Integrand size = 239, antiderivative size = 33 \[ \int \frac {e^{e^{\frac {153-24 x+x^2-120 x^3+10 x^4+25 x^6+e^{10} \left (17-16 x+4 x^2\right )+e^5 \left (-102+56 x-4 x^2+40 x^3-20 x^4\right )}{9 x-6 e^5 x+e^{10} x}}+\frac {153-24 x+x^2-120 x^3+10 x^4+25 x^6+e^{10} \left (17-16 x+4 x^2\right )+e^5 \left (-102+56 x-4 x^2+40 x^3-20 x^4\right )}{9 x-6 e^5 x+e^{10} x}} \left (-153+x^2-240 x^3+30 x^4+125 x^6+e^{10} \left (-17+4 x^2\right )+e^5 \left (102-4 x^2+80 x^3-60 x^4\right )\right )}{9 x^2-6 e^5 x^2+e^{10} x^2} \, dx=e^{e^{\frac {1+\left (-4+2 x-\frac {5 \left (-x+x^3\right )}{-3+e^5}\right )^2}{x}}} \] Output:
exp(exp(((2*x-4-5*(x^3-x)/(exp(5)-3))^2+1)/x))
Leaf count is larger than twice the leaf count of optimal. \(77\) vs. \(2(33)=66\).
Time = 1.13 (sec) , antiderivative size = 77, normalized size of antiderivative = 2.33 \[ \int \frac {e^{e^{\frac {153-24 x+x^2-120 x^3+10 x^4+25 x^6+e^{10} \left (17-16 x+4 x^2\right )+e^5 \left (-102+56 x-4 x^2+40 x^3-20 x^4\right )}{9 x-6 e^5 x+e^{10} x}}+\frac {153-24 x+x^2-120 x^3+10 x^4+25 x^6+e^{10} \left (17-16 x+4 x^2\right )+e^5 \left (-102+56 x-4 x^2+40 x^3-20 x^4\right )}{9 x-6 e^5 x+e^{10} x}} \left (-153+x^2-240 x^3+30 x^4+125 x^6+e^{10} \left (-17+4 x^2\right )+e^5 \left (102-4 x^2+80 x^3-60 x^4\right )\right )}{9 x^2-6 e^5 x^2+e^{10} x^2} \, dx=e^{e^{\frac {153-24 x+x^2-120 x^3+10 x^4+25 x^6+e^{10} \left (17-16 x+4 x^2\right )-2 e^5 \left (51-28 x+2 x^2-20 x^3+10 x^4\right )}{\left (-3+e^5\right )^2 x}}} \] Input:
Integrate[(E^(E^((153 - 24*x + x^2 - 120*x^3 + 10*x^4 + 25*x^6 + E^10*(17 - 16*x + 4*x^2) + E^5*(-102 + 56*x - 4*x^2 + 40*x^3 - 20*x^4))/(9*x - 6*E^ 5*x + E^10*x)) + (153 - 24*x + x^2 - 120*x^3 + 10*x^4 + 25*x^6 + E^10*(17 - 16*x + 4*x^2) + E^5*(-102 + 56*x - 4*x^2 + 40*x^3 - 20*x^4))/(9*x - 6*E^ 5*x + E^10*x))*(-153 + x^2 - 240*x^3 + 30*x^4 + 125*x^6 + E^10*(-17 + 4*x^ 2) + E^5*(102 - 4*x^2 + 80*x^3 - 60*x^4)))/(9*x^2 - 6*E^5*x^2 + E^10*x^2), x]
Output:
E^E^((153 - 24*x + x^2 - 120*x^3 + 10*x^4 + 25*x^6 + E^10*(17 - 16*x + 4*x ^2) - 2*E^5*(51 - 28*x + 2*x^2 - 20*x^3 + 10*x^4))/((-3 + E^5)^2*x))
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {\left (125 x^6+30 x^4-240 x^3+x^2+e^{10} \left (4 x^2-17\right )+e^5 \left (-60 x^4+80 x^3-4 x^2+102\right )-153\right ) \exp \left (\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2+e^{10} \left (4 x^2-16 x+17\right )+e^5 \left (-20 x^4+40 x^3-4 x^2+56 x-102\right )-24 x+153}{e^{10} x-6 e^5 x+9 x}\right )+\frac {25 x^6+10 x^4-120 x^3+x^2+e^{10} \left (4 x^2-16 x+17\right )+e^5 \left (-20 x^4+40 x^3-4 x^2+56 x-102\right )-24 x+153}{e^{10} x-6 e^5 x+9 x}\right )}{e^{10} x^2-6 e^5 x^2+9 x^2} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {\left (125 x^6+30 x^4-240 x^3+x^2+e^{10} \left (4 x^2-17\right )+e^5 \left (-60 x^4+80 x^3-4 x^2+102\right )-153\right ) \exp \left (\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2+e^{10} \left (4 x^2-16 x+17\right )+e^5 \left (-20 x^4+40 x^3-4 x^2+56 x-102\right )-24 x+153}{e^{10} x-6 e^5 x+9 x}\right )+\frac {25 x^6+10 x^4-120 x^3+x^2+e^{10} \left (4 x^2-16 x+17\right )+e^5 \left (-20 x^4+40 x^3-4 x^2+56 x-102\right )-24 x+153}{e^{10} x-6 e^5 x+9 x}\right )}{\left (9-6 e^5\right ) x^2+e^{10} x^2}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {\left (125 x^6+30 x^4-240 x^3+x^2+e^{10} \left (4 x^2-17\right )+e^5 \left (-60 x^4+80 x^3-4 x^2+102\right )-153\right ) \exp \left (\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2+e^{10} \left (4 x^2-16 x+17\right )+e^5 \left (-20 x^4+40 x^3-4 x^2+56 x-102\right )-24 x+153}{e^{10} x-6 e^5 x+9 x}\right )+\frac {25 x^6+10 x^4-120 x^3+x^2+e^{10} \left (4 x^2-16 x+17\right )+e^5 \left (-20 x^4+40 x^3-4 x^2+56 x-102\right )-24 x+153}{e^{10} x-6 e^5 x+9 x}\right )}{\left (9-6 e^5+e^{10}\right ) x^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {\int -\frac {\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (3-e^5\right )^2 x}+\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (3-e^5\right )^2 x}\right )\right ) \left (-125 x^6-30 x^4+240 x^3-x^2+e^{10} \left (17-4 x^2\right )-2 e^5 \left (-30 x^4+40 x^3-2 x^2+51\right )+153\right )}{x^2}dx}{\left (3-e^5\right )^2}\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -\frac {\int \frac {\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (3-e^5\right )^2 x}+\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (3-e^5\right )^2 x}\right )\right ) \left (-125 x^6-30 x^4+240 x^3-x^2+e^{10} \left (17-4 x^2\right )-2 e^5 \left (-30 x^4+40 x^3-2 x^2+51\right )+153\right )}{x^2}dx}{\left (3-e^5\right )^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {\int \left (-125 e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (3-e^5\right )^2 x}+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (3-e^5\right )^2 x}}} x^4+30 e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (3-e^5\right )^2 x}+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (3-e^5\right )^2 x}}} \left (-1+2 e^5\right ) x^2-80 e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (3-e^5\right )^2 x}+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (3-e^5\right )^2 x}}} \left (-3+e^5\right ) x-e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (3-e^5\right )^2 x}+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (3-e^5\right )^2 x}}} \left (-1+2 e^5\right )^2+\frac {17 e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (3-e^5\right )^2 x}+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (3-e^5\right )^2 x}}} \left (-3+e^5\right )^2}{x^2}\right )dx}{\left (3-e^5\right )^2}\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {\int \frac {\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2+\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}\right ) \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}\right ) \left (-125 x^6-30 x^4+240 x^3-x^2-e^{10} \left (4 x^2-17\right )-e^5 \left (-60 x^4+80 x^3-4 x^2+102\right )+153\right )}{x^2}dx}{\left (3-e^5\right )^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {\int \left (-125 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} x^4+30 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-1+2 e^5\right ) x^2-80 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right ) x-e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-1+2 e^5\right )^2+\frac {17 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2}{x^2}\right )dx}{\left (3-e^5\right )^2}\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {\int \frac {\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2+\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}\right ) \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}\right ) \left (-125 x^6-30 x^4+240 x^3-x^2-e^{10} \left (4 x^2-17\right )-e^5 \left (-60 x^4+80 x^3-4 x^2+102\right )+153\right )}{x^2}dx}{\left (3-e^5\right )^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {\int \left (-125 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} x^4+30 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-1+2 e^5\right ) x^2-80 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right ) x-e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-1+2 e^5\right )^2+\frac {17 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2}{x^2}\right )dx}{\left (3-e^5\right )^2}\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {\int \frac {\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2+\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}\right ) \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}\right ) \left (-125 x^6-30 x^4+240 x^3-x^2-e^{10} \left (4 x^2-17\right )-e^5 \left (-60 x^4+80 x^3-4 x^2+102\right )+153\right )}{x^2}dx}{\left (3-e^5\right )^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {\int \left (-125 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} x^4+30 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-1+2 e^5\right ) x^2-80 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right ) x-e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-1+2 e^5\right )^2+\frac {17 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2}{x^2}\right )dx}{\left (3-e^5\right )^2}\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {\int \frac {\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2+\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}\right ) \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}\right ) \left (-125 x^6-30 x^4+240 x^3-x^2-e^{10} \left (4 x^2-17\right )-e^5 \left (-60 x^4+80 x^3-4 x^2+102\right )+153\right )}{x^2}dx}{\left (3-e^5\right )^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {\int \left (-125 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} x^4+30 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-1+2 e^5\right ) x^2-80 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right ) x-e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-1+2 e^5\right )^2+\frac {17 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2}{x^2}\right )dx}{\left (3-e^5\right )^2}\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {\int \frac {\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2+\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}\right ) \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}\right ) \left (-125 x^6-30 x^4+240 x^3-x^2-e^{10} \left (4 x^2-17\right )-e^5 \left (-60 x^4+80 x^3-4 x^2+102\right )+153\right )}{x^2}dx}{\left (3-e^5\right )^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {\int \left (-125 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} x^4+30 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-1+2 e^5\right ) x^2-80 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right ) x-e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-1+2 e^5\right )^2+\frac {17 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2}{x^2}\right )dx}{\left (3-e^5\right )^2}\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {\int \frac {\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2+\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}\right ) \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}\right ) \left (-125 x^6-30 x^4+240 x^3-x^2-e^{10} \left (4 x^2-17\right )-e^5 \left (-60 x^4+80 x^3-4 x^2+102\right )+153\right )}{x^2}dx}{\left (3-e^5\right )^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {\int \left (-125 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} x^4+30 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-1+2 e^5\right ) x^2-80 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right ) x-e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-1+2 e^5\right )^2+\frac {17 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2}{x^2}\right )dx}{\left (3-e^5\right )^2}\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {\int \frac {\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2+\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}\right ) \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}\right ) \left (-125 x^6-30 x^4+240 x^3-x^2-e^{10} \left (4 x^2-17\right )-e^5 \left (-60 x^4+80 x^3-4 x^2+102\right )+153\right )}{x^2}dx}{\left (3-e^5\right )^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {\int \left (-125 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} x^4+30 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-1+2 e^5\right ) x^2-80 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right ) x-e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-1+2 e^5\right )^2+\frac {17 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2}{x^2}\right )dx}{\left (3-e^5\right )^2}\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {\int \frac {\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2+\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}\right ) \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}\right ) \left (-125 x^6-30 x^4+240 x^3-x^2-e^{10} \left (4 x^2-17\right )-e^5 \left (-60 x^4+80 x^3-4 x^2+102\right )+153\right )}{x^2}dx}{\left (3-e^5\right )^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {\int \left (-125 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} x^4+30 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-1+2 e^5\right ) x^2-80 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right ) x-e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-1+2 e^5\right )^2+\frac {17 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2}{x^2}\right )dx}{\left (3-e^5\right )^2}\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {\int \frac {\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2+\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}\right ) \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}\right ) \left (-125 x^6-30 x^4+240 x^3-x^2-e^{10} \left (4 x^2-17\right )-e^5 \left (-60 x^4+80 x^3-4 x^2+102\right )+153\right )}{x^2}dx}{\left (3-e^5\right )^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {\int \left (-125 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} x^4+30 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-1+2 e^5\right ) x^2-80 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right ) x-e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-1+2 e^5\right )^2+\frac {17 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2}{x^2}\right )dx}{\left (3-e^5\right )^2}\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {\int \frac {\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2+\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}\right ) \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}\right ) \left (-125 x^6-30 x^4+240 x^3-x^2-e^{10} \left (4 x^2-17\right )-e^5 \left (-60 x^4+80 x^3-4 x^2+102\right )+153\right )}{x^2}dx}{\left (3-e^5\right )^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {\int \left (-125 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} x^4+30 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-1+2 e^5\right ) x^2-80 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right ) x-e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-1+2 e^5\right )^2+\frac {17 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2}{x^2}\right )dx}{\left (3-e^5\right )^2}\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {\int \frac {\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2+\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}\right ) \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}\right ) \left (-125 x^6-30 x^4+240 x^3-x^2-e^{10} \left (4 x^2-17\right )-e^5 \left (-60 x^4+80 x^3-4 x^2+102\right )+153\right )}{x^2}dx}{\left (3-e^5\right )^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {\int \left (-125 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} x^4+30 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-1+2 e^5\right ) x^2-80 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right ) x-e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-1+2 e^5\right )^2+\frac {17 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2}{x^2}\right )dx}{\left (3-e^5\right )^2}\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {\int \frac {\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2+\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}\right ) \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}\right ) \left (-125 x^6-30 x^4+240 x^3-x^2-e^{10} \left (4 x^2-17\right )-e^5 \left (-60 x^4+80 x^3-4 x^2+102\right )+153\right )}{x^2}dx}{\left (3-e^5\right )^2}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {\int \left (-125 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} x^4+30 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-1+2 e^5\right ) x^2-80 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right ) x-e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-1+2 e^5\right )^2+\frac {17 e^{\frac {25 x^6+10 x^4-120 x^3+x^2+e^{\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}} \left (-3+e^5\right )^2}{x^2}\right )dx}{\left (3-e^5\right )^2}\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {\int \frac {\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2+\exp \left (\frac {25 x^6+10 x^4-120 x^3+x^2-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}\right ) \left (-3+e^5\right )^2 x-24 x+e^{10} \left (4 x^2-16 x+17\right )-2 e^5 \left (10 x^4-20 x^3+2 x^2-28 x+51\right )+153}{\left (-3+e^5\right )^2 x}\right ) \left (-125 x^6-30 x^4+240 x^3-x^2-e^{10} \left (4 x^2-17\right )-e^5 \left (-60 x^4+80 x^3-4 x^2+102\right )+153\right )}{x^2}dx}{\left (3-e^5\right )^2}\) |
Input:
Int[(E^(E^((153 - 24*x + x^2 - 120*x^3 + 10*x^4 + 25*x^6 + E^10*(17 - 16*x + 4*x^2) + E^5*(-102 + 56*x - 4*x^2 + 40*x^3 - 20*x^4))/(9*x - 6*E^5*x + E^10*x)) + (153 - 24*x + x^2 - 120*x^3 + 10*x^4 + 25*x^6 + E^10*(17 - 16*x + 4*x^2) + E^5*(-102 + 56*x - 4*x^2 + 40*x^3 - 20*x^4))/(9*x - 6*E^5*x + E^10*x))*(-153 + x^2 - 240*x^3 + 30*x^4 + 125*x^6 + E^10*(-17 + 4*x^2) + E ^5*(102 - 4*x^2 + 80*x^3 - 60*x^4)))/(9*x^2 - 6*E^5*x^2 + E^10*x^2),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(81\) vs. \(2(30)=60\).
Time = 39.51 (sec) , antiderivative size = 82, normalized size of antiderivative = 2.48
| method | result | size |
| norman | \({\mathrm e}^{{\mathrm e}^{\frac {\left (4 x^{2}-16 x +17\right ) {\mathrm e}^{10}+\left (-20 x^{4}+40 x^{3}-4 x^{2}+56 x -102\right ) {\mathrm e}^{5}+25 x^{6}+10 x^{4}-120 x^{3}+x^{2}-24 x +153}{x \,{\mathrm e}^{10}-6 x \,{\mathrm e}^{5}+9 x}}}\) | \(82\) |
| risch | \({\mathrm e}^{{\mathrm e}^{\frac {4 x^{2} {\mathrm e}^{10}-16 x \,{\mathrm e}^{10}+17 \,{\mathrm e}^{10}-20 x^{4} {\mathrm e}^{5}+40 x^{3} {\mathrm e}^{5}-4 x^{2} {\mathrm e}^{5}+56 x \,{\mathrm e}^{5}-102 \,{\mathrm e}^{5}+25 x^{6}+10 x^{4}-120 x^{3}+x^{2}-24 x +153}{x \left ({\mathrm e}^{10}-6 \,{\mathrm e}^{5}+9\right )}}}\) | \(86\) |
| parallelrisch | \(\frac {{\mathrm e}^{10} {\mathrm e}^{{\mathrm e}^{\frac {\left (4 x^{2}-16 x +17\right ) {\mathrm e}^{10}+\left (-20 x^{4}+40 x^{3}-4 x^{2}+56 x -102\right ) {\mathrm e}^{5}+25 x^{6}+10 x^{4}-120 x^{3}+x^{2}-24 x +153}{x \left ({\mathrm e}^{10}-6 \,{\mathrm e}^{5}+9\right )}}}-6 \,{\mathrm e}^{5} {\mathrm e}^{{\mathrm e}^{\frac {\left (4 x^{2}-16 x +17\right ) {\mathrm e}^{10}+\left (-20 x^{4}+40 x^{3}-4 x^{2}+56 x -102\right ) {\mathrm e}^{5}+25 x^{6}+10 x^{4}-120 x^{3}+x^{2}-24 x +153}{x \left ({\mathrm e}^{10}-6 \,{\mathrm e}^{5}+9\right )}}}+9 \,{\mathrm e}^{{\mathrm e}^{\frac {\left (4 x^{2}-16 x +17\right ) {\mathrm e}^{10}+\left (-20 x^{4}+40 x^{3}-4 x^{2}+56 x -102\right ) {\mathrm e}^{5}+25 x^{6}+10 x^{4}-120 x^{3}+x^{2}-24 x +153}{x \left ({\mathrm e}^{10}-6 \,{\mathrm e}^{5}+9\right )}}}}{{\mathrm e}^{10}-6 \,{\mathrm e}^{5}+9}\) | \(263\) |
Input:
int(((4*x^2-17)*exp(5)^2+(-60*x^4+80*x^3-4*x^2+102)*exp(5)+125*x^6+30*x^4- 240*x^3+x^2-153)*exp(((4*x^2-16*x+17)*exp(5)^2+(-20*x^4+40*x^3-4*x^2+56*x- 102)*exp(5)+25*x^6+10*x^4-120*x^3+x^2-24*x+153)/(x*exp(5)^2-6*x*exp(5)+9*x ))*exp(exp(((4*x^2-16*x+17)*exp(5)^2+(-20*x^4+40*x^3-4*x^2+56*x-102)*exp(5 )+25*x^6+10*x^4-120*x^3+x^2-24*x+153)/(x*exp(5)^2-6*x*exp(5)+9*x)))/(x^2*e xp(5)^2-6*x^2*exp(5)+9*x^2),x,method=_RETURNVERBOSE)
Output:
exp(exp(((4*x^2-16*x+17)*exp(5)^2+(-20*x^4+40*x^3-4*x^2+56*x-102)*exp(5)+2 5*x^6+10*x^4-120*x^3+x^2-24*x+153)/(x*exp(5)^2-6*x*exp(5)+9*x)))
Leaf count of result is larger than twice the leaf count of optimal. 246 vs. \(2 (30) = 60\).
Time = 0.11 (sec) , antiderivative size = 246, normalized size of antiderivative = 7.45 \[ \int \frac {e^{e^{\frac {153-24 x+x^2-120 x^3+10 x^4+25 x^6+e^{10} \left (17-16 x+4 x^2\right )+e^5 \left (-102+56 x-4 x^2+40 x^3-20 x^4\right )}{9 x-6 e^5 x+e^{10} x}}+\frac {153-24 x+x^2-120 x^3+10 x^4+25 x^6+e^{10} \left (17-16 x+4 x^2\right )+e^5 \left (-102+56 x-4 x^2+40 x^3-20 x^4\right )}{9 x-6 e^5 x+e^{10} x}} \left (-153+x^2-240 x^3+30 x^4+125 x^6+e^{10} \left (-17+4 x^2\right )+e^5 \left (102-4 x^2+80 x^3-60 x^4\right )\right )}{9 x^2-6 e^5 x^2+e^{10} x^2} \, dx=e^{\left (\frac {25 \, x^{6} + 10 \, x^{4} - 120 \, x^{3} + x^{2} + {\left (4 \, x^{2} - 16 \, x + 17\right )} e^{10} - 2 \, {\left (10 \, x^{4} - 20 \, x^{3} + 2 \, x^{2} - 28 \, x + 51\right )} e^{5} + {\left (x e^{10} - 6 \, x e^{5} + 9 \, x\right )} e^{\left (\frac {25 \, x^{6} + 10 \, x^{4} - 120 \, x^{3} + x^{2} + {\left (4 \, x^{2} - 16 \, x + 17\right )} e^{10} - 2 \, {\left (10 \, x^{4} - 20 \, x^{3} + 2 \, x^{2} - 28 \, x + 51\right )} e^{5} - 24 \, x + 153}{x e^{10} - 6 \, x e^{5} + 9 \, x}\right )} - 24 \, x + 153}{x e^{10} - 6 \, x e^{5} + 9 \, x} - \frac {25 \, x^{6} + 10 \, x^{4} - 120 \, x^{3} + x^{2} + {\left (4 \, x^{2} - 16 \, x + 17\right )} e^{10} - 2 \, {\left (10 \, x^{4} - 20 \, x^{3} + 2 \, x^{2} - 28 \, x + 51\right )} e^{5} - 24 \, x + 153}{x e^{10} - 6 \, x e^{5} + 9 \, x}\right )} \] Input:
integrate(((4*x^2-17)*exp(5)^2+(-60*x^4+80*x^3-4*x^2+102)*exp(5)+125*x^6+3 0*x^4-240*x^3+x^2-153)*exp(((4*x^2-16*x+17)*exp(5)^2+(-20*x^4+40*x^3-4*x^2 +56*x-102)*exp(5)+25*x^6+10*x^4-120*x^3+x^2-24*x+153)/(x*exp(5)^2-6*x*exp( 5)+9*x))*exp(exp(((4*x^2-16*x+17)*exp(5)^2+(-20*x^4+40*x^3-4*x^2+56*x-102) *exp(5)+25*x^6+10*x^4-120*x^3+x^2-24*x+153)/(x*exp(5)^2-6*x*exp(5)+9*x)))/ (x^2*exp(5)^2-6*x^2*exp(5)+9*x^2),x, algorithm="fricas")
Output:
e^((25*x^6 + 10*x^4 - 120*x^3 + x^2 + (4*x^2 - 16*x + 17)*e^10 - 2*(10*x^4 - 20*x^3 + 2*x^2 - 28*x + 51)*e^5 + (x*e^10 - 6*x*e^5 + 9*x)*e^((25*x^6 + 10*x^4 - 120*x^3 + x^2 + (4*x^2 - 16*x + 17)*e^10 - 2*(10*x^4 - 20*x^3 + 2*x^2 - 28*x + 51)*e^5 - 24*x + 153)/(x*e^10 - 6*x*e^5 + 9*x)) - 24*x + 15 3)/(x*e^10 - 6*x*e^5 + 9*x) - (25*x^6 + 10*x^4 - 120*x^3 + x^2 + (4*x^2 - 16*x + 17)*e^10 - 2*(10*x^4 - 20*x^3 + 2*x^2 - 28*x + 51)*e^5 - 24*x + 153 )/(x*e^10 - 6*x*e^5 + 9*x))
Leaf count of result is larger than twice the leaf count of optimal. 78 vs. \(2 (26) = 52\).
Time = 0.61 (sec) , antiderivative size = 78, normalized size of antiderivative = 2.36 \[ \int \frac {e^{e^{\frac {153-24 x+x^2-120 x^3+10 x^4+25 x^6+e^{10} \left (17-16 x+4 x^2\right )+e^5 \left (-102+56 x-4 x^2+40 x^3-20 x^4\right )}{9 x-6 e^5 x+e^{10} x}}+\frac {153-24 x+x^2-120 x^3+10 x^4+25 x^6+e^{10} \left (17-16 x+4 x^2\right )+e^5 \left (-102+56 x-4 x^2+40 x^3-20 x^4\right )}{9 x-6 e^5 x+e^{10} x}} \left (-153+x^2-240 x^3+30 x^4+125 x^6+e^{10} \left (-17+4 x^2\right )+e^5 \left (102-4 x^2+80 x^3-60 x^4\right )\right )}{9 x^2-6 e^5 x^2+e^{10} x^2} \, dx=e^{e^{\frac {25 x^{6} + 10 x^{4} - 120 x^{3} + x^{2} - 24 x + \left (4 x^{2} - 16 x + 17\right ) e^{10} + \left (- 20 x^{4} + 40 x^{3} - 4 x^{2} + 56 x - 102\right ) e^{5} + 153}{- 6 x e^{5} + 9 x + x e^{10}}}} \] Input:
integrate(((4*x**2-17)*exp(5)**2+(-60*x**4+80*x**3-4*x**2+102)*exp(5)+125* x**6+30*x**4-240*x**3+x**2-153)*exp(((4*x**2-16*x+17)*exp(5)**2+(-20*x**4+ 40*x**3-4*x**2+56*x-102)*exp(5)+25*x**6+10*x**4-120*x**3+x**2-24*x+153)/(x *exp(5)**2-6*x*exp(5)+9*x))*exp(exp(((4*x**2-16*x+17)*exp(5)**2+(-20*x**4+ 40*x**3-4*x**2+56*x-102)*exp(5)+25*x**6+10*x**4-120*x**3+x**2-24*x+153)/(x *exp(5)**2-6*x*exp(5)+9*x)))/(x**2*exp(5)**2-6*x**2*exp(5)+9*x**2),x)
Output:
exp(exp((25*x**6 + 10*x**4 - 120*x**3 + x**2 - 24*x + (4*x**2 - 16*x + 17) *exp(10) + (-20*x**4 + 40*x**3 - 4*x**2 + 56*x - 102)*exp(5) + 153)/(-6*x* exp(5) + 9*x + x*exp(10))))
Leaf count of result is larger than twice the leaf count of optimal. 213 vs. \(2 (30) = 60\).
Time = 1.93 (sec) , antiderivative size = 213, normalized size of antiderivative = 6.45 \[ \int \frac {e^{e^{\frac {153-24 x+x^2-120 x^3+10 x^4+25 x^6+e^{10} \left (17-16 x+4 x^2\right )+e^5 \left (-102+56 x-4 x^2+40 x^3-20 x^4\right )}{9 x-6 e^5 x+e^{10} x}}+\frac {153-24 x+x^2-120 x^3+10 x^4+25 x^6+e^{10} \left (17-16 x+4 x^2\right )+e^5 \left (-102+56 x-4 x^2+40 x^3-20 x^4\right )}{9 x-6 e^5 x+e^{10} x}} \left (-153+x^2-240 x^3+30 x^4+125 x^6+e^{10} \left (-17+4 x^2\right )+e^5 \left (102-4 x^2+80 x^3-60 x^4\right )\right )}{9 x^2-6 e^5 x^2+e^{10} x^2} \, dx=e^{\left (e^{\left (\frac {25 \, x^{5}}{e^{10} - 6 \, e^{5} + 9} - \frac {20 \, x^{3} e^{5}}{e^{10} - 6 \, e^{5} + 9} + \frac {10 \, x^{3}}{e^{10} - 6 \, e^{5} + 9} + \frac {40 \, x^{2} e^{5}}{e^{10} - 6 \, e^{5} + 9} - \frac {120 \, x^{2}}{e^{10} - 6 \, e^{5} + 9} + \frac {4 \, x e^{10}}{e^{10} - 6 \, e^{5} + 9} - \frac {4 \, x e^{5}}{e^{10} - 6 \, e^{5} + 9} + \frac {x}{e^{10} - 6 \, e^{5} + 9} - \frac {16 \, e^{10}}{e^{10} - 6 \, e^{5} + 9} + \frac {56 \, e^{5}}{e^{10} - 6 \, e^{5} + 9} - \frac {24}{e^{10} - 6 \, e^{5} + 9} + \frac {17 \, e^{10}}{x {\left (e^{10} - 6 \, e^{5} + 9\right )}} - \frac {102 \, e^{5}}{x {\left (e^{10} - 6 \, e^{5} + 9\right )}} + \frac {153}{x {\left (e^{10} - 6 \, e^{5} + 9\right )}}\right )}\right )} \] Input:
integrate(((4*x^2-17)*exp(5)^2+(-60*x^4+80*x^3-4*x^2+102)*exp(5)+125*x^6+3 0*x^4-240*x^3+x^2-153)*exp(((4*x^2-16*x+17)*exp(5)^2+(-20*x^4+40*x^3-4*x^2 +56*x-102)*exp(5)+25*x^6+10*x^4-120*x^3+x^2-24*x+153)/(x*exp(5)^2-6*x*exp( 5)+9*x))*exp(exp(((4*x^2-16*x+17)*exp(5)^2+(-20*x^4+40*x^3-4*x^2+56*x-102) *exp(5)+25*x^6+10*x^4-120*x^3+x^2-24*x+153)/(x*exp(5)^2-6*x*exp(5)+9*x)))/ (x^2*exp(5)^2-6*x^2*exp(5)+9*x^2),x, algorithm="maxima")
Output:
e^(e^(25*x^5/(e^10 - 6*e^5 + 9) - 20*x^3*e^5/(e^10 - 6*e^5 + 9) + 10*x^3/( e^10 - 6*e^5 + 9) + 40*x^2*e^5/(e^10 - 6*e^5 + 9) - 120*x^2/(e^10 - 6*e^5 + 9) + 4*x*e^10/(e^10 - 6*e^5 + 9) - 4*x*e^5/(e^10 - 6*e^5 + 9) + x/(e^10 - 6*e^5 + 9) - 16*e^10/(e^10 - 6*e^5 + 9) + 56*e^5/(e^10 - 6*e^5 + 9) - 24 /(e^10 - 6*e^5 + 9) + 17*e^10/(x*(e^10 - 6*e^5 + 9)) - 102*e^5/(x*(e^10 - 6*e^5 + 9)) + 153/(x*(e^10 - 6*e^5 + 9))))
\[ \int \frac {e^{e^{\frac {153-24 x+x^2-120 x^3+10 x^4+25 x^6+e^{10} \left (17-16 x+4 x^2\right )+e^5 \left (-102+56 x-4 x^2+40 x^3-20 x^4\right )}{9 x-6 e^5 x+e^{10} x}}+\frac {153-24 x+x^2-120 x^3+10 x^4+25 x^6+e^{10} \left (17-16 x+4 x^2\right )+e^5 \left (-102+56 x-4 x^2+40 x^3-20 x^4\right )}{9 x-6 e^5 x+e^{10} x}} \left (-153+x^2-240 x^3+30 x^4+125 x^6+e^{10} \left (-17+4 x^2\right )+e^5 \left (102-4 x^2+80 x^3-60 x^4\right )\right )}{9 x^2-6 e^5 x^2+e^{10} x^2} \, dx=\int { \frac {{\left (125 \, x^{6} + 30 \, x^{4} - 240 \, x^{3} + x^{2} + {\left (4 \, x^{2} - 17\right )} e^{10} - 2 \, {\left (30 \, x^{4} - 40 \, x^{3} + 2 \, x^{2} - 51\right )} e^{5} - 153\right )} e^{\left (\frac {25 \, x^{6} + 10 \, x^{4} - 120 \, x^{3} + x^{2} + {\left (4 \, x^{2} - 16 \, x + 17\right )} e^{10} - 2 \, {\left (10 \, x^{4} - 20 \, x^{3} + 2 \, x^{2} - 28 \, x + 51\right )} e^{5} - 24 \, x + 153}{x e^{10} - 6 \, x e^{5} + 9 \, x} + e^{\left (\frac {25 \, x^{6} + 10 \, x^{4} - 120 \, x^{3} + x^{2} + {\left (4 \, x^{2} - 16 \, x + 17\right )} e^{10} - 2 \, {\left (10 \, x^{4} - 20 \, x^{3} + 2 \, x^{2} - 28 \, x + 51\right )} e^{5} - 24 \, x + 153}{x e^{10} - 6 \, x e^{5} + 9 \, x}\right )}\right )}}{x^{2} e^{10} - 6 \, x^{2} e^{5} + 9 \, x^{2}} \,d x } \] Input:
integrate(((4*x^2-17)*exp(5)^2+(-60*x^4+80*x^3-4*x^2+102)*exp(5)+125*x^6+3 0*x^4-240*x^3+x^2-153)*exp(((4*x^2-16*x+17)*exp(5)^2+(-20*x^4+40*x^3-4*x^2 +56*x-102)*exp(5)+25*x^6+10*x^4-120*x^3+x^2-24*x+153)/(x*exp(5)^2-6*x*exp( 5)+9*x))*exp(exp(((4*x^2-16*x+17)*exp(5)^2+(-20*x^4+40*x^3-4*x^2+56*x-102) *exp(5)+25*x^6+10*x^4-120*x^3+x^2-24*x+153)/(x*exp(5)^2-6*x*exp(5)+9*x)))/ (x^2*exp(5)^2-6*x^2*exp(5)+9*x^2),x, algorithm="giac")
Output:
integrate((125*x^6 + 30*x^4 - 240*x^3 + x^2 + (4*x^2 - 17)*e^10 - 2*(30*x^ 4 - 40*x^3 + 2*x^2 - 51)*e^5 - 153)*e^((25*x^6 + 10*x^4 - 120*x^3 + x^2 + (4*x^2 - 16*x + 17)*e^10 - 2*(10*x^4 - 20*x^3 + 2*x^2 - 28*x + 51)*e^5 - 2 4*x + 153)/(x*e^10 - 6*x*e^5 + 9*x) + e^((25*x^6 + 10*x^4 - 120*x^3 + x^2 + (4*x^2 - 16*x + 17)*e^10 - 2*(10*x^4 - 20*x^3 + 2*x^2 - 28*x + 51)*e^5 - 24*x + 153)/(x*e^10 - 6*x*e^5 + 9*x)))/(x^2*e^10 - 6*x^2*e^5 + 9*x^2), x)
Time = 3.53 (sec) , antiderivative size = 232, normalized size of antiderivative = 7.03 \[ \int \frac {e^{e^{\frac {153-24 x+x^2-120 x^3+10 x^4+25 x^6+e^{10} \left (17-16 x+4 x^2\right )+e^5 \left (-102+56 x-4 x^2+40 x^3-20 x^4\right )}{9 x-6 e^5 x+e^{10} x}}+\frac {153-24 x+x^2-120 x^3+10 x^4+25 x^6+e^{10} \left (17-16 x+4 x^2\right )+e^5 \left (-102+56 x-4 x^2+40 x^3-20 x^4\right )}{9 x-6 e^5 x+e^{10} x}} \left (-153+x^2-240 x^3+30 x^4+125 x^6+e^{10} \left (-17+4 x^2\right )+e^5 \left (102-4 x^2+80 x^3-60 x^4\right )\right )}{9 x^2-6 e^5 x^2+e^{10} x^2} \, dx={\mathrm {e}}^{{\mathrm {e}}^{-\frac {16\,{\mathrm {e}}^{10}}{{\mathrm {e}}^{10}-6\,{\mathrm {e}}^5+9}}\,{\mathrm {e}}^{\frac {56\,{\mathrm {e}}^5}{{\mathrm {e}}^{10}-6\,{\mathrm {e}}^5+9}}\,{\mathrm {e}}^{\frac {x}{{\mathrm {e}}^{10}-6\,{\mathrm {e}}^5+9}}\,{\mathrm {e}}^{\frac {17\,{\mathrm {e}}^{10}}{9\,x-6\,x\,{\mathrm {e}}^5+x\,{\mathrm {e}}^{10}}}\,{\mathrm {e}}^{-\frac {102\,{\mathrm {e}}^5}{9\,x-6\,x\,{\mathrm {e}}^5+x\,{\mathrm {e}}^{10}}}\,{\mathrm {e}}^{\frac {10\,x^3}{{\mathrm {e}}^{10}-6\,{\mathrm {e}}^5+9}}\,{\mathrm {e}}^{\frac {25\,x^5}{{\mathrm {e}}^{10}-6\,{\mathrm {e}}^5+9}}\,{\mathrm {e}}^{-\frac {120\,x^2}{{\mathrm {e}}^{10}-6\,{\mathrm {e}}^5+9}}\,{\mathrm {e}}^{-\frac {4\,x\,{\mathrm {e}}^5}{{\mathrm {e}}^{10}-6\,{\mathrm {e}}^5+9}}\,{\mathrm {e}}^{\frac {4\,x\,{\mathrm {e}}^{10}}{{\mathrm {e}}^{10}-6\,{\mathrm {e}}^5+9}}\,{\mathrm {e}}^{-\frac {24}{{\mathrm {e}}^{10}-6\,{\mathrm {e}}^5+9}}\,{\mathrm {e}}^{\frac {153}{9\,x-6\,x\,{\mathrm {e}}^5+x\,{\mathrm {e}}^{10}}}\,{\mathrm {e}}^{-\frac {20\,x^3\,{\mathrm {e}}^5}{{\mathrm {e}}^{10}-6\,{\mathrm {e}}^5+9}}\,{\mathrm {e}}^{\frac {40\,x^2\,{\mathrm {e}}^5}{{\mathrm {e}}^{10}-6\,{\mathrm {e}}^5+9}}} \] Input:
int((exp((exp(10)*(4*x^2 - 16*x + 17) - 24*x - exp(5)*(4*x^2 - 56*x - 40*x ^3 + 20*x^4 + 102) + x^2 - 120*x^3 + 10*x^4 + 25*x^6 + 153)/(9*x - 6*x*exp (5) + x*exp(10)))*exp(exp((exp(10)*(4*x^2 - 16*x + 17) - 24*x - exp(5)*(4* x^2 - 56*x - 40*x^3 + 20*x^4 + 102) + x^2 - 120*x^3 + 10*x^4 + 25*x^6 + 15 3)/(9*x - 6*x*exp(5) + x*exp(10))))*(exp(10)*(4*x^2 - 17) - exp(5)*(4*x^2 - 80*x^3 + 60*x^4 - 102) + x^2 - 240*x^3 + 30*x^4 + 125*x^6 - 153))/(x^2*e xp(10) - 6*x^2*exp(5) + 9*x^2),x)
Output:
exp(exp(-(16*exp(10))/(exp(10) - 6*exp(5) + 9))*exp((56*exp(5))/(exp(10) - 6*exp(5) + 9))*exp(x/(exp(10) - 6*exp(5) + 9))*exp((17*exp(10))/(9*x - 6* x*exp(5) + x*exp(10)))*exp(-(102*exp(5))/(9*x - 6*x*exp(5) + x*exp(10)))*e xp((10*x^3)/(exp(10) - 6*exp(5) + 9))*exp((25*x^5)/(exp(10) - 6*exp(5) + 9 ))*exp(-(120*x^2)/(exp(10) - 6*exp(5) + 9))*exp(-(4*x*exp(5))/(exp(10) - 6 *exp(5) + 9))*exp((4*x*exp(10))/(exp(10) - 6*exp(5) + 9))*exp(-24/(exp(10) - 6*exp(5) + 9))*exp(153/(9*x - 6*x*exp(5) + x*exp(10)))*exp(-(20*x^3*exp (5))/(exp(10) - 6*exp(5) + 9))*exp((40*x^2*exp(5))/(exp(10) - 6*exp(5) + 9 )))
\[ \int \frac {e^{e^{\frac {153-24 x+x^2-120 x^3+10 x^4+25 x^6+e^{10} \left (17-16 x+4 x^2\right )+e^5 \left (-102+56 x-4 x^2+40 x^3-20 x^4\right )}{9 x-6 e^5 x+e^{10} x}}+\frac {153-24 x+x^2-120 x^3+10 x^4+25 x^6+e^{10} \left (17-16 x+4 x^2\right )+e^5 \left (-102+56 x-4 x^2+40 x^3-20 x^4\right )}{9 x-6 e^5 x+e^{10} x}} \left (-153+x^2-240 x^3+30 x^4+125 x^6+e^{10} \left (-17+4 x^2\right )+e^5 \left (102-4 x^2+80 x^3-60 x^4\right )\right )}{9 x^2-6 e^5 x^2+e^{10} x^2} \, dx=\text {too large to display} \] Input:
int(((4*x^2-17)*exp(5)^2+(-60*x^4+80*x^3-4*x^2+102)*exp(5)+125*x^6+30*x^4- 240*x^3+x^2-153)*exp(((4*x^2-16*x+17)*exp(5)^2+(-20*x^4+40*x^3-4*x^2+56*x- 102)*exp(5)+25*x^6+10*x^4-120*x^3+x^2-24*x+153)/(x*exp(5)^2-6*x*exp(5)+9*x ))*exp(exp(((4*x^2-16*x+17)*exp(5)^2+(-20*x^4+40*x^3-4*x^2+56*x-102)*exp(5 )+25*x^6+10*x^4-120*x^3+x^2-24*x+153)/(x*exp(5)^2-6*x*exp(5)+9*x)))/(x^2*e xp(5)^2-6*x^2*exp(5)+9*x^2),x)
Output:
(4*int(e**((e**((4*e**10*x**2 + 17*e**10 + 40*e**5*x**3 - 4*e**5*x**2 + 25 *x**6 + 10*x**4 + 36*x**2 + 120*x + 153)/(e**10*x - 6*e**5*x + 9*x))*e**10 *x + 9*e**((4*e**10*x**2 + 17*e**10 + 40*e**5*x**3 - 4*e**5*x**2 + 25*x**6 + 10*x**4 + 36*x**2 + 120*x + 153)/(e**10*x - 6*e**5*x + 9*x))*x + 4*e**( (20*e**5*x**4 + 40*e**5*x + 102*e**5 + 120*x**3 + 35*x**2)/(e**10*x - 6*e* *5*x + 9*x))*e**26*x**2 + 17*e**((20*e**5*x**4 + 40*e**5*x + 102*e**5 + 12 0*x**3 + 35*x**2)/(e**10*x - 6*e**5*x + 9*x))*e**26 + 40*e**((20*e**5*x**4 + 40*e**5*x + 102*e**5 + 120*x**3 + 35*x**2)/(e**10*x - 6*e**5*x + 9*x))* e**21*x**3 - 4*e**((20*e**5*x**4 + 40*e**5*x + 102*e**5 + 120*x**3 + 35*x* *2)/(e**10*x - 6*e**5*x + 9*x))*e**21*x**2 + 25*e**((20*e**5*x**4 + 40*e** 5*x + 102*e**5 + 120*x**3 + 35*x**2)/(e**10*x - 6*e**5*x + 9*x))*e**16*x** 6 + 10*e**((20*e**5*x**4 + 40*e**5*x + 102*e**5 + 120*x**3 + 35*x**2)/(e** 10*x - 6*e**5*x + 9*x))*e**16*x**4 + 36*e**((20*e**5*x**4 + 40*e**5*x + 10 2*e**5 + 120*x**3 + 35*x**2)/(e**10*x - 6*e**5*x + 9*x))*e**16*x**2 + 120* e**((20*e**5*x**4 + 40*e**5*x + 102*e**5 + 120*x**3 + 35*x**2)/(e**10*x - 6*e**5*x + 9*x))*e**16*x + 153*e**((20*e**5*x**4 + 40*e**5*x + 102*e**5 + 120*x**3 + 35*x**2)/(e**10*x - 6*e**5*x + 9*x))*e**16)/(e**((20*e**5*x**4 + 40*e**5*x + 102*e**5 + 120*x**3 + 35*x**2)/(e**10*x - 6*e**5*x + 9*x))*e **26*x - 6*e**((20*e**5*x**4 + 40*e**5*x + 102*e**5 + 120*x**3 + 35*x**2)/ (e**10*x - 6*e**5*x + 9*x))*e**21*x + 9*e**((20*e**5*x**4 + 40*e**5*x +...