Optimal. Leaf size=24 \[ -\frac {1}{3} b^5 f^a \log ^5(f) \Gamma \left (-5,-\frac {b \log (f)}{x^3}\right ) \]
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Rubi [A] time = 0.03, 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} \[ -\frac {1}{3} b^5 f^a \log ^5(f) \text {Gamma}\left (-5,-\frac {b \log (f)}{x^3}\right ) \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin {align*} \int f^{a+\frac {b}{x^3}} x^{14} \, dx &=-\frac {1}{3} b^5 f^a \Gamma \left (-5,-\frac {b \log (f)}{x^3}\right ) \log ^5(f)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 24, normalized size = 1.00 \[ -\frac {1}{3} b^5 f^a \log ^5(f) \Gamma \left (-5,-\frac {b \log (f)}{x^3}\right ) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.44, size = 84, normalized size = 3.50 \[ -\frac {1}{360} \, b^{5} f^{a} {\rm Ei}\left (\frac {b \log \relax (f)}{x^{3}}\right ) \log \relax (f)^{5} + \frac {1}{360} \, {\left (24 \, x^{15} + 6 \, b x^{12} \log \relax (f) + 2 \, b^{2} x^{9} \log \relax (f)^{2} + b^{3} x^{6} \log \relax (f)^{3} + b^{4} x^{3} \log \relax (f)^{4}\right )} f^{\frac {a x^{3} + b}{x^{3}}} \]
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 \[ \int f^{a + \frac {b}{x^{3}}} x^{14}\,{d x} \]
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 \[ \frac {\left (\frac {\left (\frac {36 b \ln \relax (f )}{x^{3}}+\frac {12 b^{2} \ln \relax (f )^{2}}{x^{6}}+\frac {6 b^{3} \ln \relax (f )^{3}}{x^{9}}+\frac {6 b^{4} \ln \relax (f )^{4}}{x^{12}}+144\right ) x^{15} {\mathrm e}^{\frac {b \ln \relax (f )}{x^{3}}}}{720 b^{5} \ln \relax (f )^{5}}-\frac {\left (\frac {1800 b \ln \relax (f )}{x^{3}}+\frac {1200 b^{2} \ln \relax (f )^{2}}{x^{6}}+\frac {600 b^{3} \ln \relax (f )^{3}}{x^{9}}+\frac {300 b^{4} \ln \relax (f )^{4}}{x^{12}}+\frac {137 b^{5} \ln \relax (f )^{5}}{x^{15}}+1440\right ) x^{15}}{7200 b^{5} \ln \relax (f )^{5}}+\frac {x^{15}}{5 b^{5} \ln \relax (f )^{5}}+\frac {x^{12}}{4 b^{4} \ln \relax (f )^{4}}+\frac {x^{9}}{6 b^{3} \ln \relax (f )^{3}}+\frac {x^{6}}{12 b^{2} \ln \relax (f )^{2}}+\frac {x^{3}}{24 b \ln \relax (f )}+\frac {\Ei \left (1, -\frac {b \ln \relax (f )}{x^{3}}\right )}{120}+\frac {\ln \relax (x )}{40}-\frac {\ln \left (-b \right )}{120}+\frac {\ln \left (-\frac {b \ln \relax (f )}{x^{3}}\right )}{120}-\frac {\ln \left (\ln \relax (f )\right )}{120}+\frac {137}{7200}\right ) b^{5} f^{a} \ln \relax (f )^{5}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.63, size = 22, normalized size = 0.92 \[ -\frac {1}{3} \, b^{5} f^{a} \Gamma \left (-5, -\frac {b \log \relax (f)}{x^{3}}\right ) \log \relax (f)^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.83, size = 102, normalized size = 4.25 \[ \frac {b^5\,f^a\,{\ln \relax (f)}^5\,\mathrm {expint}\left (-\frac {b\,\ln \relax (f)}{x^3}\right )}{360}+\frac {b^5\,f^a\,f^{\frac {b}{x^3}}\,{\ln \relax (f)}^5\,\left (\frac {x^3}{120\,b\,\ln \relax (f)}+\frac {x^6}{120\,b^2\,{\ln \relax (f)}^2}+\frac {x^9}{60\,b^3\,{\ln \relax (f)}^3}+\frac {x^{12}}{20\,b^4\,{\ln \relax (f)}^4}+\frac {x^{15}}{5\,b^5\,{\ln \relax (f)}^5}\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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