Optimal. Leaf size=82 \[ \frac {f^{a+\frac {b}{x^3}} \left (-b^5 \log ^5(f)+5 b^4 x^3 \log ^4(f)-20 b^3 x^6 \log ^3(f)+60 b^2 x^9 \log ^2(f)-120 b x^{12} \log (f)+120 x^{15}\right )}{3 b^6 x^{15} \log ^6(f)} \]
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Rubi [C] time = 0.02, antiderivative size = 24, normalized size of antiderivative = 0.29, 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} \[ \frac {f^a \text {Gamma}\left (6,-\frac {b \log (f)}{x^3}\right )}{3 b^6 \log ^6(f)} \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin {align*} \int \frac {f^{a+\frac {b}{x^3}}}{x^{19}} \, dx &=\frac {f^a \Gamma \left (6,-\frac {b \log (f)}{x^3}\right )}{3 b^6 \log ^6(f)}\\ \end {align*}
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Mathematica [C] time = 0.00, size = 24, normalized size = 0.29 \[ \frac {f^a \Gamma \left (6,-\frac {b \log (f)}{x^3}\right )}{3 b^6 \log ^6(f)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 84, normalized size = 1.02 \[ \frac {{\left (120 \, x^{15} - 120 \, b x^{12} \log \relax (f) + 60 \, b^{2} x^{9} \log \relax (f)^{2} - 20 \, b^{3} x^{6} \log \relax (f)^{3} + 5 \, b^{4} x^{3} \log \relax (f)^{4} - b^{5} \log \relax (f)^{5}\right )} f^{\frac {a x^{3} + b}{x^{3}}}}{3 \, b^{6} x^{15} \log \relax (f)^{6}} \]
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 \[ \int \frac {f^{a + \frac {b}{x^{3}}}}{x^{19}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 84, normalized size = 1.02 \[ -\frac {\left (-120 x^{15}+120 b \,x^{12} \ln \relax (f )-60 b^{2} x^{9} \ln \relax (f )^{2}+20 b^{3} x^{6} \ln \relax (f )^{3}-5 b^{4} x^{3} \ln \relax (f )^{4}+b^{5} \ln \relax (f )^{5}\right ) f^{\frac {a \,x^{3}+b}{x^{3}}}}{3 b^{6} x^{15} \ln \relax (f )^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 1.13, size = 22, normalized size = 0.27 \[ \frac {f^{a} \Gamma \left (6, -\frac {b \log \relax (f)}{x^{3}}\right )}{3 \, b^{6} \log \relax (f)^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.59, size = 84, normalized size = 1.02 \[ -\frac {f^{a+\frac {b}{x^3}}\,\left (\frac {1}{3\,b\,\ln \relax (f)}-\frac {5\,x^3}{3\,b^2\,{\ln \relax (f)}^2}+\frac {20\,x^6}{3\,b^3\,{\ln \relax (f)}^3}-\frac {20\,x^9}{b^4\,{\ln \relax (f)}^4}+\frac {40\,x^{12}}{b^5\,{\ln \relax (f)}^5}-\frac {40\,x^{15}}{b^6\,{\ln \relax (f)}^6}\right )}{x^{15}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 85, normalized size = 1.04 \[ \frac {f^{a + \frac {b}{x^{3}}} \left (- b^{5} \log {\relax (f )}^{5} + 5 b^{4} x^{3} \log {\relax (f )}^{4} - 20 b^{3} x^{6} \log {\relax (f )}^{3} + 60 b^{2} x^{9} \log {\relax (f )}^{2} - 120 b x^{12} \log {\relax (f )} + 120 x^{15}\right )}{3 b^{6} x^{15} \log {\relax (f )}^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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