Integrand size = 65, antiderivative size = 28 \[ \int \frac {e^{\frac {1}{5} \left (-12+e^{e^3} (-3-5 x)-5 x+25 x^2+(-3-5 x) \log (x)\right )} \left (-3-10 x-5 e^{e^3} x+50 x^2-5 x \log (x)\right )}{5 x} \, dx=e^{\left (\frac {3}{5}+x\right ) \left (-e^{e^3}-4 (1-x)+x-\log (x)\right )} \]
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\[ \int \frac {e^{\frac {1}{5} \left (-12+e^{e^3} (-3-5 x)-5 x+25 x^2+(-3-5 x) \log (x)\right )} \left (-3-10 x-5 e^{e^3} x+50 x^2-5 x \log (x)\right )}{5 x} \, dx=\int \frac {\exp \left (\frac {1}{5} \left (-12+e^{e^3} (-3-5 x)-5 x+25 x^2+(-3-5 x) \log (x)\right )\right ) \left (-3-10 x-5 e^{e^3} x+50 x^2-5 x \log (x)\right )}{5 x} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\exp \left (\frac {1}{5} \left (-12+e^{e^3} (-3-5 x)-5 x+25 x^2+(-3-5 x) \log (x)\right )\right ) \left (-3+\left (-10-5 e^{e^3}\right ) x+50 x^2-5 x \log (x)\right )}{5 x} \, dx \\ & = \frac {1}{5} \int \frac {\exp \left (\frac {1}{5} \left (-12+e^{e^3} (-3-5 x)-5 x+25 x^2+(-3-5 x) \log (x)\right )\right ) \left (-3+\left (-10-5 e^{e^3}\right ) x+50 x^2-5 x \log (x)\right )}{x} \, dx \\ & = \frac {1}{5} \int \frac {\exp \left (\frac {1}{5} (3+5 x) \left (-4 \left (1+\frac {e^{e^3}}{4}\right )+5 x-\log (x)\right )\right ) \left (-3+\left (-10-5 e^{e^3}\right ) x+50 x^2-5 x \log (x)\right )}{x} \, dx \\ & = \frac {1}{5} \int \left (\frac {\exp \left (\frac {1}{5} (3+5 x) \left (-4 \left (1+\frac {e^{e^3}}{4}\right )+5 x-\log (x)\right )\right ) \left (-3-5 \left (2+e^{e^3}\right ) x+50 x^2\right )}{x}-5 \exp \left (\frac {1}{5} (3+5 x) \left (-4 \left (1+\frac {e^{e^3}}{4}\right )+5 x-\log (x)\right )\right ) \log (x)\right ) \, dx \\ & = \frac {1}{5} \int \frac {\exp \left (\frac {1}{5} (3+5 x) \left (-4 \left (1+\frac {e^{e^3}}{4}\right )+5 x-\log (x)\right )\right ) \left (-3-5 \left (2+e^{e^3}\right ) x+50 x^2\right )}{x} \, dx-\int \exp \left (\frac {1}{5} (3+5 x) \left (-4 \left (1+\frac {e^{e^3}}{4}\right )+5 x-\log (x)\right )\right ) \log (x) \, dx \\ & = \frac {1}{5} \int \left (-5 \exp \left (\frac {1}{5} (3+5 x) \left (-4 \left (1+\frac {e^{e^3}}{4}\right )+5 x-\log (x)\right )\right ) \left (2+e^{e^3}\right )-\frac {3 \exp \left (\frac {1}{5} (3+5 x) \left (-4 \left (1+\frac {e^{e^3}}{4}\right )+5 x-\log (x)\right )\right )}{x}+50 \exp \left (\frac {1}{5} (3+5 x) \left (-4 \left (1+\frac {e^{e^3}}{4}\right )+5 x-\log (x)\right )\right ) x\right ) \, dx-\int \exp \left (\frac {1}{5} (3+5 x) \left (-4 \left (1+\frac {e^{e^3}}{4}\right )+5 x-\log (x)\right )\right ) \log (x) \, dx \\ & = -\left (\frac {3}{5} \int \frac {\exp \left (\frac {1}{5} (3+5 x) \left (-4 \left (1+\frac {e^{e^3}}{4}\right )+5 x-\log (x)\right )\right )}{x} \, dx\right )+10 \int \exp \left (\frac {1}{5} (3+5 x) \left (-4 \left (1+\frac {e^{e^3}}{4}\right )+5 x-\log (x)\right )\right ) x \, dx+\left (-2-e^{e^3}\right ) \int \exp \left (\frac {1}{5} (3+5 x) \left (-4 \left (1+\frac {e^{e^3}}{4}\right )+5 x-\log (x)\right )\right ) \, dx-\int \exp \left (\frac {1}{5} (3+5 x) \left (-4 \left (1+\frac {e^{e^3}}{4}\right )+5 x-\log (x)\right )\right ) \log (x) \, dx \\ \end{align*}
Time = 1.33 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.11 \[ \int \frac {e^{\frac {1}{5} \left (-12+e^{e^3} (-3-5 x)-5 x+25 x^2+(-3-5 x) \log (x)\right )} \left (-3-10 x-5 e^{e^3} x+50 x^2-5 x \log (x)\right )}{5 x} \, dx=e^{-\frac {1}{5} \left (4+e^{e^3}-5 x\right ) (3+5 x)} x^{-\frac {3}{5}-x} \]
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Time = 0.24 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.96
method | result | size |
risch | \(x^{-\frac {3}{5}-x} {\mathrm e}^{\frac {\left (5 x +3\right ) \left (5 x -{\mathrm e}^{{\mathrm e}^{3}}-4\right )}{5}}\) | \(27\) |
norman | \({\mathrm e}^{\frac {\left (-5 x -3\right ) \ln \left (x \right )}{5}+\frac {\left (-5 x -3\right ) {\mathrm e}^{{\mathrm e}^{3}}}{5}+5 x^{2}-x -\frac {12}{5}}\) | \(31\) |
parallelrisch | \({\mathrm e}^{\frac {\left (-5 x -3\right ) \ln \left (x \right )}{5}+\frac {\left (-5 x -3\right ) {\mathrm e}^{{\mathrm e}^{3}}}{5}+5 x^{2}-x -\frac {12}{5}}\) | \(31\) |
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Time = 0.44 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.07 \[ \int \frac {e^{\frac {1}{5} \left (-12+e^{e^3} (-3-5 x)-5 x+25 x^2+(-3-5 x) \log (x)\right )} \left (-3-10 x-5 e^{e^3} x+50 x^2-5 x \log (x)\right )}{5 x} \, dx=e^{\left (5 \, x^{2} - \frac {1}{5} \, {\left (5 \, x + 3\right )} e^{\left (e^{3}\right )} - \frac {1}{5} \, {\left (5 \, x + 3\right )} \log \left (x\right ) - x - \frac {12}{5}\right )} \]
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Time = 0.15 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.14 \[ \int \frac {e^{\frac {1}{5} \left (-12+e^{e^3} (-3-5 x)-5 x+25 x^2+(-3-5 x) \log (x)\right )} \left (-3-10 x-5 e^{e^3} x+50 x^2-5 x \log (x)\right )}{5 x} \, dx=e^{5 x^{2} - x + \left (- x - \frac {3}{5}\right ) \log {\left (x \right )} + \left (- x - \frac {3}{5}\right ) e^{e^{3}} - \frac {12}{5}} \]
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\[ \int \frac {e^{\frac {1}{5} \left (-12+e^{e^3} (-3-5 x)-5 x+25 x^2+(-3-5 x) \log (x)\right )} \left (-3-10 x-5 e^{e^3} x+50 x^2-5 x \log (x)\right )}{5 x} \, dx=\int { \frac {{\left (50 \, x^{2} - 5 \, x e^{\left (e^{3}\right )} - 5 \, x \log \left (x\right ) - 10 \, x - 3\right )} e^{\left (5 \, x^{2} - \frac {1}{5} \, {\left (5 \, x + 3\right )} e^{\left (e^{3}\right )} - \frac {1}{5} \, {\left (5 \, x + 3\right )} \log \left (x\right ) - x - \frac {12}{5}\right )}}{5 \, x} \,d x } \]
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Time = 0.28 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.11 \[ \int \frac {e^{\frac {1}{5} \left (-12+e^{e^3} (-3-5 x)-5 x+25 x^2+(-3-5 x) \log (x)\right )} \left (-3-10 x-5 e^{e^3} x+50 x^2-5 x \log (x)\right )}{5 x} \, dx=e^{\left (5 \, x^{2} - x e^{\left (e^{3}\right )} - x \log \left (x\right ) - x - \frac {3}{5} \, e^{\left (e^{3}\right )} - \frac {3}{5} \, \log \left (x\right ) - \frac {12}{5}\right )} \]
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Time = 12.73 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.18 \[ \int \frac {e^{\frac {1}{5} \left (-12+e^{e^3} (-3-5 x)-5 x+25 x^2+(-3-5 x) \log (x)\right )} \left (-3-10 x-5 e^{e^3} x+50 x^2-5 x \log (x)\right )}{5 x} \, dx=\frac {{\mathrm {e}}^{-x\,{\mathrm {e}}^{{\mathrm {e}}^3}}\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{-\frac {12}{5}}\,{\mathrm {e}}^{-\frac {3\,{\mathrm {e}}^{{\mathrm {e}}^3}}{5}}\,{\mathrm {e}}^{5\,x^2}}{x^{x+\frac {3}{5}}} \]
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