Optimal. Leaf size=19 \[ e^{\frac {1}{x+10 \log (25)+\log \left (\frac {\log (4)}{-16+x}\right )}} \]
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Rubi [A] time = 0.56, antiderivative size = 22, normalized size of antiderivative = 1.16, number of steps used = 2, number of rules used = 2, integrand size = 100, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.020, Rules used = {6688, 6706} \begin {gather*} e^{\frac {1}{x+\log \left (-\frac {\log (4)}{16-x}\right )+10 \log (25)}} \end {gather*}
Antiderivative was successfully verified.
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Rule 6688
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{\frac {1}{x+10 \log (25)+\log \left (\frac {\log (4)}{-16+x}\right )}} (-17+x)}{(16-x) \left (x+10 \log (25)+\log \left (\frac {\log (4)}{-16+x}\right )\right )^2} \, dx\\ &=e^{\frac {1}{x+10 \log (25)+\log \left (-\frac {\log (4)}{16-x}\right )}}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.68, size = 19, normalized size = 1.00 \begin {gather*} e^{\frac {1}{x+10 \log (25)+\log \left (\frac {\log (4)}{-16+x}\right )}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.94, size = 19, normalized size = 1.00 \begin {gather*} e^{\left (\frac {1}{x + 20 \, \log \relax (5) + \log \left (\frac {2 \, \log \relax (2)}{x - 16}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.33, size = 19, normalized size = 1.00 \begin {gather*} e^{\left (\frac {1}{x + 20 \, \log \relax (5) + \log \left (\frac {2 \, \log \relax (2)}{x - 16}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.26, size = 20, normalized size = 1.05
method | result | size |
risch | \({\mathrm e}^{\frac {1}{\ln \left (\frac {2 \ln \relax (2)}{x -16}\right )+20 \ln \relax (5)+x}}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.61, size = 55, normalized size = 2.89 \begin {gather*} \frac {x e^{\left (\frac {1}{x + 20 \, \log \relax (5) + \log \relax (2) - \log \left (x - 16\right ) + \log \left (\log \relax (2)\right )}\right )}}{x - 17} - \frac {17 \, e^{\left (\frac {1}{x + 20 \, \log \relax (5) + \log \relax (2) - \log \left (x - 16\right ) + \log \left (\log \relax (2)\right )}\right )}}{x - 17} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.85, size = 15, normalized size = 0.79 \begin {gather*} {\mathrm {e}}^{\frac {1}{x+\ln \left (\frac {190734863281250\,\ln \relax (2)}{x-16}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.62, size = 19, normalized size = 1.00 \begin {gather*} e^{\frac {1}{x + \log {\left (\frac {2 \log {\relax (2 )}}{x - 16} \right )} + 20 \log {\relax (5 )}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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