Integrand size = 131, antiderivative size = 27 \[ \int \frac {-837 x+e^x \left (-3-279 x-279 x^2\right ) \log (3)+\left (-567 x+e^x \left (-189 x-189 x^2\right ) \log (3)\right ) \log (x)+\left (-96 x+e^x \left (-32 x-32 x^2\right ) \log (3)\right ) \log ^2(x)+\left (-279 e^x x \log (3)-189 e^x x \log (3) \log (x)-32 e^x x \log (3) \log ^2(x)\right ) \log \left (\frac {93+32 \log (x)}{3+\log (x)}\right )}{837 x+567 x \log (x)+96 x \log ^2(x)} \, dx=3-x-\frac {1}{3} e^x \log (3) \left (x+\log \left (32-\frac {3}{3+\log (x)}\right )\right ) \]
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Leaf count is larger than twice the leaf count of optimal. \(109\) vs. \(2(27)=54\).
Time = 2.67 (sec) , antiderivative size = 109, normalized size of antiderivative = 4.04, number of steps used = 5, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.031, Rules used = {6873, 12, 6874, 2326} \[ \int \frac {-837 x+e^x \left (-3-279 x-279 x^2\right ) \log (3)+\left (-567 x+e^x \left (-189 x-189 x^2\right ) \log (3)\right ) \log (x)+\left (-96 x+e^x \left (-32 x-32 x^2\right ) \log (3)\right ) \log ^2(x)+\left (-279 e^x x \log (3)-189 e^x x \log (3) \log (x)-32 e^x x \log (3) \log ^2(x)\right ) \log \left (\frac {93+32 \log (x)}{3+\log (x)}\right )}{837 x+567 x \log (x)+96 x \log ^2(x)} \, dx=-\frac {e^x \log (3) \left (279 x^2+32 x^2 \log ^2(x)+189 x^2 \log (x)+32 x \log ^2(x) \log \left (\frac {32 \log (x)+93}{\log (x)+3}\right )+189 x \log (x) \log \left (\frac {32 \log (x)+93}{\log (x)+3}\right )+279 x \log \left (\frac {32 \log (x)+93}{\log (x)+3}\right )\right )}{3 x (\log (x)+3) (32 \log (x)+93)}-x \]
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Rule 12
Rule 2326
Rule 6873
Rule 6874
Rubi steps \begin{align*} \text {integral}& = \int \frac {-837 x+e^x \left (-3-279 x-279 x^2\right ) \log (3)+\left (-567 x+e^x \left (-189 x-189 x^2\right ) \log (3)\right ) \log (x)+\left (-96 x+e^x \left (-32 x-32 x^2\right ) \log (3)\right ) \log ^2(x)+\left (-279 e^x x \log (3)-189 e^x x \log (3) \log (x)-32 e^x x \log (3) \log ^2(x)\right ) \log \left (\frac {93+32 \log (x)}{3+\log (x)}\right )}{3 x \left (279+189 \log (x)+32 \log ^2(x)\right )} \, dx \\ & = \frac {1}{3} \int \frac {-837 x+e^x \left (-3-279 x-279 x^2\right ) \log (3)+\left (-567 x+e^x \left (-189 x-189 x^2\right ) \log (3)\right ) \log (x)+\left (-96 x+e^x \left (-32 x-32 x^2\right ) \log (3)\right ) \log ^2(x)+\left (-279 e^x x \log (3)-189 e^x x \log (3) \log (x)-32 e^x x \log (3) \log ^2(x)\right ) \log \left (\frac {93+32 \log (x)}{3+\log (x)}\right )}{x \left (279+189 \log (x)+32 \log ^2(x)\right )} \, dx \\ & = \frac {1}{3} \int \left (-3-\frac {e^x \log (3) \left (3+279 x+279 x^2+189 x \log (x)+189 x^2 \log (x)+32 x \log ^2(x)+32 x^2 \log ^2(x)+279 x \log \left (\frac {93+32 \log (x)}{3+\log (x)}\right )+189 x \log (x) \log \left (\frac {93+32 \log (x)}{3+\log (x)}\right )+32 x \log ^2(x) \log \left (\frac {93+32 \log (x)}{3+\log (x)}\right )\right )}{x (3+\log (x)) (93+32 \log (x))}\right ) \, dx \\ & = -x-\frac {1}{3} \log (3) \int \frac {e^x \left (3+279 x+279 x^2+189 x \log (x)+189 x^2 \log (x)+32 x \log ^2(x)+32 x^2 \log ^2(x)+279 x \log \left (\frac {93+32 \log (x)}{3+\log (x)}\right )+189 x \log (x) \log \left (\frac {93+32 \log (x)}{3+\log (x)}\right )+32 x \log ^2(x) \log \left (\frac {93+32 \log (x)}{3+\log (x)}\right )\right )}{x (3+\log (x)) (93+32 \log (x))} \, dx \\ & = -x-\frac {e^x \log (3) \left (279 x^2+189 x^2 \log (x)+32 x^2 \log ^2(x)+279 x \log \left (\frac {93+32 \log (x)}{3+\log (x)}\right )+189 x \log (x) \log \left (\frac {93+32 \log (x)}{3+\log (x)}\right )+32 x \log ^2(x) \log \left (\frac {93+32 \log (x)}{3+\log (x)}\right )\right )}{3 x (3+\log (x)) (93+32 \log (x))} \\ \end{align*}
Time = 0.70 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.37 \[ \int \frac {-837 x+e^x \left (-3-279 x-279 x^2\right ) \log (3)+\left (-567 x+e^x \left (-189 x-189 x^2\right ) \log (3)\right ) \log (x)+\left (-96 x+e^x \left (-32 x-32 x^2\right ) \log (3)\right ) \log ^2(x)+\left (-279 e^x x \log (3)-189 e^x x \log (3) \log (x)-32 e^x x \log (3) \log ^2(x)\right ) \log \left (\frac {93+32 \log (x)}{3+\log (x)}\right )}{837 x+567 x \log (x)+96 x \log ^2(x)} \, dx=\frac {1}{3} \left (-3 x-e^x x \log (3)-e^x \log (3) \log \left (\frac {93+32 \log (x)}{3+\log (x)}\right )\right ) \]
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Time = 12.41 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.19
method | result | size |
parallelrisch | \(-\frac {x \ln \left (3\right ) {\mathrm e}^{x}}{3}-\frac {\ln \left (3\right ) \ln \left (\frac {32 \ln \left (x \right )+93}{3+\ln \left (x \right )}\right ) {\mathrm e}^{x}}{3}-x\) | \(32\) |
risch | \(-\frac {\ln \left (3\right ) {\mathrm e}^{x} \ln \left (\frac {93}{32}+\ln \left (x \right )\right )}{3}+\frac {\ln \left (3\right ) {\mathrm e}^{x} \ln \left (3+\ln \left (x \right )\right )}{3}-x +\frac {i \pi \ln \left (3\right ) \operatorname {csgn}\left (\frac {i}{3+\ln \left (x \right )}\right ) \operatorname {csgn}\left (i \left (\frac {93}{32}+\ln \left (x \right )\right )\right ) \operatorname {csgn}\left (\frac {i \left (\frac {93}{32}+\ln \left (x \right )\right )}{3+\ln \left (x \right )}\right ) {\mathrm e}^{x}}{6}-\frac {i \pi \ln \left (3\right ) \operatorname {csgn}\left (\frac {i}{3+\ln \left (x \right )}\right ) \operatorname {csgn}\left (\frac {i \left (\frac {93}{32}+\ln \left (x \right )\right )}{3+\ln \left (x \right )}\right )^{2} {\mathrm e}^{x}}{6}-\frac {i \pi \ln \left (3\right ) \operatorname {csgn}\left (i \left (\frac {93}{32}+\ln \left (x \right )\right )\right ) \operatorname {csgn}\left (\frac {i \left (\frac {93}{32}+\ln \left (x \right )\right )}{3+\ln \left (x \right )}\right )^{2} {\mathrm e}^{x}}{6}+\frac {i \pi \ln \left (3\right ) \operatorname {csgn}\left (\frac {i \left (\frac {93}{32}+\ln \left (x \right )\right )}{3+\ln \left (x \right )}\right )^{3} {\mathrm e}^{x}}{6}-\frac {5 \ln \left (2\right ) \ln \left (3\right ) {\mathrm e}^{x}}{3}-\frac {x \ln \left (3\right ) {\mathrm e}^{x}}{3}\) | \(172\) |
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Time = 0.26 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.15 \[ \int \frac {-837 x+e^x \left (-3-279 x-279 x^2\right ) \log (3)+\left (-567 x+e^x \left (-189 x-189 x^2\right ) \log (3)\right ) \log (x)+\left (-96 x+e^x \left (-32 x-32 x^2\right ) \log (3)\right ) \log ^2(x)+\left (-279 e^x x \log (3)-189 e^x x \log (3) \log (x)-32 e^x x \log (3) \log ^2(x)\right ) \log \left (\frac {93+32 \log (x)}{3+\log (x)}\right )}{837 x+567 x \log (x)+96 x \log ^2(x)} \, dx=-\frac {1}{3} \, x e^{x} \log \left (3\right ) - \frac {1}{3} \, e^{x} \log \left (3\right ) \log \left (\frac {32 \, \log \left (x\right ) + 93}{\log \left (x\right ) + 3}\right ) - x \]
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Time = 7.75 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.07 \[ \int \frac {-837 x+e^x \left (-3-279 x-279 x^2\right ) \log (3)+\left (-567 x+e^x \left (-189 x-189 x^2\right ) \log (3)\right ) \log (x)+\left (-96 x+e^x \left (-32 x-32 x^2\right ) \log (3)\right ) \log ^2(x)+\left (-279 e^x x \log (3)-189 e^x x \log (3) \log (x)-32 e^x x \log (3) \log ^2(x)\right ) \log \left (\frac {93+32 \log (x)}{3+\log (x)}\right )}{837 x+567 x \log (x)+96 x \log ^2(x)} \, dx=- x + \frac {\left (- x \log {\left (3 \right )} - \log {\left (3 \right )} \log {\left (\frac {32 \log {\left (x \right )} + 93}{\log {\left (x \right )} + 3} \right )}\right ) e^{x}}{3} \]
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Time = 0.31 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.30 \[ \int \frac {-837 x+e^x \left (-3-279 x-279 x^2\right ) \log (3)+\left (-567 x+e^x \left (-189 x-189 x^2\right ) \log (3)\right ) \log (x)+\left (-96 x+e^x \left (-32 x-32 x^2\right ) \log (3)\right ) \log ^2(x)+\left (-279 e^x x \log (3)-189 e^x x \log (3) \log (x)-32 e^x x \log (3) \log ^2(x)\right ) \log \left (\frac {93+32 \log (x)}{3+\log (x)}\right )}{837 x+567 x \log (x)+96 x \log ^2(x)} \, dx=-\frac {1}{3} \, x e^{x} \log \left (3\right ) - \frac {1}{3} \, e^{x} \log \left (3\right ) \log \left (32 \, \log \left (x\right ) + 93\right ) + \frac {1}{3} \, e^{x} \log \left (3\right ) \log \left (\log \left (x\right ) + 3\right ) - x \]
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Time = 0.31 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.30 \[ \int \frac {-837 x+e^x \left (-3-279 x-279 x^2\right ) \log (3)+\left (-567 x+e^x \left (-189 x-189 x^2\right ) \log (3)\right ) \log (x)+\left (-96 x+e^x \left (-32 x-32 x^2\right ) \log (3)\right ) \log ^2(x)+\left (-279 e^x x \log (3)-189 e^x x \log (3) \log (x)-32 e^x x \log (3) \log ^2(x)\right ) \log \left (\frac {93+32 \log (x)}{3+\log (x)}\right )}{837 x+567 x \log (x)+96 x \log ^2(x)} \, dx=-\frac {1}{3} \, x e^{x} \log \left (3\right ) - \frac {1}{3} \, e^{x} \log \left (3\right ) \log \left (32 \, \log \left (x\right ) + 93\right ) + \frac {1}{3} \, e^{x} \log \left (3\right ) \log \left (\log \left (x\right ) + 3\right ) - x \]
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Time = 15.38 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.15 \[ \int \frac {-837 x+e^x \left (-3-279 x-279 x^2\right ) \log (3)+\left (-567 x+e^x \left (-189 x-189 x^2\right ) \log (3)\right ) \log (x)+\left (-96 x+e^x \left (-32 x-32 x^2\right ) \log (3)\right ) \log ^2(x)+\left (-279 e^x x \log (3)-189 e^x x \log (3) \log (x)-32 e^x x \log (3) \log ^2(x)\right ) \log \left (\frac {93+32 \log (x)}{3+\log (x)}\right )}{837 x+567 x \log (x)+96 x \log ^2(x)} \, dx=-x-\frac {x\,{\mathrm {e}}^x\,\ln \left (3\right )}{3}-\frac {\ln \left (\frac {32\,\ln \left (x\right )+93}{\ln \left (x\right )+3}\right )\,{\mathrm {e}}^x\,\ln \left (3\right )}{3} \]
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