Integrand size = 223, antiderivative size = 35 \[ \int \frac {1875 x+e^x \left (750 x-750 x^2\right )+e^{2 x} \left (75 x-150 x^2\right )+\left (-375+e^{2 x} (-15+30 x)+e^x (-150+150 x)\right ) \log \left (x^2\right )+\log \left (\frac {25+10 e^x+e^{2 x}-2 x}{x}\right ) \left (750+300 e^x+30 e^{2 x}-60 x+\left (-375-150 e^x-15 e^{2 x}+30 x\right ) \log \left (x^2\right )\right )}{\log ^2\left (\frac {25+10 e^x+e^{2 x}-2 x}{x}\right ) \left (625 x^2+250 e^x x^2+25 e^{2 x} x^2-50 x^3+\left (-250 x-100 e^x x-10 e^{2 x} x+20 x^2\right ) \log \left (x^2\right )+\left (25+10 e^x+e^{2 x}-2 x\right ) \log ^2\left (x^2\right )\right )} \, dx=1-\frac {3 x}{\log \left (-2+\frac {\left (5+e^x\right )^2}{x}\right ) \left (-x+\frac {\log \left (x^2\right )}{5}\right )} \]
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\[ \int \frac {1875 x+e^x \left (750 x-750 x^2\right )+e^{2 x} \left (75 x-150 x^2\right )+\left (-375+e^{2 x} (-15+30 x)+e^x (-150+150 x)\right ) \log \left (x^2\right )+\log \left (\frac {25+10 e^x+e^{2 x}-2 x}{x}\right ) \left (750+300 e^x+30 e^{2 x}-60 x+\left (-375-150 e^x-15 e^{2 x}+30 x\right ) \log \left (x^2\right )\right )}{\log ^2\left (\frac {25+10 e^x+e^{2 x}-2 x}{x}\right ) \left (625 x^2+250 e^x x^2+25 e^{2 x} x^2-50 x^3+\left (-250 x-100 e^x x-10 e^{2 x} x+20 x^2\right ) \log \left (x^2\right )+\left (25+10 e^x+e^{2 x}-2 x\right ) \log ^2\left (x^2\right )\right )} \, dx=\int \frac {1875 x+e^x \left (750 x-750 x^2\right )+e^{2 x} \left (75 x-150 x^2\right )+\left (-375+e^{2 x} (-15+30 x)+e^x (-150+150 x)\right ) \log \left (x^2\right )+\log \left (\frac {25+10 e^x+e^{2 x}-2 x}{x}\right ) \left (750+300 e^x+30 e^{2 x}-60 x+\left (-375-150 e^x-15 e^{2 x}+30 x\right ) \log \left (x^2\right )\right )}{\log ^2\left (\frac {25+10 e^x+e^{2 x}-2 x}{x}\right ) \left (625 x^2+250 e^x x^2+25 e^{2 x} x^2-50 x^3+\left (-250 x-100 e^x x-10 e^{2 x} x+20 x^2\right ) \log \left (x^2\right )+\left (25+10 e^x+e^{2 x}-2 x\right ) \log ^2\left (x^2\right )\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {15 \left (-\frac {\left (5+e^x\right ) \left (-5+e^x (-1+2 x)\right ) \left (5 x-\log \left (x^2\right )\right )}{25+10 e^x+e^{2 x}-2 x}-\log \left (\frac {25+10 e^x+e^{2 x}-2 x}{x}\right ) \left (-2+\log \left (x^2\right )\right )\right )}{\log ^2\left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )^2} \, dx \\ & = 15 \int \frac {-\frac {\left (5+e^x\right ) \left (-5+e^x (-1+2 x)\right ) \left (5 x-\log \left (x^2\right )\right )}{25+10 e^x+e^{2 x}-2 x}-\log \left (\frac {25+10 e^x+e^{2 x}-2 x}{x}\right ) \left (-2+\log \left (x^2\right )\right )}{\log ^2\left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )^2} \, dx \\ & = 15 \int \left (\frac {2 \left (26+5 e^x-2 x\right ) x}{\left (25+10 e^x+e^{2 x}-2 x\right ) \log ^2\left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )}+\frac {5 x-10 x^2+2 \log \left (\frac {25+10 e^x+e^{2 x}-2 x}{x}\right )-\log \left (x^2\right )+2 x \log \left (x^2\right )-\log \left (\frac {25+10 e^x+e^{2 x}-2 x}{x}\right ) \log \left (x^2\right )}{\log ^2\left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )^2}\right ) \, dx \\ & = 15 \int \frac {5 x-10 x^2+2 \log \left (\frac {25+10 e^x+e^{2 x}-2 x}{x}\right )-\log \left (x^2\right )+2 x \log \left (x^2\right )-\log \left (\frac {25+10 e^x+e^{2 x}-2 x}{x}\right ) \log \left (x^2\right )}{\log ^2\left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )^2} \, dx+30 \int \frac {\left (26+5 e^x-2 x\right ) x}{\left (25+10 e^x+e^{2 x}-2 x\right ) \log ^2\left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )} \, dx \\ & = 15 \int \frac {-\left ((-1+2 x) \left (5 x-\log \left (x^2\right )\right )\right )-\log \left (\frac {25+10 e^x+e^{2 x}-2 x}{x}\right ) \left (-2+\log \left (x^2\right )\right )}{\log ^2\left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )^2} \, dx+30 \int \left (\frac {26 x}{\left (25+10 e^x+e^{2 x}-2 x\right ) \log ^2\left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )}+\frac {5 e^x x}{\left (25+10 e^x+e^{2 x}-2 x\right ) \log ^2\left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )}+\frac {2 x^2}{\left (-25-10 e^x-e^{2 x}+2 x\right ) \log ^2\left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )}\right ) \, dx \\ & = 15 \int \left (\frac {2-5 x}{\log \left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )^2}+\frac {1-2 x+\log \left (\frac {25+10 e^x+e^{2 x}-2 x}{x}\right )}{\log ^2\left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )}\right ) \, dx+60 \int \frac {x^2}{\left (-25-10 e^x-e^{2 x}+2 x\right ) \log ^2\left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )} \, dx+150 \int \frac {e^x x}{\left (25+10 e^x+e^{2 x}-2 x\right ) \log ^2\left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )} \, dx+780 \int \frac {x}{\left (25+10 e^x+e^{2 x}-2 x\right ) \log ^2\left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )} \, dx \\ & = 15 \int \frac {2-5 x}{\log \left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )^2} \, dx+15 \int \frac {1-2 x+\log \left (\frac {25+10 e^x+e^{2 x}-2 x}{x}\right )}{\log ^2\left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )} \, dx+60 \int \frac {x^2}{\left (-25-10 e^x-e^{2 x}+2 x\right ) \log ^2\left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )} \, dx+150 \int \frac {e^x x}{\left (25+10 e^x+e^{2 x}-2 x\right ) \log ^2\left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )} \, dx+780 \int \frac {x}{\left (25+10 e^x+e^{2 x}-2 x\right ) \log ^2\left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )} \, dx \\ & = 15 \int \left (\frac {2}{\log \left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )^2}-\frac {5 x}{\log \left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )^2}\right ) \, dx+15 \int \left (\frac {1}{\log ^2\left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )}+\frac {1}{\log \left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )}+\frac {2 x}{\log ^2\left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (-5 x+\log \left (x^2\right )\right )}\right ) \, dx+60 \int \frac {x^2}{\left (-25-10 e^x-e^{2 x}+2 x\right ) \log ^2\left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )} \, dx+150 \int \frac {e^x x}{\left (25+10 e^x+e^{2 x}-2 x\right ) \log ^2\left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )} \, dx+780 \int \frac {x}{\left (25+10 e^x+e^{2 x}-2 x\right ) \log ^2\left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )} \, dx \\ & = 15 \int \frac {1}{\log ^2\left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )} \, dx+15 \int \frac {1}{\log \left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )} \, dx+30 \int \frac {1}{\log \left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )^2} \, dx+30 \int \frac {x}{\log ^2\left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (-5 x+\log \left (x^2\right )\right )} \, dx+60 \int \frac {x^2}{\left (-25-10 e^x-e^{2 x}+2 x\right ) \log ^2\left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )} \, dx-75 \int \frac {x}{\log \left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )^2} \, dx+150 \int \frac {e^x x}{\left (25+10 e^x+e^{2 x}-2 x\right ) \log ^2\left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )} \, dx+780 \int \frac {x}{\left (25+10 e^x+e^{2 x}-2 x\right ) \log ^2\left (-2+\frac {25}{x}+\frac {10 e^x}{x}+\frac {e^{2 x}}{x}\right ) \left (5 x-\log \left (x^2\right )\right )} \, dx \\ \end{align*}
Time = 0.15 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.06 \[ \int \frac {1875 x+e^x \left (750 x-750 x^2\right )+e^{2 x} \left (75 x-150 x^2\right )+\left (-375+e^{2 x} (-15+30 x)+e^x (-150+150 x)\right ) \log \left (x^2\right )+\log \left (\frac {25+10 e^x+e^{2 x}-2 x}{x}\right ) \left (750+300 e^x+30 e^{2 x}-60 x+\left (-375-150 e^x-15 e^{2 x}+30 x\right ) \log \left (x^2\right )\right )}{\log ^2\left (\frac {25+10 e^x+e^{2 x}-2 x}{x}\right ) \left (625 x^2+250 e^x x^2+25 e^{2 x} x^2-50 x^3+\left (-250 x-100 e^x x-10 e^{2 x} x+20 x^2\right ) \log \left (x^2\right )+\left (25+10 e^x+e^{2 x}-2 x\right ) \log ^2\left (x^2\right )\right )} \, dx=\frac {15 x}{\log \left (\frac {25+10 e^x+e^{2 x}-2 x}{x}\right ) \left (5 x-\log \left (x^2\right )\right )} \]
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Time = 32.59 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.03
method | result | size |
parallelrisch | \(\frac {15 x}{\left (5 x -\ln \left (x^{2}\right )\right ) \ln \left (\frac {{\mathrm e}^{2 x}+10 \,{\mathrm e}^{x}+25-2 x}{x}\right )}\) | \(36\) |
risch | \(-\frac {60 i x}{\left (i \pi \,\operatorname {csgn}\left (i x^{2}\right ) \operatorname {csgn}\left (i x \right )^{2}-2 i \pi \operatorname {csgn}\left (i x^{2}\right )^{2} \operatorname {csgn}\left (i x \right )+i \pi \operatorname {csgn}\left (i x^{2}\right )^{3}+10 x -4 \ln \left (x \right )\right ) \left (-2 \pi {\operatorname {csgn}\left (\frac {i \left (\frac {{\mathrm e}^{2 x}}{2}-x +5 \,{\mathrm e}^{x}+\frac {25}{2}\right )}{x}\right )}^{2}-\pi \,\operatorname {csgn}\left (i \left (\frac {{\mathrm e}^{2 x}}{2}-x +5 \,{\mathrm e}^{x}+\frac {25}{2}\right )\right ) {\operatorname {csgn}\left (\frac {i \left (\frac {{\mathrm e}^{2 x}}{2}-x +5 \,{\mathrm e}^{x}+\frac {25}{2}\right )}{x}\right )}^{2}-\pi \,\operatorname {csgn}\left (i \left (\frac {{\mathrm e}^{2 x}}{2}-x +5 \,{\mathrm e}^{x}+\frac {25}{2}\right )\right ) \operatorname {csgn}\left (\frac {i \left (\frac {{\mathrm e}^{2 x}}{2}-x +5 \,{\mathrm e}^{x}+\frac {25}{2}\right )}{x}\right ) \operatorname {csgn}\left (\frac {i}{x}\right )-\pi {\operatorname {csgn}\left (\frac {i \left (\frac {{\mathrm e}^{2 x}}{2}-x +5 \,{\mathrm e}^{x}+\frac {25}{2}\right )}{x}\right )}^{3}+\pi {\operatorname {csgn}\left (\frac {i \left (\frac {{\mathrm e}^{2 x}}{2}-x +5 \,{\mathrm e}^{x}+\frac {25}{2}\right )}{x}\right )}^{2} \operatorname {csgn}\left (\frac {i}{x}\right )+2 \pi -2 i \ln \left (2\right )+2 i \ln \left (x \right )-2 i \ln \left (-\frac {{\mathrm e}^{2 x}}{2}+x -5 \,{\mathrm e}^{x}-\frac {25}{2}\right )\right )}\) | \(281\) |
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Time = 0.25 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.09 \[ \int \frac {1875 x+e^x \left (750 x-750 x^2\right )+e^{2 x} \left (75 x-150 x^2\right )+\left (-375+e^{2 x} (-15+30 x)+e^x (-150+150 x)\right ) \log \left (x^2\right )+\log \left (\frac {25+10 e^x+e^{2 x}-2 x}{x}\right ) \left (750+300 e^x+30 e^{2 x}-60 x+\left (-375-150 e^x-15 e^{2 x}+30 x\right ) \log \left (x^2\right )\right )}{\log ^2\left (\frac {25+10 e^x+e^{2 x}-2 x}{x}\right ) \left (625 x^2+250 e^x x^2+25 e^{2 x} x^2-50 x^3+\left (-250 x-100 e^x x-10 e^{2 x} x+20 x^2\right ) \log \left (x^2\right )+\left (25+10 e^x+e^{2 x}-2 x\right ) \log ^2\left (x^2\right )\right )} \, dx=\frac {15 \, x}{{\left (5 \, x - \log \left (x^{2}\right )\right )} \log \left (-\frac {2 \, x - e^{\left (2 \, x\right )} - 10 \, e^{x} - 25}{x}\right )} \]
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Time = 0.39 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.83 \[ \int \frac {1875 x+e^x \left (750 x-750 x^2\right )+e^{2 x} \left (75 x-150 x^2\right )+\left (-375+e^{2 x} (-15+30 x)+e^x (-150+150 x)\right ) \log \left (x^2\right )+\log \left (\frac {25+10 e^x+e^{2 x}-2 x}{x}\right ) \left (750+300 e^x+30 e^{2 x}-60 x+\left (-375-150 e^x-15 e^{2 x}+30 x\right ) \log \left (x^2\right )\right )}{\log ^2\left (\frac {25+10 e^x+e^{2 x}-2 x}{x}\right ) \left (625 x^2+250 e^x x^2+25 e^{2 x} x^2-50 x^3+\left (-250 x-100 e^x x-10 e^{2 x} x+20 x^2\right ) \log \left (x^2\right )+\left (25+10 e^x+e^{2 x}-2 x\right ) \log ^2\left (x^2\right )\right )} \, dx=\frac {15 x}{\left (5 x - \log {\left (x^{2} \right )}\right ) \log {\left (\frac {- 2 x + e^{2 x} + 10 e^{x} + 25}{x} \right )}} \]
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Time = 0.56 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.17 \[ \int \frac {1875 x+e^x \left (750 x-750 x^2\right )+e^{2 x} \left (75 x-150 x^2\right )+\left (-375+e^{2 x} (-15+30 x)+e^x (-150+150 x)\right ) \log \left (x^2\right )+\log \left (\frac {25+10 e^x+e^{2 x}-2 x}{x}\right ) \left (750+300 e^x+30 e^{2 x}-60 x+\left (-375-150 e^x-15 e^{2 x}+30 x\right ) \log \left (x^2\right )\right )}{\log ^2\left (\frac {25+10 e^x+e^{2 x}-2 x}{x}\right ) \left (625 x^2+250 e^x x^2+25 e^{2 x} x^2-50 x^3+\left (-250 x-100 e^x x-10 e^{2 x} x+20 x^2\right ) \log \left (x^2\right )+\left (25+10 e^x+e^{2 x}-2 x\right ) \log ^2\left (x^2\right )\right )} \, dx=-\frac {15 \, x}{5 \, x \log \left (x\right ) - 2 \, \log \left (x\right )^{2} - {\left (5 \, x - 2 \, \log \left (x\right )\right )} \log \left (-2 \, x + e^{\left (2 \, x\right )} + 10 \, e^{x} + 25\right )} \]
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Time = 0.66 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.49 \[ \int \frac {1875 x+e^x \left (750 x-750 x^2\right )+e^{2 x} \left (75 x-150 x^2\right )+\left (-375+e^{2 x} (-15+30 x)+e^x (-150+150 x)\right ) \log \left (x^2\right )+\log \left (\frac {25+10 e^x+e^{2 x}-2 x}{x}\right ) \left (750+300 e^x+30 e^{2 x}-60 x+\left (-375-150 e^x-15 e^{2 x}+30 x\right ) \log \left (x^2\right )\right )}{\log ^2\left (\frac {25+10 e^x+e^{2 x}-2 x}{x}\right ) \left (625 x^2+250 e^x x^2+25 e^{2 x} x^2-50 x^3+\left (-250 x-100 e^x x-10 e^{2 x} x+20 x^2\right ) \log \left (x^2\right )+\left (25+10 e^x+e^{2 x}-2 x\right ) \log ^2\left (x^2\right )\right )} \, dx=-\frac {15 \, x}{5 \, x \log \left (x\right ) - 2 \, \log \left (x\right )^{2} - 5 \, x \log \left (-2 \, x + e^{\left (2 \, x\right )} + 10 \, e^{x} + 25\right ) + 2 \, \log \left (x\right ) \log \left (-2 \, x + e^{\left (2 \, x\right )} + 10 \, e^{x} + 25\right )} \]
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Timed out. \[ \int \frac {1875 x+e^x \left (750 x-750 x^2\right )+e^{2 x} \left (75 x-150 x^2\right )+\left (-375+e^{2 x} (-15+30 x)+e^x (-150+150 x)\right ) \log \left (x^2\right )+\log \left (\frac {25+10 e^x+e^{2 x}-2 x}{x}\right ) \left (750+300 e^x+30 e^{2 x}-60 x+\left (-375-150 e^x-15 e^{2 x}+30 x\right ) \log \left (x^2\right )\right )}{\log ^2\left (\frac {25+10 e^x+e^{2 x}-2 x}{x}\right ) \left (625 x^2+250 e^x x^2+25 e^{2 x} x^2-50 x^3+\left (-250 x-100 e^x x-10 e^{2 x} x+20 x^2\right ) \log \left (x^2\right )+\left (25+10 e^x+e^{2 x}-2 x\right ) \log ^2\left (x^2\right )\right )} \, dx=\int \frac {1875\,x+{\mathrm {e}}^{2\,x}\,\left (75\,x-150\,x^2\right )+\ln \left (x^2\right )\,\left ({\mathrm {e}}^x\,\left (150\,x-150\right )+{\mathrm {e}}^{2\,x}\,\left (30\,x-15\right )-375\right )+\ln \left (\frac {{\mathrm {e}}^{2\,x}-2\,x+10\,{\mathrm {e}}^x+25}{x}\right )\,\left (30\,{\mathrm {e}}^{2\,x}-60\,x+300\,{\mathrm {e}}^x-\ln \left (x^2\right )\,\left (15\,{\mathrm {e}}^{2\,x}-30\,x+150\,{\mathrm {e}}^x+375\right )+750\right )+{\mathrm {e}}^x\,\left (750\,x-750\,x^2\right )}{{\ln \left (\frac {{\mathrm {e}}^{2\,x}-2\,x+10\,{\mathrm {e}}^x+25}{x}\right )}^2\,\left (250\,x^2\,{\mathrm {e}}^x+25\,x^2\,{\mathrm {e}}^{2\,x}+{\ln \left (x^2\right )}^2\,\left ({\mathrm {e}}^{2\,x}-2\,x+10\,{\mathrm {e}}^x+25\right )+625\,x^2-50\,x^3-\ln \left (x^2\right )\,\left (250\,x+10\,x\,{\mathrm {e}}^{2\,x}+100\,x\,{\mathrm {e}}^x-20\,x^2\right )\right )} \,d x \]
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