Integrand size = 166, antiderivative size = 31 \[ \int \frac {10 e^{-2-6 x+x^2}+e^{-4-12 x+2 x^2} \left (-59 x+20 x^2\right )+\left (-10+e^{-2-6 x+x^2} \left (58 x-20 x^2\right )\right ) \log \left (\frac {3}{x}\right )+x \log ^2\left (\frac {3}{x}\right )+\left (2 e^{-2-6 x+x^2} x+e^{-4-12 x+2 x^2} \left (x-12 x^2+4 x^3\right )+\left (-2 x+e^{-2-6 x+x^2} \left (-2 x+12 x^2-4 x^3\right )\right ) \log \left (\frac {3}{x}\right )+x \log ^2\left (\frac {3}{x}\right )\right ) \log (x)}{x} \, dx=x \left (e^{-2-6 x+x^2}-\log \left (\frac {3}{x}\right )\right )^2 \left (\frac {5}{x}+\log (x)\right ) \]
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\[ \int \frac {10 e^{-2-6 x+x^2}+e^{-4-12 x+2 x^2} \left (-59 x+20 x^2\right )+\left (-10+e^{-2-6 x+x^2} \left (58 x-20 x^2\right )\right ) \log \left (\frac {3}{x}\right )+x \log ^2\left (\frac {3}{x}\right )+\left (2 e^{-2-6 x+x^2} x+e^{-4-12 x+2 x^2} \left (x-12 x^2+4 x^3\right )+\left (-2 x+e^{-2-6 x+x^2} \left (-2 x+12 x^2-4 x^3\right )\right ) \log \left (\frac {3}{x}\right )+x \log ^2\left (\frac {3}{x}\right )\right ) \log (x)}{x} \, dx=\int \frac {10 e^{-2-6 x+x^2}+e^{-4-12 x+2 x^2} \left (-59 x+20 x^2\right )+\left (-10+e^{-2-6 x+x^2} \left (58 x-20 x^2\right )\right ) \log \left (\frac {3}{x}\right )+x \log ^2\left (\frac {3}{x}\right )+\left (2 e^{-2-6 x+x^2} x+e^{-4-12 x+2 x^2} \left (x-12 x^2+4 x^3\right )+\left (-2 x+e^{-2-6 x+x^2} \left (-2 x+12 x^2-4 x^3\right )\right ) \log \left (\frac {3}{x}\right )+x \log ^2\left (\frac {3}{x}\right )\right ) \log (x)}{x} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \left (e^{-4-12 x+2 x^2} \left (-59+20 x+\log (x)-12 x \log (x)+4 x^2 \log (x)\right )+\frac {\log \left (\frac {3}{x}\right ) \left (-10+x \log \left (\frac {3}{x}\right )-2 x \log (x)+x \log \left (\frac {3}{x}\right ) \log (x)\right )}{x}-\frac {2 e^{-2-6 x+x^2} \left (-5-29 x \log \left (\frac {3}{x}\right )+10 x^2 \log \left (\frac {3}{x}\right )-x \log (x)+x \log \left (\frac {3}{x}\right ) \log (x)-6 x^2 \log \left (\frac {3}{x}\right ) \log (x)+2 x^3 \log \left (\frac {3}{x}\right ) \log (x)\right )}{x}\right ) \, dx \\ & = -\left (2 \int \frac {e^{-2-6 x+x^2} \left (-5-29 x \log \left (\frac {3}{x}\right )+10 x^2 \log \left (\frac {3}{x}\right )-x \log (x)+x \log \left (\frac {3}{x}\right ) \log (x)-6 x^2 \log \left (\frac {3}{x}\right ) \log (x)+2 x^3 \log \left (\frac {3}{x}\right ) \log (x)\right )}{x} \, dx\right )+\int e^{-4-12 x+2 x^2} \left (-59+20 x+\log (x)-12 x \log (x)+4 x^2 \log (x)\right ) \, dx+\int \frac {\log \left (\frac {3}{x}\right ) \left (-10+x \log \left (\frac {3}{x}\right )-2 x \log (x)+x \log \left (\frac {3}{x}\right ) \log (x)\right )}{x} \, dx \\ & = -\left (2 \int \frac {e^{-2-6 x+x^2} \left (-5-x \log (x)+x \log \left (\frac {3}{x}\right ) \left (-29+10 x+\left (1-6 x+2 x^2\right ) \log (x)\right )\right )}{x} \, dx\right )+\int \left (-59 e^{-4-12 x+2 x^2}+20 e^{-4-12 x+2 x^2} x+e^{-4-12 x+2 x^2} \log (x)-12 e^{-4-12 x+2 x^2} x \log (x)+4 e^{-4-12 x+2 x^2} x^2 \log (x)\right ) \, dx+\int \left (\frac {\log \left (\frac {3}{x}\right ) \left (-10+x \log \left (\frac {3}{x}\right )\right )}{x}+\left (-2+\log \left (\frac {3}{x}\right )\right ) \log \left (\frac {3}{x}\right ) \log (x)\right ) \, dx \\ & = -\left (2 \int \left (\frac {e^{-2-6 x+x^2} \left (-5-29 x \log \left (\frac {3}{x}\right )+10 x^2 \log \left (\frac {3}{x}\right )\right )}{x}+e^{-2-6 x+x^2} \left (-1+\log \left (\frac {3}{x}\right )-6 x \log \left (\frac {3}{x}\right )+2 x^2 \log \left (\frac {3}{x}\right )\right ) \log (x)\right ) \, dx\right )+4 \int e^{-4-12 x+2 x^2} x^2 \log (x) \, dx-12 \int e^{-4-12 x+2 x^2} x \log (x) \, dx+20 \int e^{-4-12 x+2 x^2} x \, dx-59 \int e^{-4-12 x+2 x^2} \, dx+\int \frac {\log \left (\frac {3}{x}\right ) \left (-10+x \log \left (\frac {3}{x}\right )\right )}{x} \, dx+\int e^{-4-12 x+2 x^2} \log (x) \, dx+\int \left (-2+\log \left (\frac {3}{x}\right )\right ) \log \left (\frac {3}{x}\right ) \log (x) \, dx \\ & = 5 e^{-4-12 x+2 x^2}+e^{-4-12 x+2 x^2} x \log (x)-2 \int \frac {e^{-2-6 x+x^2} \left (-5-29 x \log \left (\frac {3}{x}\right )+10 x^2 \log \left (\frac {3}{x}\right )\right )}{x} \, dx-2 \int e^{-2-6 x+x^2} \left (-1+\log \left (\frac {3}{x}\right )-6 x \log \left (\frac {3}{x}\right )+2 x^2 \log \left (\frac {3}{x}\right )\right ) \log (x) \, dx-4 \int \frac {e^{-22-12 x} \left (4 e^{2 \left (9+x^2\right )} (3+x)-35 e^{12 x} \sqrt {2 \pi } \text {erfi}\left (\sqrt {2} (3-x)\right )\right )}{16 x} \, dx+12 \int \frac {e^{2 (-3+x)^2}-3 \sqrt {2 \pi } \text {erfi}\left (\sqrt {2} (3-x)\right )}{4 e^{22} x} \, dx+60 \int e^{-4-12 x+2 x^2} \, dx-\frac {59 \int e^{\frac {1}{8} (-12+4 x)^2} \, dx}{e^{22}}-\int -\frac {\sqrt {\frac {\pi }{2}} \text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{2 e^{22} x} \, dx+\int \left (-\frac {10 \log \left (\frac {3}{x}\right )}{x}+\log ^2\left (\frac {3}{x}\right )\right ) \, dx+\int \left (-2 \log \left (\frac {3}{x}\right ) \log (x)+\log ^2\left (\frac {3}{x}\right ) \log (x)\right ) \, dx \\ & = 5 e^{-4-12 x+2 x^2}+\frac {59 \sqrt {\frac {\pi }{2}} \text {erfi}\left (\sqrt {2} (3-x)\right )}{2 e^{22}}+e^{-4-12 x+2 x^2} x \log (x)-\frac {1}{4} \int \frac {e^{-22-12 x} \left (4 e^{2 \left (9+x^2\right )} (3+x)-35 e^{12 x} \sqrt {2 \pi } \text {erfi}\left (\sqrt {2} (3-x)\right )\right )}{x} \, dx-2 \int \frac {e^{-2-6 x+x^2} \left (-5+x (-29+10 x) \log \left (\frac {3}{x}\right )\right )}{x} \, dx-2 \int \log \left (\frac {3}{x}\right ) \log (x) \, dx-2 \int e^{-2-6 x+x^2} \left (-1+\left (1-6 x+2 x^2\right ) \log \left (\frac {3}{x}\right )\right ) \log (x) \, dx-10 \int \frac {\log \left (\frac {3}{x}\right )}{x} \, dx+\frac {3 \int \frac {e^{2 (-3+x)^2}-3 \sqrt {2 \pi } \text {erfi}\left (\sqrt {2} (3-x)\right )}{x} \, dx}{e^{22}}+\frac {60 \int e^{\frac {1}{8} (-12+4 x)^2} \, dx}{e^{22}}+\frac {\sqrt {\frac {\pi }{2}} \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{2 e^{22}}+\int \log ^2\left (\frac {3}{x}\right ) \, dx+\int \log ^2\left (\frac {3}{x}\right ) \log (x) \, dx \\ & = 5 e^{-4-12 x+2 x^2}+\frac {59 \sqrt {\frac {\pi }{2}} \text {erfi}\left (\sqrt {2} (3-x)\right )}{2 e^{22}}-\frac {15 \sqrt {2 \pi } \text {erfi}\left (\sqrt {2} (3-x)\right )}{e^{22}}+5 \log ^2\left (\frac {3}{x}\right )+x \log ^2\left (\frac {3}{x}\right )+e^{-4-12 x+2 x^2} x \log (x)+x \log ^2\left (\frac {3}{x}\right ) \log (x)-\frac {1}{4} \int \left (\frac {4 e^{-4-12 x+2 x^2} (3+x)}{x}-\frac {35 \sqrt {2 \pi } \text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{e^{22} x}\right ) \, dx+2 \int \log \left (\frac {3}{x}\right ) \, dx+2 \int \left (1+\log \left (\frac {3}{x}\right )\right ) \, dx-2 \int \left (-\frac {5 e^{-2-6 x+x^2}}{x}+e^{-2-6 x+x^2} (-29+10 x) \log \left (\frac {3}{x}\right )\right ) \, dx-2 \int \left (-e^{-2-6 x+x^2} \log (x)+e^{-2-6 x+x^2} \log \left (\frac {3}{x}\right ) \log (x)-6 e^{-2-6 x+x^2} x \log \left (\frac {3}{x}\right ) \log (x)+2 e^{-2-6 x+x^2} x^2 \log \left (\frac {3}{x}\right ) \log (x)\right ) \, dx+\frac {3 \int \left (\frac {e^{2 (-3+x)^2}}{x}-\frac {3 \sqrt {2 \pi } \text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x}\right ) \, dx}{e^{22}}+\frac {\sqrt {\frac {\pi }{2}} \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{2 e^{22}}-\int \left (2+2 \log \left (\frac {3}{x}\right )+\log ^2\left (\frac {3}{x}\right )\right ) \, dx \\ & = 5 e^{-4-12 x+2 x^2}+2 x+\frac {59 \sqrt {\frac {\pi }{2}} \text {erfi}\left (\sqrt {2} (3-x)\right )}{2 e^{22}}-\frac {15 \sqrt {2 \pi } \text {erfi}\left (\sqrt {2} (3-x)\right )}{e^{22}}+2 x \log \left (\frac {3}{x}\right )+5 \log ^2\left (\frac {3}{x}\right )+x \log ^2\left (\frac {3}{x}\right )+e^{-4-12 x+2 x^2} x \log (x)+x \log ^2\left (\frac {3}{x}\right ) \log (x)-2 \int e^{-2-6 x+x^2} (-29+10 x) \log \left (\frac {3}{x}\right ) \, dx+2 \int e^{-2-6 x+x^2} \log (x) \, dx-2 \int e^{-2-6 x+x^2} \log \left (\frac {3}{x}\right ) \log (x) \, dx-4 \int e^{-2-6 x+x^2} x^2 \log \left (\frac {3}{x}\right ) \log (x) \, dx+10 \int \frac {e^{-2-6 x+x^2}}{x} \, dx+12 \int e^{-2-6 x+x^2} x \log \left (\frac {3}{x}\right ) \log (x) \, dx+\frac {3 \int \frac {e^{2 (-3+x)^2}}{x} \, dx}{e^{22}}+\frac {\sqrt {\frac {\pi }{2}} \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{2 e^{22}}+\frac {\left (35 \sqrt {\frac {\pi }{2}}\right ) \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{2 e^{22}}-\frac {\left (9 \sqrt {2 \pi }\right ) \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{e^{22}}-\int \frac {e^{-4-12 x+2 x^2} (3+x)}{x} \, dx-\int \log ^2\left (\frac {3}{x}\right ) \, dx \\ & = 5 e^{-4-12 x+2 x^2}+2 x+\frac {59 \sqrt {\frac {\pi }{2}} \text {erfi}\left (\sqrt {2} (3-x)\right )}{2 e^{22}}-\frac {15 \sqrt {2 \pi } \text {erfi}\left (\sqrt {2} (3-x)\right )}{e^{22}}-10 e^{-2-6 x+x^2} \log \left (\frac {3}{x}\right )+2 x \log \left (\frac {3}{x}\right )+\frac {\sqrt {\pi } \text {erfi}(3-x) \log \left (\frac {3}{x}\right )}{e^{11}}+5 \log ^2\left (\frac {3}{x}\right )+e^{-4-12 x+2 x^2} x \log (x)-\frac {\sqrt {\pi } \text {erfi}(3-x) \log (x)}{e^{11}}-2 e^{-2-6 x+x^2} x \log \left (\frac {3}{x}\right ) \log (x)+x \log ^2\left (\frac {3}{x}\right ) \log (x)-2 \int -\frac {\sqrt {\pi } \text {erfi}(3-x)}{2 e^{11} x} \, dx-2 \int \frac {5 e^{-2-6 x+x^2}-\frac {\sqrt {\pi } \text {erfi}(3-x)}{2 e^{11}}}{x} \, dx-2 \int \log \left (\frac {3}{x}\right ) \, dx+2 \int -\frac {\sqrt {\pi } \text {erfi}(3-x) \log \left (\frac {3}{x}\right )}{2 e^{11} x} \, dx+2 \int \frac {\sqrt {\pi } \text {erfi}(3-x) \log (x)}{2 e^{11} x} \, dx+4 \int \frac {e^{-11-6 x} \left (2 e^{9+x^2} (3+x)-17 e^{6 x} \sqrt {\pi } \text {erfi}(3-x)\right ) \log \left (\frac {3}{x}\right )}{4 x} \, dx+4 \int \frac {e^{-11-6 x} \left (-2 e^{9+x^2} (3+x)+17 e^{6 x} \sqrt {\pi } \text {erfi}(3-x)\right ) \log (x)}{4 x} \, dx+10 \int \frac {e^{-2-6 x+x^2}}{x} \, dx-12 \int \frac {\left (e^{(-3+x)^2}-3 \sqrt {\pi } \text {erfi}(3-x)\right ) \log \left (\frac {3}{x}\right )}{2 e^{11} x} \, dx-12 \int \frac {\left (-e^{(-3+x)^2}+3 \sqrt {\pi } \text {erfi}(3-x)\right ) \log (x)}{2 e^{11} x} \, dx+\frac {3 \int \frac {e^{2 (-3+x)^2}}{x} \, dx}{e^{22}}+\frac {\sqrt {\frac {\pi }{2}} \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{2 e^{22}}+\frac {\left (35 \sqrt {\frac {\pi }{2}}\right ) \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{2 e^{22}}-\frac {\left (9 \sqrt {2 \pi }\right ) \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{e^{22}}-\int \left (e^{-4-12 x+2 x^2}+\frac {3 e^{-4-12 x+2 x^2}}{x}\right ) \, dx \\ & = 5 e^{-4-12 x+2 x^2}+\frac {59 \sqrt {\frac {\pi }{2}} \text {erfi}\left (\sqrt {2} (3-x)\right )}{2 e^{22}}-\frac {15 \sqrt {2 \pi } \text {erfi}\left (\sqrt {2} (3-x)\right )}{e^{22}}-10 e^{-2-6 x+x^2} \log \left (\frac {3}{x}\right )+\frac {\sqrt {\pi } \text {erfi}(3-x) \log \left (\frac {3}{x}\right )}{e^{11}}+5 \log ^2\left (\frac {3}{x}\right )+e^{-4-12 x+2 x^2} x \log (x)-\frac {\sqrt {\pi } \text {erfi}(3-x) \log (x)}{e^{11}}-2 e^{-2-6 x+x^2} x \log \left (\frac {3}{x}\right ) \log (x)+x \log ^2\left (\frac {3}{x}\right ) \log (x)-2 \int \left (\frac {5 e^{-2-6 x+x^2}}{x}-\frac {\sqrt {\pi } \text {erfi}(3-x)}{2 e^{11} x}\right ) \, dx-3 \int \frac {e^{-4-12 x+2 x^2}}{x} \, dx+10 \int \frac {e^{-2-6 x+x^2}}{x} \, dx+\frac {3 \int \frac {e^{2 (-3+x)^2}}{x} \, dx}{e^{22}}-\frac {6 \int \frac {\left (e^{(-3+x)^2}-3 \sqrt {\pi } \text {erfi}(3-x)\right ) \log \left (\frac {3}{x}\right )}{x} \, dx}{e^{11}}-\frac {6 \int \frac {\left (-e^{(-3+x)^2}+3 \sqrt {\pi } \text {erfi}(3-x)\right ) \log (x)}{x} \, dx}{e^{11}}+\frac {\sqrt {\frac {\pi }{2}} \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{2 e^{22}}+\frac {\left (35 \sqrt {\frac {\pi }{2}}\right ) \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{2 e^{22}}+\frac {\sqrt {\pi } \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}-\frac {\sqrt {\pi } \int \frac {\text {erfi}(3-x) \log \left (\frac {3}{x}\right )}{x} \, dx}{e^{11}}+\frac {\sqrt {\pi } \int \frac {\text {erfi}(3-x) \log (x)}{x} \, dx}{e^{11}}-\frac {\left (9 \sqrt {2 \pi }\right ) \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{e^{22}}-\int e^{-4-12 x+2 x^2} \, dx+\int \frac {e^{-11-6 x} \left (2 e^{9+x^2} (3+x)-17 e^{6 x} \sqrt {\pi } \text {erfi}(3-x)\right ) \log \left (\frac {3}{x}\right )}{x} \, dx+\int \frac {e^{-11-6 x} \left (-2 e^{9+x^2} (3+x)+17 e^{6 x} \sqrt {\pi } \text {erfi}(3-x)\right ) \log (x)}{x} \, dx \\ & = 5 e^{-4-12 x+2 x^2}+\frac {59 \sqrt {\frac {\pi }{2}} \text {erfi}\left (\sqrt {2} (3-x)\right )}{2 e^{22}}-\frac {15 \sqrt {2 \pi } \text {erfi}\left (\sqrt {2} (3-x)\right )}{e^{22}}-10 e^{-2-6 x+x^2} \log \left (\frac {3}{x}\right )+5 \log ^2\left (\frac {3}{x}\right )+e^{-4-12 x+2 x^2} x \log (x)-2 e^{-2-6 x+x^2} x \log \left (\frac {3}{x}\right ) \log (x)+x \log ^2\left (\frac {3}{x}\right ) \log (x)-3 \int \frac {e^{-4-12 x+2 x^2}}{x} \, dx-\frac {\int e^{\frac {1}{8} (-12+4 x)^2} \, dx}{e^{22}}+\frac {3 \int \frac {e^{2 (-3+x)^2}}{x} \, dx}{e^{22}}+2 \frac {6 \int \frac {-\int \frac {e^{(-3+x)^2}}{x} \, dx+3 \sqrt {\pi } \int \frac {\text {erfi}(3-x)}{x} \, dx}{x} \, dx}{e^{11}}+\frac {\sqrt {\frac {\pi }{2}} \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{2 e^{22}}+\frac {\left (35 \sqrt {\frac {\pi }{2}}\right ) \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{2 e^{22}}+2 \frac {\sqrt {\pi } \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}-2 \frac {\sqrt {\pi } \int \frac {\int \frac {\text {erfi}(3-x)}{x} \, dx}{x} \, dx}{e^{11}}-\frac {\left (9 \sqrt {2 \pi }\right ) \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{e^{22}}+\left (6 \log \left (\frac {3}{x}\right )\right ) \int \frac {e^{-2-6 x+x^2}}{x} \, dx-\frac {\left (6 \log \left (\frac {3}{x}\right )\right ) \int \frac {e^{9-6 x+x^2}}{x} \, dx}{e^{11}}-\frac {\left (\sqrt {\pi } \log \left (\frac {3}{x}\right )\right ) \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}-\frac {\left (17 \sqrt {\pi } \log \left (\frac {3}{x}\right )\right ) \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}+\frac {\left (18 \sqrt {\pi } \log \left (\frac {3}{x}\right )\right ) \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}-(6 \log (x)) \int \frac {e^{-2-6 x+x^2}}{x} \, dx+\frac {(6 \log (x)) \int \frac {e^{9-6 x+x^2}}{x} \, dx}{e^{11}}+\frac {\left (\sqrt {\pi } \log (x)\right ) \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}+\frac {\left (17 \sqrt {\pi } \log (x)\right ) \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}-\frac {\left (18 \sqrt {\pi } \log (x)\right ) \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}-2 \int \frac {-6 \int \frac {e^{-2-6 x+x^2}}{x} \, dx+\frac {\sqrt {\pi } \left (\text {erfi}(3-x)+17 \int \frac {\text {erfi}(3-x)}{x} \, dx\right )}{e^{11}}}{x} \, dx \\ & = 5 e^{-4-12 x+2 x^2}-10 e^{-2-6 x+x^2} \log \left (\frac {3}{x}\right )+5 \log ^2\left (\frac {3}{x}\right )+e^{-4-12 x+2 x^2} x \log (x)-2 e^{-2-6 x+x^2} x \log \left (\frac {3}{x}\right ) \log (x)+x \log ^2\left (\frac {3}{x}\right ) \log (x)-3 \int \frac {e^{-4-12 x+2 x^2}}{x} \, dx+\frac {3 \int \frac {e^{2 (-3+x)^2}}{x} \, dx}{e^{22}}+2 \frac {6 \int \left (-\frac {\int \frac {e^{9-6 x+x^2}}{x} \, dx}{x}+\frac {3 \sqrt {\pi } \int \frac {\text {erfi}(3-x)}{x} \, dx}{x}\right ) \, dx}{e^{11}}+\frac {\sqrt {\frac {\pi }{2}} \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{2 e^{22}}+\frac {\left (35 \sqrt {\frac {\pi }{2}}\right ) \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{2 e^{22}}+2 \frac {\sqrt {\pi } \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}-2 \frac {\sqrt {\pi } \int \frac {\int \frac {\text {erfi}(3-x)}{x} \, dx}{x} \, dx}{e^{11}}-\frac {\left (9 \sqrt {2 \pi }\right ) \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{e^{22}}+\left (6 \log \left (\frac {3}{x}\right )\right ) \int \frac {e^{-2-6 x+x^2}}{x} \, dx-\frac {\left (6 \log \left (\frac {3}{x}\right )\right ) \int \frac {e^{9-6 x+x^2}}{x} \, dx}{e^{11}}-\frac {\left (\sqrt {\pi } \log \left (\frac {3}{x}\right )\right ) \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}-\frac {\left (17 \sqrt {\pi } \log \left (\frac {3}{x}\right )\right ) \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}+\frac {\left (18 \sqrt {\pi } \log \left (\frac {3}{x}\right )\right ) \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}-(6 \log (x)) \int \frac {e^{-2-6 x+x^2}}{x} \, dx+\frac {(6 \log (x)) \int \frac {e^{9-6 x+x^2}}{x} \, dx}{e^{11}}+\frac {\left (\sqrt {\pi } \log (x)\right ) \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}+\frac {\left (17 \sqrt {\pi } \log (x)\right ) \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}-\frac {\left (18 \sqrt {\pi } \log (x)\right ) \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}-2 \int \left (\frac {\sqrt {\pi } \text {erfi}(3-x)-6 e^{11} \int \frac {e^{-2-6 x+x^2}}{x} \, dx}{e^{11} x}+\frac {17 \sqrt {\pi } \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11} x}\right ) \, dx \\ & = 5 e^{-4-12 x+2 x^2}-10 e^{-2-6 x+x^2} \log \left (\frac {3}{x}\right )+5 \log ^2\left (\frac {3}{x}\right )+e^{-4-12 x+2 x^2} x \log (x)-2 e^{-2-6 x+x^2} x \log \left (\frac {3}{x}\right ) \log (x)+x \log ^2\left (\frac {3}{x}\right ) \log (x)-3 \int \frac {e^{-4-12 x+2 x^2}}{x} \, dx+\frac {3 \int \frac {e^{2 (-3+x)^2}}{x} \, dx}{e^{22}}+\frac {\sqrt {\frac {\pi }{2}} \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{2 e^{22}}+\frac {\left (35 \sqrt {\frac {\pi }{2}}\right ) \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{2 e^{22}}+2 \frac {\sqrt {\pi } \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}-2 \frac {\sqrt {\pi } \int \frac {\int \frac {\text {erfi}(3-x)}{x} \, dx}{x} \, dx}{e^{11}}-2 \left (\frac {\int \frac {\sqrt {\pi } \text {erfi}(3-x)-6 e^{11} \int \frac {e^{-2-6 x+x^2}}{x} \, dx}{x} \, dx}{e^{11}}+\frac {\left (17 \sqrt {\pi }\right ) \int \frac {\int \frac {\text {erfi}(3-x)}{x} \, dx}{x} \, dx}{e^{11}}\right )+2 \left (-\frac {6 \int \frac {\int \frac {e^{9-6 x+x^2}}{x} \, dx}{x} \, dx}{e^{11}}+\frac {\left (18 \sqrt {\pi }\right ) \int \frac {\int \frac {\text {erfi}(3-x)}{x} \, dx}{x} \, dx}{e^{11}}\right )-\frac {\left (9 \sqrt {2 \pi }\right ) \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{e^{22}}+\left (6 \log \left (\frac {3}{x}\right )\right ) \int \frac {e^{-2-6 x+x^2}}{x} \, dx-\frac {\left (6 \log \left (\frac {3}{x}\right )\right ) \int \frac {e^{9-6 x+x^2}}{x} \, dx}{e^{11}}-\frac {\left (\sqrt {\pi } \log \left (\frac {3}{x}\right )\right ) \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}-\frac {\left (17 \sqrt {\pi } \log \left (\frac {3}{x}\right )\right ) \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}+\frac {\left (18 \sqrt {\pi } \log \left (\frac {3}{x}\right )\right ) \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}-(6 \log (x)) \int \frac {e^{-2-6 x+x^2}}{x} \, dx+\frac {(6 \log (x)) \int \frac {e^{9-6 x+x^2}}{x} \, dx}{e^{11}}+\frac {\left (\sqrt {\pi } \log (x)\right ) \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}+\frac {\left (17 \sqrt {\pi } \log (x)\right ) \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}-\frac {\left (18 \sqrt {\pi } \log (x)\right ) \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}} \\ & = 5 e^{-4-12 x+2 x^2}-10 e^{-2-6 x+x^2} \log \left (\frac {3}{x}\right )+5 \log ^2\left (\frac {3}{x}\right )+e^{-4-12 x+2 x^2} x \log (x)-2 e^{-2-6 x+x^2} x \log \left (\frac {3}{x}\right ) \log (x)+x \log ^2\left (\frac {3}{x}\right ) \log (x)-3 \int \frac {e^{-4-12 x+2 x^2}}{x} \, dx+\frac {3 \int \frac {e^{2 (-3+x)^2}}{x} \, dx}{e^{22}}+\frac {\sqrt {\frac {\pi }{2}} \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{2 e^{22}}+\frac {\left (35 \sqrt {\frac {\pi }{2}}\right ) \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{2 e^{22}}+2 \frac {\sqrt {\pi } \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}-2 \frac {\sqrt {\pi } \int \frac {\int \frac {\text {erfi}(3-x)}{x} \, dx}{x} \, dx}{e^{11}}-2 \left (\frac {\int \left (\frac {\sqrt {\pi } \text {erfi}(3-x)}{x}-\frac {6 e^{11} \int \frac {e^{-2-6 x+x^2}}{x} \, dx}{x}\right ) \, dx}{e^{11}}+\frac {\left (17 \sqrt {\pi }\right ) \int \frac {\int \frac {\text {erfi}(3-x)}{x} \, dx}{x} \, dx}{e^{11}}\right )+2 \left (-\frac {6 \int \frac {\int \frac {e^{9-6 x+x^2}}{x} \, dx}{x} \, dx}{e^{11}}+\frac {\left (18 \sqrt {\pi }\right ) \int \frac {\int \frac {\text {erfi}(3-x)}{x} \, dx}{x} \, dx}{e^{11}}\right )-\frac {\left (9 \sqrt {2 \pi }\right ) \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{e^{22}}+\left (6 \log \left (\frac {3}{x}\right )\right ) \int \frac {e^{-2-6 x+x^2}}{x} \, dx-\frac {\left (6 \log \left (\frac {3}{x}\right )\right ) \int \frac {e^{9-6 x+x^2}}{x} \, dx}{e^{11}}-\frac {\left (\sqrt {\pi } \log \left (\frac {3}{x}\right )\right ) \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}-\frac {\left (17 \sqrt {\pi } \log \left (\frac {3}{x}\right )\right ) \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}+\frac {\left (18 \sqrt {\pi } \log \left (\frac {3}{x}\right )\right ) \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}-(6 \log (x)) \int \frac {e^{-2-6 x+x^2}}{x} \, dx+\frac {(6 \log (x)) \int \frac {e^{9-6 x+x^2}}{x} \, dx}{e^{11}}+\frac {\left (\sqrt {\pi } \log (x)\right ) \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}+\frac {\left (17 \sqrt {\pi } \log (x)\right ) \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}-\frac {\left (18 \sqrt {\pi } \log (x)\right ) \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}} \\ & = 5 e^{-4-12 x+2 x^2}-10 e^{-2-6 x+x^2} \log \left (\frac {3}{x}\right )+5 \log ^2\left (\frac {3}{x}\right )+e^{-4-12 x+2 x^2} x \log (x)-2 e^{-2-6 x+x^2} x \log \left (\frac {3}{x}\right ) \log (x)+x \log ^2\left (\frac {3}{x}\right ) \log (x)-3 \int \frac {e^{-4-12 x+2 x^2}}{x} \, dx+\frac {3 \int \frac {e^{2 (-3+x)^2}}{x} \, dx}{e^{22}}+\frac {\sqrt {\frac {\pi }{2}} \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{2 e^{22}}+\frac {\left (35 \sqrt {\frac {\pi }{2}}\right ) \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{2 e^{22}}+2 \frac {\sqrt {\pi } \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}-2 \frac {\sqrt {\pi } \int \frac {\int \frac {\text {erfi}(3-x)}{x} \, dx}{x} \, dx}{e^{11}}-2 \left (-\left (6 \int \frac {\int \frac {e^{-2-6 x+x^2}}{x} \, dx}{x} \, dx\right )+\frac {\sqrt {\pi } \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}+\frac {\left (17 \sqrt {\pi }\right ) \int \frac {\int \frac {\text {erfi}(3-x)}{x} \, dx}{x} \, dx}{e^{11}}\right )+2 \left (-\frac {6 \int \frac {\int \frac {e^{9-6 x+x^2}}{x} \, dx}{x} \, dx}{e^{11}}+\frac {\left (18 \sqrt {\pi }\right ) \int \frac {\int \frac {\text {erfi}(3-x)}{x} \, dx}{x} \, dx}{e^{11}}\right )-\frac {\left (9 \sqrt {2 \pi }\right ) \int \frac {\text {erfi}\left (3 \sqrt {2}-\sqrt {2} x\right )}{x} \, dx}{e^{22}}+\left (6 \log \left (\frac {3}{x}\right )\right ) \int \frac {e^{-2-6 x+x^2}}{x} \, dx-\frac {\left (6 \log \left (\frac {3}{x}\right )\right ) \int \frac {e^{9-6 x+x^2}}{x} \, dx}{e^{11}}-\frac {\left (\sqrt {\pi } \log \left (\frac {3}{x}\right )\right ) \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}-\frac {\left (17 \sqrt {\pi } \log \left (\frac {3}{x}\right )\right ) \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}+\frac {\left (18 \sqrt {\pi } \log \left (\frac {3}{x}\right )\right ) \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}-(6 \log (x)) \int \frac {e^{-2-6 x+x^2}}{x} \, dx+\frac {(6 \log (x)) \int \frac {e^{9-6 x+x^2}}{x} \, dx}{e^{11}}+\frac {\left (\sqrt {\pi } \log (x)\right ) \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}+\frac {\left (17 \sqrt {\pi } \log (x)\right ) \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}}-\frac {\left (18 \sqrt {\pi } \log (x)\right ) \int \frac {\text {erfi}(3-x)}{x} \, dx}{e^{11}} \\ \end{align*}
Time = 0.17 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.19 \[ \int \frac {10 e^{-2-6 x+x^2}+e^{-4-12 x+2 x^2} \left (-59 x+20 x^2\right )+\left (-10+e^{-2-6 x+x^2} \left (58 x-20 x^2\right )\right ) \log \left (\frac {3}{x}\right )+x \log ^2\left (\frac {3}{x}\right )+\left (2 e^{-2-6 x+x^2} x+e^{-4-12 x+2 x^2} \left (x-12 x^2+4 x^3\right )+\left (-2 x+e^{-2-6 x+x^2} \left (-2 x+12 x^2-4 x^3\right )\right ) \log \left (\frac {3}{x}\right )+x \log ^2\left (\frac {3}{x}\right )\right ) \log (x)}{x} \, dx=e^{-4-12 x} \left (e^{x^2}-e^{2+6 x} \log \left (\frac {3}{x}\right )\right )^2 (5+x \log (x)) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(88\) vs. \(2(30)=60\).
Time = 6.08 (sec) , antiderivative size = 89, normalized size of antiderivative = 2.87
method | result | size |
parallelrisch | \(-2 \ln \left (\frac {3}{x}\right ) {\mathrm e}^{x^{2}-6 x -2} \ln \left (x \right ) x +5 \ln \left (\frac {3}{x}\right )^{2}+\ln \left (\frac {3}{x}\right )^{2} \ln \left (x \right ) x +\ln \left (x \right ) {\mathrm e}^{2 x^{2}-12 x -4} x +5 \,{\mathrm e}^{2 x^{2}-12 x -4}-10 \ln \left (\frac {3}{x}\right ) {\mathrm e}^{x^{2}-6 x -2}\) | \(89\) |
risch | \(x \ln \left (x \right )^{3}+\left (5-2 x \ln \left (3\right )+2 x \,{\mathrm e}^{x^{2}-6 x -2}\right ) \ln \left (x \right )^{2}+\left (x \ln \left (3\right )^{2}+{\mathrm e}^{2 x^{2}-12 x -4} x -2 \,{\mathrm e}^{x^{2}-6 x -2} \ln \left (3\right ) x +10 \,{\mathrm e}^{x^{2}-6 x -2}\right ) \ln \left (x \right )-10 \ln \left (3\right ) \ln \left (x \right )-10 \ln \left (3\right ) {\mathrm e}^{x^{2}-6 x -2}+5 \,{\mathrm e}^{2 x^{2}-12 x -4}\) | \(112\) |
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Leaf count of result is larger than twice the leaf count of optimal. 96 vs. \(2 (30) = 60\).
Time = 0.27 (sec) , antiderivative size = 96, normalized size of antiderivative = 3.10 \[ \int \frac {10 e^{-2-6 x+x^2}+e^{-4-12 x+2 x^2} \left (-59 x+20 x^2\right )+\left (-10+e^{-2-6 x+x^2} \left (58 x-20 x^2\right )\right ) \log \left (\frac {3}{x}\right )+x \log ^2\left (\frac {3}{x}\right )+\left (2 e^{-2-6 x+x^2} x+e^{-4-12 x+2 x^2} \left (x-12 x^2+4 x^3\right )+\left (-2 x+e^{-2-6 x+x^2} \left (-2 x+12 x^2-4 x^3\right )\right ) \log \left (\frac {3}{x}\right )+x \log ^2\left (\frac {3}{x}\right )\right ) \log (x)}{x} \, dx=-x \log \left (\frac {3}{x}\right )^{3} + {\left (2 \, x e^{\left (x^{2} - 6 \, x - 2\right )} + x \log \left (3\right ) + 5\right )} \log \left (\frac {3}{x}\right )^{2} + {\left (x \log \left (3\right ) + 5\right )} e^{\left (2 \, x^{2} - 12 \, x - 4\right )} - {\left (x e^{\left (2 \, x^{2} - 12 \, x - 4\right )} + 2 \, {\left (x \log \left (3\right ) + 5\right )} e^{\left (x^{2} - 6 \, x - 2\right )}\right )} \log \left (\frac {3}{x}\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 95 vs. \(2 (24) = 48\).
Time = 0.41 (sec) , antiderivative size = 95, normalized size of antiderivative = 3.06 \[ \int \frac {10 e^{-2-6 x+x^2}+e^{-4-12 x+2 x^2} \left (-59 x+20 x^2\right )+\left (-10+e^{-2-6 x+x^2} \left (58 x-20 x^2\right )\right ) \log \left (\frac {3}{x}\right )+x \log ^2\left (\frac {3}{x}\right )+\left (2 e^{-2-6 x+x^2} x+e^{-4-12 x+2 x^2} \left (x-12 x^2+4 x^3\right )+\left (-2 x+e^{-2-6 x+x^2} \left (-2 x+12 x^2-4 x^3\right )\right ) \log \left (\frac {3}{x}\right )+x \log ^2\left (\frac {3}{x}\right )\right ) \log (x)}{x} \, dx=x \log {\left (x \right )}^{3} + x \log {\left (3 \right )}^{2} \log {\left (x \right )} + \left (- 2 x \log {\left (3 \right )} + 5\right ) \log {\left (x \right )}^{2} + \left (x \log {\left (x \right )} + 5\right ) e^{2 x^{2} - 12 x - 4} + \left (2 x \log {\left (x \right )}^{2} - 2 x \log {\left (3 \right )} \log {\left (x \right )} + 10 \log {\left (x \right )} - 10 \log {\left (3 \right )}\right ) e^{x^{2} - 6 x - 2} - 10 \log {\left (3 \right )} \log {\left (x \right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 155 vs. \(2 (30) = 60\).
Time = 0.34 (sec) , antiderivative size = 155, normalized size of antiderivative = 5.00 \[ \int \frac {10 e^{-2-6 x+x^2}+e^{-4-12 x+2 x^2} \left (-59 x+20 x^2\right )+\left (-10+e^{-2-6 x+x^2} \left (58 x-20 x^2\right )\right ) \log \left (\frac {3}{x}\right )+x \log ^2\left (\frac {3}{x}\right )+\left (2 e^{-2-6 x+x^2} x+e^{-4-12 x+2 x^2} \left (x-12 x^2+4 x^3\right )+\left (-2 x+e^{-2-6 x+x^2} \left (-2 x+12 x^2-4 x^3\right )\right ) \log \left (\frac {3}{x}\right )+x \log ^2\left (\frac {3}{x}\right )\right ) \log (x)}{x} \, dx=x \log \left (\frac {3}{x}\right )^{2} + {\left ({\left (x \log \left (x\right ) + 5\right )} e^{\left (2 \, x^{2}\right )} + 2 \, {\left (x e^{2} \log \left (x\right )^{2} - 5 \, e^{2} \log \left (3\right ) - {\left (x e^{2} \log \left (3\right ) - 5 \, e^{2}\right )} \log \left (x\right )\right )} e^{\left (x^{2} + 6 \, x\right )} - {\left (x {\left (2 \, \log \left (3\right ) + 1\right )} e^{4} \log \left (x\right )^{2} - x e^{4} \log \left (x\right )^{3} - {\left (\log \left (3\right )^{2} + 2 \, \log \left (3\right ) + 2\right )} x e^{4} \log \left (x\right ) + {\left (\log \left (3\right )^{2} + 2 \, \log \left (3\right ) + 2\right )} x e^{4}\right )} e^{\left (12 \, x\right )}\right )} e^{\left (-12 \, x - 4\right )} + 2 \, x \log \left (\frac {3}{x}\right ) + 5 \, \log \left (\frac {3}{x}\right )^{2} + 2 \, x \]
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Leaf count of result is larger than twice the leaf count of optimal. 135 vs. \(2 (30) = 60\).
Time = 0.31 (sec) , antiderivative size = 135, normalized size of antiderivative = 4.35 \[ \int \frac {10 e^{-2-6 x+x^2}+e^{-4-12 x+2 x^2} \left (-59 x+20 x^2\right )+\left (-10+e^{-2-6 x+x^2} \left (58 x-20 x^2\right )\right ) \log \left (\frac {3}{x}\right )+x \log ^2\left (\frac {3}{x}\right )+\left (2 e^{-2-6 x+x^2} x+e^{-4-12 x+2 x^2} \left (x-12 x^2+4 x^3\right )+\left (-2 x+e^{-2-6 x+x^2} \left (-2 x+12 x^2-4 x^3\right )\right ) \log \left (\frac {3}{x}\right )+x \log ^2\left (\frac {3}{x}\right )\right ) \log (x)}{x} \, dx={\left (x e^{6} \log \left (3\right )^{2} \log \left (x\right ) - 2 \, x e^{6} \log \left (3\right ) \log \left (x\right )^{2} + x e^{6} \log \left (x\right )^{3} - 2 \, x e^{\left (x^{2} - 6 \, x + 4\right )} \log \left (3\right ) \log \left (x\right ) + 2 \, x e^{\left (x^{2} - 6 \, x + 4\right )} \log \left (x\right )^{2} + x e^{\left (2 \, x^{2} - 12 \, x + 2\right )} \log \left (x\right ) - 10 \, e^{6} \log \left (3\right ) \log \left (x\right ) + 5 \, e^{6} \log \left (x\right )^{2} - 10 \, e^{\left (x^{2} - 6 \, x + 4\right )} \log \left (3\right ) + 10 \, e^{\left (x^{2} - 6 \, x + 4\right )} \log \left (x\right ) + 5 \, e^{\left (2 \, x^{2} - 12 \, x + 2\right )}\right )} e^{\left (-6\right )} \]
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Timed out. \[ \int \frac {10 e^{-2-6 x+x^2}+e^{-4-12 x+2 x^2} \left (-59 x+20 x^2\right )+\left (-10+e^{-2-6 x+x^2} \left (58 x-20 x^2\right )\right ) \log \left (\frac {3}{x}\right )+x \log ^2\left (\frac {3}{x}\right )+\left (2 e^{-2-6 x+x^2} x+e^{-4-12 x+2 x^2} \left (x-12 x^2+4 x^3\right )+\left (-2 x+e^{-2-6 x+x^2} \left (-2 x+12 x^2-4 x^3\right )\right ) \log \left (\frac {3}{x}\right )+x \log ^2\left (\frac {3}{x}\right )\right ) \log (x)}{x} \, dx=\int \frac {10\,{\mathrm {e}}^{x^2-6\,x-2}-{\mathrm {e}}^{2\,x^2-12\,x-4}\,\left (59\,x-20\,x^2\right )+\ln \left (\frac {3}{x}\right )\,\left ({\mathrm {e}}^{x^2-6\,x-2}\,\left (58\,x-20\,x^2\right )-10\right )+x\,{\ln \left (\frac {3}{x}\right )}^2+\ln \left (x\right )\,\left (x\,{\ln \left (\frac {3}{x}\right )}^2+\left (-2\,x-{\mathrm {e}}^{x^2-6\,x-2}\,\left (4\,x^3-12\,x^2+2\,x\right )\right )\,\ln \left (\frac {3}{x}\right )+2\,x\,{\mathrm {e}}^{x^2-6\,x-2}+{\mathrm {e}}^{2\,x^2-12\,x-4}\,\left (4\,x^3-12\,x^2+x\right )\right )}{x} \,d x \]
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