Integrand size = 382, antiderivative size = 27 \[ \int \frac {-20000 x^2-2500 x^3+e (800+96 x)+e^{3 x} \left (-640 x^2-80 x^3\right )+e^{4 x} \left (-32 x^2-4 x^3\right )+e^{2 x} \left (-4800 x^2-600 x^3+e \left (32+68 x+8 x^2\right )\right )+e^x \left (-16000 x^2-2000 x^3+e \left (320+360 x+40 x^2\right )\right )+\left (e (-32-4 x)+1600 x^2+200 x^3+e^{2 x} \left (64 x^2+8 x^3\right )+e^x \left (640 x^2+80 x^3\right )\right ) \log (8+x)+\left (-32 x^2-4 x^3\right ) \log ^2(8+x)}{5000 x^4+625 x^5+e^2 (8+x)+e \left (400 x^2+50 x^3\right )+e^{4 x} \left (8 x^4+x^5\right )+e^{3 x} \left (160 x^4+20 x^5\right )+e^{2 x} \left (1200 x^4+150 x^5+e \left (16 x^2+2 x^3\right )\right )+e^x \left (4000 x^4+500 x^5+e \left (160 x^2+20 x^3\right )\right )+\left (-400 x^4-50 x^5+e \left (-16 x^2-2 x^3\right )+e^x \left (-160 x^4-20 x^5\right )+e^{2 x} \left (-16 x^4-2 x^5\right )\right ) \log (8+x)+\left (8 x^4+x^5\right ) \log ^2(8+x)} \, dx=\frac {4 x}{x^2+\frac {e}{\left (5+e^x\right )^2-\log (8+x)}} \]
[Out]
\[ \int \frac {-20000 x^2-2500 x^3+e (800+96 x)+e^{3 x} \left (-640 x^2-80 x^3\right )+e^{4 x} \left (-32 x^2-4 x^3\right )+e^{2 x} \left (-4800 x^2-600 x^3+e \left (32+68 x+8 x^2\right )\right )+e^x \left (-16000 x^2-2000 x^3+e \left (320+360 x+40 x^2\right )\right )+\left (e (-32-4 x)+1600 x^2+200 x^3+e^{2 x} \left (64 x^2+8 x^3\right )+e^x \left (640 x^2+80 x^3\right )\right ) \log (8+x)+\left (-32 x^2-4 x^3\right ) \log ^2(8+x)}{5000 x^4+625 x^5+e^2 (8+x)+e \left (400 x^2+50 x^3\right )+e^{4 x} \left (8 x^4+x^5\right )+e^{3 x} \left (160 x^4+20 x^5\right )+e^{2 x} \left (1200 x^4+150 x^5+e \left (16 x^2+2 x^3\right )\right )+e^x \left (4000 x^4+500 x^5+e \left (160 x^2+20 x^3\right )\right )+\left (-400 x^4-50 x^5+e \left (-16 x^2-2 x^3\right )+e^x \left (-160 x^4-20 x^5\right )+e^{2 x} \left (-16 x^4-2 x^5\right )\right ) \log (8+x)+\left (8 x^4+x^5\right ) \log ^2(8+x)} \, dx=\int \frac {-20000 x^2-2500 x^3+e (800+96 x)+e^{3 x} \left (-640 x^2-80 x^3\right )+e^{4 x} \left (-32 x^2-4 x^3\right )+e^{2 x} \left (-4800 x^2-600 x^3+e \left (32+68 x+8 x^2\right )\right )+e^x \left (-16000 x^2-2000 x^3+e \left (320+360 x+40 x^2\right )\right )+\left (e (-32-4 x)+1600 x^2+200 x^3+e^{2 x} \left (64 x^2+8 x^3\right )+e^x \left (640 x^2+80 x^3\right )\right ) \log (8+x)+\left (-32 x^2-4 x^3\right ) \log ^2(8+x)}{5000 x^4+625 x^5+e^2 (8+x)+e \left (400 x^2+50 x^3\right )+e^{4 x} \left (8 x^4+x^5\right )+e^{3 x} \left (160 x^4+20 x^5\right )+e^{2 x} \left (1200 x^4+150 x^5+e \left (16 x^2+2 x^3\right )\right )+e^x \left (4000 x^4+500 x^5+e \left (160 x^2+20 x^3\right )\right )+\left (-400 x^4-50 x^5+e \left (-16 x^2-2 x^3\right )+e^x \left (-160 x^4-20 x^5\right )+e^{2 x} \left (-16 x^4-2 x^5\right )\right ) \log (8+x)+\left (8 x^4+x^5\right ) \log ^2(8+x)} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {4 \left (-625 x^2 (8+x)-500 e^x x^2 (8+x)-150 e^{2 x} x^2 (8+x)-20 e^{3 x} x^2 (8+x)-e^{4 x} x^2 (8+x)+8 e (25+3 x)+10 e^{1+x} \left (8+9 x+x^2\right )+e^{1+2 x} \left (8+17 x+2 x^2\right )-(8+x) \left (e-50 x^2-20 e^x x^2-2 e^{2 x} x^2\right ) \log (8+x)-x^2 (8+x) \log ^2(8+x)\right )}{(8+x) \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2} \, dx \\ & = 4 \int \frac {-625 x^2 (8+x)-500 e^x x^2 (8+x)-150 e^{2 x} x^2 (8+x)-20 e^{3 x} x^2 (8+x)-e^{4 x} x^2 (8+x)+8 e (25+3 x)+10 e^{1+x} \left (8+9 x+x^2\right )+e^{1+2 x} \left (8+17 x+2 x^2\right )-(8+x) \left (e-50 x^2-20 e^x x^2-2 e^{2 x} x^2\right ) \log (8+x)-x^2 (8+x) \log ^2(8+x)}{(8+x) \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2} \, dx \\ & = 4 \int \left (-\frac {1}{x^2}+\frac {e (3+2 x)}{x^2 \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )}-\frac {e \left (16 e+18 e x+2 e x^2+401 x^3+80 e^x x^3+50 x^4+10 e^x x^4-16 x^3 \log (8+x)-2 x^4 \log (8+x)\right )}{x^2 (8+x) \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2}\right ) \, dx \\ & = \frac {4}{x}+(4 e) \int \frac {3+2 x}{x^2 \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )} \, dx-(4 e) \int \frac {16 e+18 e x+2 e x^2+401 x^3+80 e^x x^3+50 x^4+10 e^x x^4-16 x^3 \log (8+x)-2 x^4 \log (8+x)}{x^2 (8+x) \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2} \, dx \\ & = \frac {4}{x}+(4 e) \int \left (\frac {3}{x^2 \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )}+\frac {2}{x \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )}\right ) \, dx-(4 e) \int \left (\frac {16 e+18 e x+2 e x^2+401 x^3+80 e^x x^3+50 x^4+10 e^x x^4-16 x^3 \log (8+x)-2 x^4 \log (8+x)}{8 x^2 \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2}-\frac {16 e+18 e x+2 e x^2+401 x^3+80 e^x x^3+50 x^4+10 e^x x^4-16 x^3 \log (8+x)-2 x^4 \log (8+x)}{64 x \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2}+\frac {16 e+18 e x+2 e x^2+401 x^3+80 e^x x^3+50 x^4+10 e^x x^4-16 x^3 \log (8+x)-2 x^4 \log (8+x)}{64 (8+x) \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2}\right ) \, dx \\ & = \frac {4}{x}+\frac {1}{16} e \int \frac {16 e+18 e x+2 e x^2+401 x^3+80 e^x x^3+50 x^4+10 e^x x^4-16 x^3 \log (8+x)-2 x^4 \log (8+x)}{x \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2} \, dx-\frac {1}{16} e \int \frac {16 e+18 e x+2 e x^2+401 x^3+80 e^x x^3+50 x^4+10 e^x x^4-16 x^3 \log (8+x)-2 x^4 \log (8+x)}{(8+x) \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2} \, dx-\frac {1}{2} e \int \frac {16 e+18 e x+2 e x^2+401 x^3+80 e^x x^3+50 x^4+10 e^x x^4-16 x^3 \log (8+x)-2 x^4 \log (8+x)}{x^2 \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2} \, dx+(8 e) \int \frac {1}{x \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )} \, dx+(12 e) \int \frac {1}{x^2 \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )} \, dx \\ & = \frac {4}{x}+\frac {1}{16} e \int \left (\frac {18 e}{\left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2}+\frac {16 e}{x \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2}+\frac {2 e x}{\left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2}+\frac {401 x^2}{\left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2}+\frac {80 e^x x^2}{\left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2}+\frac {50 x^3}{\left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2}+\frac {10 e^x x^3}{\left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2}-\frac {16 x^2 \log (8+x)}{\left (-e-25 x^2-10 e^x x^2-e^{2 x} x^2+x^2 \log (8+x)\right )^2}-\frac {2 x^3 \log (8+x)}{\left (-e-25 x^2-10 e^x x^2-e^{2 x} x^2+x^2 \log (8+x)\right )^2}\right ) \, dx-\frac {1}{16} e \int \left (\frac {16 e}{(8+x) \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2}+\frac {18 e x}{(8+x) \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2}+\frac {2 e x^2}{(8+x) \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2}+\frac {401 x^3}{(8+x) \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2}+\frac {80 e^x x^3}{(8+x) \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2}+\frac {50 x^4}{(8+x) \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2}+\frac {10 e^x x^4}{(8+x) \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2}-\frac {16 x^3 \log (8+x)}{(8+x) \left (-e-25 x^2-10 e^x x^2-e^{2 x} x^2+x^2 \log (8+x)\right )^2}-\frac {2 x^4 \log (8+x)}{(8+x) \left (-e-25 x^2-10 e^x x^2-e^{2 x} x^2+x^2 \log (8+x)\right )^2}\right ) \, dx-\frac {1}{2} e \int \left (\frac {2 e}{\left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2}+\frac {16 e}{x^2 \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2}+\frac {18 e}{x \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2}+\frac {401 x}{\left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2}+\frac {80 e^x x}{\left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2}+\frac {50 x^2}{\left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2}+\frac {10 e^x x^2}{\left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2}-\frac {16 x \log (8+x)}{\left (-e-25 x^2-10 e^x x^2-e^{2 x} x^2+x^2 \log (8+x)\right )^2}-\frac {2 x^2 \log (8+x)}{\left (-e-25 x^2-10 e^x x^2-e^{2 x} x^2+x^2 \log (8+x)\right )^2}\right ) \, dx+(8 e) \int \frac {1}{x \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )} \, dx+(12 e) \int \frac {1}{x^2 \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )} \, dx \\ & = \frac {4}{x}-\frac {1}{8} e \int \frac {x^3 \log (8+x)}{\left (-e-25 x^2-10 e^x x^2-e^{2 x} x^2+x^2 \log (8+x)\right )^2} \, dx+\frac {1}{8} e \int \frac {x^4 \log (8+x)}{(8+x) \left (-e-25 x^2-10 e^x x^2-e^{2 x} x^2+x^2 \log (8+x)\right )^2} \, dx+\frac {1}{8} (5 e) \int \frac {e^x x^3}{\left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2} \, dx-\frac {1}{8} (5 e) \int \frac {e^x x^4}{(8+x) \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2} \, dx+e \int \frac {x^3 \log (8+x)}{(8+x) \left (-e-25 x^2-10 e^x x^2-e^{2 x} x^2+x^2 \log (8+x)\right )^2} \, dx+\frac {1}{8} (25 e) \int \frac {x^3}{\left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2} \, dx-\frac {1}{8} (25 e) \int \frac {x^4}{(8+x) \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2} \, dx-(5 e) \int \frac {e^x x^3}{(8+x) \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2} \, dx+(8 e) \int \frac {1}{x \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )} \, dx+(8 e) \int \frac {x \log (8+x)}{\left (-e-25 x^2-10 e^x x^2-e^{2 x} x^2+x^2 \log (8+x)\right )^2} \, dx+(12 e) \int \frac {1}{x^2 \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )} \, dx-(25 e) \int \frac {x^2}{\left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2} \, dx+\frac {1}{16} (401 e) \int \frac {x^2}{\left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2} \, dx-\frac {1}{16} (401 e) \int \frac {x^3}{(8+x) \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2} \, dx-(40 e) \int \frac {e^x x}{\left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2} \, dx-\frac {1}{2} (401 e) \int \frac {x}{\left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2} \, dx+\frac {1}{8} e^2 \int \frac {x}{\left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2} \, dx-\frac {1}{8} e^2 \int \frac {x^2}{(8+x) \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2} \, dx-e^2 \int \frac {1}{\left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2} \, dx+e^2 \int \frac {1}{x \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2} \, dx-e^2 \int \frac {1}{(8+x) \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2} \, dx+\frac {1}{8} \left (9 e^2\right ) \int \frac {1}{\left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2} \, dx-\frac {1}{8} \left (9 e^2\right ) \int \frac {x}{(8+x) \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2} \, dx-\left (8 e^2\right ) \int \frac {1}{x^2 \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2} \, dx-\left (9 e^2\right ) \int \frac {1}{x \left (e+25 x^2+10 e^x x^2+e^{2 x} x^2-x^2 \log (8+x)\right )^2} \, dx \\ & = \text {Too large to display} \\ \end{align*}
Time = 0.18 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.89 \[ \int \frac {-20000 x^2-2500 x^3+e (800+96 x)+e^{3 x} \left (-640 x^2-80 x^3\right )+e^{4 x} \left (-32 x^2-4 x^3\right )+e^{2 x} \left (-4800 x^2-600 x^3+e \left (32+68 x+8 x^2\right )\right )+e^x \left (-16000 x^2-2000 x^3+e \left (320+360 x+40 x^2\right )\right )+\left (e (-32-4 x)+1600 x^2+200 x^3+e^{2 x} \left (64 x^2+8 x^3\right )+e^x \left (640 x^2+80 x^3\right )\right ) \log (8+x)+\left (-32 x^2-4 x^3\right ) \log ^2(8+x)}{5000 x^4+625 x^5+e^2 (8+x)+e \left (400 x^2+50 x^3\right )+e^{4 x} \left (8 x^4+x^5\right )+e^{3 x} \left (160 x^4+20 x^5\right )+e^{2 x} \left (1200 x^4+150 x^5+e \left (16 x^2+2 x^3\right )\right )+e^x \left (4000 x^4+500 x^5+e \left (160 x^2+20 x^3\right )\right )+\left (-400 x^4-50 x^5+e \left (-16 x^2-2 x^3\right )+e^x \left (-160 x^4-20 x^5\right )+e^{2 x} \left (-16 x^4-2 x^5\right )\right ) \log (8+x)+\left (8 x^4+x^5\right ) \log ^2(8+x)} \, dx=-4 \left (-\frac {1}{x}-\frac {e}{x \left (-e-25 x^2-10 e^x x^2-e^{2 x} x^2+x^2 \log (8+x)\right )}\right ) \]
[In]
[Out]
Time = 5.16 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.78
method | result | size |
risch | \(\frac {4}{x}-\frac {4 \,{\mathrm e}}{x \left ({\mathrm e}^{2 x} x^{2}+10 \,{\mathrm e}^{x} x^{2}-x^{2} \ln \left (x +8\right )+25 x^{2}+{\mathrm e}\right )}\) | \(48\) |
parallelrisch | \(\frac {4 x \,{\mathrm e}^{2 x}+40 \,{\mathrm e}^{x} x -4 x \ln \left (x +8\right )+100 x}{{\mathrm e}^{2 x} x^{2}+10 \,{\mathrm e}^{x} x^{2}-x^{2} \ln \left (x +8\right )+25 x^{2}+{\mathrm e}}\) | \(59\) |
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 58 vs. \(2 (27) = 54\).
Time = 0.27 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.15 \[ \int \frac {-20000 x^2-2500 x^3+e (800+96 x)+e^{3 x} \left (-640 x^2-80 x^3\right )+e^{4 x} \left (-32 x^2-4 x^3\right )+e^{2 x} \left (-4800 x^2-600 x^3+e \left (32+68 x+8 x^2\right )\right )+e^x \left (-16000 x^2-2000 x^3+e \left (320+360 x+40 x^2\right )\right )+\left (e (-32-4 x)+1600 x^2+200 x^3+e^{2 x} \left (64 x^2+8 x^3\right )+e^x \left (640 x^2+80 x^3\right )\right ) \log (8+x)+\left (-32 x^2-4 x^3\right ) \log ^2(8+x)}{5000 x^4+625 x^5+e^2 (8+x)+e \left (400 x^2+50 x^3\right )+e^{4 x} \left (8 x^4+x^5\right )+e^{3 x} \left (160 x^4+20 x^5\right )+e^{2 x} \left (1200 x^4+150 x^5+e \left (16 x^2+2 x^3\right )\right )+e^x \left (4000 x^4+500 x^5+e \left (160 x^2+20 x^3\right )\right )+\left (-400 x^4-50 x^5+e \left (-16 x^2-2 x^3\right )+e^x \left (-160 x^4-20 x^5\right )+e^{2 x} \left (-16 x^4-2 x^5\right )\right ) \log (8+x)+\left (8 x^4+x^5\right ) \log ^2(8+x)} \, dx=\frac {4 \, {\left (x e^{\left (2 \, x\right )} + 10 \, x e^{x} - x \log \left (x + 8\right ) + 25 \, x\right )}}{x^{2} e^{\left (2 \, x\right )} + 10 \, x^{2} e^{x} - x^{2} \log \left (x + 8\right ) + 25 \, x^{2} + e} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 42 vs. \(2 (20) = 40\).
Time = 0.34 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.56 \[ \int \frac {-20000 x^2-2500 x^3+e (800+96 x)+e^{3 x} \left (-640 x^2-80 x^3\right )+e^{4 x} \left (-32 x^2-4 x^3\right )+e^{2 x} \left (-4800 x^2-600 x^3+e \left (32+68 x+8 x^2\right )\right )+e^x \left (-16000 x^2-2000 x^3+e \left (320+360 x+40 x^2\right )\right )+\left (e (-32-4 x)+1600 x^2+200 x^3+e^{2 x} \left (64 x^2+8 x^3\right )+e^x \left (640 x^2+80 x^3\right )\right ) \log (8+x)+\left (-32 x^2-4 x^3\right ) \log ^2(8+x)}{5000 x^4+625 x^5+e^2 (8+x)+e \left (400 x^2+50 x^3\right )+e^{4 x} \left (8 x^4+x^5\right )+e^{3 x} \left (160 x^4+20 x^5\right )+e^{2 x} \left (1200 x^4+150 x^5+e \left (16 x^2+2 x^3\right )\right )+e^x \left (4000 x^4+500 x^5+e \left (160 x^2+20 x^3\right )\right )+\left (-400 x^4-50 x^5+e \left (-16 x^2-2 x^3\right )+e^x \left (-160 x^4-20 x^5\right )+e^{2 x} \left (-16 x^4-2 x^5\right )\right ) \log (8+x)+\left (8 x^4+x^5\right ) \log ^2(8+x)} \, dx=- \frac {4 e}{x^{3} e^{2 x} + 10 x^{3} e^{x} - x^{3} \log {\left (x + 8 \right )} + 25 x^{3} + e x} + \frac {4}{x} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 58 vs. \(2 (27) = 54\).
Time = 0.42 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.15 \[ \int \frac {-20000 x^2-2500 x^3+e (800+96 x)+e^{3 x} \left (-640 x^2-80 x^3\right )+e^{4 x} \left (-32 x^2-4 x^3\right )+e^{2 x} \left (-4800 x^2-600 x^3+e \left (32+68 x+8 x^2\right )\right )+e^x \left (-16000 x^2-2000 x^3+e \left (320+360 x+40 x^2\right )\right )+\left (e (-32-4 x)+1600 x^2+200 x^3+e^{2 x} \left (64 x^2+8 x^3\right )+e^x \left (640 x^2+80 x^3\right )\right ) \log (8+x)+\left (-32 x^2-4 x^3\right ) \log ^2(8+x)}{5000 x^4+625 x^5+e^2 (8+x)+e \left (400 x^2+50 x^3\right )+e^{4 x} \left (8 x^4+x^5\right )+e^{3 x} \left (160 x^4+20 x^5\right )+e^{2 x} \left (1200 x^4+150 x^5+e \left (16 x^2+2 x^3\right )\right )+e^x \left (4000 x^4+500 x^5+e \left (160 x^2+20 x^3\right )\right )+\left (-400 x^4-50 x^5+e \left (-16 x^2-2 x^3\right )+e^x \left (-160 x^4-20 x^5\right )+e^{2 x} \left (-16 x^4-2 x^5\right )\right ) \log (8+x)+\left (8 x^4+x^5\right ) \log ^2(8+x)} \, dx=\frac {4 \, {\left (x e^{\left (2 \, x\right )} + 10 \, x e^{x} - x \log \left (x + 8\right ) + 25 \, x\right )}}{x^{2} e^{\left (2 \, x\right )} + 10 \, x^{2} e^{x} - x^{2} \log \left (x + 8\right ) + 25 \, x^{2} + e} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 4300 vs. \(2 (27) = 54\).
Time = 6.88 (sec) , antiderivative size = 4300, normalized size of antiderivative = 159.26 \[ \int \frac {-20000 x^2-2500 x^3+e (800+96 x)+e^{3 x} \left (-640 x^2-80 x^3\right )+e^{4 x} \left (-32 x^2-4 x^3\right )+e^{2 x} \left (-4800 x^2-600 x^3+e \left (32+68 x+8 x^2\right )\right )+e^x \left (-16000 x^2-2000 x^3+e \left (320+360 x+40 x^2\right )\right )+\left (e (-32-4 x)+1600 x^2+200 x^3+e^{2 x} \left (64 x^2+8 x^3\right )+e^x \left (640 x^2+80 x^3\right )\right ) \log (8+x)+\left (-32 x^2-4 x^3\right ) \log ^2(8+x)}{5000 x^4+625 x^5+e^2 (8+x)+e \left (400 x^2+50 x^3\right )+e^{4 x} \left (8 x^4+x^5\right )+e^{3 x} \left (160 x^4+20 x^5\right )+e^{2 x} \left (1200 x^4+150 x^5+e \left (16 x^2+2 x^3\right )\right )+e^x \left (4000 x^4+500 x^5+e \left (160 x^2+20 x^3\right )\right )+\left (-400 x^4-50 x^5+e \left (-16 x^2-2 x^3\right )+e^x \left (-160 x^4-20 x^5\right )+e^{2 x} \left (-16 x^4-2 x^5\right )\right ) \log (8+x)+\left (8 x^4+x^5\right ) \log ^2(8+x)} \, dx=\text {Too large to display} \]
[In]
[Out]
Timed out. \[ \int \frac {-20000 x^2-2500 x^3+e (800+96 x)+e^{3 x} \left (-640 x^2-80 x^3\right )+e^{4 x} \left (-32 x^2-4 x^3\right )+e^{2 x} \left (-4800 x^2-600 x^3+e \left (32+68 x+8 x^2\right )\right )+e^x \left (-16000 x^2-2000 x^3+e \left (320+360 x+40 x^2\right )\right )+\left (e (-32-4 x)+1600 x^2+200 x^3+e^{2 x} \left (64 x^2+8 x^3\right )+e^x \left (640 x^2+80 x^3\right )\right ) \log (8+x)+\left (-32 x^2-4 x^3\right ) \log ^2(8+x)}{5000 x^4+625 x^5+e^2 (8+x)+e \left (400 x^2+50 x^3\right )+e^{4 x} \left (8 x^4+x^5\right )+e^{3 x} \left (160 x^4+20 x^5\right )+e^{2 x} \left (1200 x^4+150 x^5+e \left (16 x^2+2 x^3\right )\right )+e^x \left (4000 x^4+500 x^5+e \left (160 x^2+20 x^3\right )\right )+\left (-400 x^4-50 x^5+e \left (-16 x^2-2 x^3\right )+e^x \left (-160 x^4-20 x^5\right )+e^{2 x} \left (-16 x^4-2 x^5\right )\right ) \log (8+x)+\left (8 x^4+x^5\right ) \log ^2(8+x)} \, dx=-\int \frac {{\mathrm {e}}^x\,\left (16000\,x^2-\mathrm {e}\,\left (40\,x^2+360\,x+320\right )+2000\,x^3\right )+{\mathrm {e}}^{4\,x}\,\left (4\,x^3+32\,x^2\right )+{\mathrm {e}}^{3\,x}\,\left (80\,x^3+640\,x^2\right )+{\mathrm {e}}^{2\,x}\,\left (4800\,x^2-\mathrm {e}\,\left (8\,x^2+68\,x+32\right )+600\,x^3\right )+{\ln \left (x+8\right )}^2\,\left (4\,x^3+32\,x^2\right )+20000\,x^2+2500\,x^3-\ln \left (x+8\right )\,\left ({\mathrm {e}}^x\,\left (80\,x^3+640\,x^2\right )+{\mathrm {e}}^{2\,x}\,\left (8\,x^3+64\,x^2\right )+1600\,x^2+200\,x^3-\mathrm {e}\,\left (4\,x+32\right )\right )-\mathrm {e}\,\left (96\,x+800\right )}{{\mathrm {e}}^{4\,x}\,\left (x^5+8\,x^4\right )+{\mathrm {e}}^{3\,x}\,\left (20\,x^5+160\,x^4\right )+{\ln \left (x+8\right )}^2\,\left (x^5+8\,x^4\right )-\ln \left (x+8\right )\,\left ({\mathrm {e}}^x\,\left (20\,x^5+160\,x^4\right )+{\mathrm {e}}^{2\,x}\,\left (2\,x^5+16\,x^4\right )+\mathrm {e}\,\left (2\,x^3+16\,x^2\right )+400\,x^4+50\,x^5\right )+\mathrm {e}\,\left (50\,x^3+400\,x^2\right )+{\mathrm {e}}^x\,\left (\mathrm {e}\,\left (20\,x^3+160\,x^2\right )+4000\,x^4+500\,x^5\right )+{\mathrm {e}}^2\,\left (x+8\right )+5000\,x^4+625\,x^5+{\mathrm {e}}^{2\,x}\,\left (\mathrm {e}\,\left (2\,x^3+16\,x^2\right )+1200\,x^4+150\,x^5\right )} \,d x \]
[In]
[Out]