x^{2}}}{8 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.62, size = 22, normalized size = 0.92 \[ -\frac {1}{2} \, b^{4} f^{a} \Gamma \left (-4, -b x^{2} \log \relax (f)\right ) \log \relax (f)^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.57, size = 90, normalized size = 3.75 \[ -\frac {b^4\,f^a\,{\ln \relax (f)}^4\,\mathrm {expint}\left (-b\,x^2\,\ln \relax (f)\right )}{48}-\frac {b^4\,f^a\,f^{b\,x^2}\,{\ln \relax (f)}^4\,\left (\frac {1}{24\,b\,x^2\,\ln \relax (f)}+\frac {1}{24\,b^2\,x^4\,{\ln \relax (f)}^2}+\frac {1}{12\,b^3\,x^6\,{\ln \relax (f)}^3}+\frac {1}{4\,b^4\,x^8\,{\ln \relax (f)}^4}\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {f^{a + b x^{2}}}{x^{9}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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