Optimal. Leaf size=24 \[ \frac {1}{3} b^5 f^a \log ^5(f) \Gamma \left (-5,-b x^3 \log (f)\right ) \]
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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} \[ \frac {1}{3} b^5 f^a \log ^5(f) \text {Gamma}\left (-5,-b x^3 \log (f)\right ) \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin {align*} \int \frac {f^{a+b x^3}}{x^{16}} \, dx &=\frac {1}{3} b^5 f^a \Gamma \left (-5,-b x^3 \log (f)\right ) \log ^5(f)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 24, normalized size = 1.00 \[ \frac {1}{3} b^5 f^a \log ^5(f) \Gamma \left (-5,-b x^3 \log (f)\right ) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.40, size = 83, normalized size = 3.46 \[ \frac {b^{5} f^{a} x^{15} {\rm Ei}\left (b x^{3} \log \relax (f)\right ) \log \relax (f)^{5} - {\left (b^{4} x^{12} \log \relax (f)^{4} + b^{3} x^{9} \log \relax (f)^{3} + 2 \, b^{2} x^{6} \log \relax (f)^{2} + 6 \, b x^{3} \log \relax (f) + 24\right )} f^{b x^{3} + a}}{360 \, x^{15}} \]
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 \[ \int \frac {f^{b x^{3} + a}}{x^{16}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.09, size = 249, normalized size = 10.38 \[ -\frac {\left (\frac {\Ei \left (1, -b \,x^{3} \ln \relax (f )\right )}{120}-\frac {\ln \relax (x )}{40}-\frac {\ln \left (-b \right )}{120}+\frac {\ln \left (-b \,x^{3} \ln \relax (f )\right )}{120}-\frac {\ln \left (\ln \relax (f )\right )}{120}+\frac {1}{24 b \,x^{3} \ln \relax (f )}+\frac {1}{12 b^{2} x^{6} \ln \relax (f )^{2}}+\frac {1}{6 b^{3} x^{9} \ln \relax (f )^{3}}+\frac {1}{4 b^{4} x^{12} \ln \relax (f )^{4}}+\frac {\left (6 b^{4} x^{12} \ln \relax (f )^{4}+6 b^{3} x^{9} \ln \relax (f )^{3}+12 b^{2} x^{6} \ln \relax (f )^{2}+36 b \,x^{3} \ln \relax (f )+144\right ) {\mathrm e}^{b \,x^{3} \ln \relax (f )}}{720 b^{5} x^{15} \ln \relax (f )^{5}}-\frac {137 b^{5} x^{15} \ln \relax (f )^{5}+300 b^{4} x^{12} \ln \relax (f )^{4}+600 b^{3} x^{9} \ln \relax (f )^{3}+1200 b^{2} x^{6} \ln \relax (f )^{2}+1800 b \,x^{3} \ln \relax (f )+1440}{7200 b^{5} x^{15} \ln \relax (f )^{5}}+\frac {1}{5 b^{5} x^{15} \ln \relax (f )^{5}}+\frac {137}{7200}\right ) b^{5} f^{a} \ln \relax (f )^{5}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.29, size = 22, normalized size = 0.92 \[ \frac {1}{3} \, b^{5} f^{a} \Gamma \left (-5, -b x^{3} \log \relax (f)\right ) \log \relax (f)^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.47, size = 102, normalized size = 4.25 \[ -\frac {b^5\,f^a\,{\ln \relax (f)}^5\,\mathrm {expint}\left (-b\,x^3\,\ln \relax (f)\right )}{360}-\frac {b^5\,f^a\,f^{b\,x^3}\,{\ln \relax (f)}^5\,\left (\frac {1}{120\,b\,x^3\,\ln \relax (f)}+\frac {1}{120\,b^2\,x^6\,{\ln \relax (f)}^2}+\frac {1}{60\,b^3\,x^9\,{\ln \relax (f)}^3}+\frac {1}{20\,b^4\,x^{12}\,{\ln \relax (f)}^4}+\frac {1}{5\,b^5\,x^{15}\,{\ln \relax (f)}^5}\right )}{3} \]
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 \[ \int \frac {f^{a + b x^{3}}}{x^{16}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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