Integrand size = 326, antiderivative size = 29 \[ \int \frac {e^x \left (-4050 x-2025 x^2+81 x^3+\left (-2025-2106 x+81 x^2\right ) \log (5)\right )+e^{2+e^x} \left (e^{2 x} \left (2700 x^2-108 x^3+\left (2700 x-108 x^2\right ) \log (5)\right )+e^x \left (5400 x+2700 x^2-108 x^3+\left (2700+2808 x-108 x^2\right ) \log (5)\right )\right )+e^{6+3 e^x} \left (e^{2 x} \left (900 x^2-36 x^3+\left (900 x-36 x^2\right ) \log (5)\right )+e^x \left (600 x+300 x^2-12 x^3+\left (300+312 x-12 x^2\right ) \log (5)\right )\right )+e^{8+4 e^x} \left (e^x \left (-50 x-25 x^2+x^3+\left (-25-26 x+x^2\right ) \log (5)\right )+e^{2 x} \left (-100 x^2+4 x^3+\left (-100 x+4 x^2\right ) \log (5)\right )\right )+e^{4+2 e^x} \left (e^x \left (-2700 x-1350 x^2+54 x^3+\left (-1350-1404 x+54 x^2\right ) \log (5)\right )+e^{2 x} \left (-2700 x^2+108 x^3+\left (-2700 x+108 x^2\right ) \log (5)\right )\right )}{-15625+1875 x-75 x^2+x^3} \, dx=\frac {e^x \left (3-e^{2+e^x}\right )^4 x (x+\log (5))}{(25-x)^2} \]
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\[ \int \frac {e^x \left (-4050 x-2025 x^2+81 x^3+\left (-2025-2106 x+81 x^2\right ) \log (5)\right )+e^{2+e^x} \left (e^{2 x} \left (2700 x^2-108 x^3+\left (2700 x-108 x^2\right ) \log (5)\right )+e^x \left (5400 x+2700 x^2-108 x^3+\left (2700+2808 x-108 x^2\right ) \log (5)\right )\right )+e^{6+3 e^x} \left (e^{2 x} \left (900 x^2-36 x^3+\left (900 x-36 x^2\right ) \log (5)\right )+e^x \left (600 x+300 x^2-12 x^3+\left (300+312 x-12 x^2\right ) \log (5)\right )\right )+e^{8+4 e^x} \left (e^x \left (-50 x-25 x^2+x^3+\left (-25-26 x+x^2\right ) \log (5)\right )+e^{2 x} \left (-100 x^2+4 x^3+\left (-100 x+4 x^2\right ) \log (5)\right )\right )+e^{4+2 e^x} \left (e^x \left (-2700 x-1350 x^2+54 x^3+\left (-1350-1404 x+54 x^2\right ) \log (5)\right )+e^{2 x} \left (-2700 x^2+108 x^3+\left (-2700 x+108 x^2\right ) \log (5)\right )\right )}{-15625+1875 x-75 x^2+x^3} \, dx=\int \frac {e^x \left (-4050 x-2025 x^2+81 x^3+\left (-2025-2106 x+81 x^2\right ) \log (5)\right )+e^{2+e^x} \left (e^{2 x} \left (2700 x^2-108 x^3+\left (2700 x-108 x^2\right ) \log (5)\right )+e^x \left (5400 x+2700 x^2-108 x^3+\left (2700+2808 x-108 x^2\right ) \log (5)\right )\right )+e^{6+3 e^x} \left (e^{2 x} \left (900 x^2-36 x^3+\left (900 x-36 x^2\right ) \log (5)\right )+e^x \left (600 x+300 x^2-12 x^3+\left (300+312 x-12 x^2\right ) \log (5)\right )\right )+e^{8+4 e^x} \left (e^x \left (-50 x-25 x^2+x^3+\left (-25-26 x+x^2\right ) \log (5)\right )+e^{2 x} \left (-100 x^2+4 x^3+\left (-100 x+4 x^2\right ) \log (5)\right )\right )+e^{4+2 e^x} \left (e^x \left (-2700 x-1350 x^2+54 x^3+\left (-1350-1404 x+54 x^2\right ) \log (5)\right )+e^{2 x} \left (-2700 x^2+108 x^3+\left (-2700 x+108 x^2\right ) \log (5)\right )\right )}{-15625+1875 x-75 x^2+x^3} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {e^x \left (3-e^{2+e^x}\right )^3 \left (\left (-3+e^{2+e^x}+4 e^{2+e^x+x}\right ) x^3+\left (-3+e^{2+e^x}+4 e^{2+e^x+x}\right ) x^2 (-25+\log (5))-25 \left (-3+e^{2+e^x}\right ) \log (5)-2 x \left (-75-39 \log (5)+50 e^{2+e^x+x} \log (5)+e^{2+e^x} (25+13 \log (5))\right )\right )}{(25-x)^3} \, dx \\ & = \int \left (-\frac {3 e^x \left (-3+e^{2+e^x}\right )^3 x^3}{(-25+x)^3}+\frac {e^{2+e^x+x} \left (-3+e^{2+e^x}\right )^3 x^3}{(-25+x)^3}+\frac {150 e^x \left (-3+e^{2+e^x}\right )^3 x \left (1+\frac {13 \log (5)}{25}\right )}{(-25+x)^3}-\frac {3 e^x \left (-3+e^{2+e^x}\right )^3 x^2 (-25+\log (5))}{(-25+x)^3}+\frac {e^{2+e^x+x} \left (-3+e^{2+e^x}\right )^3 x^2 (-25+\log (5))}{(-25+x)^3}-\frac {25 e^x \left (-3+e^{2+e^x}\right )^4 \log (5)}{(-25+x)^3}+\frac {4 e^{2+e^x+2 x} \left (-3+e^{2+e^x}\right )^3 x (x+\log (5))}{(-25+x)^2}-\frac {2 e^{2+e^x+x} \left (-3+e^{2+e^x}\right )^3 x (25+13 \log (5))}{(-25+x)^3}\right ) \, dx \\ & = -\left (3 \int \frac {e^x \left (-3+e^{2+e^x}\right )^3 x^3}{(-25+x)^3} \, dx\right )+4 \int \frac {e^{2+e^x+2 x} \left (-3+e^{2+e^x}\right )^3 x (x+\log (5))}{(-25+x)^2} \, dx+(-25+\log (5)) \int \frac {e^{2+e^x+x} \left (-3+e^{2+e^x}\right )^3 x^2}{(-25+x)^3} \, dx-(3 (-25+\log (5))) \int \frac {e^x \left (-3+e^{2+e^x}\right )^3 x^2}{(-25+x)^3} \, dx-(25 \log (5)) \int \frac {e^x \left (-3+e^{2+e^x}\right )^4}{(-25+x)^3} \, dx-(2 (25+13 \log (5))) \int \frac {e^{2+e^x+x} \left (-3+e^{2+e^x}\right )^3 x}{(-25+x)^3} \, dx+(6 (25+13 \log (5))) \int \frac {e^x \left (-3+e^{2+e^x}\right )^3 x}{(-25+x)^3} \, dx+\int \frac {e^{2+e^x+x} \left (-3+e^{2+e^x}\right )^3 x^3}{(-25+x)^3} \, dx \\ & = -\left (3 \int \left (\frac {9 e^{2 \left (2+e^x\right )+x} x^3}{(25-x)^3}-\frac {27 e^x x^3}{(-25+x)^3}+\frac {27 e^{2+e^x+x} x^3}{(-25+x)^3}+\frac {e^{3 \left (2+e^x\right )+x} x^3}{(-25+x)^3}\right ) \, dx\right )+4 \int \left (\frac {9 e^{2+e^x+2 \left (2+e^x\right )+2 x} x (-x-\log (5))}{(25-x)^2}+\frac {e^{2+e^x+3 \left (2+e^x\right )+2 x} x (x+\log (5))}{(25-x)^2}-\frac {27 e^{2+e^x+2 x} x (x+\log (5))}{(-25+x)^2}+\frac {27 e^{4+2 e^x+2 x} x (x+\log (5))}{(-25+x)^2}\right ) \, dx+(-25+\log (5)) \int \left (\frac {9 e^{2+e^x+2 \left (2+e^x\right )+x} x^2}{(25-x)^3}-\frac {27 e^{2+e^x+x} x^2}{(-25+x)^3}+\frac {27 e^{4+2 e^x+x} x^2}{(-25+x)^3}+\frac {e^{2+e^x+3 \left (2+e^x\right )+x} x^2}{(-25+x)^3}\right ) \, dx-(3 (-25+\log (5))) \int \left (\frac {9 e^{2 \left (2+e^x\right )+x} x^2}{(25-x)^3}-\frac {27 e^x x^2}{(-25+x)^3}+\frac {27 e^{2+e^x+x} x^2}{(-25+x)^3}+\frac {e^{3 \left (2+e^x\right )+x} x^2}{(-25+x)^3}\right ) \, dx-(25 \log (5)) \int \left (\frac {12 e^{3 \left (2+e^x\right )+x}}{(25-x)^3}+\frac {81 e^x}{(-25+x)^3}-\frac {108 e^{2+e^x+x}}{(-25+x)^3}+\frac {54 e^{2 \left (2+e^x\right )+x}}{(-25+x)^3}+\frac {e^{4 \left (2+e^x\right )+x}}{(-25+x)^3}\right ) \, dx-(2 (25+13 \log (5))) \int \left (\frac {9 e^{2+e^x+2 \left (2+e^x\right )+x} x}{(25-x)^3}-\frac {27 e^{2+e^x+x} x}{(-25+x)^3}+\frac {27 e^{4+2 e^x+x} x}{(-25+x)^3}+\frac {e^{2+e^x+3 \left (2+e^x\right )+x} x}{(-25+x)^3}\right ) \, dx+(6 (25+13 \log (5))) \int \left (\frac {9 e^{2 \left (2+e^x\right )+x} x}{(25-x)^3}-\frac {27 e^x x}{(-25+x)^3}+\frac {27 e^{2+e^x+x} x}{(-25+x)^3}+\frac {e^{3 \left (2+e^x\right )+x} x}{(-25+x)^3}\right ) \, dx+\int \left (\frac {9 e^{2+e^x+2 \left (2+e^x\right )+x} x^3}{(25-x)^3}-\frac {27 e^{2+e^x+x} x^3}{(-25+x)^3}+\frac {27 e^{4+2 e^x+x} x^3}{(-25+x)^3}+\frac {e^{2+e^x+3 \left (2+e^x\right )+x} x^3}{(-25+x)^3}\right ) \, dx \\ & = -\left (3 \int \frac {e^{3 \left (2+e^x\right )+x} x^3}{(-25+x)^3} \, dx\right )+4 \int \frac {e^{2+e^x+3 \left (2+e^x\right )+2 x} x (x+\log (5))}{(25-x)^2} \, dx+9 \int \frac {e^{2+e^x+2 \left (2+e^x\right )+x} x^3}{(25-x)^3} \, dx-27 \int \frac {e^{2 \left (2+e^x\right )+x} x^3}{(25-x)^3} \, dx-27 \int \frac {e^{2+e^x+x} x^3}{(-25+x)^3} \, dx+27 \int \frac {e^{4+2 e^x+x} x^3}{(-25+x)^3} \, dx+36 \int \frac {e^{2+e^x+2 \left (2+e^x\right )+2 x} x (-x-\log (5))}{(25-x)^2} \, dx+81 \int \frac {e^x x^3}{(-25+x)^3} \, dx-81 \int \frac {e^{2+e^x+x} x^3}{(-25+x)^3} \, dx-108 \int \frac {e^{2+e^x+2 x} x (x+\log (5))}{(-25+x)^2} \, dx+108 \int \frac {e^{4+2 e^x+2 x} x (x+\log (5))}{(-25+x)^2} \, dx-(9 (25-\log (5))) \int \frac {e^{2+e^x+2 \left (2+e^x\right )+x} x^2}{(25-x)^3} \, dx+(27 (25-\log (5))) \int \frac {e^{2 \left (2+e^x\right )+x} x^2}{(25-x)^3} \, dx+(27 (25-\log (5))) \int \frac {e^{2+e^x+x} x^2}{(-25+x)^3} \, dx-(27 (25-\log (5))) \int \frac {e^{4+2 e^x+x} x^2}{(-25+x)^3} \, dx-(81 (25-\log (5))) \int \frac {e^x x^2}{(-25+x)^3} \, dx+(81 (25-\log (5))) \int \frac {e^{2+e^x+x} x^2}{(-25+x)^3} \, dx+(-25+\log (5)) \int \frac {e^{2+e^x+3 \left (2+e^x\right )+x} x^2}{(-25+x)^3} \, dx-(3 (-25+\log (5))) \int \frac {e^{3 \left (2+e^x\right )+x} x^2}{(-25+x)^3} \, dx-(25 \log (5)) \int \frac {e^{4 \left (2+e^x\right )+x}}{(-25+x)^3} \, dx-(300 \log (5)) \int \frac {e^{3 \left (2+e^x\right )+x}}{(25-x)^3} \, dx-(1350 \log (5)) \int \frac {e^{2 \left (2+e^x\right )+x}}{(-25+x)^3} \, dx-(2025 \log (5)) \int \frac {e^x}{(-25+x)^3} \, dx+(2700 \log (5)) \int \frac {e^{2+e^x+x}}{(-25+x)^3} \, dx-(2 (25+13 \log (5))) \int \frac {e^{2+e^x+3 \left (2+e^x\right )+x} x}{(-25+x)^3} \, dx+(6 (25+13 \log (5))) \int \frac {e^{3 \left (2+e^x\right )+x} x}{(-25+x)^3} \, dx-(18 (25+13 \log (5))) \int \frac {e^{2+e^x+2 \left (2+e^x\right )+x} x}{(25-x)^3} \, dx+(54 (25+13 \log (5))) \int \frac {e^{2 \left (2+e^x\right )+x} x}{(25-x)^3} \, dx+(54 (25+13 \log (5))) \int \frac {e^{2+e^x+x} x}{(-25+x)^3} \, dx-(54 (25+13 \log (5))) \int \frac {e^{4+2 e^x+x} x}{(-25+x)^3} \, dx-(162 (25+13 \log (5))) \int \frac {e^x x}{(-25+x)^3} \, dx+(162 (25+13 \log (5))) \int \frac {e^{2+e^x+x} x}{(-25+x)^3} \, dx+\int \frac {e^{2+e^x+3 \left (2+e^x\right )+x} x^3}{(-25+x)^3} \, dx \\ & = \text {Too large to display} \\ \end{align*}
Time = 0.31 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.86 \[ \int \frac {e^x \left (-4050 x-2025 x^2+81 x^3+\left (-2025-2106 x+81 x^2\right ) \log (5)\right )+e^{2+e^x} \left (e^{2 x} \left (2700 x^2-108 x^3+\left (2700 x-108 x^2\right ) \log (5)\right )+e^x \left (5400 x+2700 x^2-108 x^3+\left (2700+2808 x-108 x^2\right ) \log (5)\right )\right )+e^{6+3 e^x} \left (e^{2 x} \left (900 x^2-36 x^3+\left (900 x-36 x^2\right ) \log (5)\right )+e^x \left (600 x+300 x^2-12 x^3+\left (300+312 x-12 x^2\right ) \log (5)\right )\right )+e^{8+4 e^x} \left (e^x \left (-50 x-25 x^2+x^3+\left (-25-26 x+x^2\right ) \log (5)\right )+e^{2 x} \left (-100 x^2+4 x^3+\left (-100 x+4 x^2\right ) \log (5)\right )\right )+e^{4+2 e^x} \left (e^x \left (-2700 x-1350 x^2+54 x^3+\left (-1350-1404 x+54 x^2\right ) \log (5)\right )+e^{2 x} \left (-2700 x^2+108 x^3+\left (-2700 x+108 x^2\right ) \log (5)\right )\right )}{-15625+1875 x-75 x^2+x^3} \, dx=\frac {e^x \left (-3+e^{2+e^x}\right )^4 x (x+\log (5))}{(-25+x)^2} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(112\) vs. \(2(26)=52\).
Time = 2.49 (sec) , antiderivative size = 113, normalized size of antiderivative = 3.90
method | result | size |
risch | \(\frac {81 x \left (\ln \left (5\right )+x \right ) {\mathrm e}^{x}}{\left (x -25\right )^{2}}+\frac {x \left (\ln \left (5\right )+x \right ) {\mathrm e}^{x +4 \,{\mathrm e}^{x}+8}}{x^{2}-50 x +625}-\frac {12 x \left (\ln \left (5\right )+x \right ) {\mathrm e}^{x +3 \,{\mathrm e}^{x}+6}}{x^{2}-50 x +625}+\frac {54 x \left (\ln \left (5\right )+x \right ) {\mathrm e}^{x +2 \,{\mathrm e}^{x}+4}}{x^{2}-50 x +625}-\frac {108 x \left (\ln \left (5\right )+x \right ) {\mathrm e}^{{\mathrm e}^{x}+2+x}}{x^{2}-50 x +625}\) | \(113\) |
parallelrisch | \(\frac {\ln \left (5\right ) {\mathrm e}^{x} {\mathrm e}^{4 \,{\mathrm e}^{x}+8} x +{\mathrm e}^{x} {\mathrm e}^{4 \,{\mathrm e}^{x}+8} x^{2}-12 \ln \left (5\right ) {\mathrm e}^{x} {\mathrm e}^{3 \,{\mathrm e}^{x}+6} x -12 \,{\mathrm e}^{x} {\mathrm e}^{3 \,{\mathrm e}^{x}+6} x^{2}+54 \ln \left (5\right ) {\mathrm e}^{x} {\mathrm e}^{2 \,{\mathrm e}^{x}+4} x +54 \,{\mathrm e}^{x} {\mathrm e}^{2 \,{\mathrm e}^{x}+4} x^{2}-108 \ln \left (5\right ) {\mathrm e}^{x} {\mathrm e}^{{\mathrm e}^{x}+2} x -108 \,{\mathrm e}^{x} {\mathrm e}^{{\mathrm e}^{x}+2} x^{2}+81 x \,{\mathrm e}^{x} \ln \left (5\right )+81 \,{\mathrm e}^{x} x^{2}}{x^{2}-50 x +625}\) | \(133\) |
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Leaf count of result is larger than twice the leaf count of optimal. 93 vs. \(2 (22) = 44\).
Time = 0.27 (sec) , antiderivative size = 93, normalized size of antiderivative = 3.21 \[ \int \frac {e^x \left (-4050 x-2025 x^2+81 x^3+\left (-2025-2106 x+81 x^2\right ) \log (5)\right )+e^{2+e^x} \left (e^{2 x} \left (2700 x^2-108 x^3+\left (2700 x-108 x^2\right ) \log (5)\right )+e^x \left (5400 x+2700 x^2-108 x^3+\left (2700+2808 x-108 x^2\right ) \log (5)\right )\right )+e^{6+3 e^x} \left (e^{2 x} \left (900 x^2-36 x^3+\left (900 x-36 x^2\right ) \log (5)\right )+e^x \left (600 x+300 x^2-12 x^3+\left (300+312 x-12 x^2\right ) \log (5)\right )\right )+e^{8+4 e^x} \left (e^x \left (-50 x-25 x^2+x^3+\left (-25-26 x+x^2\right ) \log (5)\right )+e^{2 x} \left (-100 x^2+4 x^3+\left (-100 x+4 x^2\right ) \log (5)\right )\right )+e^{4+2 e^x} \left (e^x \left (-2700 x-1350 x^2+54 x^3+\left (-1350-1404 x+54 x^2\right ) \log (5)\right )+e^{2 x} \left (-2700 x^2+108 x^3+\left (-2700 x+108 x^2\right ) \log (5)\right )\right )}{-15625+1875 x-75 x^2+x^3} \, dx=\frac {{\left (x^{2} + x \log \left (5\right )\right )} e^{\left (x + 4 \, e^{x} + 8\right )} - 12 \, {\left (x^{2} + x \log \left (5\right )\right )} e^{\left (x + 3 \, e^{x} + 6\right )} + 54 \, {\left (x^{2} + x \log \left (5\right )\right )} e^{\left (x + 2 \, e^{x} + 4\right )} - 108 \, {\left (x^{2} + x \log \left (5\right )\right )} e^{\left (x + e^{x} + 2\right )} + 81 \, {\left (x^{2} + x \log \left (5\right )\right )} e^{x}}{x^{2} - 50 \, x + 625} \]
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Leaf count of result is larger than twice the leaf count of optimal. 654 vs. \(2 (24) = 48\).
Time = 0.39 (sec) , antiderivative size = 654, normalized size of antiderivative = 22.55 \[ \int \frac {e^x \left (-4050 x-2025 x^2+81 x^3+\left (-2025-2106 x+81 x^2\right ) \log (5)\right )+e^{2+e^x} \left (e^{2 x} \left (2700 x^2-108 x^3+\left (2700 x-108 x^2\right ) \log (5)\right )+e^x \left (5400 x+2700 x^2-108 x^3+\left (2700+2808 x-108 x^2\right ) \log (5)\right )\right )+e^{6+3 e^x} \left (e^{2 x} \left (900 x^2-36 x^3+\left (900 x-36 x^2\right ) \log (5)\right )+e^x \left (600 x+300 x^2-12 x^3+\left (300+312 x-12 x^2\right ) \log (5)\right )\right )+e^{8+4 e^x} \left (e^x \left (-50 x-25 x^2+x^3+\left (-25-26 x+x^2\right ) \log (5)\right )+e^{2 x} \left (-100 x^2+4 x^3+\left (-100 x+4 x^2\right ) \log (5)\right )\right )+e^{4+2 e^x} \left (e^x \left (-2700 x-1350 x^2+54 x^3+\left (-1350-1404 x+54 x^2\right ) \log (5)\right )+e^{2 x} \left (-2700 x^2+108 x^3+\left (-2700 x+108 x^2\right ) \log (5)\right )\right )}{-15625+1875 x-75 x^2+x^3} \, dx=\frac {\left (81 x^{2} + 81 x \log {\left (5 \right )}\right ) e^{x}}{x^{2} - 50 x + 625} + \frac {\left (- 108 x^{8} e^{x} - 108 x^{7} e^{x} \log {\left (5 \right )} + 16200 x^{7} e^{x} - 1012500 x^{6} e^{x} + 16200 x^{6} e^{x} \log {\left (5 \right )} - 1012500 x^{5} e^{x} \log {\left (5 \right )} + 33750000 x^{5} e^{x} - 632812500 x^{4} e^{x} + 33750000 x^{4} e^{x} \log {\left (5 \right )} - 632812500 x^{3} e^{x} \log {\left (5 \right )} + 6328125000 x^{3} e^{x} - 26367187500 x^{2} e^{x} + 6328125000 x^{2} e^{x} \log {\left (5 \right )} - 26367187500 x e^{x} \log {\left (5 \right )}\right ) e^{e^{x} + 2} + \left (- 12 x^{8} e^{x} - 12 x^{7} e^{x} \log {\left (5 \right )} + 1800 x^{7} e^{x} - 112500 x^{6} e^{x} + 1800 x^{6} e^{x} \log {\left (5 \right )} - 112500 x^{5} e^{x} \log {\left (5 \right )} + 3750000 x^{5} e^{x} - 70312500 x^{4} e^{x} + 3750000 x^{4} e^{x} \log {\left (5 \right )} - 70312500 x^{3} e^{x} \log {\left (5 \right )} + 703125000 x^{3} e^{x} - 2929687500 x^{2} e^{x} + 703125000 x^{2} e^{x} \log {\left (5 \right )} - 2929687500 x e^{x} \log {\left (5 \right )}\right ) e^{3 e^{x} + 6} + \left (x^{8} e^{x} - 150 x^{7} e^{x} + x^{7} e^{x} \log {\left (5 \right )} - 150 x^{6} e^{x} \log {\left (5 \right )} + 9375 x^{6} e^{x} - 312500 x^{5} e^{x} + 9375 x^{5} e^{x} \log {\left (5 \right )} - 312500 x^{4} e^{x} \log {\left (5 \right )} + 5859375 x^{4} e^{x} - 58593750 x^{3} e^{x} + 5859375 x^{3} e^{x} \log {\left (5 \right )} - 58593750 x^{2} e^{x} \log {\left (5 \right )} + 244140625 x^{2} e^{x} + 244140625 x e^{x} \log {\left (5 \right )}\right ) e^{4 e^{x} + 8} + \left (54 x^{8} e^{x} - 8100 x^{7} e^{x} + 54 x^{7} e^{x} \log {\left (5 \right )} - 8100 x^{6} e^{x} \log {\left (5 \right )} + 506250 x^{6} e^{x} - 16875000 x^{5} e^{x} + 506250 x^{5} e^{x} \log {\left (5 \right )} - 16875000 x^{4} e^{x} \log {\left (5 \right )} + 316406250 x^{4} e^{x} - 3164062500 x^{3} e^{x} + 316406250 x^{3} e^{x} \log {\left (5 \right )} - 3164062500 x^{2} e^{x} \log {\left (5 \right )} + 13183593750 x^{2} e^{x} + 13183593750 x e^{x} \log {\left (5 \right )}\right ) e^{2 e^{x} + 4}}{x^{8} - 200 x^{7} + 17500 x^{6} - 875000 x^{5} + 27343750 x^{4} - 546875000 x^{3} + 6835937500 x^{2} - 48828125000 x + 152587890625} \]
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\[ \int \frac {e^x \left (-4050 x-2025 x^2+81 x^3+\left (-2025-2106 x+81 x^2\right ) \log (5)\right )+e^{2+e^x} \left (e^{2 x} \left (2700 x^2-108 x^3+\left (2700 x-108 x^2\right ) \log (5)\right )+e^x \left (5400 x+2700 x^2-108 x^3+\left (2700+2808 x-108 x^2\right ) \log (5)\right )\right )+e^{6+3 e^x} \left (e^{2 x} \left (900 x^2-36 x^3+\left (900 x-36 x^2\right ) \log (5)\right )+e^x \left (600 x+300 x^2-12 x^3+\left (300+312 x-12 x^2\right ) \log (5)\right )\right )+e^{8+4 e^x} \left (e^x \left (-50 x-25 x^2+x^3+\left (-25-26 x+x^2\right ) \log (5)\right )+e^{2 x} \left (-100 x^2+4 x^3+\left (-100 x+4 x^2\right ) \log (5)\right )\right )+e^{4+2 e^x} \left (e^x \left (-2700 x-1350 x^2+54 x^3+\left (-1350-1404 x+54 x^2\right ) \log (5)\right )+e^{2 x} \left (-2700 x^2+108 x^3+\left (-2700 x+108 x^2\right ) \log (5)\right )\right )}{-15625+1875 x-75 x^2+x^3} \, dx=\int { \frac {81 \, {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 26 \, x - 25\right )} \log \left (5\right ) - 50 \, x\right )} e^{x} + {\left (4 \, {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 25 \, x\right )} \log \left (5\right )\right )} e^{\left (2 \, x\right )} + {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 26 \, x - 25\right )} \log \left (5\right ) - 50 \, x\right )} e^{x}\right )} e^{\left (4 \, e^{x} + 8\right )} - 12 \, {\left (3 \, {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 25 \, x\right )} \log \left (5\right )\right )} e^{\left (2 \, x\right )} + {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 26 \, x - 25\right )} \log \left (5\right ) - 50 \, x\right )} e^{x}\right )} e^{\left (3 \, e^{x} + 6\right )} + 54 \, {\left (2 \, {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 25 \, x\right )} \log \left (5\right )\right )} e^{\left (2 \, x\right )} + {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 26 \, x - 25\right )} \log \left (5\right ) - 50 \, x\right )} e^{x}\right )} e^{\left (2 \, e^{x} + 4\right )} - 108 \, {\left ({\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 25 \, x\right )} \log \left (5\right )\right )} e^{\left (2 \, x\right )} + {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 26 \, x - 25\right )} \log \left (5\right ) - 50 \, x\right )} e^{x}\right )} e^{\left (e^{x} + 2\right )}}{x^{3} - 75 \, x^{2} + 1875 \, x - 15625} \,d x } \]
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\[ \int \frac {e^x \left (-4050 x-2025 x^2+81 x^3+\left (-2025-2106 x+81 x^2\right ) \log (5)\right )+e^{2+e^x} \left (e^{2 x} \left (2700 x^2-108 x^3+\left (2700 x-108 x^2\right ) \log (5)\right )+e^x \left (5400 x+2700 x^2-108 x^3+\left (2700+2808 x-108 x^2\right ) \log (5)\right )\right )+e^{6+3 e^x} \left (e^{2 x} \left (900 x^2-36 x^3+\left (900 x-36 x^2\right ) \log (5)\right )+e^x \left (600 x+300 x^2-12 x^3+\left (300+312 x-12 x^2\right ) \log (5)\right )\right )+e^{8+4 e^x} \left (e^x \left (-50 x-25 x^2+x^3+\left (-25-26 x+x^2\right ) \log (5)\right )+e^{2 x} \left (-100 x^2+4 x^3+\left (-100 x+4 x^2\right ) \log (5)\right )\right )+e^{4+2 e^x} \left (e^x \left (-2700 x-1350 x^2+54 x^3+\left (-1350-1404 x+54 x^2\right ) \log (5)\right )+e^{2 x} \left (-2700 x^2+108 x^3+\left (-2700 x+108 x^2\right ) \log (5)\right )\right )}{-15625+1875 x-75 x^2+x^3} \, dx=\int { \frac {81 \, {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 26 \, x - 25\right )} \log \left (5\right ) - 50 \, x\right )} e^{x} + {\left (4 \, {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 25 \, x\right )} \log \left (5\right )\right )} e^{\left (2 \, x\right )} + {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 26 \, x - 25\right )} \log \left (5\right ) - 50 \, x\right )} e^{x}\right )} e^{\left (4 \, e^{x} + 8\right )} - 12 \, {\left (3 \, {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 25 \, x\right )} \log \left (5\right )\right )} e^{\left (2 \, x\right )} + {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 26 \, x - 25\right )} \log \left (5\right ) - 50 \, x\right )} e^{x}\right )} e^{\left (3 \, e^{x} + 6\right )} + 54 \, {\left (2 \, {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 25 \, x\right )} \log \left (5\right )\right )} e^{\left (2 \, x\right )} + {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 26 \, x - 25\right )} \log \left (5\right ) - 50 \, x\right )} e^{x}\right )} e^{\left (2 \, e^{x} + 4\right )} - 108 \, {\left ({\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 25 \, x\right )} \log \left (5\right )\right )} e^{\left (2 \, x\right )} + {\left (x^{3} - 25 \, x^{2} + {\left (x^{2} - 26 \, x - 25\right )} \log \left (5\right ) - 50 \, x\right )} e^{x}\right )} e^{\left (e^{x} + 2\right )}}{x^{3} - 75 \, x^{2} + 1875 \, x - 15625} \,d x } \]
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Time = 13.96 (sec) , antiderivative size = 155, normalized size of antiderivative = 5.34 \[ \int \frac {e^x \left (-4050 x-2025 x^2+81 x^3+\left (-2025-2106 x+81 x^2\right ) \log (5)\right )+e^{2+e^x} \left (e^{2 x} \left (2700 x^2-108 x^3+\left (2700 x-108 x^2\right ) \log (5)\right )+e^x \left (5400 x+2700 x^2-108 x^3+\left (2700+2808 x-108 x^2\right ) \log (5)\right )\right )+e^{6+3 e^x} \left (e^{2 x} \left (900 x^2-36 x^3+\left (900 x-36 x^2\right ) \log (5)\right )+e^x \left (600 x+300 x^2-12 x^3+\left (300+312 x-12 x^2\right ) \log (5)\right )\right )+e^{8+4 e^x} \left (e^x \left (-50 x-25 x^2+x^3+\left (-25-26 x+x^2\right ) \log (5)\right )+e^{2 x} \left (-100 x^2+4 x^3+\left (-100 x+4 x^2\right ) \log (5)\right )\right )+e^{4+2 e^x} \left (e^x \left (-2700 x-1350 x^2+54 x^3+\left (-1350-1404 x+54 x^2\right ) \log (5)\right )+e^{2 x} \left (-2700 x^2+108 x^3+\left (-2700 x+108 x^2\right ) \log (5)\right )\right )}{-15625+1875 x-75 x^2+x^3} \, dx=\frac {{\mathrm {e}}^{4\,{\mathrm {e}}^x+8}\,\left (x^2\,{\mathrm {e}}^x+x\,{\mathrm {e}}^x\,\ln \left (5\right )\right )}{x^2-50\,x+625}-\frac {{\mathrm {e}}^{{\mathrm {e}}^x+2}\,\left (108\,x^2\,{\mathrm {e}}^x+108\,x\,{\mathrm {e}}^x\,\ln \left (5\right )\right )}{x^2-50\,x+625}-\frac {{\mathrm {e}}^{3\,{\mathrm {e}}^x+6}\,\left (12\,x^2\,{\mathrm {e}}^x+12\,x\,{\mathrm {e}}^x\,\ln \left (5\right )\right )}{x^2-50\,x+625}+\frac {{\mathrm {e}}^{2\,{\mathrm {e}}^x+4}\,\left (54\,x^2\,{\mathrm {e}}^x+54\,x\,{\mathrm {e}}^x\,\ln \left (5\right )\right )}{x^2-50\,x+625}+\frac {{\mathrm {e}}^x\,\left (81\,x^2+81\,\ln \left (5\right )\,x\right )}{x^2-50\,x+625} \]
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