Integrand size = 701, antiderivative size = 31 \[ \int \frac {e^{\frac {50 e^6 x^2+20 e^7 x^2+2 e^8 x^2}{x^2+e^3 \left (40 x-40 x^2\right )+e^8 \left (16-32 x+16 x^2\right )+e^6 \left (400-800 x+400 x^2\right )+e^{2 x} \left (25 e^6 x^2+10 e^7 x^2+e^8 x^2\right )+e^4 \left (8 x-8 x^2+e^3 \left (160-320 x+160 x^2\right )\right )+e^x \left (-10 e^3 x^2+e^8 \left (-8 x+8 x^2\right )+e^6 \left (-200 x+200 x^2\right )+e^4 \left (-2 x^2+e^3 \left (-80 x+80 x^2\right )\right )\right )}} \left (-2000 e^9 x-1200 e^{10} x-240 e^{11} x-16 e^{12} x+e^x \left (-500 e^9 x^3-300 e^{10} x^3-60 e^{11} x^3-4 e^{12} x^3\right )\right )}{-x^3+e^6 \left (-1200 x+2400 x^2-1200 x^3\right )+e^3 \left (-60 x^2+60 x^3\right )+e^{12} \left (-64+192 x-192 x^2+64 x^3\right )+e^9 \left (-8000+24000 x-24000 x^2+8000 x^3\right )+e^{3 x} \left (125 e^9 x^3+75 e^{10} x^3+15 e^{11} x^3+e^{12} x^3\right )+e^8 \left (-48 x+96 x^2-48 x^3+e^3 \left (-960+2880 x-2880 x^2+960 x^3\right )\right )+e^4 \left (-12 x^2+12 x^3+e^3 \left (-480 x+960 x^2-480 x^3\right )+e^6 \left (-4800+14400 x-14400 x^2+4800 x^3\right )\right )+e^{2 x} \left (-75 e^6 x^3+e^{12} \left (-12 x^2+12 x^3\right )+e^9 \left (-1500 x^2+1500 x^3\right )+e^8 \left (-3 x^3+e^3 \left (-180 x^2+180 x^3\right )\right )+e^4 \left (-30 e^3 x^3+e^6 \left (-900 x^2+900 x^3\right )\right )\right )+e^x \left (15 e^3 x^3+e^6 \left (600 x^2-600 x^3\right )+e^{12} \left (48 x-96 x^2+48 x^3\right )+e^9 \left (6000 x-12000 x^2+6000 x^3\right )+e^8 \left (24 x^2-24 x^3+e^3 \left (720 x-1440 x^2+720 x^3\right )\right )+e^4 \left (3 x^3+e^3 \left (240 x^2-240 x^3\right )+e^6 \left (3600 x-7200 x^2+3600 x^3\right )\right )\right )} \, dx=e^{\frac {2}{\left (4+e^x-\frac {4+\frac {x}{5 e^3+e^4}}{x}\right )^2}} \]
[Out]
\[ \int \frac {e^{\frac {50 e^6 x^2+20 e^7 x^2+2 e^8 x^2}{x^2+e^3 \left (40 x-40 x^2\right )+e^8 \left (16-32 x+16 x^2\right )+e^6 \left (400-800 x+400 x^2\right )+e^{2 x} \left (25 e^6 x^2+10 e^7 x^2+e^8 x^2\right )+e^4 \left (8 x-8 x^2+e^3 \left (160-320 x+160 x^2\right )\right )+e^x \left (-10 e^3 x^2+e^8 \left (-8 x+8 x^2\right )+e^6 \left (-200 x+200 x^2\right )+e^4 \left (-2 x^2+e^3 \left (-80 x+80 x^2\right )\right )\right )}} \left (-2000 e^9 x-1200 e^{10} x-240 e^{11} x-16 e^{12} x+e^x \left (-500 e^9 x^3-300 e^{10} x^3-60 e^{11} x^3-4 e^{12} x^3\right )\right )}{-x^3+e^6 \left (-1200 x+2400 x^2-1200 x^3\right )+e^3 \left (-60 x^2+60 x^3\right )+e^{12} \left (-64+192 x-192 x^2+64 x^3\right )+e^9 \left (-8000+24000 x-24000 x^2+8000 x^3\right )+e^{3 x} \left (125 e^9 x^3+75 e^{10} x^3+15 e^{11} x^3+e^{12} x^3\right )+e^8 \left (-48 x+96 x^2-48 x^3+e^3 \left (-960+2880 x-2880 x^2+960 x^3\right )\right )+e^4 \left (-12 x^2+12 x^3+e^3 \left (-480 x+960 x^2-480 x^3\right )+e^6 \left (-4800+14400 x-14400 x^2+4800 x^3\right )\right )+e^{2 x} \left (-75 e^6 x^3+e^{12} \left (-12 x^2+12 x^3\right )+e^9 \left (-1500 x^2+1500 x^3\right )+e^8 \left (-3 x^3+e^3 \left (-180 x^2+180 x^3\right )\right )+e^4 \left (-30 e^3 x^3+e^6 \left (-900 x^2+900 x^3\right )\right )\right )+e^x \left (15 e^3 x^3+e^6 \left (600 x^2-600 x^3\right )+e^{12} \left (48 x-96 x^2+48 x^3\right )+e^9 \left (6000 x-12000 x^2+6000 x^3\right )+e^8 \left (24 x^2-24 x^3+e^3 \left (720 x-1440 x^2+720 x^3\right )\right )+e^4 \left (3 x^3+e^3 \left (240 x^2-240 x^3\right )+e^6 \left (3600 x-7200 x^2+3600 x^3\right )\right )\right )} \, dx=\int \frac {\exp \left (\frac {50 e^6 x^2+20 e^7 x^2+2 e^8 x^2}{x^2+e^3 \left (40 x-40 x^2\right )+e^8 \left (16-32 x+16 x^2\right )+e^6 \left (400-800 x+400 x^2\right )+e^{2 x} \left (25 e^6 x^2+10 e^7 x^2+e^8 x^2\right )+e^4 \left (8 x-8 x^2+e^3 \left (160-320 x+160 x^2\right )\right )+e^x \left (-10 e^3 x^2+e^8 \left (-8 x+8 x^2\right )+e^6 \left (-200 x+200 x^2\right )+e^4 \left (-2 x^2+e^3 \left (-80 x+80 x^2\right )\right )\right )}\right ) \left (-2000 e^9 x-1200 e^{10} x-240 e^{11} x-16 e^{12} x+e^x \left (-500 e^9 x^3-300 e^{10} x^3-60 e^{11} x^3-4 e^{12} x^3\right )\right )}{-x^3+e^6 \left (-1200 x+2400 x^2-1200 x^3\right )+e^3 \left (-60 x^2+60 x^3\right )+e^{12} \left (-64+192 x-192 x^2+64 x^3\right )+e^9 \left (-8000+24000 x-24000 x^2+8000 x^3\right )+e^{3 x} \left (125 e^9 x^3+75 e^{10} x^3+15 e^{11} x^3+e^{12} x^3\right )+e^8 \left (-48 x+96 x^2-48 x^3+e^3 \left (-960+2880 x-2880 x^2+960 x^3\right )\right )+e^4 \left (-12 x^2+12 x^3+e^3 \left (-480 x+960 x^2-480 x^3\right )+e^6 \left (-4800+14400 x-14400 x^2+4800 x^3\right )\right )+e^{2 x} \left (-75 e^6 x^3+e^{12} \left (-12 x^2+12 x^3\right )+e^9 \left (-1500 x^2+1500 x^3\right )+e^8 \left (-3 x^3+e^3 \left (-180 x^2+180 x^3\right )\right )+e^4 \left (-30 e^3 x^3+e^6 \left (-900 x^2+900 x^3\right )\right )\right )+e^x \left (15 e^3 x^3+e^6 \left (600 x^2-600 x^3\right )+e^{12} \left (48 x-96 x^2+48 x^3\right )+e^9 \left (6000 x-12000 x^2+6000 x^3\right )+e^8 \left (24 x^2-24 x^3+e^3 \left (720 x-1440 x^2+720 x^3\right )\right )+e^4 \left (3 x^3+e^3 \left (240 x^2-240 x^3\right )+e^6 \left (3600 x-7200 x^2+3600 x^3\right )\right )\right )} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {\exp \left (\frac {50 e^6 x^2+20 e^7 x^2+2 e^8 x^2}{x^2+e^3 \left (40 x-40 x^2\right )+e^8 \left (16-32 x+16 x^2\right )+e^6 \left (400-800 x+400 x^2\right )+e^{2 x} \left (25 e^6 x^2+10 e^7 x^2+e^8 x^2\right )+e^4 \left (8 x-8 x^2+e^3 \left (160-320 x+160 x^2\right )\right )+e^x \left (-10 e^3 x^2+e^8 \left (-8 x+8 x^2\right )+e^6 \left (-200 x+200 x^2\right )+e^4 \left (-2 x^2+e^3 \left (-80 x+80 x^2\right )\right )\right )}\right ) \left (-240 e^{11} x-16 e^{12} x+\left (-2000 e^9-1200 e^{10}\right ) x+e^x \left (-500 e^9 x^3-300 e^{10} x^3-60 e^{11} x^3-4 e^{12} x^3\right )\right )}{-x^3+e^6 \left (-1200 x+2400 x^2-1200 x^3\right )+e^3 \left (-60 x^2+60 x^3\right )+e^{12} \left (-64+192 x-192 x^2+64 x^3\right )+e^9 \left (-8000+24000 x-24000 x^2+8000 x^3\right )+e^{3 x} \left (125 e^9 x^3+75 e^{10} x^3+15 e^{11} x^3+e^{12} x^3\right )+e^8 \left (-48 x+96 x^2-48 x^3+e^3 \left (-960+2880 x-2880 x^2+960 x^3\right )\right )+e^4 \left (-12 x^2+12 x^3+e^3 \left (-480 x+960 x^2-480 x^3\right )+e^6 \left (-4800+14400 x-14400 x^2+4800 x^3\right )\right )+e^{2 x} \left (-75 e^6 x^3+e^{12} \left (-12 x^2+12 x^3\right )+e^9 \left (-1500 x^2+1500 x^3\right )+e^8 \left (-3 x^3+e^3 \left (-180 x^2+180 x^3\right )\right )+e^4 \left (-30 e^3 x^3+e^6 \left (-900 x^2+900 x^3\right )\right )\right )+e^x \left (15 e^3 x^3+e^6 \left (600 x^2-600 x^3\right )+e^{12} \left (48 x-96 x^2+48 x^3\right )+e^9 \left (6000 x-12000 x^2+6000 x^3\right )+e^8 \left (24 x^2-24 x^3+e^3 \left (720 x-1440 x^2+720 x^3\right )\right )+e^4 \left (3 x^3+e^3 \left (240 x^2-240 x^3\right )+e^6 \left (3600 x-7200 x^2+3600 x^3\right )\right )\right )} \, dx \\ & = \int \frac {\exp \left (\frac {50 e^6 x^2+20 e^7 x^2+2 e^8 x^2}{x^2+e^3 \left (40 x-40 x^2\right )+e^8 \left (16-32 x+16 x^2\right )+e^6 \left (400-800 x+400 x^2\right )+e^{2 x} \left (25 e^6 x^2+10 e^7 x^2+e^8 x^2\right )+e^4 \left (8 x-8 x^2+e^3 \left (160-320 x+160 x^2\right )\right )+e^x \left (-10 e^3 x^2+e^8 \left (-8 x+8 x^2\right )+e^6 \left (-200 x+200 x^2\right )+e^4 \left (-2 x^2+e^3 \left (-80 x+80 x^2\right )\right )\right )}\right ) \left (\left (-2000 e^9-1200 e^{10}\right ) x+\left (-240 e^{11}-16 e^{12}\right ) x+e^x \left (-500 e^9 x^3-300 e^{10} x^3-60 e^{11} x^3-4 e^{12} x^3\right )\right )}{-x^3+e^6 \left (-1200 x+2400 x^2-1200 x^3\right )+e^3 \left (-60 x^2+60 x^3\right )+e^{12} \left (-64+192 x-192 x^2+64 x^3\right )+e^9 \left (-8000+24000 x-24000 x^2+8000 x^3\right )+e^{3 x} \left (125 e^9 x^3+75 e^{10} x^3+15 e^{11} x^3+e^{12} x^3\right )+e^8 \left (-48 x+96 x^2-48 x^3+e^3 \left (-960+2880 x-2880 x^2+960 x^3\right )\right )+e^4 \left (-12 x^2+12 x^3+e^3 \left (-480 x+960 x^2-480 x^3\right )+e^6 \left (-4800+14400 x-14400 x^2+4800 x^3\right )\right )+e^{2 x} \left (-75 e^6 x^3+e^{12} \left (-12 x^2+12 x^3\right )+e^9 \left (-1500 x^2+1500 x^3\right )+e^8 \left (-3 x^3+e^3 \left (-180 x^2+180 x^3\right )\right )+e^4 \left (-30 e^3 x^3+e^6 \left (-900 x^2+900 x^3\right )\right )\right )+e^x \left (15 e^3 x^3+e^6 \left (600 x^2-600 x^3\right )+e^{12} \left (48 x-96 x^2+48 x^3\right )+e^9 \left (6000 x-12000 x^2+6000 x^3\right )+e^8 \left (24 x^2-24 x^3+e^3 \left (720 x-1440 x^2+720 x^3\right )\right )+e^4 \left (3 x^3+e^3 \left (240 x^2-240 x^3\right )+e^6 \left (3600 x-7200 x^2+3600 x^3\right )\right )\right )} \, dx \\ & = \int \frac {\exp \left (\frac {50 e^6 x^2+20 e^7 x^2+2 e^8 x^2}{x^2+e^3 \left (40 x-40 x^2\right )+e^8 \left (16-32 x+16 x^2\right )+e^6 \left (400-800 x+400 x^2\right )+e^{2 x} \left (25 e^6 x^2+10 e^7 x^2+e^8 x^2\right )+e^4 \left (8 x-8 x^2+e^3 \left (160-320 x+160 x^2\right )\right )+e^x \left (-10 e^3 x^2+e^8 \left (-8 x+8 x^2\right )+e^6 \left (-200 x+200 x^2\right )+e^4 \left (-2 x^2+e^3 \left (-80 x+80 x^2\right )\right )\right )}\right ) \left (\left (-2000 e^9-1200 e^{10}-240 e^{11}-16 e^{12}\right ) x+e^x \left (-500 e^9 x^3-300 e^{10} x^3-60 e^{11} x^3-4 e^{12} x^3\right )\right )}{-x^3+e^6 \left (-1200 x+2400 x^2-1200 x^3\right )+e^3 \left (-60 x^2+60 x^3\right )+e^{12} \left (-64+192 x-192 x^2+64 x^3\right )+e^9 \left (-8000+24000 x-24000 x^2+8000 x^3\right )+e^{3 x} \left (125 e^9 x^3+75 e^{10} x^3+15 e^{11} x^3+e^{12} x^3\right )+e^8 \left (-48 x+96 x^2-48 x^3+e^3 \left (-960+2880 x-2880 x^2+960 x^3\right )\right )+e^4 \left (-12 x^2+12 x^3+e^3 \left (-480 x+960 x^2-480 x^3\right )+e^6 \left (-4800+14400 x-14400 x^2+4800 x^3\right )\right )+e^{2 x} \left (-75 e^6 x^3+e^{12} \left (-12 x^2+12 x^3\right )+e^9 \left (-1500 x^2+1500 x^3\right )+e^8 \left (-3 x^3+e^3 \left (-180 x^2+180 x^3\right )\right )+e^4 \left (-30 e^3 x^3+e^6 \left (-900 x^2+900 x^3\right )\right )\right )+e^x \left (15 e^3 x^3+e^6 \left (600 x^2-600 x^3\right )+e^{12} \left (48 x-96 x^2+48 x^3\right )+e^9 \left (6000 x-12000 x^2+6000 x^3\right )+e^8 \left (24 x^2-24 x^3+e^3 \left (720 x-1440 x^2+720 x^3\right )\right )+e^4 \left (3 x^3+e^3 \left (240 x^2-240 x^3\right )+e^6 \left (3600 x-7200 x^2+3600 x^3\right )\right )\right )} \, dx \\ & = \int \frac {4 \exp \left (\frac {-360 \left (1+\frac {e}{5}\right ) e^3 (-1+x) x+1800 e^{6+x} \left (1+\frac {1}{25} e (10+e)\right ) (-1+x) x+9 x^2-90 \left (1+\frac {e}{5}\right ) e^{3+x} x^2+225 e^{6+2 x} \left (1+\frac {1}{25} e (10+e)\right ) x^2+50 e^6 \left (1+\frac {1}{25} e (10+e)\right ) \left (72-144 x+73 x^2\right )}{\left (20 \left (1+\frac {e}{5}\right ) e^3 (-1+x)-x+5 \left (1+\frac {e}{5}\right ) e^{3+x} x\right )^2}\right ) (5+e)^3 x \left (-4-e^x x^2\right )}{\left (20 \left (1+\frac {e}{5}\right ) e^3 (-1+x)-x+5 \left (1+\frac {e}{5}\right ) e^{3+x} x\right )^3} \, dx \\ & = \left (4 (5+e)^3\right ) \int \frac {\exp \left (\frac {-360 \left (1+\frac {e}{5}\right ) e^3 (-1+x) x+1800 e^{6+x} \left (1+\frac {1}{25} e (10+e)\right ) (-1+x) x+9 x^2-90 \left (1+\frac {e}{5}\right ) e^{3+x} x^2+225 e^{6+2 x} \left (1+\frac {1}{25} e (10+e)\right ) x^2+50 e^6 \left (1+\frac {1}{25} e (10+e)\right ) \left (72-144 x+73 x^2\right )}{\left (20 \left (1+\frac {e}{5}\right ) e^3 (-1+x)-x+5 \left (1+\frac {e}{5}\right ) e^{3+x} x\right )^2}\right ) x \left (-4-e^x x^2\right )}{\left (20 \left (1+\frac {e}{5}\right ) e^3 (-1+x)-x+5 \left (1+\frac {e}{5}\right ) e^{3+x} x\right )^3} \, dx \\ & = \left (4 (5+e)^3\right ) \int \left (\frac {\exp \left (-3+\frac {-360 \left (1+\frac {e}{5}\right ) e^3 (-1+x) x+1800 e^{6+x} \left (1+\frac {1}{25} e (10+e)\right ) (-1+x) x+9 x^2-90 \left (1+\frac {e}{5}\right ) e^{3+x} x^2+225 e^{6+2 x} \left (1+\frac {1}{25} e (10+e)\right ) x^2+50 e^6 \left (1+\frac {1}{25} e (10+e)\right ) \left (72-144 x+73 x^2\right )}{\left (20 \left (1+\frac {e}{5}\right ) e^3 (-1+x)-x+5 \left (1+\frac {e}{5}\right ) e^{3+x} x\right )^2}\right ) x^2}{(-5-e) \left (20 \left (1+\frac {e}{5}\right ) e^3-5 \left (1+\frac {e}{5}\right ) e^{3+x} x+\left (1-4 e^3 (5+e)\right ) x\right )^2}+\frac {\exp \left (-3+\frac {-360 \left (1+\frac {e}{5}\right ) e^3 (-1+x) x+1800 e^{6+x} \left (1+\frac {1}{25} e (10+e)\right ) (-1+x) x+9 x^2-90 \left (1+\frac {e}{5}\right ) e^{3+x} x^2+225 e^{6+2 x} \left (1+\frac {1}{25} e (10+e)\right ) x^2+50 e^6 \left (1+\frac {1}{25} e (10+e)\right ) \left (72-144 x+73 x^2\right )}{\left (20 \left (1+\frac {e}{5}\right ) e^3 (-1+x)-x+5 \left (1+\frac {e}{5}\right ) e^{3+x} x\right )^2}\right ) x \left (4 e^3 (5+e)+4 e^3 (5+e) x+\left (1-20 e^3-4 e^4\right ) x^2\right )}{(5+e) \left (20 \left (1+\frac {e}{5}\right ) e^3-5 \left (1+\frac {e}{5}\right ) e^{3+x} x+\left (1-4 e^3 (5+e)\right ) x\right )^3}\right ) \, dx \\ & = -\left (\left (4 (5+e)^2\right ) \int \frac {\exp \left (-3+\frac {-360 \left (1+\frac {e}{5}\right ) e^3 (-1+x) x+1800 e^{6+x} \left (1+\frac {1}{25} e (10+e)\right ) (-1+x) x+9 x^2-90 \left (1+\frac {e}{5}\right ) e^{3+x} x^2+225 e^{6+2 x} \left (1+\frac {1}{25} e (10+e)\right ) x^2+50 e^6 \left (1+\frac {1}{25} e (10+e)\right ) \left (72-144 x+73 x^2\right )}{\left (20 \left (1+\frac {e}{5}\right ) e^3 (-1+x)-x+5 \left (1+\frac {e}{5}\right ) e^{3+x} x\right )^2}\right ) x^2}{\left (20 \left (1+\frac {e}{5}\right ) e^3-5 \left (1+\frac {e}{5}\right ) e^{3+x} x+\left (1-4 e^3 (5+e)\right ) x\right )^2} \, dx\right )+\left (4 (5+e)^2\right ) \int \frac {\exp \left (-3+\frac {-360 \left (1+\frac {e}{5}\right ) e^3 (-1+x) x+1800 e^{6+x} \left (1+\frac {1}{25} e (10+e)\right ) (-1+x) x+9 x^2-90 \left (1+\frac {e}{5}\right ) e^{3+x} x^2+225 e^{6+2 x} \left (1+\frac {1}{25} e (10+e)\right ) x^2+50 e^6 \left (1+\frac {1}{25} e (10+e)\right ) \left (72-144 x+73 x^2\right )}{\left (20 \left (1+\frac {e}{5}\right ) e^3 (-1+x)-x+5 \left (1+\frac {e}{5}\right ) e^{3+x} x\right )^2}\right ) x \left (4 e^3 (5+e)+4 e^3 (5+e) x+\left (1-20 e^3-4 e^4\right ) x^2\right )}{\left (20 \left (1+\frac {e}{5}\right ) e^3-5 \left (1+\frac {e}{5}\right ) e^{3+x} x+\left (1-4 e^3 (5+e)\right ) x\right )^3} \, dx \\ & = -\left (\left (4 (5+e)^2\right ) \int \frac {e^{-3+\frac {-360 \left (1+\frac {e}{5}\right ) e^3 (-1+x) x+1800 e^{6+x} \left (1+\frac {1}{25} e (10+e)\right ) (-1+x) x+9 x^2-90 \left (1+\frac {e}{5}\right ) e^{3+x} x^2+225 e^{6+2 x} \left (1+\frac {1}{25} e (10+e)\right ) x^2+50 e^6 \left (1+\frac {1}{25} e (10+e)\right ) \left (72-144 x+73 x^2\right )}{\left (20 \left (1+\frac {e}{5}\right ) e^3 (-1+x)-x+5 \left (1+\frac {e}{5}\right ) e^{3+x} x\right )^2}} x^2}{\left (20 \left (1+\frac {e}{5}\right ) e^3-5 \left (1+\frac {e}{5}\right ) e^{3+x} x+\left (1-4 e^3 (5+e)\right ) x\right )^2} \, dx\right )+\left (4 (5+e)^2\right ) \int \left (\frac {4 e^{\frac {-360 \left (1+\frac {e}{5}\right ) e^3 (-1+x) x+1800 e^{6+x} \left (1+\frac {1}{25} e (10+e)\right ) (-1+x) x+9 x^2-90 \left (1+\frac {e}{5}\right ) e^{3+x} x^2+225 e^{6+2 x} \left (1+\frac {1}{25} e (10+e)\right ) x^2+50 e^6 \left (1+\frac {1}{25} e (10+e)\right ) \left (72-144 x+73 x^2\right )}{\left (20 \left (1+\frac {e}{5}\right ) e^3 (-1+x)-x+5 \left (1+\frac {e}{5}\right ) e^{3+x} x\right )^2}} (5+e) x}{\left (20 \left (1+\frac {e}{5}\right ) e^3-5 \left (1+\frac {e}{5}\right ) e^{3+x} x+\left (1-4 e^3 (5+e)\right ) x\right )^3}+\frac {4 e^{\frac {-360 \left (1+\frac {e}{5}\right ) e^3 (-1+x) x+1800 e^{6+x} \left (1+\frac {1}{25} e (10+e)\right ) (-1+x) x+9 x^2-90 \left (1+\frac {e}{5}\right ) e^{3+x} x^2+225 e^{6+2 x} \left (1+\frac {1}{25} e (10+e)\right ) x^2+50 e^6 \left (1+\frac {1}{25} e (10+e)\right ) \left (72-144 x+73 x^2\right )}{\left (20 \left (1+\frac {e}{5}\right ) e^3 (-1+x)-x+5 \left (1+\frac {e}{5}\right ) e^{3+x} x\right )^2}} (5+e) x^2}{\left (20 \left (1+\frac {e}{5}\right ) e^3-5 \left (1+\frac {e}{5}\right ) e^{3+x} x+\left (1-4 e^3 (5+e)\right ) x\right )^3}+\frac {e^{-3+\frac {-360 \left (1+\frac {e}{5}\right ) e^3 (-1+x) x+1800 e^{6+x} \left (1+\frac {1}{25} e (10+e)\right ) (-1+x) x+9 x^2-90 \left (1+\frac {e}{5}\right ) e^{3+x} x^2+225 e^{6+2 x} \left (1+\frac {1}{25} e (10+e)\right ) x^2+50 e^6 \left (1+\frac {1}{25} e (10+e)\right ) \left (72-144 x+73 x^2\right )}{\left (20 \left (1+\frac {e}{5}\right ) e^3 (-1+x)-x+5 \left (1+\frac {e}{5}\right ) e^{3+x} x\right )^2}} \left (1-20 e^3-4 e^4\right ) x^3}{\left (20 \left (1+\frac {e}{5}\right ) e^3-5 \left (1+\frac {e}{5}\right ) e^{3+x} x+\left (1-4 e^3 (5+e)\right ) x\right )^3}\right ) \, dx \\ & = -\left (\left (4 (5+e)^2\right ) \int \frac {e^{-3+\frac {-360 \left (1+\frac {e}{5}\right ) e^3 (-1+x) x+1800 e^{6+x} \left (1+\frac {1}{25} e (10+e)\right ) (-1+x) x+9 x^2-90 \left (1+\frac {e}{5}\right ) e^{3+x} x^2+225 e^{6+2 x} \left (1+\frac {1}{25} e (10+e)\right ) x^2+50 e^6 \left (1+\frac {1}{25} e (10+e)\right ) \left (72-144 x+73 x^2\right )}{\left (20 \left (1+\frac {e}{5}\right ) e^3 (-1+x)-x+5 \left (1+\frac {e}{5}\right ) e^{3+x} x\right )^2}} x^2}{\left (20 \left (1+\frac {e}{5}\right ) e^3-5 \left (1+\frac {e}{5}\right ) e^{3+x} x+\left (1-4 e^3 (5+e)\right ) x\right )^2} \, dx\right )+\left (16 (5+e)^3\right ) \int \frac {e^{\frac {-360 \left (1+\frac {e}{5}\right ) e^3 (-1+x) x+1800 e^{6+x} \left (1+\frac {1}{25} e (10+e)\right ) (-1+x) x+9 x^2-90 \left (1+\frac {e}{5}\right ) e^{3+x} x^2+225 e^{6+2 x} \left (1+\frac {1}{25} e (10+e)\right ) x^2+50 e^6 \left (1+\frac {1}{25} e (10+e)\right ) \left (72-144 x+73 x^2\right )}{\left (20 \left (1+\frac {e}{5}\right ) e^3 (-1+x)-x+5 \left (1+\frac {e}{5}\right ) e^{3+x} x\right )^2}} x}{\left (20 \left (1+\frac {e}{5}\right ) e^3-5 \left (1+\frac {e}{5}\right ) e^{3+x} x+\left (1-4 e^3 (5+e)\right ) x\right )^3} \, dx+\left (16 (5+e)^3\right ) \int \frac {e^{\frac {-360 \left (1+\frac {e}{5}\right ) e^3 (-1+x) x+1800 e^{6+x} \left (1+\frac {1}{25} e (10+e)\right ) (-1+x) x+9 x^2-90 \left (1+\frac {e}{5}\right ) e^{3+x} x^2+225 e^{6+2 x} \left (1+\frac {1}{25} e (10+e)\right ) x^2+50 e^6 \left (1+\frac {1}{25} e (10+e)\right ) \left (72-144 x+73 x^2\right )}{\left (20 \left (1+\frac {e}{5}\right ) e^3 (-1+x)-x+5 \left (1+\frac {e}{5}\right ) e^{3+x} x\right )^2}} x^2}{\left (20 \left (1+\frac {e}{5}\right ) e^3-5 \left (1+\frac {e}{5}\right ) e^{3+x} x+\left (1-4 e^3 (5+e)\right ) x\right )^3} \, dx+\left (4 (5+e)^2 \left (1-20 e^3-4 e^4\right )\right ) \int \frac {e^{-3+\frac {-360 \left (1+\frac {e}{5}\right ) e^3 (-1+x) x+1800 e^{6+x} \left (1+\frac {1}{25} e (10+e)\right ) (-1+x) x+9 x^2-90 \left (1+\frac {e}{5}\right ) e^{3+x} x^2+225 e^{6+2 x} \left (1+\frac {1}{25} e (10+e)\right ) x^2+50 e^6 \left (1+\frac {1}{25} e (10+e)\right ) \left (72-144 x+73 x^2\right )}{\left (20 \left (1+\frac {e}{5}\right ) e^3 (-1+x)-x+5 \left (1+\frac {e}{5}\right ) e^{3+x} x\right )^2}} x^3}{\left (20 \left (1+\frac {e}{5}\right ) e^3-5 \left (1+\frac {e}{5}\right ) e^{3+x} x+\left (1-4 e^3 (5+e)\right ) x\right )^3} \, dx \\ \end{align*}
Time = 0.79 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.68 \[ \int \frac {e^{\frac {50 e^6 x^2+20 e^7 x^2+2 e^8 x^2}{x^2+e^3 \left (40 x-40 x^2\right )+e^8 \left (16-32 x+16 x^2\right )+e^6 \left (400-800 x+400 x^2\right )+e^{2 x} \left (25 e^6 x^2+10 e^7 x^2+e^8 x^2\right )+e^4 \left (8 x-8 x^2+e^3 \left (160-320 x+160 x^2\right )\right )+e^x \left (-10 e^3 x^2+e^8 \left (-8 x+8 x^2\right )+e^6 \left (-200 x+200 x^2\right )+e^4 \left (-2 x^2+e^3 \left (-80 x+80 x^2\right )\right )\right )}} \left (-2000 e^9 x-1200 e^{10} x-240 e^{11} x-16 e^{12} x+e^x \left (-500 e^9 x^3-300 e^{10} x^3-60 e^{11} x^3-4 e^{12} x^3\right )\right )}{-x^3+e^6 \left (-1200 x+2400 x^2-1200 x^3\right )+e^3 \left (-60 x^2+60 x^3\right )+e^{12} \left (-64+192 x-192 x^2+64 x^3\right )+e^9 \left (-8000+24000 x-24000 x^2+8000 x^3\right )+e^{3 x} \left (125 e^9 x^3+75 e^{10} x^3+15 e^{11} x^3+e^{12} x^3\right )+e^8 \left (-48 x+96 x^2-48 x^3+e^3 \left (-960+2880 x-2880 x^2+960 x^3\right )\right )+e^4 \left (-12 x^2+12 x^3+e^3 \left (-480 x+960 x^2-480 x^3\right )+e^6 \left (-4800+14400 x-14400 x^2+4800 x^3\right )\right )+e^{2 x} \left (-75 e^6 x^3+e^{12} \left (-12 x^2+12 x^3\right )+e^9 \left (-1500 x^2+1500 x^3\right )+e^8 \left (-3 x^3+e^3 \left (-180 x^2+180 x^3\right )\right )+e^4 \left (-30 e^3 x^3+e^6 \left (-900 x^2+900 x^3\right )\right )\right )+e^x \left (15 e^3 x^3+e^6 \left (600 x^2-600 x^3\right )+e^{12} \left (48 x-96 x^2+48 x^3\right )+e^9 \left (6000 x-12000 x^2+6000 x^3\right )+e^8 \left (24 x^2-24 x^3+e^3 \left (720 x-1440 x^2+720 x^3\right )\right )+e^4 \left (3 x^3+e^3 \left (240 x^2-240 x^3\right )+e^6 \left (3600 x-7200 x^2+3600 x^3\right )\right )\right )} \, dx=e^{\frac {2 e^6 (5+e)^2 x^2}{\left (20 e^3 (-1+x)+4 e^4 (-1+x)-x+5 e^{3+x} x+e^{4+x} x\right )^2}} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. \(196\) vs. \(2(27)=54\).
Time = 46.77 (sec) , antiderivative size = 197, normalized size of antiderivative = 6.35
method | result | size |
risch | \({\mathrm e}^{-\frac {2 x^{2} \left ({\mathrm e}^{8}+25 \,{\mathrm e}^{6}+10 \,{\mathrm e}^{7}\right )}{200 x \,{\mathrm e}^{6+x}+80 x \,{\mathrm e}^{x +7}-25 x^{2} {\mathrm e}^{2 x +6}+8 x \,{\mathrm e}^{x +8}-200 x^{2} {\mathrm e}^{6+x}-x^{2} {\mathrm e}^{2 x +8}-400 x^{2} {\mathrm e}^{6}+2 x^{2} {\mathrm e}^{4+x}+32 x \,{\mathrm e}^{8}+320 x \,{\mathrm e}^{7}+8 x^{2} {\mathrm e}^{4}+800 x \,{\mathrm e}^{6}-40 x \,{\mathrm e}^{3}+40 x^{2} {\mathrm e}^{3}-160 x^{2} {\mathrm e}^{7}+10 x^{2} {\mathrm e}^{3+x}-160 \,{\mathrm e}^{7}-16 \,{\mathrm e}^{8}-400 \,{\mathrm e}^{6}-8 x \,{\mathrm e}^{4}-x^{2}-16 x^{2} {\mathrm e}^{8}-10 x^{2} {\mathrm e}^{2 x +7}-8 x^{2} {\mathrm e}^{x +8}-80 x^{2} {\mathrm e}^{x +7}}}\) | \(197\) |
parallelrisch | \(\text {Expression too large to display}\) | \(1762\) |
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 165 vs. \(2 (28) = 56\).
Time = 0.29 (sec) , antiderivative size = 165, normalized size of antiderivative = 5.32 \[ \int \frac {e^{\frac {50 e^6 x^2+20 e^7 x^2+2 e^8 x^2}{x^2+e^3 \left (40 x-40 x^2\right )+e^8 \left (16-32 x+16 x^2\right )+e^6 \left (400-800 x+400 x^2\right )+e^{2 x} \left (25 e^6 x^2+10 e^7 x^2+e^8 x^2\right )+e^4 \left (8 x-8 x^2+e^3 \left (160-320 x+160 x^2\right )\right )+e^x \left (-10 e^3 x^2+e^8 \left (-8 x+8 x^2\right )+e^6 \left (-200 x+200 x^2\right )+e^4 \left (-2 x^2+e^3 \left (-80 x+80 x^2\right )\right )\right )}} \left (-2000 e^9 x-1200 e^{10} x-240 e^{11} x-16 e^{12} x+e^x \left (-500 e^9 x^3-300 e^{10} x^3-60 e^{11} x^3-4 e^{12} x^3\right )\right )}{-x^3+e^6 \left (-1200 x+2400 x^2-1200 x^3\right )+e^3 \left (-60 x^2+60 x^3\right )+e^{12} \left (-64+192 x-192 x^2+64 x^3\right )+e^9 \left (-8000+24000 x-24000 x^2+8000 x^3\right )+e^{3 x} \left (125 e^9 x^3+75 e^{10} x^3+15 e^{11} x^3+e^{12} x^3\right )+e^8 \left (-48 x+96 x^2-48 x^3+e^3 \left (-960+2880 x-2880 x^2+960 x^3\right )\right )+e^4 \left (-12 x^2+12 x^3+e^3 \left (-480 x+960 x^2-480 x^3\right )+e^6 \left (-4800+14400 x-14400 x^2+4800 x^3\right )\right )+e^{2 x} \left (-75 e^6 x^3+e^{12} \left (-12 x^2+12 x^3\right )+e^9 \left (-1500 x^2+1500 x^3\right )+e^8 \left (-3 x^3+e^3 \left (-180 x^2+180 x^3\right )\right )+e^4 \left (-30 e^3 x^3+e^6 \left (-900 x^2+900 x^3\right )\right )\right )+e^x \left (15 e^3 x^3+e^6 \left (600 x^2-600 x^3\right )+e^{12} \left (48 x-96 x^2+48 x^3\right )+e^9 \left (6000 x-12000 x^2+6000 x^3\right )+e^8 \left (24 x^2-24 x^3+e^3 \left (720 x-1440 x^2+720 x^3\right )\right )+e^4 \left (3 x^3+e^3 \left (240 x^2-240 x^3\right )+e^6 \left (3600 x-7200 x^2+3600 x^3\right )\right )\right )} \, dx=e^{\left (\frac {2 \, {\left (x^{2} e^{8} + 10 \, x^{2} e^{7} + 25 \, x^{2} e^{6}\right )}}{x^{2} + 16 \, {\left (x^{2} - 2 \, x + 1\right )} e^{8} + 160 \, {\left (x^{2} - 2 \, x + 1\right )} e^{7} + 400 \, {\left (x^{2} - 2 \, x + 1\right )} e^{6} - 8 \, {\left (x^{2} - x\right )} e^{4} - 40 \, {\left (x^{2} - x\right )} e^{3} + {\left (x^{2} e^{8} + 10 \, x^{2} e^{7} + 25 \, x^{2} e^{6}\right )} e^{\left (2 \, x\right )} - 2 \, {\left (x^{2} e^{4} + 5 \, x^{2} e^{3} - 4 \, {\left (x^{2} - x\right )} e^{8} - 40 \, {\left (x^{2} - x\right )} e^{7} - 100 \, {\left (x^{2} - x\right )} e^{6}\right )} e^{x}}\right )} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 178 vs. \(2 (22) = 44\).
Time = 1.81 (sec) , antiderivative size = 178, normalized size of antiderivative = 5.74 \[ \int \frac {e^{\frac {50 e^6 x^2+20 e^7 x^2+2 e^8 x^2}{x^2+e^3 \left (40 x-40 x^2\right )+e^8 \left (16-32 x+16 x^2\right )+e^6 \left (400-800 x+400 x^2\right )+e^{2 x} \left (25 e^6 x^2+10 e^7 x^2+e^8 x^2\right )+e^4 \left (8 x-8 x^2+e^3 \left (160-320 x+160 x^2\right )\right )+e^x \left (-10 e^3 x^2+e^8 \left (-8 x+8 x^2\right )+e^6 \left (-200 x+200 x^2\right )+e^4 \left (-2 x^2+e^3 \left (-80 x+80 x^2\right )\right )\right )}} \left (-2000 e^9 x-1200 e^{10} x-240 e^{11} x-16 e^{12} x+e^x \left (-500 e^9 x^3-300 e^{10} x^3-60 e^{11} x^3-4 e^{12} x^3\right )\right )}{-x^3+e^6 \left (-1200 x+2400 x^2-1200 x^3\right )+e^3 \left (-60 x^2+60 x^3\right )+e^{12} \left (-64+192 x-192 x^2+64 x^3\right )+e^9 \left (-8000+24000 x-24000 x^2+8000 x^3\right )+e^{3 x} \left (125 e^9 x^3+75 e^{10} x^3+15 e^{11} x^3+e^{12} x^3\right )+e^8 \left (-48 x+96 x^2-48 x^3+e^3 \left (-960+2880 x-2880 x^2+960 x^3\right )\right )+e^4 \left (-12 x^2+12 x^3+e^3 \left (-480 x+960 x^2-480 x^3\right )+e^6 \left (-4800+14400 x-14400 x^2+4800 x^3\right )\right )+e^{2 x} \left (-75 e^6 x^3+e^{12} \left (-12 x^2+12 x^3\right )+e^9 \left (-1500 x^2+1500 x^3\right )+e^8 \left (-3 x^3+e^3 \left (-180 x^2+180 x^3\right )\right )+e^4 \left (-30 e^3 x^3+e^6 \left (-900 x^2+900 x^3\right )\right )\right )+e^x \left (15 e^3 x^3+e^6 \left (600 x^2-600 x^3\right )+e^{12} \left (48 x-96 x^2+48 x^3\right )+e^9 \left (6000 x-12000 x^2+6000 x^3\right )+e^8 \left (24 x^2-24 x^3+e^3 \left (720 x-1440 x^2+720 x^3\right )\right )+e^4 \left (3 x^3+e^3 \left (240 x^2-240 x^3\right )+e^6 \left (3600 x-7200 x^2+3600 x^3\right )\right )\right )} \, dx=e^{\frac {2 x^{2} e^{8} + 50 x^{2} e^{6} + 20 x^{2} e^{7}}{x^{2} + \left (- 40 x^{2} + 40 x\right ) e^{3} + \left (- 8 x^{2} + 8 x + \left (160 x^{2} - 320 x + 160\right ) e^{3}\right ) e^{4} + \left (16 x^{2} - 32 x + 16\right ) e^{8} + \left (400 x^{2} - 800 x + 400\right ) e^{6} + \left (x^{2} e^{8} + 25 x^{2} e^{6} + 10 x^{2} e^{7}\right ) e^{2 x} + \left (- 10 x^{2} e^{3} + \left (- 2 x^{2} + \left (80 x^{2} - 80 x\right ) e^{3}\right ) e^{4} + \left (8 x^{2} - 8 x\right ) e^{8} + \left (200 x^{2} - 200 x\right ) e^{6}\right ) e^{x}}} \]
[In]
[Out]
Timed out. \[ \int \frac {e^{\frac {50 e^6 x^2+20 e^7 x^2+2 e^8 x^2}{x^2+e^3 \left (40 x-40 x^2\right )+e^8 \left (16-32 x+16 x^2\right )+e^6 \left (400-800 x+400 x^2\right )+e^{2 x} \left (25 e^6 x^2+10 e^7 x^2+e^8 x^2\right )+e^4 \left (8 x-8 x^2+e^3 \left (160-320 x+160 x^2\right )\right )+e^x \left (-10 e^3 x^2+e^8 \left (-8 x+8 x^2\right )+e^6 \left (-200 x+200 x^2\right )+e^4 \left (-2 x^2+e^3 \left (-80 x+80 x^2\right )\right )\right )}} \left (-2000 e^9 x-1200 e^{10} x-240 e^{11} x-16 e^{12} x+e^x \left (-500 e^9 x^3-300 e^{10} x^3-60 e^{11} x^3-4 e^{12} x^3\right )\right )}{-x^3+e^6 \left (-1200 x+2400 x^2-1200 x^3\right )+e^3 \left (-60 x^2+60 x^3\right )+e^{12} \left (-64+192 x-192 x^2+64 x^3\right )+e^9 \left (-8000+24000 x-24000 x^2+8000 x^3\right )+e^{3 x} \left (125 e^9 x^3+75 e^{10} x^3+15 e^{11} x^3+e^{12} x^3\right )+e^8 \left (-48 x+96 x^2-48 x^3+e^3 \left (-960+2880 x-2880 x^2+960 x^3\right )\right )+e^4 \left (-12 x^2+12 x^3+e^3 \left (-480 x+960 x^2-480 x^3\right )+e^6 \left (-4800+14400 x-14400 x^2+4800 x^3\right )\right )+e^{2 x} \left (-75 e^6 x^3+e^{12} \left (-12 x^2+12 x^3\right )+e^9 \left (-1500 x^2+1500 x^3\right )+e^8 \left (-3 x^3+e^3 \left (-180 x^2+180 x^3\right )\right )+e^4 \left (-30 e^3 x^3+e^6 \left (-900 x^2+900 x^3\right )\right )\right )+e^x \left (15 e^3 x^3+e^6 \left (600 x^2-600 x^3\right )+e^{12} \left (48 x-96 x^2+48 x^3\right )+e^9 \left (6000 x-12000 x^2+6000 x^3\right )+e^8 \left (24 x^2-24 x^3+e^3 \left (720 x-1440 x^2+720 x^3\right )\right )+e^4 \left (3 x^3+e^3 \left (240 x^2-240 x^3\right )+e^6 \left (3600 x-7200 x^2+3600 x^3\right )\right )\right )} \, dx=\text {Timed out} \]
[In]
[Out]
Timed out. \[ \int \frac {e^{\frac {50 e^6 x^2+20 e^7 x^2+2 e^8 x^2}{x^2+e^3 \left (40 x-40 x^2\right )+e^8 \left (16-32 x+16 x^2\right )+e^6 \left (400-800 x+400 x^2\right )+e^{2 x} \left (25 e^6 x^2+10 e^7 x^2+e^8 x^2\right )+e^4 \left (8 x-8 x^2+e^3 \left (160-320 x+160 x^2\right )\right )+e^x \left (-10 e^3 x^2+e^8 \left (-8 x+8 x^2\right )+e^6 \left (-200 x+200 x^2\right )+e^4 \left (-2 x^2+e^3 \left (-80 x+80 x^2\right )\right )\right )}} \left (-2000 e^9 x-1200 e^{10} x-240 e^{11} x-16 e^{12} x+e^x \left (-500 e^9 x^3-300 e^{10} x^3-60 e^{11} x^3-4 e^{12} x^3\right )\right )}{-x^3+e^6 \left (-1200 x+2400 x^2-1200 x^3\right )+e^3 \left (-60 x^2+60 x^3\right )+e^{12} \left (-64+192 x-192 x^2+64 x^3\right )+e^9 \left (-8000+24000 x-24000 x^2+8000 x^3\right )+e^{3 x} \left (125 e^9 x^3+75 e^{10} x^3+15 e^{11} x^3+e^{12} x^3\right )+e^8 \left (-48 x+96 x^2-48 x^3+e^3 \left (-960+2880 x-2880 x^2+960 x^3\right )\right )+e^4 \left (-12 x^2+12 x^3+e^3 \left (-480 x+960 x^2-480 x^3\right )+e^6 \left (-4800+14400 x-14400 x^2+4800 x^3\right )\right )+e^{2 x} \left (-75 e^6 x^3+e^{12} \left (-12 x^2+12 x^3\right )+e^9 \left (-1500 x^2+1500 x^3\right )+e^8 \left (-3 x^3+e^3 \left (-180 x^2+180 x^3\right )\right )+e^4 \left (-30 e^3 x^3+e^6 \left (-900 x^2+900 x^3\right )\right )\right )+e^x \left (15 e^3 x^3+e^6 \left (600 x^2-600 x^3\right )+e^{12} \left (48 x-96 x^2+48 x^3\right )+e^9 \left (6000 x-12000 x^2+6000 x^3\right )+e^8 \left (24 x^2-24 x^3+e^3 \left (720 x-1440 x^2+720 x^3\right )\right )+e^4 \left (3 x^3+e^3 \left (240 x^2-240 x^3\right )+e^6 \left (3600 x-7200 x^2+3600 x^3\right )\right )\right )} \, dx=\text {Timed out} \]
[In]
[Out]
Time = 16.08 (sec) , antiderivative size = 553, normalized size of antiderivative = 17.84 \[ \int \frac {e^{\frac {50 e^6 x^2+20 e^7 x^2+2 e^8 x^2}{x^2+e^3 \left (40 x-40 x^2\right )+e^8 \left (16-32 x+16 x^2\right )+e^6 \left (400-800 x+400 x^2\right )+e^{2 x} \left (25 e^6 x^2+10 e^7 x^2+e^8 x^2\right )+e^4 \left (8 x-8 x^2+e^3 \left (160-320 x+160 x^2\right )\right )+e^x \left (-10 e^3 x^2+e^8 \left (-8 x+8 x^2\right )+e^6 \left (-200 x+200 x^2\right )+e^4 \left (-2 x^2+e^3 \left (-80 x+80 x^2\right )\right )\right )}} \left (-2000 e^9 x-1200 e^{10} x-240 e^{11} x-16 e^{12} x+e^x \left (-500 e^9 x^3-300 e^{10} x^3-60 e^{11} x^3-4 e^{12} x^3\right )\right )}{-x^3+e^6 \left (-1200 x+2400 x^2-1200 x^3\right )+e^3 \left (-60 x^2+60 x^3\right )+e^{12} \left (-64+192 x-192 x^2+64 x^3\right )+e^9 \left (-8000+24000 x-24000 x^2+8000 x^3\right )+e^{3 x} \left (125 e^9 x^3+75 e^{10} x^3+15 e^{11} x^3+e^{12} x^3\right )+e^8 \left (-48 x+96 x^2-48 x^3+e^3 \left (-960+2880 x-2880 x^2+960 x^3\right )\right )+e^4 \left (-12 x^2+12 x^3+e^3 \left (-480 x+960 x^2-480 x^3\right )+e^6 \left (-4800+14400 x-14400 x^2+4800 x^3\right )\right )+e^{2 x} \left (-75 e^6 x^3+e^{12} \left (-12 x^2+12 x^3\right )+e^9 \left (-1500 x^2+1500 x^3\right )+e^8 \left (-3 x^3+e^3 \left (-180 x^2+180 x^3\right )\right )+e^4 \left (-30 e^3 x^3+e^6 \left (-900 x^2+900 x^3\right )\right )\right )+e^x \left (15 e^3 x^3+e^6 \left (600 x^2-600 x^3\right )+e^{12} \left (48 x-96 x^2+48 x^3\right )+e^9 \left (6000 x-12000 x^2+6000 x^3\right )+e^8 \left (24 x^2-24 x^3+e^3 \left (720 x-1440 x^2+720 x^3\right )\right )+e^4 \left (3 x^3+e^3 \left (240 x^2-240 x^3\right )+e^6 \left (3600 x-7200 x^2+3600 x^3\right )\right )\right )} \, dx={\mathrm {e}}^{\frac {2\,x^2\,{\mathrm {e}}^8}{400\,{\mathrm {e}}^6+160\,{\mathrm {e}}^7+16\,{\mathrm {e}}^8+40\,x\,{\mathrm {e}}^3+8\,x\,{\mathrm {e}}^4-800\,x\,{\mathrm {e}}^6-320\,x\,{\mathrm {e}}^7-32\,x\,{\mathrm {e}}^8-40\,x^2\,{\mathrm {e}}^3-8\,x^2\,{\mathrm {e}}^4+400\,x^2\,{\mathrm {e}}^6+160\,x^2\,{\mathrm {e}}^7+16\,x^2\,{\mathrm {e}}^8+x^2-200\,x\,{\mathrm {e}}^6\,{\mathrm {e}}^x-80\,x\,{\mathrm {e}}^7\,{\mathrm {e}}^x-8\,x\,{\mathrm {e}}^8\,{\mathrm {e}}^x-10\,x^2\,{\mathrm {e}}^3\,{\mathrm {e}}^x-2\,x^2\,{\mathrm {e}}^4\,{\mathrm {e}}^x+200\,x^2\,{\mathrm {e}}^6\,{\mathrm {e}}^x+80\,x^2\,{\mathrm {e}}^7\,{\mathrm {e}}^x+8\,x^2\,{\mathrm {e}}^8\,{\mathrm {e}}^x+25\,x^2\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^6+10\,x^2\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^7+x^2\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^8}}\,{\mathrm {e}}^{\frac {20\,x^2\,{\mathrm {e}}^7}{400\,{\mathrm {e}}^6+160\,{\mathrm {e}}^7+16\,{\mathrm {e}}^8+40\,x\,{\mathrm {e}}^3+8\,x\,{\mathrm {e}}^4-800\,x\,{\mathrm {e}}^6-320\,x\,{\mathrm {e}}^7-32\,x\,{\mathrm {e}}^8-40\,x^2\,{\mathrm {e}}^3-8\,x^2\,{\mathrm {e}}^4+400\,x^2\,{\mathrm {e}}^6+160\,x^2\,{\mathrm {e}}^7+16\,x^2\,{\mathrm {e}}^8+x^2-200\,x\,{\mathrm {e}}^6\,{\mathrm {e}}^x-80\,x\,{\mathrm {e}}^7\,{\mathrm {e}}^x-8\,x\,{\mathrm {e}}^8\,{\mathrm {e}}^x-10\,x^2\,{\mathrm {e}}^3\,{\mathrm {e}}^x-2\,x^2\,{\mathrm {e}}^4\,{\mathrm {e}}^x+200\,x^2\,{\mathrm {e}}^6\,{\mathrm {e}}^x+80\,x^2\,{\mathrm {e}}^7\,{\mathrm {e}}^x+8\,x^2\,{\mathrm {e}}^8\,{\mathrm {e}}^x+25\,x^2\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^6+10\,x^2\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^7+x^2\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^8}}\,{\mathrm {e}}^{\frac {50\,x^2\,{\mathrm {e}}^6}{400\,{\mathrm {e}}^6+160\,{\mathrm {e}}^7+16\,{\mathrm {e}}^8+40\,x\,{\mathrm {e}}^3+8\,x\,{\mathrm {e}}^4-800\,x\,{\mathrm {e}}^6-320\,x\,{\mathrm {e}}^7-32\,x\,{\mathrm {e}}^8-40\,x^2\,{\mathrm {e}}^3-8\,x^2\,{\mathrm {e}}^4+400\,x^2\,{\mathrm {e}}^6+160\,x^2\,{\mathrm {e}}^7+16\,x^2\,{\mathrm {e}}^8+x^2-200\,x\,{\mathrm {e}}^6\,{\mathrm {e}}^x-80\,x\,{\mathrm {e}}^7\,{\mathrm {e}}^x-8\,x\,{\mathrm {e}}^8\,{\mathrm {e}}^x-10\,x^2\,{\mathrm {e}}^3\,{\mathrm {e}}^x-2\,x^2\,{\mathrm {e}}^4\,{\mathrm {e}}^x+200\,x^2\,{\mathrm {e}}^6\,{\mathrm {e}}^x+80\,x^2\,{\mathrm {e}}^7\,{\mathrm {e}}^x+8\,x^2\,{\mathrm {e}}^8\,{\mathrm {e}}^x+25\,x^2\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^6+10\,x^2\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^7+x^2\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^8}} \]
[In]
[Out]