Optimal. Leaf size=27 \[ \frac {x}{1+\frac {3}{4} \left (1-e^5\right )+\frac {6 x}{5}+\log (\log (-4+x))} \]
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Rubi [F]
time = 2.12, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {-400 x+\left (-2800+e^5 (1200-300 x)+700 x\right ) \log (-4+x)+(-1600+400 x) \log (-4+x) \log (\log (-4+x))}{\left (-4900-5495 x-624 x^2+576 x^3+e^{10} (-900+225 x)+e^5 \left (4200+1830 x-720 x^2\right )\right ) \log (-4+x)+\left (-5600+e^5 (2400-600 x)-2440 x+960 x^2\right ) \log (-4+x) \log (\log (-4+x))+(-1600+400 x) \log (-4+x) \log ^2(\log (-4+x))} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {100 \left (4 x+(-4+x) \log (-4+x) \left (-7+3 e^5-4 \log (\log (-4+x))\right )\right )}{(4-x) \log (-4+x) \left (35 \left (1-\frac {3 e^5}{7}\right )+24 x+20 \log (\log (-4+x))\right )^2} \, dx\\ &=100 \int \frac {4 x+(-4+x) \log (-4+x) \left (-7+3 e^5-4 \log (\log (-4+x))\right )}{(4-x) \log (-4+x) \left (35 \left (1-\frac {3 e^5}{7}\right )+24 x+20 \log (\log (-4+x))\right )^2} \, dx\\ &=100 \int \left (\frac {4 x (5-24 \log (-4+x)+6 x \log (-4+x))}{5 (4-x) \log (-4+x) \left (35 \left (1-\frac {3 e^5}{7}\right )+24 x+20 \log (\log (-4+x))\right )^2}+\frac {1}{5 \left (35 \left (1-\frac {3 e^5}{7}\right )+24 x+20 \log (\log (-4+x))\right )}\right ) \, dx\\ &=20 \int \frac {1}{35 \left (1-\frac {3 e^5}{7}\right )+24 x+20 \log (\log (-4+x))} \, dx+80 \int \frac {x (5-24 \log (-4+x)+6 x \log (-4+x))}{(4-x) \log (-4+x) \left (35 \left (1-\frac {3 e^5}{7}\right )+24 x+20 \log (\log (-4+x))\right )^2} \, dx\\ &=20 \int \frac {1}{35 \left (1-\frac {3 e^5}{7}\right )+24 x+20 \log (\log (-4+x))} \, dx+80 \int \frac {x (5+6 (-4+x) \log (-4+x))}{(4-x) \log (-4+x) \left (35 \left (1-\frac {3 e^5}{7}\right )+24 x+20 \log (\log (-4+x))\right )^2} \, dx\\ &=20 \int \frac {1}{35 \left (1-\frac {3 e^5}{7}\right )+24 x+20 \log (\log (-4+x))} \, dx+80 \int \left (\frac {-5+24 \log (-4+x)-6 x \log (-4+x)}{\log (-4+x) \left (35 \left (1-\frac {3 e^5}{7}\right )+24 x+20 \log (\log (-4+x))\right )^2}+\frac {4 (5-24 \log (-4+x)+6 x \log (-4+x))}{(4-x) \log (-4+x) \left (35 \left (1-\frac {3 e^5}{7}\right )+24 x+20 \log (\log (-4+x))\right )^2}\right ) \, dx\\ &=20 \int \frac {1}{35 \left (1-\frac {3 e^5}{7}\right )+24 x+20 \log (\log (-4+x))} \, dx+80 \int \frac {-5+24 \log (-4+x)-6 x \log (-4+x)}{\log (-4+x) \left (35 \left (1-\frac {3 e^5}{7}\right )+24 x+20 \log (\log (-4+x))\right )^2} \, dx+320 \int \frac {5-24 \log (-4+x)+6 x \log (-4+x)}{(4-x) \log (-4+x) \left (35 \left (1-\frac {3 e^5}{7}\right )+24 x+20 \log (\log (-4+x))\right )^2} \, dx\\ &=\frac {80}{5 \left (7-3 e^5\right )+24 x+20 \log (\log (-4+x))}+20 \int \frac {1}{35 \left (1-\frac {3 e^5}{7}\right )+24 x+20 \log (\log (-4+x))} \, dx+80 \int \frac {-5-6 (-4+x) \log (-4+x)}{\log (-4+x) \left (35 \left (1-\frac {3 e^5}{7}\right )+24 x+20 \log (\log (-4+x))\right )^2} \, dx\\ &=\frac {80}{5 \left (7-3 e^5\right )+24 x+20 \log (\log (-4+x))}+20 \int \frac {1}{35 \left (1-\frac {3 e^5}{7}\right )+24 x+20 \log (\log (-4+x))} \, dx+80 \int \left (\frac {24}{\left (35 \left (1-\frac {3 e^5}{7}\right )+24 x+20 \log (\log (-4+x))\right )^2}-\frac {6 x}{\left (35 \left (1-\frac {3 e^5}{7}\right )+24 x+20 \log (\log (-4+x))\right )^2}-\frac {5}{\log (-4+x) \left (35 \left (1-\frac {3 e^5}{7}\right )+24 x+20 \log (\log (-4+x))\right )^2}\right ) \, dx\\ &=\frac {80}{5 \left (7-3 e^5\right )+24 x+20 \log (\log (-4+x))}+20 \int \frac {1}{35 \left (1-\frac {3 e^5}{7}\right )+24 x+20 \log (\log (-4+x))} \, dx-400 \int \frac {1}{\log (-4+x) \left (35 \left (1-\frac {3 e^5}{7}\right )+24 x+20 \log (\log (-4+x))\right )^2} \, dx-480 \int \frac {x}{\left (35 \left (1-\frac {3 e^5}{7}\right )+24 x+20 \log (\log (-4+x))\right )^2} \, dx+1920 \int \frac {1}{\left (35 \left (1-\frac {3 e^5}{7}\right )+24 x+20 \log (\log (-4+x))\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.24, size = 22, normalized size = 0.81 \begin {gather*} \frac {100 x}{175-75 e^5+120 x+100 \log (\log (-4+x))} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 5.39, size = 22, normalized size = 0.81
method | result | size |
risch | \(-\frac {20 x}{15 \,{\mathrm e}^{5}-20 \ln \left (\ln \left (x -4\right )\right )-24 x -35}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.34, size = 21, normalized size = 0.78 \begin {gather*} \frac {20 \, x}{24 \, x - 15 \, e^{5} + 20 \, \log \left (\log \left (x - 4\right )\right ) + 35} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 21, normalized size = 0.78 \begin {gather*} \frac {20 \, x}{24 \, x - 15 \, e^{5} + 20 \, \log \left (\log \left (x - 4\right )\right ) + 35} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.12, size = 22, normalized size = 0.81 \begin {gather*} \frac {x}{\frac {6 x}{5} + \log {\left (\log {\left (x - 4 \right )} \right )} - \frac {3 e^{5}}{4} + \frac {7}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.46, size = 21, normalized size = 0.78 \begin {gather*} \frac {20 \, x}{24 \, x - 15 \, e^{5} + 20 \, \log \left (\log \left (x - 4\right )\right ) + 35} \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 = -0.04 \begin {gather*} \int \frac {400\,x+\ln \left (x-4\right )\,\left ({\mathrm {e}}^5\,\left (300\,x-1200\right )-700\,x+2800\right )-\ln \left (x-4\right )\,\ln \left (\ln \left (x-4\right )\right )\,\left (400\,x-1600\right )}{-\ln \left (x-4\right )\,\left (400\,x-1600\right )\,{\ln \left (\ln \left (x-4\right )\right )}^2+\ln \left (x-4\right )\,\left (2440\,x-960\,x^2+{\mathrm {e}}^5\,\left (600\,x-2400\right )+5600\right )\,\ln \left (\ln \left (x-4\right )\right )+\ln \left (x-4\right )\,\left (5495\,x-{\mathrm {e}}^5\,\left (-720\,x^2+1830\,x+4200\right )+624\,x^2-576\,x^3-{\mathrm {e}}^{10}\,\left (225\,x-900\right )+4900\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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