Optimal. Leaf size=77 \[ \frac {f^{a+\frac {b}{x}} \left (-b^5 \log ^5(f)+5 b^4 x \log ^4(f)-20 b^3 x^2 \log ^3(f)+60 b^2 x^3 \log ^2(f)-120 b x^4 \log (f)+120 x^5\right )}{b^6 x^5 \log ^6(f)} \]
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Rubi [C] time = 0.02, antiderivative size = 21, normalized size of antiderivative = 0.27, 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} \[ \frac {f^a \text {Gamma}\left (6,-\frac {b \log (f)}{x}\right )}{b^6 \log ^6(f)} \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin {align*} \int \frac {f^{a+\frac {b}{x}}}{x^7} \, dx &=\frac {f^a \Gamma \left (6,-\frac {b \log (f)}{x}\right )}{b^6 \log ^6(f)}\\ \end {align*}
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Mathematica [C] time = 0.00, size = 21, normalized size = 0.27 \[ \frac {f^a \Gamma \left (6,-\frac {b \log (f)}{x}\right )}{b^6 \log ^6(f)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 79, normalized size = 1.03 \[ -\frac {{\left (b^{5} \log \relax (f)^{5} - 5 \, b^{4} x \log \relax (f)^{4} + 20 \, b^{3} x^{2} \log \relax (f)^{3} - 60 \, b^{2} x^{3} \log \relax (f)^{2} + 120 \, b x^{4} \log \relax (f) - 120 \, x^{5}\right )} f^{\frac {a x + b}{x}}}{b^{6} x^{5} \log \relax (f)^{6}} \]
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 \[ \int \frac {f^{a + \frac {b}{x}}}{x^{7}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 142, normalized size = 1.84 \[ \frac {-\frac {x \,{\mathrm e}^{\left (a +\frac {b}{x}\right ) \ln \relax (f )}}{b \ln \relax (f )}+\frac {5 x^{2} {\mathrm e}^{\left (a +\frac {b}{x}\right ) \ln \relax (f )}}{b^{2} \ln \relax (f )^{2}}-\frac {20 x^{3} {\mathrm e}^{\left (a +\frac {b}{x}\right ) \ln \relax (f )}}{b^{3} \ln \relax (f )^{3}}+\frac {60 x^{4} {\mathrm e}^{\left (a +\frac {b}{x}\right ) \ln \relax (f )}}{b^{4} \ln \relax (f )^{4}}-\frac {120 x^{5} {\mathrm e}^{\left (a +\frac {b}{x}\right ) \ln \relax (f )}}{b^{5} \ln \relax (f )^{5}}+\frac {120 x^{6} {\mathrm e}^{\left (a +\frac {b}{x}\right ) \ln \relax (f )}}{b^{6} \ln \relax (f )^{6}}}{x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 1.29, size = 21, normalized size = 0.27 \[ \frac {f^{a} \Gamma \left (6, -\frac {b \log \relax (f)}{x}\right )}{b^{6} \log \relax (f)^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.65, size = 81, normalized size = 1.05 \[ -\frac {f^{a+\frac {b}{x}}\,\left (\frac {1}{b\,\ln \relax (f)}+\frac {20\,x^2}{b^3\,{\ln \relax (f)}^3}-\frac {60\,x^3}{b^4\,{\ln \relax (f)}^4}+\frac {120\,x^4}{b^5\,{\ln \relax (f)}^5}-\frac {120\,x^5}{b^6\,{\ln \relax (f)}^6}-\frac {5\,x}{b^2\,{\ln \relax (f)}^2}\right )}{x^5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 80, normalized size = 1.04 \[ \frac {f^{a + \frac {b}{x}} \left (- b^{5} \log {\relax (f )}^{5} + 5 b^{4} x \log {\relax (f )}^{4} - 20 b^{3} x^{2} \log {\relax (f )}^{3} + 60 b^{2} x^{3} \log {\relax (f )}^{2} - 120 b x^{4} \log {\relax (f )} + 120 x^{5}\right )}{b^{6} x^{5} \log {\relax (f )}^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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