Optimal. Leaf size=65 \[ -\frac {f^{a+\frac {b}{x}} \left (b^4 \log ^4(f)-4 b^3 x \log ^3(f)+12 b^2 x^2 \log ^2(f)-24 b x^3 \log (f)+24 x^4\right )}{b^5 x^4 \log ^5(f)} \]
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Rubi [C] time = 0.02, antiderivative size = 22, normalized size of antiderivative = 0.34, 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} \[ -\frac {f^a \text {Gamma}\left (5,-\frac {b \log (f)}{x}\right )}{b^5 \log ^5(f)} \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin {align*} \int \frac {f^{a+\frac {b}{x}}}{x^6} \, dx &=-\frac {f^a \Gamma \left (5,-\frac {b \log (f)}{x}\right )}{b^5 \log ^5(f)}\\ \end {align*}
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Mathematica [C] time = 0.00, size = 22, normalized size = 0.34 \[ -\frac {f^a \Gamma \left (5,-\frac {b \log (f)}{x}\right )}{b^5 \log ^5(f)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 67, normalized size = 1.03 \[ -\frac {{\left (b^{4} \log \relax (f)^{4} - 4 \, b^{3} x \log \relax (f)^{3} + 12 \, b^{2} x^{2} \log \relax (f)^{2} - 24 \, b x^{3} \log \relax (f) + 24 \, x^{4}\right )} f^{\frac {a x + b}{x}}}{b^{5} x^{4} \log \relax (f)^{5}} \]
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 \[ \int \frac {f^{a + \frac {b}{x}}}{x^{6}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 119, normalized size = 1.83 \[ \frac {-\frac {x \,{\mathrm e}^{\left (a +\frac {b}{x}\right ) \ln \relax (f )}}{b \ln \relax (f )}+\frac {4 x^{2} {\mathrm e}^{\left (a +\frac {b}{x}\right ) \ln \relax (f )}}{b^{2} \ln \relax (f )^{2}}-\frac {12 x^{3} {\mathrm e}^{\left (a +\frac {b}{x}\right ) \ln \relax (f )}}{b^{3} \ln \relax (f )^{3}}+\frac {24 x^{4} {\mathrm e}^{\left (a +\frac {b}{x}\right ) \ln \relax (f )}}{b^{4} \ln \relax (f )^{4}}-\frac {24 x^{5} {\mathrm e}^{\left (a +\frac {b}{x}\right ) \ln \relax (f )}}{b^{5} \ln \relax (f )^{5}}}{x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 1.24, size = 22, normalized size = 0.34 \[ -\frac {f^{a} \Gamma \left (5, -\frac {b \log \relax (f)}{x}\right )}{b^{5} \log \relax (f)^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.60, size = 69, normalized size = 1.06 \[ -\frac {f^{a+\frac {b}{x}}\,\left (\frac {1}{b\,\ln \relax (f)}+\frac {12\,x^2}{b^3\,{\ln \relax (f)}^3}-\frac {24\,x^3}{b^4\,{\ln \relax (f)}^4}+\frac {24\,x^4}{b^5\,{\ln \relax (f)}^5}-\frac {4\,x}{b^2\,{\ln \relax (f)}^2}\right )}{x^4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 66, normalized size = 1.02 \[ \frac {f^{a + \frac {b}{x}} \left (- b^{4} \log {\relax (f )}^{4} + 4 b^{3} x \log {\relax (f )}^{3} - 12 b^{2} x^{2} \log {\relax (f )}^{2} + 24 b x^{3} \log {\relax (f )} - 24 x^{4}\right )}{b^{5} x^{4} \log {\relax (f )}^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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