Optimal. Leaf size=24 \[ -\frac {1}{3} b^4 f^a \log ^4(f) \Gamma \left (-4,-b x^3 \log (f)\right ) \]
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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} \[ -\frac {1}{3} b^4 f^a \log ^4(f) \text {Gamma}\left (-4,-b x^3 \log (f)\right ) \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin {align*} \int \frac {f^{a+b x^3}}{x^{13}} \, dx &=-\frac {1}{3} b^4 f^a \Gamma \left (-4,-b x^3 \log (f)\right ) \log ^4(f)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 24, normalized size = 1.00 \[ -\frac {1}{3} b^4 f^a \log ^4(f) \Gamma \left (-4,-b x^3 \log (f)\right ) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.40, size = 71, normalized size = 2.96 \[ \frac {b^{4} f^{a} x^{12} {\rm Ei}\left (b x^{3} \log \relax (f)\right ) \log \relax (f)^{4} - {\left (b^{3} x^{9} \log \relax (f)^{3} + b^{2} x^{6} \log \relax (f)^{2} + 2 \, b x^{3} \log \relax (f) + 6\right )} f^{b x^{3} + a}}{72 \, x^{12}} \]
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 \[ \int \frac {f^{b x^{3} + a}}{x^{13}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.08, size = 213, normalized size = 8.88 \[ \frac {\left (-\frac {\Ei \left (1, -b \,x^{3} \ln \relax (f )\right )}{24}+\frac {\ln \relax (x )}{8}+\frac {\ln \left (-b \right )}{24}-\frac {\ln \left (-b \,x^{3} \ln \relax (f )\right )}{24}+\frac {\ln \left (\ln \relax (f )\right )}{24}-\frac {1}{6 b \,x^{3} \ln \relax (f )}-\frac {1}{4 b^{2} x^{6} \ln \relax (f )^{2}}-\frac {1}{3 b^{3} x^{9} \ln \relax (f )^{3}}-\frac {\left (5 b^{3} x^{9} \ln \relax (f )^{3}+5 b^{2} x^{6} \ln \relax (f )^{2}+10 b \,x^{3} \ln \relax (f )+30\right ) {\mathrm e}^{b \,x^{3} \ln \relax (f )}}{120 b^{4} x^{12} \ln \relax (f )^{4}}+\frac {125 b^{4} x^{12} \ln \relax (f )^{4}+240 b^{3} x^{9} \ln \relax (f )^{3}+360 b^{2} x^{6} \ln \relax (f )^{2}+480 b \,x^{3} \ln \relax (f )+360}{1440 b^{4} x^{12} \ln \relax (f )^{4}}-\frac {1}{4 b^{4} x^{12} \ln \relax (f )^{4}}-\frac {25}{288}\right ) b^{4} f^{a} \ln \relax (f )^{4}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.14, size = 22, normalized size = 0.92 \[ -\frac {1}{3} \, b^{4} f^{a} \Gamma \left (-4, -b x^{3} \log \relax (f)\right ) \log \relax (f)^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.58, size = 90, normalized size = 3.75 \[ -\frac {b^4\,f^a\,{\ln \relax (f)}^4\,\mathrm {expint}\left (-b\,x^3\,\ln \relax (f)\right )}{72}-\frac {b^4\,f^a\,f^{b\,x^3}\,{\ln \relax (f)}^4\,\left (\frac {1}{24\,b\,x^3\,\ln \relax (f)}+\frac {1}{24\,b^2\,x^6\,{\ln \relax (f)}^2}+\frac {1}{12\,b^3\,x^9\,{\ln \relax (f)}^3}+\frac {1}{4\,b^4\,x^{12}\,{\ln \relax (f)}^4}\right )}{3} \]
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 \[ \int \frac {f^{a + b x^{3}}}{x^{13}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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