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 = 0.33, 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 = {6820, 6838}
\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 6820
Rule 6838
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 = 0.11, 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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Maple [A]
time = 0.25, size = 20, normalized size = 1.05
method | result | size |
risch | \({\mathrm e}^{\frac {1}{\ln \left (\frac {2 \ln \left (2\right )}{x -16}\right )+20 \ln \left (5\right )+x}}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 55 vs.
\(2 (19) = 38\).
time = 0.50, size = 55, normalized size = 2.89 \begin {gather*} \frac {x e^{\left (\frac {1}{x + 20 \, \log \left (5\right ) + \log \left (2\right ) - \log \left (x - 16\right ) + \log \left (\log \left (2\right )\right )}\right )}}{x - 17} - \frac {17 \, e^{\left (\frac {1}{x + 20 \, \log \left (5\right ) + \log \left (2\right ) - \log \left (x - 16\right ) + \log \left (\log \left (2\right )\right )}\right )}}{x - 17} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.30, size = 19, normalized size = 1.00 \begin {gather*} e^{\left (\frac {1}{x + 20 \, \log \left (5\right ) + \log \left (\frac {2 \, \log \left (2\right )}{x - 16}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.27, size = 19, normalized size = 1.00 \begin {gather*} e^{\frac {1}{x + \log {\left (\frac {2 \log {\left (2 \right )}}{x - 16} \right )} + 20 \log {\left (5 \right )}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 19, normalized size = 1.00 \begin {gather*} e^{\left (\frac {1}{x + 20 \, \log \left (5\right ) + \log \left (\frac {2 \, \log \left (2\right )}{x - 16}\right )}\right )} \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 \left (2\right )}{x-16}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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