Integrand size = 163, antiderivative size = 21 \[ \int \frac {e^x \left (18-18 x+27 x^2-3 x^3+e^5 \left (-75 x+15 x^2\right )\right )}{-7776 x^2-6480 x^4-2160 x^6+3125 e^{25} x^7-360 x^8-30 x^{10}-x^{12}+e^{20} \left (-18750 x^6-3125 x^8\right )+e^{15} \left (45000 x^5+15000 x^7+1250 x^9\right )+e^{10} \left (-54000 x^4-27000 x^6-4500 x^8-250 x^{10}\right )+e^5 \left (32400 x^3+21600 x^5+5400 x^7+600 x^9+25 x^{11}\right )} \, dx=\frac {3 e^x}{x \left (6-5 e^5 x+x^2\right )^4} \] Output:
3/x/(x^2-5*x*exp(5)+6)^4*exp(x)
Time = 1.86 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.00 \[ \int \frac {e^x \left (18-18 x+27 x^2-3 x^3+e^5 \left (-75 x+15 x^2\right )\right )}{-7776 x^2-6480 x^4-2160 x^6+3125 e^{25} x^7-360 x^8-30 x^{10}-x^{12}+e^{20} \left (-18750 x^6-3125 x^8\right )+e^{15} \left (45000 x^5+15000 x^7+1250 x^9\right )+e^{10} \left (-54000 x^4-27000 x^6-4500 x^8-250 x^{10}\right )+e^5 \left (32400 x^3+21600 x^5+5400 x^7+600 x^9+25 x^{11}\right )} \, dx=\frac {3 e^x}{x \left (6-5 e^5 x+x^2\right )^4} \] Input:
Integrate[(E^x*(18 - 18*x + 27*x^2 - 3*x^3 + E^5*(-75*x + 15*x^2)))/(-7776 *x^2 - 6480*x^4 - 2160*x^6 + 3125*E^25*x^7 - 360*x^8 - 30*x^10 - x^12 + E^ 20*(-18750*x^6 - 3125*x^8) + E^15*(45000*x^5 + 15000*x^7 + 1250*x^9) + E^1 0*(-54000*x^4 - 27000*x^6 - 4500*x^8 - 250*x^10) + E^5*(32400*x^3 + 21600* x^5 + 5400*x^7 + 600*x^9 + 25*x^11)),x]
Output:
(3*E^x)/(x*(6 - 5*E^5*x + x^2)^4)
Result contains higher order function than in optimal. Order 4 vs. order 3 in optimal.
Time = 23.91 (sec) , antiderivative size = 9038, normalized size of antiderivative = 430.38, number of steps used = 7, number of rules used = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {2026, 2463, 7239, 27, 25, 7293, 2009}
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.
| \(\displaystyle \int \frac {e^x \left (-3 x^3+27 x^2+e^5 \left (15 x^2-75 x\right )-18 x+18\right )}{-x^{12}-30 x^{10}-360 x^8+3125 e^{25} x^7-2160 x^6-6480 x^4-7776 x^2+e^{20} \left (-3125 x^8-18750 x^6\right )+e^{15} \left (1250 x^9+15000 x^7+45000 x^5\right )+e^{10} \left (-250 x^{10}-4500 x^8-27000 x^6-54000 x^4\right )+e^5 \left (25 x^{11}+600 x^9+5400 x^7+21600 x^5+32400 x^3\right )} \, dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {e^x \left (-3 x^3+27 x^2+e^5 \left (15 x^2-75 x\right )-18 x+18\right )}{x^2 \left (-x^{10}+25 e^5 x^9-10 \left (3+25 e^{10}\right ) x^8+50 e^5 \left (12+25 e^{10}\right ) x^7-5 \left (72+900 e^{10}+625 e^{20}\right ) x^6+25 e^5 \left (216+600 e^{10}+125 e^{20}\right ) x^5-30 \left (72+900 e^{10}+625 e^{20}\right ) x^4+1800 e^5 \left (12+25 e^{10}\right ) x^3-2160 \left (3+25 e^{10}\right ) x^2+32400 e^5 x-7776\right )}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \left (\frac {140 e^x \left (-3 x^3+27 x^2+e^5 \left (15 x^2-75 x\right )-18 x+18\right )}{\left (25 e^{10}-24\right )^{9/2} x^2 \left (2 x+\sqrt {25 e^{10}-24}-5 e^5\right )}+\frac {140 e^x \left (-3 x^3+27 x^2+e^5 \left (15 x^2-75 x\right )-18 x+18\right )}{\left (25 e^{10}-24\right )^{9/2} \left (-2 x+\sqrt {25 e^{10}-24}+5 e^5\right ) x^2}+\frac {140 e^x \left (-3 x^3+27 x^2+e^5 \left (15 x^2-75 x\right )-18 x+18\right )}{\left (25 e^{10}-24\right )^4 \left (-2 x+\sqrt {25 e^{10}-24}+5 e^5\right )^2 x^2}+\frac {120 e^x \left (-3 x^3+27 x^2+e^5 \left (15 x^2-75 x\right )-18 x+18\right )}{\left (25 e^{10}-24\right )^{7/2} \left (-2 x+\sqrt {25 e^{10}-24}+5 e^5\right )^3 x^2}+\frac {80 e^x \left (-3 x^3+27 x^2+e^5 \left (15 x^2-75 x\right )-18 x+18\right )}{\left (25 e^{10}-24\right )^3 \left (-2 x+\sqrt {25 e^{10}-24}+5 e^5\right )^4 x^2}+\frac {32 e^x \left (-3 x^3+27 x^2+e^5 \left (15 x^2-75 x\right )-18 x+18\right )}{\left (25 e^{10}-24\right )^{5/2} \left (-2 x+\sqrt {25 e^{10}-24}+5 e^5\right )^5 x^2}+\frac {140 e^x \left (-3 x^3+27 x^2+e^5 \left (15 x^2-75 x\right )-18 x+18\right )}{\left (25 e^{10}-24\right )^4 x^2 \left (2 x+\sqrt {25 e^{10}-24}-5 e^5\right )^2}+\frac {120 e^x \left (-3 x^3+27 x^2+e^5 \left (15 x^2-75 x\right )-18 x+18\right )}{\left (25 e^{10}-24\right )^{7/2} x^2 \left (2 x+\sqrt {25 e^{10}-24}-5 e^5\right )^3}+\frac {80 e^x \left (-3 x^3+27 x^2+e^5 \left (15 x^2-75 x\right )-18 x+18\right )}{\left (25 e^{10}-24\right )^3 x^2 \left (2 x+\sqrt {25 e^{10}-24}-5 e^5\right )^4}+\frac {32 e^x \left (-3 x^3+27 x^2+e^5 \left (15 x^2-75 x\right )-18 x+18\right )}{\left (25 e^{10}-24\right )^{5/2} x^2 \left (2 x+\sqrt {25 e^{10}-24}-5 e^5\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {3 e^x \left (x^3-\left (9+5 e^5\right ) x^2+\left (6+25 e^5\right ) x-6\right )}{x^2 \left (x^2-5 e^5 x+6\right )^5}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 3 \int -\frac {e^x \left (-x^3+\left (9+5 e^5\right ) x^2-\left (6+25 e^5\right ) x+6\right )}{x^2 \left (x^2-5 e^5 x+6\right )^5}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -3 \int \frac {e^x \left (-x^3+\left (9+5 e^5\right ) x^2-\left (6+25 e^5\right ) x+6\right )}{x^2 \left (x^2-5 e^5 x+6\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -3 \int \left (\frac {e^x \left (-x+5 e^5+1\right )}{1296 \left (-x^2+5 e^5 x-6\right )}-\frac {e^x}{1296 x}+\frac {e^x}{1296 x^2}+\frac {e^x \left (\left (6+5 e^5\right ) x-25 e^{10}-30 e^5-6\right )}{1296 \left (x^2-5 e^5 x+6\right )^2}+\frac {e^x \left (\left (3+5 e^5\right ) x-25 e^{10}-15 e^5-3\right )}{108 \left (x^2-5 e^5 x+6\right )^3}+\frac {e^x \left (\left (2+5 e^5\right ) x-25 e^{10}-10 e^5-2\right )}{12 \left (x^2-5 e^5 x+6\right )^4}+\frac {2 e^x \left (-5 e^5 x+25 e^{10}-12\right )}{3 \left (-x^2+5 e^5 x-6\right )^5}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -3 \left (\frac {5 e^{\frac {1}{2} \left (10+5 e^5+\sqrt {-24+25 e^{10}}\right )} \left (25 e^5+3 \sqrt {-24+25 e^{10}}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x-\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{18 \left (24-25 e^{10}\right )^3}-\frac {25 e^{\frac {1}{2} \left (10+5 e^5+\sqrt {-24+25 e^{10}}\right )} \left (35 e^5+\sqrt {-24+25 e^{10}}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x-\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{3 \left (24-25 e^{10}\right )^4}-\frac {e^{\frac {1}{2} \left (5 e^5+\sqrt {-24+25 e^{10}}\right )} \left (2+5 e^5\right ) \left (25 e^5+\sqrt {-24+25 e^{10}}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x-\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{12 \left (24-25 e^{10}\right )^3}+\frac {25 e^{\frac {1}{2} \left (10+5 e^5+\sqrt {-24+25 e^{10}}\right )} \left (15 e^5+\sqrt {-24+25 e^{10}}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x-\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{6 \left (-24+25 e^{10}\right )^{7/2}}-\frac {e^{\frac {1}{2} \left (5 e^5+\sqrt {-24+25 e^{10}}\right )} \left (3+5 e^5\right ) \left (15 e^5+\sqrt {-24+25 e^{10}}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x-\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{216 \left (24-25 e^{10}\right )^2}-\frac {e^{\frac {1}{2} \left (5 e^5+\sqrt {-24+25 e^{10}}\right )} \left (2+5 e^5\right ) \left (10 e^5+\sqrt {-24+25 e^{10}}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x-\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{24 \left (-24+25 e^{10}\right )^{5/2}}+\frac {e^{\frac {1}{2} \left (5 e^5+\sqrt {-24+25 e^{10}}\right )} \left (3+5 e^5\right ) \left (5 e^5+\sqrt {-24+25 e^{10}}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x-\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{432 \left (-24+25 e^{10}\right )^{3/2}}+\frac {5 e^{\frac {1}{2} \left (10+5 e^5+\sqrt {-24+25 e^{10}}\right )} \left (5 e^5+\sqrt {-24+25 e^{10}}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x-\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{72 \left (-24+25 e^{10}\right )^{5/2}}-\frac {e^{\frac {1}{2} \left (5 e^5+\sqrt {-24+25 e^{10}}\right )} \left (6+5 e^5\right ) \left (5 e^5+\sqrt {-24+25 e^{10}}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x-\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{2592 \left (24-25 e^{10}\right )}+\frac {e^{\frac {1}{2} \left (5 e^5+\sqrt {-24+25 e^{10}}\right )} \left (2+5 e^5\right ) \left (5 e^5+\sqrt {-24+25 e^{10}}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x-\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{144 \left (24-25 e^{10}\right )^2}+\frac {e^{\frac {1}{2} \left (5 e^5+\sqrt {-24+25 e^{10}}\right )} \left (1-\frac {2+5 e^5}{\sqrt {-24+25 e^{10}}}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x-\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{2592}+\frac {e^{\frac {1}{2} \left (5 e^5+\sqrt {-24+25 e^{10}}\right )} \left (6+5 e^5 \left (6+5 e^5\right )\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x-\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{648 \left (-24+25 e^{10}\right )^{3/2}}+\frac {e^{\frac {1}{2} \left (5 e^5+\sqrt {-24+25 e^{10}}\right )} \left (6+5 e^5 \left (6+5 e^5\right )\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x-\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{1296 \left (24-25 e^{10}\right )}-\frac {e^{\frac {1}{2} \left (5 e^5+\sqrt {-24+25 e^{10}}\right )} \left (3+5 e^5 \left (3+5 e^5\right )\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x-\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{216 \left (-24+25 e^{10}\right )^{3/2}}-\frac {e^{\frac {1}{2} \left (5 e^5+\sqrt {-24+25 e^{10}}\right )} \left (3+5 e^5 \left (3+5 e^5\right )\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x-\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{18 \left (-24+25 e^{10}\right )^{5/2}}+\frac {e^{\frac {1}{2} \left (5 e^5+\sqrt {-24+25 e^{10}}\right )} \left (3+5 e^5 \left (3+5 e^5\right )\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x-\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{36 \left (24-25 e^{10}\right )^2}+\frac {e^{\frac {1}{2} \left (5 e^5+\sqrt {-24+25 e^{10}}\right )} \left (2+5 e^5 \left (2+5 e^5\right )\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x-\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{6 \left (-24+25 e^{10}\right )^{5/2}}+\frac {5 e^{\frac {1}{2} \left (5 e^5+\sqrt {-24+25 e^{10}}\right )} \left (2+5 e^5 \left (2+5 e^5\right )\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x-\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{3 \left (-24+25 e^{10}\right )^{7/2}}-\frac {e^{\frac {1}{2} \left (5 e^5+\sqrt {-24+25 e^{10}}\right )} \left (2+5 e^5 \left (2+5 e^5\right )\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x-\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{72 \left (24-25 e^{10}\right )^2}+\frac {5 e^{\frac {1}{2} \left (5 e^5+\sqrt {-24+25 e^{10}}\right )} \left (2+5 e^5 \left (2+5 e^5\right )\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x-\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{6 \left (24-25 e^{10}\right )^3}-\frac {5 e^{\frac {1}{2} \left (10+5 e^5+\sqrt {-24+25 e^{10}}\right )} \left (6+5 e^5\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x-\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{1296 \left (-24+25 e^{10}\right )^{3/2}}+\frac {e^{\frac {1}{2} \left (5 e^5+\sqrt {-24+25 e^{10}}\right )} \left (12-25 e^{10}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x-\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{36 \left (-24+25 e^{10}\right )^{5/2}}+\frac {5 e^{\frac {1}{2} \left (10+5 e^5+\sqrt {-24+25 e^{10}}\right )} \left (3+5 e^5\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x-\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{36 \left (-24+25 e^{10}\right )^{5/2}}+\frac {5 e^{\frac {1}{2} \left (5 e^5+\sqrt {-24+25 e^{10}}\right )} \left (12-25 e^{10}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x-\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{\left (-24+25 e^{10}\right )^{7/2}}-\frac {25 e^{\frac {1}{2} \left (10+5 e^5+\sqrt {-24+25 e^{10}}\right )} \left (2+5 e^5\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x-\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{6 \left (-24+25 e^{10}\right )^{7/2}}+\frac {140 e^{\frac {1}{2} \left (5 e^5+\sqrt {-24+25 e^{10}}\right )} \left (12-25 e^{10}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x-\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{3 \left (-24+25 e^{10}\right )^{9/2}}+\frac {1750 e^{\frac {1}{2} \left (20+5 e^5+\sqrt {-24+25 e^{10}}\right )} \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x-\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{3 \left (-24+25 e^{10}\right )^{9/2}}+\frac {5 e^{\frac {1}{2} \left (5 e^5+\sqrt {-24+25 e^{10}}\right )} \left (12-25 e^{10}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x-\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{9 \left (24-25 e^{10}\right )^3}-\frac {70 e^{\frac {1}{2} \left (5 e^5+\sqrt {-24+25 e^{10}}\right )} \left (12-25 e^{10}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x-\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{3 \left (24-25 e^{10}\right )^4}-\frac {25 e^{5+\frac {5 e^5}{2}-\frac {1}{2} \sqrt {-24+25 e^{10}}} \left (35 e^5-\sqrt {-24+25 e^{10}}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x+\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{3 \left (24-25 e^{10}\right )^4}-\frac {e^{\frac {5 e^5}{2}-\frac {1}{2} \sqrt {-24+25 e^{10}}} \left (2+5 e^5\right ) \left (25 e^5-\sqrt {-24+25 e^{10}}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x+\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{12 \left (24-25 e^{10}\right )^3}-\frac {25 e^{5+\frac {5 e^5}{2}-\frac {1}{2} \sqrt {-24+25 e^{10}}} \left (15 e^5-\sqrt {-24+25 e^{10}}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x+\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{6 \left (-24+25 e^{10}\right )^{7/2}}-\frac {e^{\frac {5 e^5}{2}-\frac {1}{2} \sqrt {-24+25 e^{10}}} \left (3+5 e^5\right ) \left (15 e^5-\sqrt {-24+25 e^{10}}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x+\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{216 \left (24-25 e^{10}\right )^2}+\frac {e^{\frac {5 e^5}{2}-\frac {1}{2} \sqrt {-24+25 e^{10}}} \left (2+5 e^5\right ) \left (10 e^5-\sqrt {-24+25 e^{10}}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x+\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{24 \left (-24+25 e^{10}\right )^{5/2}}-\frac {e^{\frac {5 e^5}{2}-\frac {1}{2} \sqrt {-24+25 e^{10}}} \left (3+5 e^5\right ) \left (5 e^5-\sqrt {-24+25 e^{10}}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x+\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{432 \left (-24+25 e^{10}\right )^{3/2}}-\frac {5 e^{5+\frac {5 e^5}{2}-\frac {1}{2} \sqrt {-24+25 e^{10}}} \left (5 e^5-\sqrt {-24+25 e^{10}}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x+\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{72 \left (-24+25 e^{10}\right )^{5/2}}-\frac {e^{\frac {5 e^5}{2}-\frac {1}{2} \sqrt {-24+25 e^{10}}} \left (6+5 e^5\right ) \left (5 e^5-\sqrt {-24+25 e^{10}}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x+\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{2592 \left (24-25 e^{10}\right )}+\frac {e^{\frac {5 e^5}{2}-\frac {1}{2} \sqrt {-24+25 e^{10}}} \left (2+5 e^5\right ) \left (5 e^5-\sqrt {-24+25 e^{10}}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x+\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{144 \left (24-25 e^{10}\right )^2}+\frac {5 e^{5+\frac {5 e^5}{2}-\frac {1}{2} \sqrt {-24+25 e^{10}}} \left (25 e^5-3 \sqrt {-24+25 e^{10}}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x+\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{18 \left (24-25 e^{10}\right )^3}+\frac {e^{\frac {5 e^5}{2}-\frac {1}{2} \sqrt {-24+25 e^{10}}} \left (1+\frac {2+5 e^5}{\sqrt {-24+25 e^{10}}}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x+\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{2592}-\frac {e^{\frac {5 e^5}{2}-\frac {1}{2} \sqrt {-24+25 e^{10}}} \left (6+30 e^5+25 e^{10}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x+\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{648 \left (-24+25 e^{10}\right )^{3/2}}+\frac {e^{\frac {5 e^5}{2}-\frac {1}{2} \sqrt {-24+25 e^{10}}} \left (6+30 e^5+25 e^{10}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x+\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{1296 \left (24-25 e^{10}\right )}+\frac {e^{\frac {5 e^5}{2}-\frac {1}{2} \sqrt {-24+25 e^{10}}} \left (3+15 e^5+25 e^{10}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x+\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{216 \left (-24+25 e^{10}\right )^{3/2}}+\frac {e^{\frac {5 e^5}{2}-\frac {1}{2} \sqrt {-24+25 e^{10}}} \left (3+15 e^5+25 e^{10}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x+\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{18 \left (-24+25 e^{10}\right )^{5/2}}+\frac {e^{\frac {5 e^5}{2}-\frac {1}{2} \sqrt {-24+25 e^{10}}} \left (3+15 e^5+25 e^{10}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x+\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{36 \left (24-25 e^{10}\right )^2}-\frac {e^{\frac {5 e^5}{2}-\frac {1}{2} \sqrt {-24+25 e^{10}}} \left (2+10 e^5+25 e^{10}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x+\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{6 \left (-24+25 e^{10}\right )^{5/2}}-\frac {5 e^{\frac {5 e^5}{2}-\frac {1}{2} \sqrt {-24+25 e^{10}}} \left (2+10 e^5+25 e^{10}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x+\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{3 \left (-24+25 e^{10}\right )^{7/2}}-\frac {e^{\frac {5 e^5}{2}-\frac {1}{2} \sqrt {-24+25 e^{10}}} \left (2+10 e^5+25 e^{10}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x+\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{72 \left (24-25 e^{10}\right )^2}+\frac {5 e^{\frac {5 e^5}{2}-\frac {1}{2} \sqrt {-24+25 e^{10}}} \left (2+10 e^5+25 e^{10}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x+\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{6 \left (24-25 e^{10}\right )^3}+\frac {5 e^{5+\frac {5 e^5}{2}-\frac {1}{2} \sqrt {-24+25 e^{10}}} \left (6+5 e^5\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x+\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{1296 \left (-24+25 e^{10}\right )^{3/2}}-\frac {e^{\frac {5 e^5}{2}-\frac {1}{2} \sqrt {-24+25 e^{10}}} \left (12-25 e^{10}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x+\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{36 \left (-24+25 e^{10}\right )^{5/2}}-\frac {5 e^{5+\frac {5 e^5}{2}-\frac {1}{2} \sqrt {-24+25 e^{10}}} \left (3+5 e^5\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x+\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{36 \left (-24+25 e^{10}\right )^{5/2}}-\frac {5 e^{\frac {5 e^5}{2}-\frac {1}{2} \sqrt {-24+25 e^{10}}} \left (12-25 e^{10}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x+\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{\left (-24+25 e^{10}\right )^{7/2}}+\frac {25 e^{5+\frac {5 e^5}{2}-\frac {1}{2} \sqrt {-24+25 e^{10}}} \left (2+5 e^5\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x+\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{6 \left (-24+25 e^{10}\right )^{7/2}}-\frac {140 e^{\frac {5 e^5}{2}-\frac {1}{2} \sqrt {-24+25 e^{10}}} \left (12-25 e^{10}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x+\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{3 \left (-24+25 e^{10}\right )^{9/2}}-\frac {1750 e^{10+\frac {5 e^5}{2}-\frac {1}{2} \sqrt {-24+25 e^{10}}} \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x+\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{3 \left (-24+25 e^{10}\right )^{9/2}}+\frac {5 e^{\frac {5 e^5}{2}-\frac {1}{2} \sqrt {-24+25 e^{10}}} \left (12-25 e^{10}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x+\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{9 \left (24-25 e^{10}\right )^3}-\frac {70 e^{\frac {5 e^5}{2}-\frac {1}{2} \sqrt {-24+25 e^{10}}} \left (12-25 e^{10}\right ) \operatorname {ExpIntegralEi}\left (\frac {1}{2} \left (2 x+\sqrt {-24+25 e^{10}}-5 e^5\right )\right )}{3 \left (24-25 e^{10}\right )^4}-\frac {50 e^{x+5} \left (35 e^5-\sqrt {-24+25 e^{10}}\right )}{3 \left (24-25 e^{10}\right )^4 \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )}-\frac {e^x \left (2+5 e^5\right ) \left (25 e^5-\sqrt {-24+25 e^{10}}\right )}{6 \left (24-25 e^{10}\right )^3 \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )}-\frac {25 e^{x+5} \left (15 e^5-\sqrt {-24+25 e^{10}}\right )}{3 \left (-24+25 e^{10}\right )^{7/2} \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )}-\frac {e^x \left (3+5 e^5\right ) \left (15 e^5-\sqrt {-24+25 e^{10}}\right )}{108 \left (24-25 e^{10}\right )^2 \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )}+\frac {e^x \left (2+5 e^5\right ) \left (10 e^5-\sqrt {-24+25 e^{10}}\right )}{12 \left (-24+25 e^{10}\right )^{5/2} \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )}-\frac {e^x \left (3+5 e^5\right ) \left (5 e^5-\sqrt {-24+25 e^{10}}\right )}{216 \left (-24+25 e^{10}\right )^{3/2} \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )}-\frac {5 e^{x+5} \left (5 e^5-\sqrt {-24+25 e^{10}}\right )}{36 \left (-24+25 e^{10}\right )^{5/2} \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )}-\frac {e^x \left (6+5 e^5\right ) \left (5 e^5-\sqrt {-24+25 e^{10}}\right )}{1296 \left (24-25 e^{10}\right ) \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )}+\frac {e^x \left (2+5 e^5\right ) \left (5 e^5-\sqrt {-24+25 e^{10}}\right )}{72 \left (24-25 e^{10}\right )^2 \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )}+\frac {5 e^{x+5} \left (25 e^5-3 \sqrt {-24+25 e^{10}}\right )}{9 \left (24-25 e^{10}\right )^3 \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )}+\frac {e^x \left (6+30 e^5+25 e^{10}\right )}{648 \left (24-25 e^{10}\right ) \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )}+\frac {e^x \left (3+15 e^5+25 e^{10}\right )}{108 \left (-24+25 e^{10}\right )^{3/2} \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )}+\frac {e^x \left (3+15 e^5+25 e^{10}\right )}{18 \left (24-25 e^{10}\right )^2 \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )}-\frac {e^x \left (2+10 e^5+25 e^{10}\right )}{3 \left (-24+25 e^{10}\right )^{5/2} \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )}-\frac {e^x \left (2+10 e^5+25 e^{10}\right )}{36 \left (24-25 e^{10}\right )^2 \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )}+\frac {5 e^x \left (2+10 e^5+25 e^{10}\right )}{3 \left (24-25 e^{10}\right )^3 \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )}-\frac {e^x \left (12-25 e^{10}\right )}{18 \left (-24+25 e^{10}\right )^{5/2} \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )}-\frac {10 e^x \left (12-25 e^{10}\right )}{\left (-24+25 e^{10}\right )^{7/2} \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )}+\frac {10 e^x \left (12-25 e^{10}\right )}{9 \left (24-25 e^{10}\right )^3 \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )}-\frac {140 e^x \left (12-25 e^{10}\right )}{3 \left (24-25 e^{10}\right )^4 \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )}+\frac {5 e^{x+5} \left (25 e^5+3 \sqrt {-24+25 e^{10}}\right )}{9 \left (24-25 e^{10}\right )^3 \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )}-\frac {50 e^{x+5} \left (35 e^5+\sqrt {-24+25 e^{10}}\right )}{3 \left (24-25 e^{10}\right )^4 \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )}-\frac {e^x \left (2+5 e^5\right ) \left (25 e^5+\sqrt {-24+25 e^{10}}\right )}{6 \left (24-25 e^{10}\right )^3 \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )}+\frac {25 e^{x+5} \left (15 e^5+\sqrt {-24+25 e^{10}}\right )}{3 \left (-24+25 e^{10}\right )^{7/2} \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )}-\frac {e^x \left (3+5 e^5\right ) \left (15 e^5+\sqrt {-24+25 e^{10}}\right )}{108 \left (24-25 e^{10}\right )^2 \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )}-\frac {e^x \left (2+5 e^5\right ) \left (10 e^5+\sqrt {-24+25 e^{10}}\right )}{12 \left (-24+25 e^{10}\right )^{5/2} \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )}+\frac {e^x \left (3+5 e^5\right ) \left (5 e^5+\sqrt {-24+25 e^{10}}\right )}{216 \left (-24+25 e^{10}\right )^{3/2} \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )}+\frac {5 e^{x+5} \left (5 e^5+\sqrt {-24+25 e^{10}}\right )}{36 \left (-24+25 e^{10}\right )^{5/2} \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )}-\frac {e^x \left (6+5 e^5\right ) \left (5 e^5+\sqrt {-24+25 e^{10}}\right )}{1296 \left (24-25 e^{10}\right ) \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )}+\frac {e^x \left (2+5 e^5\right ) \left (5 e^5+\sqrt {-24+25 e^{10}}\right )}{72 \left (24-25 e^{10}\right )^2 \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )}+\frac {e^x \left (6+30 e^5+25 e^{10}\right )}{648 \left (24-25 e^{10}\right ) \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )}-\frac {e^x \left (3+15 e^5+25 e^{10}\right )}{108 \left (-24+25 e^{10}\right )^{3/2} \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )}+\frac {e^x \left (3+15 e^5+25 e^{10}\right )}{18 \left (24-25 e^{10}\right )^2 \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )}+\frac {e^x \left (2+10 e^5+25 e^{10}\right )}{3 \left (-24+25 e^{10}\right )^{5/2} \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )}-\frac {e^x \left (2+10 e^5+25 e^{10}\right )}{36 \left (24-25 e^{10}\right )^2 \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )}+\frac {5 e^x \left (2+10 e^5+25 e^{10}\right )}{3 \left (24-25 e^{10}\right )^3 \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )}+\frac {e^x \left (12-25 e^{10}\right )}{18 \left (-24+25 e^{10}\right )^{5/2} \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )}+\frac {10 e^x \left (12-25 e^{10}\right )}{\left (-24+25 e^{10}\right )^{7/2} \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )}+\frac {10 e^x \left (12-25 e^{10}\right )}{9 \left (24-25 e^{10}\right )^3 \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )}-\frac {140 e^x \left (12-25 e^{10}\right )}{3 \left (24-25 e^{10}\right )^4 \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )}-\frac {e^x}{1296 x}+\frac {50 e^{x+5} \left (15 e^5-\sqrt {-24+25 e^{10}}\right )}{3 \left (-24+25 e^{10}\right )^{7/2} \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )^2}-\frac {e^x \left (2+5 e^5\right ) \left (10 e^5-\sqrt {-24+25 e^{10}}\right )}{6 \left (-24+25 e^{10}\right )^{5/2} \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )^2}+\frac {e^x \left (3+5 e^5\right ) \left (5 e^5-\sqrt {-24+25 e^{10}}\right )}{108 \left (-24+25 e^{10}\right )^{3/2} \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )^2}+\frac {5 e^{x+5} \left (5 e^5-\sqrt {-24+25 e^{10}}\right )}{18 \left (-24+25 e^{10}\right )^{5/2} \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )^2}-\frac {e^x \left (2+5 e^5\right ) \left (5 e^5-\sqrt {-24+25 e^{10}}\right )}{36 \left (24-25 e^{10}\right )^2 \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )^2}-\frac {10 e^{x+5} \left (25 e^5-3 \sqrt {-24+25 e^{10}}\right )}{9 \left (24-25 e^{10}\right )^3 \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )^2}-\frac {e^x \left (3+15 e^5+25 e^{10}\right )}{54 \left (-24+25 e^{10}\right )^{3/2} \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )^2}+\frac {2 e^x \left (2+10 e^5+25 e^{10}\right )}{3 \left (-24+25 e^{10}\right )^{5/2} \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )^2}+\frac {e^x \left (2+10 e^5+25 e^{10}\right )}{18 \left (24-25 e^{10}\right )^2 \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )^2}+\frac {e^x \left (12-25 e^{10}\right )}{9 \left (-24+25 e^{10}\right )^{5/2} \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )^2}+\frac {20 e^x \left (12-25 e^{10}\right )}{\left (-24+25 e^{10}\right )^{7/2} \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )^2}-\frac {20 e^x \left (12-25 e^{10}\right )}{9 \left (24-25 e^{10}\right )^3 \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )^2}-\frac {10 e^{x+5} \left (25 e^5+3 \sqrt {-24+25 e^{10}}\right )}{9 \left (24-25 e^{10}\right )^3 \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )^2}-\frac {50 e^{x+5} \left (15 e^5+\sqrt {-24+25 e^{10}}\right )}{3 \left (-24+25 e^{10}\right )^{7/2} \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )^2}+\frac {e^x \left (2+5 e^5\right ) \left (10 e^5+\sqrt {-24+25 e^{10}}\right )}{6 \left (-24+25 e^{10}\right )^{5/2} \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )^2}-\frac {e^x \left (3+5 e^5\right ) \left (5 e^5+\sqrt {-24+25 e^{10}}\right )}{108 \left (-24+25 e^{10}\right )^{3/2} \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )^2}-\frac {5 e^{x+5} \left (5 e^5+\sqrt {-24+25 e^{10}}\right )}{18 \left (-24+25 e^{10}\right )^{5/2} \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )^2}-\frac {e^x \left (2+5 e^5\right ) \left (5 e^5+\sqrt {-24+25 e^{10}}\right )}{36 \left (24-25 e^{10}\right )^2 \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )^2}+\frac {e^x \left (3+15 e^5+25 e^{10}\right )}{54 \left (-24+25 e^{10}\right )^{3/2} \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )^2}-\frac {2 e^x \left (2+10 e^5+25 e^{10}\right )}{3 \left (-24+25 e^{10}\right )^{5/2} \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )^2}+\frac {e^x \left (2+10 e^5+25 e^{10}\right )}{18 \left (24-25 e^{10}\right )^2 \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )^2}-\frac {e^x \left (12-25 e^{10}\right )}{9 \left (-24+25 e^{10}\right )^{5/2} \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )^2}-\frac {20 e^x \left (12-25 e^{10}\right )}{\left (-24+25 e^{10}\right )^{7/2} \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )^2}-\frac {20 e^x \left (12-25 e^{10}\right )}{9 \left (24-25 e^{10}\right )^3 \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )^2}-\frac {10 e^{x+5} \left (5 e^5-\sqrt {-24+25 e^{10}}\right )}{9 \left (-24+25 e^{10}\right )^{5/2} \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )^3}+\frac {e^x \left (2+5 e^5\right ) \left (5 e^5-\sqrt {-24+25 e^{10}}\right )}{9 \left (24-25 e^{10}\right )^2 \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )^3}+\frac {40 e^{x+5} \left (25 e^5-3 \sqrt {-24+25 e^{10}}\right )}{9 \left (24-25 e^{10}\right )^3 \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )^3}-\frac {2 e^x \left (2+10 e^5+25 e^{10}\right )}{9 \left (24-25 e^{10}\right )^2 \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )^3}-\frac {4 e^x \left (12-25 e^{10}\right )}{9 \left (-24+25 e^{10}\right )^{5/2} \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )^3}+\frac {80 e^x \left (12-25 e^{10}\right )}{9 \left (24-25 e^{10}\right )^3 \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )^3}+\frac {40 e^{x+5} \left (25 e^5+3 \sqrt {-24+25 e^{10}}\right )}{9 \left (24-25 e^{10}\right )^3 \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )^3}+\frac {10 e^{x+5} \left (5 e^5+\sqrt {-24+25 e^{10}}\right )}{9 \left (-24+25 e^{10}\right )^{5/2} \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )^3}+\frac {e^x \left (2+5 e^5\right ) \left (5 e^5+\sqrt {-24+25 e^{10}}\right )}{9 \left (24-25 e^{10}\right )^2 \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )^3}-\frac {2 e^x \left (2+10 e^5+25 e^{10}\right )}{9 \left (24-25 e^{10}\right )^2 \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )^3}+\frac {4 e^x \left (12-25 e^{10}\right )}{9 \left (-24+25 e^{10}\right )^{5/2} \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )^3}+\frac {80 e^x \left (12-25 e^{10}\right )}{9 \left (24-25 e^{10}\right )^3 \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )^3}+\frac {20 e^{x+5} \left (5 e^5-\sqrt {-24+25 e^{10}}\right )}{3 \left (-24+25 e^{10}\right )^{5/2} \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )^4}+\frac {8 e^x \left (12-25 e^{10}\right )}{3 \left (-24+25 e^{10}\right )^{5/2} \left (-2 x-\sqrt {-24+25 e^{10}}+5 e^5\right )^4}-\frac {20 e^{x+5} \left (5 e^5+\sqrt {-24+25 e^{10}}\right )}{3 \left (-24+25 e^{10}\right )^{5/2} \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )^4}-\frac {8 e^x \left (12-25 e^{10}\right )}{3 \left (-24+25 e^{10}\right )^{5/2} \left (-2 x+\sqrt {-24+25 e^{10}}+5 e^5\right )^4}\right )\) |
Input:
Int[(E^x*(18 - 18*x + 27*x^2 - 3*x^3 + E^5*(-75*x + 15*x^2)))/(-7776*x^2 - 6480*x^4 - 2160*x^6 + 3125*E^25*x^7 - 360*x^8 - 30*x^10 - x^12 + E^20*(-1 8750*x^6 - 3125*x^8) + E^15*(45000*x^5 + 15000*x^7 + 1250*x^9) + E^10*(-54 000*x^4 - 27000*x^6 - 4500*x^8 - 250*x^10) + E^5*(32400*x^3 + 21600*x^5 + 5400*x^7 + 600*x^9 + 25*x^11)),x]
Output:
-3*((8*E^x*(12 - 25*E^10))/(3*(-24 + 25*E^10)^(5/2)*(5*E^5 - Sqrt[-24 + 25 *E^10] - 2*x)^4) + (20*E^(5 + x)*(5*E^5 - Sqrt[-24 + 25*E^10]))/(3*(-24 + 25*E^10)^(5/2)*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)^4) + (80*E^x*(12 - 25*E ^10))/(9*(24 - 25*E^10)^3*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)^3) - (4*E^x* (12 - 25*E^10))/(9*(-24 + 25*E^10)^(5/2)*(5*E^5 - Sqrt[-24 + 25*E^10] - 2* x)^3) - (2*E^x*(2 + 10*E^5 + 25*E^10))/(9*(24 - 25*E^10)^2*(5*E^5 - Sqrt[- 24 + 25*E^10] - 2*x)^3) + (40*E^(5 + x)*(25*E^5 - 3*Sqrt[-24 + 25*E^10]))/ (9*(24 - 25*E^10)^3*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)^3) + (E^x*(2 + 5*E ^5)*(5*E^5 - Sqrt[-24 + 25*E^10]))/(9*(24 - 25*E^10)^2*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)^3) - (10*E^(5 + x)*(5*E^5 - Sqrt[-24 + 25*E^10]))/(9*(-24 + 25*E^10)^(5/2)*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)^3) - (20*E^x*(12 - 2 5*E^10))/(9*(24 - 25*E^10)^3*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)^2) + (20* E^x*(12 - 25*E^10))/((-24 + 25*E^10)^(7/2)*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)^2) + (E^x*(12 - 25*E^10))/(9*(-24 + 25*E^10)^(5/2)*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)^2) + (E^x*(2 + 10*E^5 + 25*E^10))/(18*(24 - 25*E^10)^2*( 5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)^2) + (2*E^x*(2 + 10*E^5 + 25*E^10))/(3* (-24 + 25*E^10)^(5/2)*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)^2) - (E^x*(3 + 1 5*E^5 + 25*E^10))/(54*(-24 + 25*E^10)^(3/2)*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)^2) - (10*E^(5 + x)*(25*E^5 - 3*Sqrt[-24 + 25*E^10]))/(9*(24 - 25*E^1 0)^3*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)^2) - (E^x*(2 + 5*E^5)*(5*E^5 -...
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[(Fx_.)*(Px_)^(p_.), x_Symbol] :> With[{r = Expon[Px, x, Min]}, Int[x^(p *r)*ExpandToSum[Px/x^r, x]^p*Fx, x] /; IGtQ[r, 0]] /; PolyQ[Px, x] && Integ erQ[p] && !MonomialQ[Px, x] && (ILtQ[p, 0] || !PolyQ[u, x])
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{Qx = Factor[Px]}, Int[ExpandIntegr and[u, Qx^p, x], x] /; !SumQ[NonfreeFactors[Qx, x]]] /; PolyQ[Px, x] && Gt Q[Expon[Px, x], 2] && !BinomialQ[Px, x] && !TrinomialQ[Px, x] && ILtQ[p, 0]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Time = 1.08 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.05
| method | result | size |
| norman | \(\frac {3 \,{\mathrm e}^{x}}{x \left (5 x \,{\mathrm e}^{5}-x^{2}-6\right )^{4}}\) | \(22\) |
| gosper | \(\frac {3 \,{\mathrm e}^{x}}{x \left (625 \,{\mathrm e}^{20} x^{4}-500 \,{\mathrm e}^{15} x^{5}+150 \,{\mathrm e}^{10} x^{6}-20 \,{\mathrm e}^{5} x^{7}+x^{8}-3000 x^{3} {\mathrm e}^{15}+1800 \,{\mathrm e}^{10} x^{4}-360 x^{5} {\mathrm e}^{5}+24 x^{6}+5400 \,{\mathrm e}^{10} x^{2}-2160 x^{3} {\mathrm e}^{5}+216 x^{4}-4320 x \,{\mathrm e}^{5}+864 x^{2}+1296\right )}\) | \(110\) |
| parallelrisch | \(\frac {3 \,{\mathrm e}^{x}}{x \left (625 \,{\mathrm e}^{20} x^{4}-500 \,{\mathrm e}^{15} x^{5}+150 \,{\mathrm e}^{10} x^{6}-20 \,{\mathrm e}^{5} x^{7}+x^{8}-3000 x^{3} {\mathrm e}^{15}+1800 \,{\mathrm e}^{10} x^{4}-360 x^{5} {\mathrm e}^{5}+24 x^{6}+5400 \,{\mathrm e}^{10} x^{2}-2160 x^{3} {\mathrm e}^{5}+216 x^{4}-4320 x \,{\mathrm e}^{5}+864 x^{2}+1296\right )}\) | \(110\) |
| default | \(\text {Expression too large to display}\) | \(14908\) |
Input:
int(((15*x^2-75*x)*exp(5)-3*x^3+27*x^2-18*x+18)*exp(x)/(3125*x^7*exp(5)^5+ (-3125*x^8-18750*x^6)*exp(5)^4+(1250*x^9+15000*x^7+45000*x^5)*exp(5)^3+(-2 50*x^10-4500*x^8-27000*x^6-54000*x^4)*exp(5)^2+(25*x^11+600*x^9+5400*x^7+2 1600*x^5+32400*x^3)*exp(5)-x^12-30*x^10-360*x^8-2160*x^6-6480*x^4-7776*x^2 ),x,method=_RETURNVERBOSE)
Output:
3*exp(x)/x/(5*x*exp(5)-x^2-6)^4
Leaf count of result is larger than twice the leaf count of optimal. 89 vs. \(2 (19) = 38\).
Time = 0.12 (sec) , antiderivative size = 89, normalized size of antiderivative = 4.24 \[ \int \frac {e^x \left (18-18 x+27 x^2-3 x^3+e^5 \left (-75 x+15 x^2\right )\right )}{-7776 x^2-6480 x^4-2160 x^6+3125 e^{25} x^7-360 x^8-30 x^{10}-x^{12}+e^{20} \left (-18750 x^6-3125 x^8\right )+e^{15} \left (45000 x^5+15000 x^7+1250 x^9\right )+e^{10} \left (-54000 x^4-27000 x^6-4500 x^8-250 x^{10}\right )+e^5 \left (32400 x^3+21600 x^5+5400 x^7+600 x^9+25 x^{11}\right )} \, dx=\frac {3 \, e^{x}}{x^{9} + 24 \, x^{7} + 625 \, x^{5} e^{20} + 216 \, x^{5} + 864 \, x^{3} - 500 \, {\left (x^{6} + 6 \, x^{4}\right )} e^{15} + 150 \, {\left (x^{7} + 12 \, x^{5} + 36 \, x^{3}\right )} e^{10} - 20 \, {\left (x^{8} + 18 \, x^{6} + 108 \, x^{4} + 216 \, x^{2}\right )} e^{5} + 1296 \, x} \] Input:
integrate(((15*x^2-75*x)*exp(5)-3*x^3+27*x^2-18*x+18)*exp(x)/(3125*x^7*exp (5)^5+(-3125*x^8-18750*x^6)*exp(5)^4+(1250*x^9+15000*x^7+45000*x^5)*exp(5) ^3+(-250*x^10-4500*x^8-27000*x^6-54000*x^4)*exp(5)^2+(25*x^11+600*x^9+5400 *x^7+21600*x^5+32400*x^3)*exp(5)-x^12-30*x^10-360*x^8-2160*x^6-6480*x^4-77 76*x^2),x, algorithm="fricas")
Output:
3*e^x/(x^9 + 24*x^7 + 625*x^5*e^20 + 216*x^5 + 864*x^3 - 500*(x^6 + 6*x^4) *e^15 + 150*(x^7 + 12*x^5 + 36*x^3)*e^10 - 20*(x^8 + 18*x^6 + 108*x^4 + 21 6*x^2)*e^5 + 1296*x)
Leaf count of result is larger than twice the leaf count of optimal. 110 vs. \(2 (19) = 38\).
Time = 0.19 (sec) , antiderivative size = 110, normalized size of antiderivative = 5.24 \[ \int \frac {e^x \left (18-18 x+27 x^2-3 x^3+e^5 \left (-75 x+15 x^2\right )\right )}{-7776 x^2-6480 x^4-2160 x^6+3125 e^{25} x^7-360 x^8-30 x^{10}-x^{12}+e^{20} \left (-18750 x^6-3125 x^8\right )+e^{15} \left (45000 x^5+15000 x^7+1250 x^9\right )+e^{10} \left (-54000 x^4-27000 x^6-4500 x^8-250 x^{10}\right )+e^5 \left (32400 x^3+21600 x^5+5400 x^7+600 x^9+25 x^{11}\right )} \, dx=\frac {3 e^{x}}{x^{9} - 20 x^{8} e^{5} + 24 x^{7} + 150 x^{7} e^{10} - 500 x^{6} e^{15} - 360 x^{6} e^{5} + 216 x^{5} + 1800 x^{5} e^{10} + 625 x^{5} e^{20} - 3000 x^{4} e^{15} - 2160 x^{4} e^{5} + 864 x^{3} + 5400 x^{3} e^{10} - 4320 x^{2} e^{5} + 1296 x} \] Input:
integrate(((15*x**2-75*x)*exp(5)-3*x**3+27*x**2-18*x+18)*exp(x)/(3125*x**7 *exp(5)**5+(-3125*x**8-18750*x**6)*exp(5)**4+(1250*x**9+15000*x**7+45000*x **5)*exp(5)**3+(-250*x**10-4500*x**8-27000*x**6-54000*x**4)*exp(5)**2+(25* x**11+600*x**9+5400*x**7+21600*x**5+32400*x**3)*exp(5)-x**12-30*x**10-360* x**8-2160*x**6-6480*x**4-7776*x**2),x)
Output:
3*exp(x)/(x**9 - 20*x**8*exp(5) + 24*x**7 + 150*x**7*exp(10) - 500*x**6*ex p(15) - 360*x**6*exp(5) + 216*x**5 + 1800*x**5*exp(10) + 625*x**5*exp(20) - 3000*x**4*exp(15) - 2160*x**4*exp(5) + 864*x**3 + 5400*x**3*exp(10) - 43 20*x**2*exp(5) + 1296*x)
Leaf count of result is larger than twice the leaf count of optimal. 91 vs. \(2 (19) = 38\).
Time = 0.08 (sec) , antiderivative size = 91, normalized size of antiderivative = 4.33 \[ \int \frac {e^x \left (18-18 x+27 x^2-3 x^3+e^5 \left (-75 x+15 x^2\right )\right )}{-7776 x^2-6480 x^4-2160 x^6+3125 e^{25} x^7-360 x^8-30 x^{10}-x^{12}+e^{20} \left (-18750 x^6-3125 x^8\right )+e^{15} \left (45000 x^5+15000 x^7+1250 x^9\right )+e^{10} \left (-54000 x^4-27000 x^6-4500 x^8-250 x^{10}\right )+e^5 \left (32400 x^3+21600 x^5+5400 x^7+600 x^9+25 x^{11}\right )} \, dx=\frac {3 \, e^{x}}{x^{9} - 20 \, x^{8} e^{5} + 6 \, x^{7} {\left (25 \, e^{10} + 4\right )} - 20 \, x^{6} {\left (25 \, e^{15} + 18 \, e^{5}\right )} + x^{5} {\left (625 \, e^{20} + 1800 \, e^{10} + 216\right )} - 120 \, x^{4} {\left (25 \, e^{15} + 18 \, e^{5}\right )} + 216 \, x^{3} {\left (25 \, e^{10} + 4\right )} - 4320 \, x^{2} e^{5} + 1296 \, x} \] Input:
integrate(((15*x^2-75*x)*exp(5)-3*x^3+27*x^2-18*x+18)*exp(x)/(3125*x^7*exp (5)^5+(-3125*x^8-18750*x^6)*exp(5)^4+(1250*x^9+15000*x^7+45000*x^5)*exp(5) ^3+(-250*x^10-4500*x^8-27000*x^6-54000*x^4)*exp(5)^2+(25*x^11+600*x^9+5400 *x^7+21600*x^5+32400*x^3)*exp(5)-x^12-30*x^10-360*x^8-2160*x^6-6480*x^4-77 76*x^2),x, algorithm="maxima")
Output:
3*e^x/(x^9 - 20*x^8*e^5 + 6*x^7*(25*e^10 + 4) - 20*x^6*(25*e^15 + 18*e^5) + x^5*(625*e^20 + 1800*e^10 + 216) - 120*x^4*(25*e^15 + 18*e^5) + 216*x^3* (25*e^10 + 4) - 4320*x^2*e^5 + 1296*x)
Leaf count of result is larger than twice the leaf count of optimal. 216 vs. \(2 (19) = 38\).
Time = 0.22 (sec) , antiderivative size = 216, normalized size of antiderivative = 10.29 \[ \int \frac {e^x \left (18-18 x+27 x^2-3 x^3+e^5 \left (-75 x+15 x^2\right )\right )}{-7776 x^2-6480 x^4-2160 x^6+3125 e^{25} x^7-360 x^8-30 x^{10}-x^{12}+e^{20} \left (-18750 x^6-3125 x^8\right )+e^{15} \left (45000 x^5+15000 x^7+1250 x^9\right )+e^{10} \left (-54000 x^4-27000 x^6-4500 x^8-250 x^{10}\right )+e^5 \left (32400 x^3+21600 x^5+5400 x^7+600 x^9+25 x^{11}\right )} \, dx=-\frac {x^{8} e^{x} - 20 \, x^{7} e^{\left (x + 5\right )} + 150 \, x^{6} e^{\left (x + 10\right )} + 24 \, x^{6} e^{x} - 500 \, x^{5} e^{\left (x + 15\right )} - 360 \, x^{5} e^{\left (x + 5\right )} + 625 \, x^{4} e^{\left (x + 20\right )} + 1800 \, x^{4} e^{\left (x + 10\right )} + 216 \, x^{4} e^{x} - 3000 \, x^{3} e^{\left (x + 15\right )} - 2160 \, x^{3} e^{\left (x + 5\right )} + 5400 \, x^{2} e^{\left (x + 10\right )} + 864 \, x^{2} e^{x} - 4320 \, x e^{\left (x + 5\right )} - 1296 \, e^{x}}{432 \, {\left (x^{9} - 20 \, x^{8} e^{5} + 150 \, x^{7} e^{10} + 24 \, x^{7} - 500 \, x^{6} e^{15} - 360 \, x^{6} e^{5} + 625 \, x^{5} e^{20} + 1800 \, x^{5} e^{10} + 216 \, x^{5} - 3000 \, x^{4} e^{15} - 2160 \, x^{4} e^{5} + 5400 \, x^{3} e^{10} + 864 \, x^{3} - 4320 \, x^{2} e^{5} + 1296 \, x\right )}} \] Input:
integrate(((15*x^2-75*x)*exp(5)-3*x^3+27*x^2-18*x+18)*exp(x)/(3125*x^7*exp (5)^5+(-3125*x^8-18750*x^6)*exp(5)^4+(1250*x^9+15000*x^7+45000*x^5)*exp(5) ^3+(-250*x^10-4500*x^8-27000*x^6-54000*x^4)*exp(5)^2+(25*x^11+600*x^9+5400 *x^7+21600*x^5+32400*x^3)*exp(5)-x^12-30*x^10-360*x^8-2160*x^6-6480*x^4-77 76*x^2),x, algorithm="giac")
Output:
-1/432*(x^8*e^x - 20*x^7*e^(x + 5) + 150*x^6*e^(x + 10) + 24*x^6*e^x - 500 *x^5*e^(x + 15) - 360*x^5*e^(x + 5) + 625*x^4*e^(x + 20) + 1800*x^4*e^(x + 10) + 216*x^4*e^x - 3000*x^3*e^(x + 15) - 2160*x^3*e^(x + 5) + 5400*x^2*e ^(x + 10) + 864*x^2*e^x - 4320*x*e^(x + 5) - 1296*e^x)/(x^9 - 20*x^8*e^5 + 150*x^7*e^10 + 24*x^7 - 500*x^6*e^15 - 360*x^6*e^5 + 625*x^5*e^20 + 1800* x^5*e^10 + 216*x^5 - 3000*x^4*e^15 - 2160*x^4*e^5 + 5400*x^3*e^10 + 864*x^ 3 - 4320*x^2*e^5 + 1296*x)
Timed out. \[ \int \frac {e^x \left (18-18 x+27 x^2-3 x^3+e^5 \left (-75 x+15 x^2\right )\right )}{-7776 x^2-6480 x^4-2160 x^6+3125 e^{25} x^7-360 x^8-30 x^{10}-x^{12}+e^{20} \left (-18750 x^6-3125 x^8\right )+e^{15} \left (45000 x^5+15000 x^7+1250 x^9\right )+e^{10} \left (-54000 x^4-27000 x^6-4500 x^8-250 x^{10}\right )+e^5 \left (32400 x^3+21600 x^5+5400 x^7+600 x^9+25 x^{11}\right )} \, dx=\text {Hanged} \] Input:
int((exp(x)*(18*x + exp(5)*(75*x - 15*x^2) - 27*x^2 + 3*x^3 - 18))/(exp(20 )*(18750*x^6 + 3125*x^8) - exp(5)*(32400*x^3 + 21600*x^5 + 5400*x^7 + 600* x^9 + 25*x^11) - 3125*x^7*exp(25) - exp(15)*(45000*x^5 + 15000*x^7 + 1250* x^9) + 7776*x^2 + 6480*x^4 + 2160*x^6 + 360*x^8 + 30*x^10 + x^12 + exp(10) *(54000*x^4 + 27000*x^6 + 4500*x^8 + 250*x^10)),x)
Output:
\text{Hanged}
Time = 0.16 (sec) , antiderivative size = 108, normalized size of antiderivative = 5.14 \[ \int \frac {e^x \left (18-18 x+27 x^2-3 x^3+e^5 \left (-75 x+15 x^2\right )\right )}{-7776 x^2-6480 x^4-2160 x^6+3125 e^{25} x^7-360 x^8-30 x^{10}-x^{12}+e^{20} \left (-18750 x^6-3125 x^8\right )+e^{15} \left (45000 x^5+15000 x^7+1250 x^9\right )+e^{10} \left (-54000 x^4-27000 x^6-4500 x^8-250 x^{10}\right )+e^5 \left (32400 x^3+21600 x^5+5400 x^7+600 x^9+25 x^{11}\right )} \, dx=\frac {3 e^{x}}{x \left (625 e^{20} x^{4}-500 e^{15} x^{5}-3000 e^{15} x^{3}+150 e^{10} x^{6}+1800 e^{10} x^{4}+5400 e^{10} x^{2}-20 e^{5} x^{7}-360 e^{5} x^{5}-2160 e^{5} x^{3}+x^{8}-4320 e^{5} x +24 x^{6}+216 x^{4}+864 x^{2}+1296\right )} \] Input:
int(((15*x^2-75*x)*exp(5)-3*x^3+27*x^2-18*x+18)*exp(x)/(3125*x^7*exp(5)^5+ (-3125*x^8-18750*x^6)*exp(5)^4+(1250*x^9+15000*x^7+45000*x^5)*exp(5)^3+(-2 50*x^10-4500*x^8-27000*x^6-54000*x^4)*exp(5)^2+(25*x^11+600*x^9+5400*x^7+2 1600*x^5+32400*x^3)*exp(5)-x^12-30*x^10-360*x^8-2160*x^6-6480*x^4-7776*x^2 ),x)
Output:
(3*e**x)/(x*(625*e**20*x**4 - 500*e**15*x**5 - 3000*e**15*x**3 + 150*e**10 *x**6 + 1800*e**10*x**4 + 5400*e**10*x**2 - 20*e**5*x**7 - 360*e**5*x**5 - 2160*e**5*x**3 - 4320*e**5*x + x**8 + 24*x**6 + 216*x**4 + 864*x**2 + 129 6))