Integrand size = 231, antiderivative size = 28 \[ \int \frac {9796900-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+31285 x+e^{2 x} \left (10945000+7500 x-7500 x^2\right )+e^{4 x} \left (1093800+50 x-100 x^2\right )+e^{3 x} \left (-4376000-1000 x+1500 x^2\right )+e^x \left (-15650000-25000 x+12500 x^2\right )+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}+30 x\right ) \log (x)+9 \log ^2(x)}{9796900-15650000 e^x+10945000 e^{2 x}-4376000 e^{3 x}+1093800 e^{4 x}-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}\right ) \log (x)+9 \log ^2(x)} \, dx=x+\frac {x^2}{\left (5-e^x\right )^4+\frac {1}{5} (5+3 \log (x))} \]
Time = 0.19 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.46 \[ \int \frac {9796900-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+31285 x+e^{2 x} \left (10945000+7500 x-7500 x^2\right )+e^{4 x} \left (1093800+50 x-100 x^2\right )+e^{3 x} \left (-4376000-1000 x+1500 x^2\right )+e^x \left (-15650000-25000 x+12500 x^2\right )+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}+30 x\right ) \log (x)+9 \log ^2(x)}{9796900-15650000 e^x+10945000 e^{2 x}-4376000 e^{3 x}+1093800 e^{4 x}-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}\right ) \log (x)+9 \log ^2(x)} \, dx=x+\frac {5 x^2}{3130-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3 \log (x)} \]
Integrate[(9796900 - 175000*E^(5*x) + 17500*E^(6*x) - 1000*E^(7*x) + 25*E^ (8*x) + 31285*x + E^(2*x)*(10945000 + 7500*x - 7500*x^2) + E^(4*x)*(109380 0 + 50*x - 100*x^2) + E^(3*x)*(-4376000 - 1000*x + 1500*x^2) + E^x*(-15650 000 - 25000*x + 12500*x^2) + (18780 - 15000*E^x + 4500*E^(2*x) - 600*E^(3* x) + 30*E^(4*x) + 30*x)*Log[x] + 9*Log[x]^2)/(9796900 - 15650000*E^x + 109 45000*E^(2*x) - 4376000*E^(3*x) + 1093800*E^(4*x) - 175000*E^(5*x) + 17500 *E^(6*x) - 1000*E^(7*x) + 25*E^(8*x) + (18780 - 15000*E^x + 4500*E^(2*x) - 600*E^(3*x) + 30*E^(4*x))*Log[x] + 9*Log[x]^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.
| \(\displaystyle \int \frac {e^{2 x} \left (-7500 x^2+7500 x+10945000\right )+e^{4 x} \left (-100 x^2+50 x+1093800\right )+e^{3 x} \left (1500 x^2-1000 x-4376000\right )+e^x \left (12500 x^2-25000 x-15650000\right )-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+31285 x+9 \log ^2(x)+\left (30 x-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}+18780\right ) \log (x)+9796900}{-15650000 e^x+10945000 e^{2 x}-4376000 e^{3 x}+1093800 e^{4 x}-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+9 \log ^2(x)+\left (-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}+18780\right ) \log (x)+9796900} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {e^{2 x} \left (-7500 x^2+7500 x+10945000\right )+e^{4 x} \left (-100 x^2+50 x+1093800\right )+e^{3 x} \left (1500 x^2-1000 x-4376000\right )+e^x \left (12500 x^2-25000 x-15650000\right )-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+31285 x+9 \log ^2(x)+\left (30 x-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}+18780\right ) \log (x)+9796900}{\left (-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3 \log (x)+3130\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {10 x (2 x-1)}{-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3 \log (x)+3130}-\frac {5 x \left (7500 e^x x-1500 e^{2 x} x+100 e^{3 x} x-12520 x-12 x \log (x)+3\right )}{\left (-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3 \log (x)+3130\right )^2}+1\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 62600 \int \frac {x^2}{\left (3 \log (x)-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3130\right )^2}dx-37500 \int \frac {e^x x^2}{\left (3 \log (x)-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3130\right )^2}dx+7500 \int \frac {e^{2 x} x^2}{\left (3 \log (x)-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3130\right )^2}dx-500 \int \frac {e^{3 x} x^2}{\left (3 \log (x)-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3130\right )^2}dx+60 \int \frac {x^2 \log (x)}{\left (3 \log (x)-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3130\right )^2}dx-20 \int \frac {x^2}{3 \log (x)-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3130}dx-15 \int \frac {x}{\left (3 \log (x)-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3130\right )^2}dx+10 \int \frac {x}{3 \log (x)-2500 e^x+750 e^{2 x}-100 e^{3 x}+5 e^{4 x}+3130}dx+x\) |
Int[(9796900 - 175000*E^(5*x) + 17500*E^(6*x) - 1000*E^(7*x) + 25*E^(8*x) + 31285*x + E^(2*x)*(10945000 + 7500*x - 7500*x^2) + E^(4*x)*(1093800 + 50 *x - 100*x^2) + E^(3*x)*(-4376000 - 1000*x + 1500*x^2) + E^x*(-15650000 - 25000*x + 12500*x^2) + (18780 - 15000*E^x + 4500*E^(2*x) - 600*E^(3*x) + 3 0*E^(4*x) + 30*x)*Log[x] + 9*Log[x]^2)/(9796900 - 15650000*E^x + 10945000* E^(2*x) - 4376000*E^(3*x) + 1093800*E^(4*x) - 175000*E^(5*x) + 17500*E^(6* x) - 1000*E^(7*x) + 25*E^(8*x) + (18780 - 15000*E^x + 4500*E^(2*x) - 600*E ^(3*x) + 30*E^(4*x))*Log[x] + 9*Log[x]^2),x]
3.6.83.3.1 Defintions of rubi rules used
Time = 0.84 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.36
| method | result | size |
| risch | \(x +\frac {5 x^{2}}{5 \,{\mathrm e}^{4 x}-100 \,{\mathrm e}^{3 x}+750 \,{\mathrm e}^{2 x}+3 \ln \left (x \right )-2500 \,{\mathrm e}^{x}+3130}\) | \(38\) |
| parallelrisch | \(\frac {939000 x +225000 x \,{\mathrm e}^{2 x}-30000 x \,{\mathrm e}^{3 x}-750000 \,{\mathrm e}^{x} x +900 x \ln \left (x \right )+1500 x \,{\mathrm e}^{4 x}+1500 x^{2}}{1500 \,{\mathrm e}^{4 x}-30000 \,{\mathrm e}^{3 x}+225000 \,{\mathrm e}^{2 x}+900 \ln \left (x \right )-750000 \,{\mathrm e}^{x}+939000}\) | \(73\) |
int((9*ln(x)^2+(30*exp(x)^4-600*exp(x)^3+4500*exp(x)^2-15000*exp(x)+30*x+1 8780)*ln(x)+25*exp(x)^8-1000*exp(x)^7+17500*exp(x)^6-175000*exp(x)^5+(-100 *x^2+50*x+1093800)*exp(x)^4+(1500*x^2-1000*x-4376000)*exp(x)^3+(-7500*x^2+ 7500*x+10945000)*exp(x)^2+(12500*x^2-25000*x-15650000)*exp(x)+31285*x+9796 900)/(9*ln(x)^2+(30*exp(x)^4-600*exp(x)^3+4500*exp(x)^2-15000*exp(x)+18780 )*ln(x)+25*exp(x)^8-1000*exp(x)^7+17500*exp(x)^6-175000*exp(x)^5+1093800*e xp(x)^4-4376000*exp(x)^3+10945000*exp(x)^2-15650000*exp(x)+9796900),x,meth od=_RETURNVERBOSE)
Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (23) = 46\).
Time = 0.26 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.54 \[ \int \frac {9796900-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+31285 x+e^{2 x} \left (10945000+7500 x-7500 x^2\right )+e^{4 x} \left (1093800+50 x-100 x^2\right )+e^{3 x} \left (-4376000-1000 x+1500 x^2\right )+e^x \left (-15650000-25000 x+12500 x^2\right )+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}+30 x\right ) \log (x)+9 \log ^2(x)}{9796900-15650000 e^x+10945000 e^{2 x}-4376000 e^{3 x}+1093800 e^{4 x}-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}\right ) \log (x)+9 \log ^2(x)} \, dx=\frac {5 \, x^{2} + 5 \, x e^{\left (4 \, x\right )} - 100 \, x e^{\left (3 \, x\right )} + 750 \, x e^{\left (2 \, x\right )} - 2500 \, x e^{x} + 3 \, x \log \left (x\right ) + 3130 \, x}{5 \, e^{\left (4 \, x\right )} - 100 \, e^{\left (3 \, x\right )} + 750 \, e^{\left (2 \, x\right )} - 2500 \, e^{x} + 3 \, \log \left (x\right ) + 3130} \]
integrate((9*log(x)^2+(30*exp(x)^4-600*exp(x)^3+4500*exp(x)^2-15000*exp(x) +30*x+18780)*log(x)+25*exp(x)^8-1000*exp(x)^7+17500*exp(x)^6-175000*exp(x) ^5+(-100*x^2+50*x+1093800)*exp(x)^4+(1500*x^2-1000*x-4376000)*exp(x)^3+(-7 500*x^2+7500*x+10945000)*exp(x)^2+(12500*x^2-25000*x-15650000)*exp(x)+3128 5*x+9796900)/(9*log(x)^2+(30*exp(x)^4-600*exp(x)^3+4500*exp(x)^2-15000*exp (x)+18780)*log(x)+25*exp(x)^8-1000*exp(x)^7+17500*exp(x)^6-175000*exp(x)^5 +1093800*exp(x)^4-4376000*exp(x)^3+10945000*exp(x)^2-15650000*exp(x)+97969 00),x, algorithm=\
(5*x^2 + 5*x*e^(4*x) - 100*x*e^(3*x) + 750*x*e^(2*x) - 2500*x*e^x + 3*x*lo g(x) + 3130*x)/(5*e^(4*x) - 100*e^(3*x) + 750*e^(2*x) - 2500*e^x + 3*log(x ) + 3130)
Time = 0.23 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.29 \[ \int \frac {9796900-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+31285 x+e^{2 x} \left (10945000+7500 x-7500 x^2\right )+e^{4 x} \left (1093800+50 x-100 x^2\right )+e^{3 x} \left (-4376000-1000 x+1500 x^2\right )+e^x \left (-15650000-25000 x+12500 x^2\right )+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}+30 x\right ) \log (x)+9 \log ^2(x)}{9796900-15650000 e^x+10945000 e^{2 x}-4376000 e^{3 x}+1093800 e^{4 x}-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}\right ) \log (x)+9 \log ^2(x)} \, dx=\frac {x^{2}}{e^{4 x} - 20 e^{3 x} + 150 e^{2 x} - 500 e^{x} + \frac {3 \log {\left (x \right )}}{5} + 626} + x \]
integrate((9*ln(x)**2+(30*exp(x)**4-600*exp(x)**3+4500*exp(x)**2-15000*exp (x)+30*x+18780)*ln(x)+25*exp(x)**8-1000*exp(x)**7+17500*exp(x)**6-175000*e xp(x)**5+(-100*x**2+50*x+1093800)*exp(x)**4+(1500*x**2-1000*x-4376000)*exp (x)**3+(-7500*x**2+7500*x+10945000)*exp(x)**2+(12500*x**2-25000*x-15650000 )*exp(x)+31285*x+9796900)/(9*ln(x)**2+(30*exp(x)**4-600*exp(x)**3+4500*exp (x)**2-15000*exp(x)+18780)*ln(x)+25*exp(x)**8-1000*exp(x)**7+17500*exp(x)* *6-175000*exp(x)**5+1093800*exp(x)**4-4376000*exp(x)**3+10945000*exp(x)**2 -15650000*exp(x)+9796900),x)
Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (23) = 46\).
Time = 0.37 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.54 \[ \int \frac {9796900-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+31285 x+e^{2 x} \left (10945000+7500 x-7500 x^2\right )+e^{4 x} \left (1093800+50 x-100 x^2\right )+e^{3 x} \left (-4376000-1000 x+1500 x^2\right )+e^x \left (-15650000-25000 x+12500 x^2\right )+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}+30 x\right ) \log (x)+9 \log ^2(x)}{9796900-15650000 e^x+10945000 e^{2 x}-4376000 e^{3 x}+1093800 e^{4 x}-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}\right ) \log (x)+9 \log ^2(x)} \, dx=\frac {5 \, x^{2} + 5 \, x e^{\left (4 \, x\right )} - 100 \, x e^{\left (3 \, x\right )} + 750 \, x e^{\left (2 \, x\right )} - 2500 \, x e^{x} + 3 \, x \log \left (x\right ) + 3130 \, x}{5 \, e^{\left (4 \, x\right )} - 100 \, e^{\left (3 \, x\right )} + 750 \, e^{\left (2 \, x\right )} - 2500 \, e^{x} + 3 \, \log \left (x\right ) + 3130} \]
integrate((9*log(x)^2+(30*exp(x)^4-600*exp(x)^3+4500*exp(x)^2-15000*exp(x) +30*x+18780)*log(x)+25*exp(x)^8-1000*exp(x)^7+17500*exp(x)^6-175000*exp(x) ^5+(-100*x^2+50*x+1093800)*exp(x)^4+(1500*x^2-1000*x-4376000)*exp(x)^3+(-7 500*x^2+7500*x+10945000)*exp(x)^2+(12500*x^2-25000*x-15650000)*exp(x)+3128 5*x+9796900)/(9*log(x)^2+(30*exp(x)^4-600*exp(x)^3+4500*exp(x)^2-15000*exp (x)+18780)*log(x)+25*exp(x)^8-1000*exp(x)^7+17500*exp(x)^6-175000*exp(x)^5 +1093800*exp(x)^4-4376000*exp(x)^3+10945000*exp(x)^2-15650000*exp(x)+97969 00),x, algorithm=\
(5*x^2 + 5*x*e^(4*x) - 100*x*e^(3*x) + 750*x*e^(2*x) - 2500*x*e^x + 3*x*lo g(x) + 3130*x)/(5*e^(4*x) - 100*e^(3*x) + 750*e^(2*x) - 2500*e^x + 3*log(x ) + 3130)
Leaf count of result is larger than twice the leaf count of optimal. 1712 vs. \(2 (23) = 46\).
Time = 25.33 (sec) , antiderivative size = 1712, normalized size of antiderivative = 61.14 \[ \int \frac {9796900-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+31285 x+e^{2 x} \left (10945000+7500 x-7500 x^2\right )+e^{4 x} \left (1093800+50 x-100 x^2\right )+e^{3 x} \left (-4376000-1000 x+1500 x^2\right )+e^x \left (-15650000-25000 x+12500 x^2\right )+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}+30 x\right ) \log (x)+9 \log ^2(x)}{9796900-15650000 e^x+10945000 e^{2 x}-4376000 e^{3 x}+1093800 e^{4 x}-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}\right ) \log (x)+9 \log ^2(x)} \, dx=\text {Too large to display} \]
integrate((9*log(x)^2+(30*exp(x)^4-600*exp(x)^3+4500*exp(x)^2-15000*exp(x) +30*x+18780)*log(x)+25*exp(x)^8-1000*exp(x)^7+17500*exp(x)^6-175000*exp(x) ^5+(-100*x^2+50*x+1093800)*exp(x)^4+(1500*x^2-1000*x-4376000)*exp(x)^3+(-7 500*x^2+7500*x+10945000)*exp(x)^2+(12500*x^2-25000*x-15650000)*exp(x)+3128 5*x+9796900)/(9*log(x)^2+(30*exp(x)^4-600*exp(x)^3+4500*exp(x)^2-15000*exp (x)+18780)*log(x)+25*exp(x)^8-1000*exp(x)^7+17500*exp(x)^6-175000*exp(x)^5 +1093800*exp(x)^4-4376000*exp(x)^3+10945000*exp(x)^2-15650000*exp(x)+97969 00),x, algorithm=\
(103680*x^6*log(x)^4 + 103680*x^5*e^(4*x)*log(x)^4 - 2073600*x^5*e^(3*x)*l og(x)^4 + 15552000*x^5*e^(2*x)*log(x)^4 - 51840000*x^5*e^x*log(x)^4 + 6220 8*x^5*log(x)^5 + 108691200*x^6*log(x)^3 + 108691200*x^5*e^(4*x)*log(x)^3 - 2173392000*x^5*e^(3*x)*log(x)^3 + 16295040000*x^5*e^(2*x)*log(x)^3 - 5428 0800000*x^5*e^x*log(x)^3 + 130170240*x^5*log(x)^4 + 129600*x^4*e^(3*x)*log (x)^4 - 2592000*x^4*e^(2*x)*log(x)^4 + 19440000*x^4*e^x*log(x)^4 + 15552*x ^4*log(x)^5 + 541728000*x^6*log(x)^2 + 541728000*x^5*e^(4*x)*log(x)^2 - 10 382616000*x^5*e^(3*x)*log(x)^2 + 72220320000*x^5*e^(2*x)*log(x)^2 - 203072 400000*x^5*e^x*log(x)^2 + 68257944000*x^5*log(x)^3 - 103680*x^4*e^(4*x)*lo g(x)^3 + 272937600*x^4*e^(3*x)*log(x)^3 - 5432832000*x^4*e^(2*x)*log(x)^3 + 40681440000*x^4*e^x*log(x)^3 - 16132608*x^4*log(x)^4 + 901920000*x^6*log (x) + 901920000*x^5*e^(4*x)*log(x) - 16535520000*x^5*e^(3*x)*log(x) + 1052 30400000*x^5*e^(2*x)*log(x) - 225528000000*x^5*e^x*log(x) + 170454096000*x ^5*log(x)^2 - 518400*x^4*e^(4*x)*log(x)^2 + 141987312000*x^4*e^(3*x)*log(x )^2 - 2839617180000*x^4*e^(2*x)*log(x)^2 + 21296811600000*x^4*e^x*log(x)^2 - 84547821600*x^4*log(x)^3 - 64800*x^3*e^(3*x)*log(x)^3 + 1134000*x^3*e^( 2*x)*log(x)^3 - 6480000*x^3*e^x*log(x)^3 - 11664*x^3*log(x)^4 + 500800000* x^6 + 500800000*x^5*e^(4*x) - 8764600000*x^5*e^(3*x) + 50092000000*x^5*e^( 2*x) - 62690000000*x^5*e^x + 1772280000*x^5*log(x) - 864000*x^4*e^(4*x)*lo g(x) + 470794068000*x^4*e^(3*x)*log(x) - 9416229390000*x^4*e^(2*x)*log(...
Timed out. \[ \int \frac {9796900-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+31285 x+e^{2 x} \left (10945000+7500 x-7500 x^2\right )+e^{4 x} \left (1093800+50 x-100 x^2\right )+e^{3 x} \left (-4376000-1000 x+1500 x^2\right )+e^x \left (-15650000-25000 x+12500 x^2\right )+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}+30 x\right ) \log (x)+9 \log ^2(x)}{9796900-15650000 e^x+10945000 e^{2 x}-4376000 e^{3 x}+1093800 e^{4 x}-175000 e^{5 x}+17500 e^{6 x}-1000 e^{7 x}+25 e^{8 x}+\left (18780-15000 e^x+4500 e^{2 x}-600 e^{3 x}+30 e^{4 x}\right ) \log (x)+9 \log ^2(x)} \, dx=\int \frac {9\,{\ln \left (x\right )}^2+\left (30\,x+4500\,{\mathrm {e}}^{2\,x}-600\,{\mathrm {e}}^{3\,x}+30\,{\mathrm {e}}^{4\,x}-15000\,{\mathrm {e}}^x+18780\right )\,\ln \left (x\right )+31285\,x-175000\,{\mathrm {e}}^{5\,x}+17500\,{\mathrm {e}}^{6\,x}-1000\,{\mathrm {e}}^{7\,x}+25\,{\mathrm {e}}^{8\,x}+{\mathrm {e}}^{4\,x}\,\left (-100\,x^2+50\,x+1093800\right )-{\mathrm {e}}^{3\,x}\,\left (-1500\,x^2+1000\,x+4376000\right )+{\mathrm {e}}^{2\,x}\,\left (-7500\,x^2+7500\,x+10945000\right )-{\mathrm {e}}^x\,\left (-12500\,x^2+25000\,x+15650000\right )+9796900}{9\,{\ln \left (x\right )}^2+\left (4500\,{\mathrm {e}}^{2\,x}-600\,{\mathrm {e}}^{3\,x}+30\,{\mathrm {e}}^{4\,x}-15000\,{\mathrm {e}}^x+18780\right )\,\ln \left (x\right )+10945000\,{\mathrm {e}}^{2\,x}-4376000\,{\mathrm {e}}^{3\,x}+1093800\,{\mathrm {e}}^{4\,x}-175000\,{\mathrm {e}}^{5\,x}+17500\,{\mathrm {e}}^{6\,x}-1000\,{\mathrm {e}}^{7\,x}+25\,{\mathrm {e}}^{8\,x}-15650000\,{\mathrm {e}}^x+9796900} \,d x \]
int((31285*x - 175000*exp(5*x) + 17500*exp(6*x) - 1000*exp(7*x) + 25*exp(8 *x) + exp(4*x)*(50*x - 100*x^2 + 1093800) - exp(3*x)*(1000*x - 1500*x^2 + 4376000) + exp(2*x)*(7500*x - 7500*x^2 + 10945000) + 9*log(x)^2 + log(x)*( 30*x + 4500*exp(2*x) - 600*exp(3*x) + 30*exp(4*x) - 15000*exp(x) + 18780) - exp(x)*(25000*x - 12500*x^2 + 15650000) + 9796900)/(10945000*exp(2*x) - 4376000*exp(3*x) + 1093800*exp(4*x) - 175000*exp(5*x) + 17500*exp(6*x) - 1 000*exp(7*x) + 25*exp(8*x) - 15650000*exp(x) + 9*log(x)^2 + log(x)*(4500*e xp(2*x) - 600*exp(3*x) + 30*exp(4*x) - 15000*exp(x) + 18780) + 9796900),x)
int((31285*x - 175000*exp(5*x) + 17500*exp(6*x) - 1000*exp(7*x) + 25*exp(8 *x) + exp(4*x)*(50*x - 100*x^2 + 1093800) - exp(3*x)*(1000*x - 1500*x^2 + 4376000) + exp(2*x)*(7500*x - 7500*x^2 + 10945000) + 9*log(x)^2 + log(x)*( 30*x + 4500*exp(2*x) - 600*exp(3*x) + 30*exp(4*x) - 15000*exp(x) + 18780) - exp(x)*(25000*x - 12500*x^2 + 15650000) + 9796900)/(10945000*exp(2*x) - 4376000*exp(3*x) + 1093800*exp(4*x) - 175000*exp(5*x) + 17500*exp(6*x) - 1 000*exp(7*x) + 25*exp(8*x) - 15650000*exp(x) + 9*log(x)^2 + log(x)*(4500*e xp(2*x) - 600*exp(3*x) + 30*exp(4*x) - 15000*exp(x) + 18780) + 9796900), x )