Optimal. Leaf size=19 \[ \left (4+e^{19 x}\right ) \log (5-x-\log (\log (x))) \]
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Rubi [B] time = 1.37, antiderivative size = 93, normalized size of antiderivative = 4.89, number of steps used = 5, number of rules used = 4, integrand size = 106, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.038, Rules used = {6688, 6742, 6684, 2288} \begin {gather*} \frac {e^{19 x} \left (x^2 (-\log (x)) \log (-x-\log (\log (x))+5)+5 x \log (x) \log (-x-\log (\log (x))+5)-x \log (x) \log (\log (x)) \log (-x-\log (\log (x))+5)\right )}{x \log (x) (-x-\log (\log (x))+5)}+4 \log (-x-\log (\log (x))+5) \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rule 6684
Rule 6688
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-4-e^{19 x}-x \log (x) \left (4+e^{19 x}+19 e^{19 x} (-5+x+\log (\log (x))) \log (5-x-\log (\log (x)))\right )}{x \log (x) (5-x-\log (\log (x)))} \, dx\\ &=\int \left (\frac {4 (1+x \log (x))}{x \log (x) (-5+x+\log (\log (x)))}+\frac {e^{19 x} \left (1+x \log (x)-95 x \log (x) \log (5-x-\log (\log (x)))+19 x^2 \log (x) \log (5-x-\log (\log (x)))+19 x \log (x) \log (\log (x)) \log (5-x-\log (\log (x)))\right )}{x \log (x) (-5+x+\log (\log (x)))}\right ) \, dx\\ &=4 \int \frac {1+x \log (x)}{x \log (x) (-5+x+\log (\log (x)))} \, dx+\int \frac {e^{19 x} \left (1+x \log (x)-95 x \log (x) \log (5-x-\log (\log (x)))+19 x^2 \log (x) \log (5-x-\log (\log (x)))+19 x \log (x) \log (\log (x)) \log (5-x-\log (\log (x)))\right )}{x \log (x) (-5+x+\log (\log (x)))} \, dx\\ &=4 \log (5-x-\log (\log (x)))+\frac {e^{19 x} \left (5 x \log (x) \log (5-x-\log (\log (x)))-x^2 \log (x) \log (5-x-\log (\log (x)))-x \log (x) \log (\log (x)) \log (5-x-\log (\log (x)))\right )}{x \log (x) (5-x-\log (\log (x)))}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.31, size = 19, normalized size = 1.00 \begin {gather*} \left (4+e^{19 x}\right ) \log (5-x-\log (\log (x))) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.51, size = 18, normalized size = 0.95 \begin {gather*} {\left (e^{\left (19 \, x\right )} + 4\right )} \log \left (-x - \log \left (\log \relax (x)\right ) + 5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.25, size = 26, normalized size = 1.37 \begin {gather*} e^{\left (19 \, x\right )} \log \left (-x - \log \left (\log \relax (x)\right ) + 5\right ) + 4 \, \log \left (x + \log \left (\log \relax (x)\right ) - 5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 27, normalized size = 1.42
method | result | size |
risch | \({\mathrm e}^{19 x} \ln \left (-\ln \left (\ln \relax (x )\right )+5-x \right )+4 \ln \left (\ln \left (\ln \relax (x )\right )+x -5\right )\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 18, normalized size = 0.95 \begin {gather*} {\left (e^{\left (19 \, x\right )} + 4\right )} \log \left (-x - \log \left (\log \relax (x)\right ) + 5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} -\int \frac {4\,{\mathrm {e}}^{5\,x}+{\mathrm {e}}^{24\,x}-\ln \left (5-\ln \left (\ln \relax (x)\right )-x\right )\,\left ({\mathrm {e}}^{24\,x}\,\ln \relax (x)\,\left (95\,x-19\,x^2\right )-19\,x\,\ln \left (\ln \relax (x)\right )\,{\mathrm {e}}^{24\,x}\,\ln \relax (x)\right )+\ln \relax (x)\,\left (4\,x\,{\mathrm {e}}^{5\,x}+x\,{\mathrm {e}}^{24\,x}\right )}{{\mathrm {e}}^{5\,x}\,\ln \relax (x)\,\left (5\,x-x^2\right )-x\,\ln \left (\ln \relax (x)\right )\,{\mathrm {e}}^{5\,x}\,\ln \relax (x)} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 13.95, size = 26, normalized size = 1.37 \begin {gather*} e^{19 x} \log {\left (- x - \log {\left (\log {\relax (x )} \right )} + 5 \right )} + 4 \log {\left (x + \log {\left (\log {\relax (x )} \right )} - 5 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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