Integrand size = 206, antiderivative size = 29 \[ \int \frac {e^{\frac {-1+\log (5)}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \left (-9 x+9 x \log (5)+(-6 x+6 x \log (5)) \log (x)+(-x+x \log (5)) \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (-75+59 x+(75-59 x) \log (5)+(31 x-31 x \log (5)) \log (x)+(x-x \log (5)) \log ^2(x)\right )\right )}{\left (-9 x^2-6 x^2 \log (x)-x^2 \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (9 x+6 x \log (x)+x \log ^2(x)\right )\right ) \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx=e^{\frac {-1+\log (5)}{\log \left (-e^{x+\frac {25 (3+x)}{3+\log (x)}}+x\right )}} \]
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\[ \int \frac {e^{\frac {-1+\log (5)}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \left (-9 x+9 x \log (5)+(-6 x+6 x \log (5)) \log (x)+(-x+x \log (5)) \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (-75+59 x+(75-59 x) \log (5)+(31 x-31 x \log (5)) \log (x)+(x-x \log (5)) \log ^2(x)\right )\right )}{\left (-9 x^2-6 x^2 \log (x)-x^2 \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (9 x+6 x \log (x)+x \log ^2(x)\right )\right ) \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx=\int \frac {\exp \left (\frac {-1+\log (5)}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}\right ) \left (-9 x+9 x \log (5)+(-6 x+6 x \log (5)) \log (x)+(-x+x \log (5)) \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (-75+59 x+(75-59 x) \log (5)+(31 x-31 x \log (5)) \log (x)+(x-x \log (5)) \log ^2(x)\right )\right )}{\left (-9 x^2-6 x^2 \log (x)-x^2 \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (9 x+6 x \log (x)+x \log ^2(x)\right )\right ) \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\exp \left (\frac {-1+\log (5)}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}\right ) \left (x (-9+9 \log (5))+(-6 x+6 x \log (5)) \log (x)+(-x+x \log (5)) \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (-75+59 x+(75-59 x) \log (5)+(31 x-31 x \log (5)) \log (x)+(x-x \log (5)) \log ^2(x)\right )\right )}{\left (-9 x^2-6 x^2 \log (x)-x^2 \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (9 x+6 x \log (x)+x \log ^2(x)\right )\right ) \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx \\ & = \int \frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} (1-\log (5)) \left (9 x+6 x \log (x)+x \log ^2(x)-e^{\frac {75+28 x}{3+\log (x)}} x^{\frac {x}{3+\log (x)}} \left (-75+59 x+31 x \log (x)+x \log ^2(x)\right )\right )}{x \left (x-e^{\frac {75+28 x}{3+\log (x)}} x^{\frac {x}{3+\log (x)}}\right ) (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx \\ & = (1-\log (5)) \int \frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \left (9 x+6 x \log (x)+x \log ^2(x)-e^{\frac {75+28 x}{3+\log (x)}} x^{\frac {x}{3+\log (x)}} \left (-75+59 x+31 x \log (x)+x \log ^2(x)\right )\right )}{x \left (x-e^{\frac {75+28 x}{3+\log (x)}} x^{\frac {x}{3+\log (x)}}\right ) (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx \\ & = (1-\log (5)) \int \left (\frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \left (-75+59 x+31 x \log (x)+x \log ^2(x)\right )}{x (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}+\frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \left (-84+59 x-6 \log (x)+31 x \log (x)-\log ^2(x)+x \log ^2(x)\right )}{\left (-x+e^{\frac {75}{3+\log (x)}+\frac {28 x}{3+\log (x)}} x^{\frac {x}{3+\log (x)}}\right ) (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}\right ) \, dx \\ & = (1-\log (5)) \int \frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \left (-75+59 x+31 x \log (x)+x \log ^2(x)\right )}{x (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx+(1-\log (5)) \int \frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \left (-84+59 x-6 \log (x)+31 x \log (x)-\log ^2(x)+x \log ^2(x)\right )}{\left (-x+e^{\frac {75}{3+\log (x)}+\frac {28 x}{3+\log (x)}} x^{\frac {x}{3+\log (x)}}\right ) (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx \\ & = (1-\log (5)) \int \left (\frac {59 \left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}}}{(3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}-\frac {3\ 5^{2+\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} e^{-\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}}}{x (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}+\frac {31 \left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \log (x)}{(3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}+\frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \log ^2(x)}{(3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}\right ) \, dx+(1-\log (5)) \int \left (-\frac {84 \left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}}}{\left (-x+e^{\frac {75}{3+\log (x)}+\frac {28 x}{3+\log (x)}} x^{\frac {x}{3+\log (x)}}\right ) (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}+\frac {59 \left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} x}{\left (-x+e^{\frac {75}{3+\log (x)}+\frac {28 x}{3+\log (x)}} x^{\frac {x}{3+\log (x)}}\right ) (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}-\frac {6 \left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \log (x)}{\left (-x+e^{\frac {75}{3+\log (x)}+\frac {28 x}{3+\log (x)}} x^{\frac {x}{3+\log (x)}}\right ) (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}+\frac {31 \left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} x \log (x)}{\left (-x+e^{\frac {75}{3+\log (x)}+\frac {28 x}{3+\log (x)}} x^{\frac {x}{3+\log (x)}}\right ) (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}-\frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \log ^2(x)}{\left (-x+e^{\frac {75}{3+\log (x)}+\frac {28 x}{3+\log (x)}} x^{\frac {x}{3+\log (x)}}\right ) (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}+\frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} x \log ^2(x)}{\left (-x+e^{\frac {75}{3+\log (x)}+\frac {28 x}{3+\log (x)}} x^{\frac {x}{3+\log (x)}}\right ) (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}\right ) \, dx \\ & = (1-\log (5)) \int \frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \log ^2(x)}{(3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx+(1-\log (5)) \int \frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} x \log ^2(x)}{\left (-x+e^{\frac {75}{3+\log (x)}+\frac {28 x}{3+\log (x)}} x^{\frac {x}{3+\log (x)}}\right ) (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx-(6 (1-\log (5))) \int \frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \log (x)}{\left (-x+e^{\frac {75}{3+\log (x)}+\frac {28 x}{3+\log (x)}} x^{\frac {x}{3+\log (x)}}\right ) (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx+(31 (1-\log (5))) \int \frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \log (x)}{(3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx+(31 (1-\log (5))) \int \frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} x \log (x)}{\left (-x+e^{\frac {75}{3+\log (x)}+\frac {28 x}{3+\log (x)}} x^{\frac {x}{3+\log (x)}}\right ) (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx+(59 (1-\log (5))) \int \frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}}}{(3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx+(59 (1-\log (5))) \int \frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} x}{\left (-x+e^{\frac {75}{3+\log (x)}+\frac {28 x}{3+\log (x)}} x^{\frac {x}{3+\log (x)}}\right ) (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx-(84 (1-\log (5))) \int \frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}}}{\left (-x+e^{\frac {75}{3+\log (x)}+\frac {28 x}{3+\log (x)}} x^{\frac {x}{3+\log (x)}}\right ) (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx+(-1+\log (5)) \int \frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \log ^2(x)}{\left (-x+e^{\frac {75}{3+\log (x)}+\frac {28 x}{3+\log (x)}} x^{\frac {x}{3+\log (x)}}\right ) (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx+(3 (-1+\log (5))) \int \frac {5^{2+\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} e^{-\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}}}{x (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx \\ \end{align*}
Time = 0.40 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.07 \[ \int \frac {e^{\frac {-1+\log (5)}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \left (-9 x+9 x \log (5)+(-6 x+6 x \log (5)) \log (x)+(-x+x \log (5)) \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (-75+59 x+(75-59 x) \log (5)+(31 x-31 x \log (5)) \log (x)+(x-x \log (5)) \log ^2(x)\right )\right )}{\left (-9 x^2-6 x^2 \log (x)-x^2 \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (9 x+6 x \log (x)+x \log ^2(x)\right )\right ) \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx=\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \]
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Time = 0.04 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.07
\[{\mathrm e}^{\frac {\ln \left (5\right )-1}{\ln \left (-{\mathrm e}^{\frac {x \ln \left (x \right )+28 x +75}{3+\ln \left (x \right )}}+x \right )}}\]
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Time = 0.24 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.03 \[ \int \frac {e^{\frac {-1+\log (5)}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \left (-9 x+9 x \log (5)+(-6 x+6 x \log (5)) \log (x)+(-x+x \log (5)) \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (-75+59 x+(75-59 x) \log (5)+(31 x-31 x \log (5)) \log (x)+(x-x \log (5)) \log ^2(x)\right )\right )}{\left (-9 x^2-6 x^2 \log (x)-x^2 \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (9 x+6 x \log (x)+x \log ^2(x)\right )\right ) \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx=e^{\left (\frac {\log \left (5\right ) - 1}{\log \left (x - e^{\left (\frac {x \log \left (x\right ) + 28 \, x + 75}{\log \left (x\right ) + 3}\right )}\right )}\right )} \]
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Timed out. \[ \int \frac {e^{\frac {-1+\log (5)}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \left (-9 x+9 x \log (5)+(-6 x+6 x \log (5)) \log (x)+(-x+x \log (5)) \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (-75+59 x+(75-59 x) \log (5)+(31 x-31 x \log (5)) \log (x)+(x-x \log (5)) \log ^2(x)\right )\right )}{\left (-9 x^2-6 x^2 \log (x)-x^2 \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (9 x+6 x \log (x)+x \log ^2(x)\right )\right ) \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx=\text {Timed out} \]
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Leaf count of result is larger than twice the leaf count of optimal. 79 vs. \(2 (27) = 54\).
Time = 0.66 (sec) , antiderivative size = 79, normalized size of antiderivative = 2.72 \[ \int \frac {e^{\frac {-1+\log (5)}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \left (-9 x+9 x \log (5)+(-6 x+6 x \log (5)) \log (x)+(-x+x \log (5)) \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (-75+59 x+(75-59 x) \log (5)+(31 x-31 x \log (5)) \log (x)+(x-x \log (5)) \log ^2(x)\right )\right )}{\left (-9 x^2-6 x^2 \log (x)-x^2 \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (9 x+6 x \log (x)+x \log ^2(x)\right )\right ) \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx=e^{\left (\frac {\log \left (5\right )}{\log \left (x - e^{\left (\frac {x \log \left (x\right )}{\log \left (x\right ) + 3} + \frac {28 \, x}{\log \left (x\right ) + 3} + \frac {75}{\log \left (x\right ) + 3}\right )}\right )} - \frac {1}{\log \left (x - e^{\left (\frac {x \log \left (x\right )}{\log \left (x\right ) + 3} + \frac {28 \, x}{\log \left (x\right ) + 3} + \frac {75}{\log \left (x\right ) + 3}\right )}\right )}\right )} \]
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Timed out. \[ \int \frac {e^{\frac {-1+\log (5)}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \left (-9 x+9 x \log (5)+(-6 x+6 x \log (5)) \log (x)+(-x+x \log (5)) \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (-75+59 x+(75-59 x) \log (5)+(31 x-31 x \log (5)) \log (x)+(x-x \log (5)) \log ^2(x)\right )\right )}{\left (-9 x^2-6 x^2 \log (x)-x^2 \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (9 x+6 x \log (x)+x \log ^2(x)\right )\right ) \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx=\text {Timed out} \]
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Time = 8.68 (sec) , antiderivative size = 78, normalized size of antiderivative = 2.69 \[ \int \frac {e^{\frac {-1+\log (5)}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \left (-9 x+9 x \log (5)+(-6 x+6 x \log (5)) \log (x)+(-x+x \log (5)) \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (-75+59 x+(75-59 x) \log (5)+(31 x-31 x \log (5)) \log (x)+(x-x \log (5)) \log ^2(x)\right )\right )}{\left (-9 x^2-6 x^2 \log (x)-x^2 \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (9 x+6 x \log (x)+x \log ^2(x)\right )\right ) \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx=5^{\frac {1}{\ln \left (x-x^{\frac {x}{\ln \left (x\right )+3}}\,{\mathrm {e}}^{\frac {75}{\ln \left (x\right )+3}}\,{\mathrm {e}}^{\frac {28\,x}{\ln \left (x\right )+3}}\right )}}\,{\mathrm {e}}^{-\frac {1}{\ln \left (x-x^{\frac {x}{\ln \left (x\right )+3}}\,{\mathrm {e}}^{\frac {75}{\ln \left (x\right )+3}}\,{\mathrm {e}}^{\frac {28\,x}{\ln \left (x\right )+3}}\right )}} \]
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