\(\int \frac {-26244+13122 e^{10}-26244 x+7776 x^2+62208 x^3+174960 x^4+209952 x^5+91854 x^6+e^5 (-23328 x-104976 x^2-104976 x^3)+e^{4 x} (486 x^2+648 x^3)+e^{3 x} (-3888 x^2-11664 x^3-5832 x^4)+(-26244 e^5+23328 x+104976 x^2+104976 x^3) \log (3)+13122 \log ^2(3)+e^{2 x} (11664 x^2+54432 x^3+67068 x^4+17496 x^5+e^5 (-5832 x-5832 x^2)+(5832 x+5832 x^2) \log (3))+e^x (-15552 x^2-98496 x^3-198288 x^4-139968 x^5-17496 x^6+e^5 (23328 x+64152 x^2+17496 x^3)+(-23328 x-64152 x^2-17496 x^3) \log (3))}{26244 x^2+6561 e^{20} x^2+26244 x^3+1377 x^4-33696 x^5-85280 x^6+e^{8 x} x^6-101904 x^7-45108 x^8+35262 x^9+90720 x^{10}+108864 x^{11}+81648 x^{12}+34992 x^{13}+6561 x^{14}+e^{15} (-11664 x^3-34992 x^4-26244 x^5)+e^{7 x} (-16 x^6-24 x^7)+e^{10} (-26244 x^2-13122 x^3+7776 x^4+46656 x^5+104976 x^6+104976 x^7+39366 x^8)+e^5 (23328 x^3+81648 x^4+85176 x^5+5508 x^6-77760 x^7-155520 x^8-174960 x^9-104976 x^{10}-26244 x^{11})+(-26244 e^{15} x^2-23328 x^3-81648 x^4-85176 x^5-5508 x^6+77760 x^7+155520 x^8+174960 x^9+104976 x^{10}+26244 x^{11}+e^{10} (34992 x^3+104976 x^4+78732 x^5)+e^5 (52488 x^2+26244 x^3-15552 x^4-93312 x^5-209952 x^6-209952 x^7-78732 x^8)) \log (3)+(-26244 x^2+39366 e^{10} x^2-13122 x^3+7776 x^4+46656 x^5+104976 x^6+104976 x^7+39366 x^8+e^5 (-34992 x^3-104976 x^4-78732 x^5)) \log ^2(3)+(-26244 e^5 x^2+11664 x^3+34992 x^4+26244 x^5) \log ^3(3)+6561 x^2 \log ^4(3)+e^{6 x} (-36 e^5 x^5+112 x^6+336 x^7+252 x^8+36 x^5 \log (3))+e^{5 x} (-448 x^6-2016 x^7-3024 x^8-1512 x^9+e^5 (432 x^5+648 x^6)+(-432 x^5-648 x^6) \log (3))+e^{4 x} (-324 x^4+486 e^{10} x^4-162 x^5+1120 x^6+6720 x^7+15120 x^8+15120 x^9+5670 x^{10}+e^5 (-2160 x^5-6480 x^6-4860 x^7)+(-972 e^5 x^4+2160 x^5+6480 x^6+4860 x^7) \log (3)+486 x^4 \log ^2(3))+e^{3 x} (2592 x^4+5184 x^5+152 x^6-13440 x^7-40320 x^8-60480 x^9-45360 x^{10}-13608 x^{11}+e^{10} (-3888 x^4-5832 x^5)+e^5 (5760 x^5+25920 x^6+38880 x^7+19440 x^8)+(-5760 x^5-25920 x^6-38880 x^7-19440 x^8+e^5 (7776 x^4+11664 x^5)) \log (3)+(-3888 x^4-5832 x^5) \log ^2(3))+e^{2 x} (-2916 e^{15} x^3-7776 x^4-27216 x^5-27368 x^6+7380 x^7+60480 x^8+120960 x^9+136080 x^{10}+81648 x^{11}+20412 x^{12}+e^{10} (11664 x^4+34992 x^5+26244 x^6)+e^5 (5832 x^3+2916 x^4-8640 x^5-51840 x^6-116640 x^7-116640 x^8-43740 x^9)+(-5832 x^3+8748 e^{10} x^3-2916 x^4+8640 x^5+51840 x^6+116640 x^7+116640 x^8+43740 x^9+e^5 (-23328 x^4-69984 x^5-52488 x^6)) \log (3)+(-8748 e^5 x^3+11664 x^4+34992 x^5+26244 x^6) \log ^2(3)+2916 x^3 \log ^3(3))+e^x (10368 x^4+51840 x^5+92288 x^6+59232 x^7-30888 x^8-120960 x^9-181440 x^{10}-163296 x^{11}-81648 x^{12}-17496 x^{13}+e^{15} (11664 x^3+17496 x^4)+e^{10} (-15552 x^4-69984 x^5-104976 x^6-52488 x^7)+e^5 (-23328 x^3-46656 x^4-10584 x^5+51840 x^6+155520 x^7+233280 x^8+174960 x^9+52488 x^{10})+(23328 x^3+46656 x^4+10584 x^5-51840 x^6-155520 x^7-233280 x^8-174960 x^9-52488 x^{10}+e^{10} (-34992 x^3-52488 x^4)+e^5 (31104 x^4+139968 x^5+209952 x^6+104976 x^7)) \log (3)+(-15552 x^4-69984 x^5-104976 x^6-52488 x^7+e^5 (34992 x^3+52488 x^4)) \log ^2(3)+(-11664 x^3-17496 x^4) \log ^3(3))} \, dx\) [710]

Optimal result

Integrand size = 1521, antiderivative size = 39 \[ \text {the integral} =\frac {2}{x \left (2+x-\left (-e^5+\left (\frac {1}{3} \left (-2+e^x\right )-x\right )^2 x+\log (3)\right )^2\right )} \] Output:

2/(2-(x*(1/3*exp(x)-2/3-x)^2-exp(5)+ln(3))^2+x)/x
                                                                                    
                                                                                    
 

Mathematica [F(-1)]

Timed out. \[ \text {the integral} =\text {\$Aborted} \] Input:

Integrate[(-26244 + 13122*E^10 - 26244*x + 7776*x^2 + 62208*x^3 + 174960*x 
^4 + 209952*x^5 + 91854*x^6 + E^5*(-23328*x - 104976*x^2 - 104976*x^3) + E 
^(4*x)*(486*x^2 + 648*x^3) + E^(3*x)*(-3888*x^2 - 11664*x^3 - 5832*x^4) + 
(-26244*E^5 + 23328*x + 104976*x^2 + 104976*x^3)*Log[3] + 13122*Log[3]^2 + 
 E^(2*x)*(11664*x^2 + 54432*x^3 + 67068*x^4 + 17496*x^5 + E^5*(-5832*x - 5 
832*x^2) + (5832*x + 5832*x^2)*Log[3]) + E^x*(-15552*x^2 - 98496*x^3 - 198 
288*x^4 - 139968*x^5 - 17496*x^6 + E^5*(23328*x + 64152*x^2 + 17496*x^3) + 
 (-23328*x - 64152*x^2 - 17496*x^3)*Log[3]))/(26244*x^2 + 6561*E^20*x^2 + 
26244*x^3 + 1377*x^4 - 33696*x^5 - 85280*x^6 + E^(8*x)*x^6 - 101904*x^7 - 
45108*x^8 + 35262*x^9 + 90720*x^10 + 108864*x^11 + 81648*x^12 + 34992*x^13 
 + 6561*x^14 + E^15*(-11664*x^3 - 34992*x^4 - 26244*x^5) + E^(7*x)*(-16*x^ 
6 - 24*x^7) + E^10*(-26244*x^2 - 13122*x^3 + 7776*x^4 + 46656*x^5 + 104976 
*x^6 + 104976*x^7 + 39366*x^8) + E^5*(23328*x^3 + 81648*x^4 + 85176*x^5 + 
5508*x^6 - 77760*x^7 - 155520*x^8 - 174960*x^9 - 104976*x^10 - 26244*x^11) 
 + (-26244*E^15*x^2 - 23328*x^3 - 81648*x^4 - 85176*x^5 - 5508*x^6 + 77760 
*x^7 + 155520*x^8 + 174960*x^9 + 104976*x^10 + 26244*x^11 + E^10*(34992*x^ 
3 + 104976*x^4 + 78732*x^5) + E^5*(52488*x^2 + 26244*x^3 - 15552*x^4 - 933 
12*x^5 - 209952*x^6 - 209952*x^7 - 78732*x^8))*Log[3] + (-26244*x^2 + 3936 
6*E^10*x^2 - 13122*x^3 + 7776*x^4 + 46656*x^5 + 104976*x^6 + 104976*x^7 + 
39366*x^8 + E^5*(-34992*x^3 - 104976*x^4 - 78732*x^5))*Log[3]^2 + (-26244* 
E^5*x^2 + 11664*x^3 + 34992*x^4 + 26244*x^5)*Log[3]^3 + 6561*x^2*Log[3]^4 
+ E^(6*x)*(-36*E^5*x^5 + 112*x^6 + 336*x^7 + 252*x^8 + 36*x^5*Log[3]) + E^ 
(5*x)*(-448*x^6 - 2016*x^7 - 3024*x^8 - 1512*x^9 + E^5*(432*x^5 + 648*x^6) 
 + (-432*x^5 - 648*x^6)*Log[3]) + E^(4*x)*(-324*x^4 + 486*E^10*x^4 - 162*x 
^5 + 1120*x^6 + 6720*x^7 + 15120*x^8 + 15120*x^9 + 5670*x^10 + E^5*(-2160* 
x^5 - 6480*x^6 - 4860*x^7) + (-972*E^5*x^4 + 2160*x^5 + 6480*x^6 + 4860*x^ 
7)*Log[3] + 486*x^4*Log[3]^2) + E^(3*x)*(2592*x^4 + 5184*x^5 + 152*x^6 - 1 
3440*x^7 - 40320*x^8 - 60480*x^9 - 45360*x^10 - 13608*x^11 + E^10*(-3888*x 
^4 - 5832*x^5) + E^5*(5760*x^5 + 25920*x^6 + 38880*x^7 + 19440*x^8) + (-57 
60*x^5 - 25920*x^6 - 38880*x^7 - 19440*x^8 + E^5*(7776*x^4 + 11664*x^5))*L 
og[3] + (-3888*x^4 - 5832*x^5)*Log[3]^2) + E^(2*x)*(-2916*E^15*x^3 - 7776* 
x^4 - 27216*x^5 - 27368*x^6 + 7380*x^7 + 60480*x^8 + 120960*x^9 + 136080*x 
^10 + 81648*x^11 + 20412*x^12 + E^10*(11664*x^4 + 34992*x^5 + 26244*x^6) + 
 E^5*(5832*x^3 + 2916*x^4 - 8640*x^5 - 51840*x^6 - 116640*x^7 - 116640*x^8 
 - 43740*x^9) + (-5832*x^3 + 8748*E^10*x^3 - 2916*x^4 + 8640*x^5 + 51840*x 
^6 + 116640*x^7 + 116640*x^8 + 43740*x^9 + E^5*(-23328*x^4 - 69984*x^5 - 5 
2488*x^6))*Log[3] + (-8748*E^5*x^3 + 11664*x^4 + 34992*x^5 + 26244*x^6)*Lo 
g[3]^2 + 2916*x^3*Log[3]^3) + E^x*(10368*x^4 + 51840*x^5 + 92288*x^6 + 592 
32*x^7 - 30888*x^8 - 120960*x^9 - 181440*x^10 - 163296*x^11 - 81648*x^12 - 
 17496*x^13 + E^15*(11664*x^3 + 17496*x^4) + E^10*(-15552*x^4 - 69984*x^5 
- 104976*x^6 - 52488*x^7) + E^5*(-23328*x^3 - 46656*x^4 - 10584*x^5 + 5184 
0*x^6 + 155520*x^7 + 233280*x^8 + 174960*x^9 + 52488*x^10) + (23328*x^3 + 
46656*x^4 + 10584*x^5 - 51840*x^6 - 155520*x^7 - 233280*x^8 - 174960*x^9 - 
 52488*x^10 + E^10*(-34992*x^3 - 52488*x^4) + E^5*(31104*x^4 + 139968*x^5 
+ 209952*x^6 + 104976*x^7))*Log[3] + (-15552*x^4 - 69984*x^5 - 104976*x^6 
- 52488*x^7 + E^5*(34992*x^3 + 52488*x^4))*Log[3]^2 + (-11664*x^3 - 17496* 
x^4)*Log[3]^3)),x]
 

Output:

$Aborted
 

Rubi [F]

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 {91854 x^6+209952 x^5+174960 x^4+62208 x^3+7776 x^2-26244 x+e^5 \left (-104976 x^3-104976 x^2-23328 x\right )+e^{4 x} \left (648 x^3+486 x^2\right )+e^{3 x} \left (-5832 x^4-11664 x^3-3888 x^2\right )+e^{2 x} \left (17496 x^5+67068 x^4+54432 x^3+11664 x^2+e^5 \left (-5832 x^2-5832 x\right )+\left (5832 x^2+5832 x\right ) \log (3)\right )+e^x \left (-17496 x^6-139968 x^5-198288 x^4-98496 x^3-15552 x^2+e^5 \left (17496 x^3+64152 x^2+23328 x\right )+\left (-17496 x^3-64152 x^2-23328 x\right ) \log (3)\right )+13122 \log ^2(3)+\left (104976 x^3+104976 x^2+23328 x-26244 e^5\right ) \log (3)+13122 e^{10}-26244}{6561 x^{14}+34992 x^{13}+81648 x^{12}+108864 x^{11}+90720 x^{10}+35262 x^9-45108 x^8-101904 x^7+e^{8 x} x^6-85280 x^6-33696 x^5+1377 x^4+26244 x^3+6561 \log ^4(3) x^2+6561 e^{20} x^2+26244 x^2+e^{15} \left (-26244 x^5-34992 x^4-11664 x^3\right )+e^{7 x} \left (-24 x^7-16 x^6\right )+e^{10} \left (39366 x^8+104976 x^7+104976 x^6+46656 x^5+7776 x^4-13122 x^3-26244 x^2\right )+e^5 \left (-26244 x^{11}-104976 x^{10}-174960 x^9-155520 x^8-77760 x^7+5508 x^6+85176 x^5+81648 x^4+23328 x^3\right )+e^{6 x} \left (252 x^8+336 x^7+112 x^6+36 \log (3) x^5-36 e^5 x^5\right )+e^{5 x} \left (-1512 x^9-3024 x^8-2016 x^7-448 x^6+e^5 \left (648 x^6+432 x^5\right )+\left (-648 x^6-432 x^5\right ) \log (3)\right )+e^{4 x} \left (5670 x^{10}+15120 x^9+15120 x^8+6720 x^7+1120 x^6-162 x^5+486 \log ^2(3) x^4+486 e^{10} x^4-324 x^4+e^5 \left (-4860 x^7-6480 x^6-2160 x^5\right )+\left (4860 x^7+6480 x^6+2160 x^5-972 e^5 x^4\right ) \log (3)\right )+e^{3 x} \left (-13608 x^{11}-45360 x^{10}-60480 x^9-40320 x^8-13440 x^7+152 x^6+5184 x^5+2592 x^4+e^{10} \left (-5832 x^5-3888 x^4\right )+e^5 \left (19440 x^8+38880 x^7+25920 x^6+5760 x^5\right )+\left (-5832 x^5-3888 x^4\right ) \log ^2(3)+\left (-19440 x^8-38880 x^7-25920 x^6-5760 x^5+e^5 \left (11664 x^5+7776 x^4\right )\right ) \log (3)\right )+e^{2 x} \left (20412 x^{12}+81648 x^{11}+136080 x^{10}+120960 x^9+60480 x^8+7380 x^7-27368 x^6-27216 x^5-7776 x^4+2916 \log ^3(3) x^3-2916 e^{15} x^3+e^{10} \left (26244 x^6+34992 x^5+11664 x^4\right )+e^5 \left (-43740 x^9-116640 x^8-116640 x^7-51840 x^6-8640 x^5+2916 x^4+5832 x^3\right )+\left (26244 x^6+34992 x^5+11664 x^4-8748 e^5 x^3\right ) \log ^2(3)+\left (43740 x^9+116640 x^8+116640 x^7+51840 x^6+8640 x^5-2916 x^4+8748 e^{10} x^3-5832 x^3+e^5 \left (-52488 x^6-69984 x^5-23328 x^4\right )\right ) \log (3)\right )+e^x \left (-17496 x^{13}-81648 x^{12}-163296 x^{11}-181440 x^{10}-120960 x^9-30888 x^8+59232 x^7+92288 x^6+51840 x^5+10368 x^4+e^{15} \left (17496 x^4+11664 x^3\right )+e^{10} \left (-52488 x^7-104976 x^6-69984 x^5-15552 x^4\right )+e^5 \left (52488 x^{10}+174960 x^9+233280 x^8+155520 x^7+51840 x^6-10584 x^5-46656 x^4-23328 x^3\right )+\left (-17496 x^4-11664 x^3\right ) \log ^3(3)+\left (-52488 x^7-104976 x^6-69984 x^5-15552 x^4+e^5 \left (52488 x^4+34992 x^3\right )\right ) \log ^2(3)+\left (-52488 x^{10}-174960 x^9-233280 x^8-155520 x^7-51840 x^6+10584 x^5+46656 x^4+23328 x^3+e^{10} \left (-52488 x^4-34992 x^3\right )+e^5 \left (104976 x^7+209952 x^6+139968 x^5+31104 x^4\right )\right ) \log (3)\right )+\left (26244 x^5+34992 x^4+11664 x^3-26244 e^5 x^2\right ) \log ^3(3)+\left (39366 x^8+104976 x^7+104976 x^6+46656 x^5+7776 x^4-13122 x^3+39366 e^{10} x^2-26244 x^2+e^5 \left (-78732 x^5-104976 x^4-34992 x^3\right )\right ) \log ^2(3)+\left (26244 x^{11}+104976 x^{10}+174960 x^9+155520 x^8+77760 x^7-5508 x^6-85176 x^5-81648 x^4-23328 x^3-26244 e^{15} x^2+e^{10} \left (78732 x^5+104976 x^4+34992 x^3\right )+e^5 \left (-78732 x^8-209952 x^7-209952 x^6-93312 x^5-15552 x^4+26244 x^3+52488 x^2\right )\right ) \log (3)} \, dx\)

\(\Big \downarrow \) 6

\(\displaystyle \int \frac {91854 x^6+209952 x^5+174960 x^4+62208 x^3+7776 x^2-26244 x+e^5 \left (-104976 x^3-104976 x^2-23328 x\right )+e^{4 x} \left (648 x^3+486 x^2\right )+e^{3 x} \left (-5832 x^4-11664 x^3-3888 x^2\right )+e^{2 x} \left (17496 x^5+67068 x^4+54432 x^3+11664 x^2+e^5 \left (-5832 x^2-5832 x\right )+\left (5832 x^2+5832 x\right ) \log (3)\right )+e^x \left (-17496 x^6-139968 x^5-198288 x^4-98496 x^3-15552 x^2+e^5 \left (17496 x^3+64152 x^2+23328 x\right )+\left (-17496 x^3-64152 x^2-23328 x\right ) \log (3)\right )+13122 \log ^2(3)+\left (104976 x^3+104976 x^2+23328 x-26244 e^5\right ) \log (3)+13122 e^{10}-26244}{6561 x^{14}+34992 x^{13}+81648 x^{12}+108864 x^{11}+90720 x^{10}+35262 x^9-45108 x^8-101904 x^7+e^{8 x} x^6-85280 x^6-33696 x^5+1377 x^4+26244 x^3+6561 \log ^4(3) x^2+\left (26244+6561 e^{20}\right ) x^2+e^{15} \left (-26244 x^5-34992 x^4-11664 x^3\right )+e^{7 x} \left (-24 x^7-16 x^6\right )+e^{10} \left (39366 x^8+104976 x^7+104976 x^6+46656 x^5+7776 x^4-13122 x^3-26244 x^2\right )+e^5 \left (-26244 x^{11}-104976 x^{10}-174960 x^9-155520 x^8-77760 x^7+5508 x^6+85176 x^5+81648 x^4+23328 x^3\right )+e^{6 x} \left (252 x^8+336 x^7+112 x^6+36 \log (3) x^5-36 e^5 x^5\right )+e^{5 x} \left (-1512 x^9-3024 x^8-2016 x^7-448 x^6+e^5 \left (648 x^6+432 x^5\right )+\left (-648 x^6-432 x^5\right ) \log (3)\right )+e^{4 x} \left (5670 x^{10}+15120 x^9+15120 x^8+6720 x^7+1120 x^6-162 x^5+486 \log ^2(3) x^4+486 e^{10} x^4-324 x^4+e^5 \left (-4860 x^7-6480 x^6-2160 x^5\right )+\left (4860 x^7+6480 x^6+2160 x^5-972 e^5 x^4\right ) \log (3)\right )+e^{3 x} \left (-13608 x^{11}-45360 x^{10}-60480 x^9-40320 x^8-13440 x^7+152 x^6+5184 x^5+2592 x^4+e^{10} \left (-5832 x^5-3888 x^4\right )+e^5 \left (19440 x^8+38880 x^7+25920 x^6+5760 x^5\right )+\left (-5832 x^5-3888 x^4\right ) \log ^2(3)+\left (-19440 x^8-38880 x^7-25920 x^6-5760 x^5+e^5 \left (11664 x^5+7776 x^4\right )\right ) \log (3)\right )+e^{2 x} \left (20412 x^{12}+81648 x^{11}+136080 x^{10}+120960 x^9+60480 x^8+7380 x^7-27368 x^6-27216 x^5-7776 x^4+2916 \log ^3(3) x^3-2916 e^{15} x^3+e^{10} \left (26244 x^6+34992 x^5+11664 x^4\right )+e^5 \left (-43740 x^9-116640 x^8-116640 x^7-51840 x^6-8640 x^5+2916 x^4+5832 x^3\right )+\left (26244 x^6+34992 x^5+11664 x^4-8748 e^5 x^3\right ) \log ^2(3)+\left (43740 x^9+116640 x^8+116640 x^7+51840 x^6+8640 x^5-2916 x^4+8748 e^{10} x^3-5832 x^3+e^5 \left (-52488 x^6-69984 x^5-23328 x^4\right )\right ) \log (3)\right )+e^x \left (-17496 x^{13}-81648 x^{12}-163296 x^{11}-181440 x^{10}-120960 x^9-30888 x^8+59232 x^7+92288 x^6+51840 x^5+10368 x^4+e^{15} \left (17496 x^4+11664 x^3\right )+e^{10} \left (-52488 x^7-104976 x^6-69984 x^5-15552 x^4\right )+e^5 \left (52488 x^{10}+174960 x^9+233280 x^8+155520 x^7+51840 x^6-10584 x^5-46656 x^4-23328 x^3\right )+\left (-17496 x^4-11664 x^3\right ) \log ^3(3)+\left (-52488 x^7-104976 x^6-69984 x^5-15552 x^4+e^5 \left (52488 x^4+34992 x^3\right )\right ) \log ^2(3)+\left (-52488 x^{10}-174960 x^9-233280 x^8-155520 x^7-51840 x^6+10584 x^5+46656 x^4+23328 x^3+e^{10} \left (-52488 x^4-34992 x^3\right )+e^5 \left (104976 x^7+209952 x^6+139968 x^5+31104 x^4\right )\right ) \log (3)\right )+\left (26244 x^5+34992 x^4+11664 x^3-26244 e^5 x^2\right ) \log ^3(3)+\left (39366 x^8+104976 x^7+104976 x^6+46656 x^5+7776 x^4-13122 x^3+39366 e^{10} x^2-26244 x^2+e^5 \left (-78732 x^5-104976 x^4-34992 x^3\right )\right ) \log ^2(3)+\left (26244 x^{11}+104976 x^{10}+174960 x^9+155520 x^8+77760 x^7-5508 x^6-85176 x^5-81648 x^4-23328 x^3-26244 e^{15} x^2+e^{10} \left (78732 x^5+104976 x^4+34992 x^3\right )+e^5 \left (-78732 x^8-209952 x^7-209952 x^6-93312 x^5-15552 x^4+26244 x^3+52488 x^2\right )\right ) \log (3)}dx\)

\(\Big \downarrow \) 6

\(\displaystyle \int \frac {91854 x^6+209952 x^5+174960 x^4+62208 x^3+7776 x^2-26244 x+e^5 \left (-104976 x^3-104976 x^2-23328 x\right )+e^{4 x} \left (648 x^3+486 x^2\right )+e^{3 x} \left (-5832 x^4-11664 x^3-3888 x^2\right )+e^{2 x} \left (17496 x^5+67068 x^4+54432 x^3+11664 x^2+e^5 \left (-5832 x^2-5832 x\right )+\left (5832 x^2+5832 x\right ) \log (3)\right )+e^x \left (-17496 x^6-139968 x^5-198288 x^4-98496 x^3-15552 x^2+e^5 \left (17496 x^3+64152 x^2+23328 x\right )+\left (-17496 x^3-64152 x^2-23328 x\right ) \log (3)\right )+13122 \log ^2(3)+\left (104976 x^3+104976 x^2+23328 x-26244 e^5\right ) \log (3)+13122 e^{10}-26244}{6561 x^{14}+34992 x^{13}+81648 x^{12}+108864 x^{11}+90720 x^{10}+35262 x^9-45108 x^8-101904 x^7+e^{8 x} x^6-85280 x^6-33696 x^5+1377 x^4+26244 x^3+\left (26244+6561 e^{20}+6561 \log ^4(3)\right ) x^2+e^{15} \left (-26244 x^5-34992 x^4-11664 x^3\right )+e^{7 x} \left (-24 x^7-16 x^6\right )+e^{10} \left (39366 x^8+104976 x^7+104976 x^6+46656 x^5+7776 x^4-13122 x^3-26244 x^2\right )+e^5 \left (-26244 x^{11}-104976 x^{10}-174960 x^9-155520 x^8-77760 x^7+5508 x^6+85176 x^5+81648 x^4+23328 x^3\right )+e^{6 x} \left (252 x^8+336 x^7+112 x^6+36 \log (3) x^5-36 e^5 x^5\right )+e^{5 x} \left (-1512 x^9-3024 x^8-2016 x^7-448 x^6+e^5 \left (648 x^6+432 x^5\right )+\left (-648 x^6-432 x^5\right ) \log (3)\right )+e^{4 x} \left (5670 x^{10}+15120 x^9+15120 x^8+6720 x^7+1120 x^6-162 x^5+486 \log ^2(3) x^4+486 e^{10} x^4-324 x^4+e^5 \left (-4860 x^7-6480 x^6-2160 x^5\right )+\left (4860 x^7+6480 x^6+2160 x^5-972 e^5 x^4\right ) \log (3)\right )+e^{3 x} \left (-13608 x^{11}-45360 x^{10}-60480 x^9-40320 x^8-13440 x^7+152 x^6+5184 x^5+2592 x^4+e^{10} \left (-5832 x^5-3888 x^4\right )+e^5 \left (19440 x^8+38880 x^7+25920 x^6+5760 x^5\right )+\left (-5832 x^5-3888 x^4\right ) \log ^2(3)+\left (-19440 x^8-38880 x^7-25920 x^6-5760 x^5+e^5 \left (11664 x^5+7776 x^4\right )\right ) \log (3)\right )+e^{2 x} \left (20412 x^{12}+81648 x^{11}+136080 x^{10}+120960 x^9+60480 x^8+7380 x^7-27368 x^6-27216 x^5-7776 x^4+2916 \log ^3(3) x^3-2916 e^{15} x^3+e^{10} \left (26244 x^6+34992 x^5+11664 x^4\right )+e^5 \left (-43740 x^9-116640 x^8-116640 x^7-51840 x^6-8640 x^5+2916 x^4+5832 x^3\right )+\left (26244 x^6+34992 x^5+11664 x^4-8748 e^5 x^3\right ) \log ^2(3)+\left (43740 x^9+116640 x^8+116640 x^7+51840 x^6+8640 x^5-2916 x^4+8748 e^{10} x^3-5832 x^3+e^5 \left (-52488 x^6-69984 x^5-23328 x^4\right )\right ) \log (3)\right )+e^x \left (-17496 x^{13}-81648 x^{12}-163296 x^{11}-181440 x^{10}-120960 x^9-30888 x^8+59232 x^7+92288 x^6+51840 x^5+10368 x^4+e^{15} \left (17496 x^4+11664 x^3\right )+e^{10} \left (-52488 x^7-104976 x^6-69984 x^5-15552 x^4\right )+e^5 \left (52488 x^{10}+174960 x^9+233280 x^8+155520 x^7+51840 x^6-10584 x^5-46656 x^4-23328 x^3\right )+\left (-17496 x^4-11664 x^3\right ) \log ^3(3)+\left (-52488 x^7-104976 x^6-69984 x^5-15552 x^4+e^5 \left (52488 x^4+34992 x^3\right )\right ) \log ^2(3)+\left (-52488 x^{10}-174960 x^9-233280 x^8-155520 x^7-51840 x^6+10584 x^5+46656 x^4+23328 x^3+e^{10} \left (-52488 x^4-34992 x^3\right )+e^5 \left (104976 x^7+209952 x^6+139968 x^5+31104 x^4\right )\right ) \log (3)\right )+\left (26244 x^5+34992 x^4+11664 x^3-26244 e^5 x^2\right ) \log ^3(3)+\left (39366 x^8+104976 x^7+104976 x^6+46656 x^5+7776 x^4-13122 x^3+39366 e^{10} x^2-26244 x^2+e^5 \left (-78732 x^5-104976 x^4-34992 x^3\right )\right ) \log ^2(3)+\left (26244 x^{11}+104976 x^{10}+174960 x^9+155520 x^8+77760 x^7-5508 x^6-85176 x^5-81648 x^4-23328 x^3-26244 e^{15} x^2+e^{10} \left (78732 x^5+104976 x^4+34992 x^3\right )+e^5 \left (-78732 x^8-209952 x^7-209952 x^6-93312 x^5-15552 x^4+26244 x^3+52488 x^2\right )\right ) \log (3)}dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {162 \left (e^{4 x} (4 x+3) x^2-12 e^{3 x} \left (3 x^2+6 x+2\right ) x^2+36 e^{x+5} \left (3 x^2+11 x+4\right ) x-18 e^5 \left (36 x^3+36 x^2+8 x+9 \log (3)\right )+6 e^{2 x} x \left (18 x^4+69 x^3+56 x^2+6 x (2+\log (3))+\log (729)\right )-4 e^x x \left (27 x^5+216 x^4+306 x^3+x^2 (152+27 \log (3))+3 x (8+33 \log (3))+36 \log (3)\right )+3 \left (189 x^6+432 x^5+360 x^4+8 x^3 (16+27 \log (3))+8 x^2 (2+27 \log (3))+6 x (8 \log (3)-9)+27 \left (\log ^2(3)-2\right )\right )-36 e^{2 x+5} (x+1) x+81 e^{10}\right )}{x^2 \left (-81 x^6-216 x^5-216 x^4-6 x^3 (16+27 \log (3))-e^{4 x} x^2+4 e^{3 x} (3 x+2) x^2-8 x^2 (2+27 \log (3))+4 e^x (3 x+2) x \left (9 x^3+12 x^2+4 x+9 \log (3)\right )-6 e^{2 x} x \left (9 x^3+12 x^2+4 x+\log (27)\right )+18 e^5 \left (9 x^3+12 x^2+4 x+9 \log (3)\right )+18 e^{2 x+5} x-36 e^{x+5} (3 x+2) x-9 x (8 \log (3)-9)-81 e^{10} \left (1+\frac {\log ^2(3)-2}{e^{10}}\right )\right )^2}dx\)

\(\Big \downarrow \) 27

\(\displaystyle 162 \int \frac {e^{4 x} (4 x+3) x^2-12 e^{3 x} \left (3 x^2+6 x+2\right ) x^2-36 e^{2 x+5} (x+1) x+36 e^{x+5} \left (3 x^2+11 x+4\right ) x-4 e^x \left (27 x^5+216 x^4+306 x^3+(152+27 \log (3)) x^2+3 (8+33 \log (3)) x+36 \log (3)\right ) x+6 e^{2 x} \left (18 x^4+69 x^3+56 x^2+6 (2+\log (3)) x+\log (729)\right ) x-18 e^5 \left (36 x^3+36 x^2+8 x+9 \log (3)\right )+3 \left (189 x^6+432 x^5+360 x^4+8 (16+27 \log (3)) x^3+8 (2+27 \log (3)) x^2-6 (9-8 \log (3)) x-27 \left (2-\log ^2(3)\right )\right )+81 e^{10}}{x^2 \left (-81 x^6-216 x^5-216 x^4-6 (16+27 \log (3)) x^3-e^{4 x} x^2+4 e^{3 x} (3 x+2) x^2-8 (2+27 \log (3)) x^2+18 e^{2 x+5} x-36 e^{x+5} (3 x+2) x+4 e^x (3 x+2) \left (9 x^3+12 x^2+4 x+9 \log (3)\right ) x-6 e^{2 x} \left (9 x^3+12 x^2+4 x+\log (27)\right ) x+9 (9-8 \log (3)) x+18 e^5 \left (9 x^3+12 x^2+4 x+9 \log (3)\right )+81 \left (2-e^{10}-\log ^2(3)\right )\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 162 \int \left (\frac {4 x+3}{x^2 \left (81 x^6-108 e^x x^5+216 x^5-216 e^x x^4+54 e^{2 x} x^4+216 x^4-144 e^x x^3+72 e^{2 x} x^3-12 e^{3 x} x^3+96 \left (1-\frac {27}{16} \left (e^5-\log (3)\right )\right ) x^3+24 e^{2 x} x^2-8 e^{3 x} x^2+e^{4 x} x^2-32 e^x \left (1-\frac {27}{8} \left (e^5-\log (3)\right )\right ) x^2+16 \left (1-\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^2-18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+72 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x-81 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x-162 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )\right )}+\frac {-324 x^7+324 e^x x^6-540 x^6+324 e^x x^5-108 e^{2 x} x^5-216 x^5-36 e^{2 x} x^4+12 e^{3 x} x^4+48 \left (1+\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^4+24 e^{2 x} x^3-4 e^{3 x} x^3+32 \left (1+\frac {351}{16} \left (e^5-\log (3)\right )\right ) x^3-48 e^x \left (1+\frac {27}{4} \left (e^5-\log (3)\right )\right ) x^3+36 e^{2 x+5} \left (1-\frac {\log (729)}{6 e^5}\right ) x^2-216 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x^2+324 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x^2-72 e^{x+5} \left (1-\frac {\log (729)}{6 e^5}\right ) x+18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+729 \left (1-\frac {4}{81} \left (9 e^{10}+9 \log ^2(3)-2 e^5 (1+9 \log (3))+\log (9)\right )\right ) x+324 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )}{x^2 \left (81 x^6-108 e^x x^5+216 x^5-216 e^x x^4+54 e^{2 x} x^4+216 x^4-144 e^x x^3+72 e^{2 x} x^3-12 e^{3 x} x^3+96 \left (1-\frac {27}{16} \left (e^5-\log (3)\right )\right ) x^3+24 e^{2 x} x^2-8 e^{3 x} x^2+e^{4 x} x^2-32 e^x \left (1-\frac {27}{8} \left (e^5-\log (3)\right )\right ) x^2+16 \left (1-\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^2-18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+72 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x-81 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x-162 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 162 \int \frac {e^{4 x} (4 x+3) x^2-12 e^{3 x} \left (3 x^2+6 x+2\right ) x^2-36 e^{2 x+5} (x+1) x+36 e^{x+5} \left (3 x^2+11 x+4\right ) x-4 e^x \left (27 x^5+216 x^4+306 x^3+(152+27 \log (3)) x^2+3 (8+33 \log (3)) x-3 \log (729)+54 \log (3)\right ) x+6 e^{2 x} \left (18 x^4+69 x^3+56 x^2+(12+\log (729)) x+\log (729)\right ) x-18 e^5 \left (36 x^3+36 x^2+8 x+9 \log (3)\right )+3 \left (189 x^6+432 x^5+360 x^4+8 (16+27 \log (3)) x^3+8 (2+27 \log (3)) x^2+6 (-9+\log (6561)) x+27 \left (-2+\log ^2(3)\right )\right )+81 e^{10}}{x^2 \left (-81 x^6-216 x^5-216 x^4-6 (16+27 \log (3)) x^3-e^{4 x} x^2+4 e^{3 x} (3 x+2) x^2-8 (2+27 \log (3)) x^2+18 e^{2 x+5} x-36 e^{x+5} (3 x+2) x+4 e^x (3 x+2) \left (9 x^3+12 x^2+4 x+9 \log (3)\right ) x-6 e^{2 x} \left (9 x^3+12 x^2+4 x+\log (27)\right ) x-9 (-9+8 \log (3)) x+18 e^5 \left (9 x^3+12 x^2+4 x+9 \log (3)\right )-81 e^{10} \left (1+\frac {-2+\log ^2(3)}{e^{10}}\right )\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 162 \int \left (\frac {4 x+3}{x^2 \left (81 x^6-108 e^x x^5+216 x^5-216 e^x x^4+54 e^{2 x} x^4+216 x^4-144 e^x x^3+72 e^{2 x} x^3-12 e^{3 x} x^3+96 \left (1-\frac {27}{16} \left (e^5-\log (3)\right )\right ) x^3+24 e^{2 x} x^2-8 e^{3 x} x^2+e^{4 x} x^2-32 e^x \left (1-\frac {27}{8} \left (e^5-\log (3)\right )\right ) x^2+16 \left (1-\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^2-18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+72 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x-81 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x-162 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )\right )}+\frac {-324 x^7+324 e^x x^6-540 x^6+324 e^x x^5-108 e^{2 x} x^5-216 x^5-36 e^{2 x} x^4+12 e^{3 x} x^4+48 \left (1+\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^4+24 e^{2 x} x^3-4 e^{3 x} x^3+32 \left (1+\frac {351}{16} \left (e^5-\log (3)\right )\right ) x^3-48 e^x \left (1+\frac {27}{4} \left (e^5-\log (3)\right )\right ) x^3+36 e^{2 x+5} \left (1-\frac {\log (729)}{6 e^5}\right ) x^2-216 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x^2+324 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x^2+729 \left (1+\frac {1}{81} \left (-36 e^{10}-36 \log ^2(3)+8 e^5 (1+9 \log (3))-\log (6561)\right )\right ) x-72 e^{x+5} \left (1-\frac {\log (729)}{6 e^5}\right ) x+18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+324 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )}{x^2 \left (81 x^6-108 e^x x^5+216 x^5-216 e^x x^4+54 e^{2 x} x^4+216 x^4-144 e^x x^3+72 e^{2 x} x^3-12 e^{3 x} x^3+96 \left (1-\frac {27}{16} \left (e^5-\log (3)\right )\right ) x^3+24 e^{2 x} x^2-8 e^{3 x} x^2+e^{4 x} x^2-32 e^x \left (1-\frac {27}{8} \left (e^5-\log (3)\right )\right ) x^2+16 \left (1-\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^2-18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+72 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x-81 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x-162 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 162 \int \frac {e^{4 x} (4 x+3) x^2-12 e^{3 x} \left (3 x^2+6 x+2\right ) x^2-36 e^{2 x+5} (x+1) x+36 e^{x+5} \left (3 x^2+11 x+4\right ) x-4 e^x \left (27 x^5+216 x^4+306 x^3+(152+27 \log (3)) x^2+3 (8+33 \log (3)) x-3 \log (729)+54 \log (3)\right ) x+6 e^{2 x} \left (18 x^4+69 x^3+56 x^2+(12+\log (729)) x+\log (729)\right ) x-18 e^5 \left (36 x^3+36 x^2+8 x+9 \log (3)\right )+3 \left (189 x^6+432 x^5+360 x^4+8 (16+27 \log (3)) x^3+8 (2+27 \log (3)) x^2-3 (18+\log (6561)) x+72 \log (3) x+27 \left (-2+\log ^2(3)\right )\right )+81 e^{10}}{x^2 \left (-81 x^6-216 x^5-216 x^4-6 (16+27 \log (3)) x^3-e^{4 x} x^2+4 e^{3 x} (3 x+2) x^2-8 (2+27 \log (3)) x^2+18 e^{2 x+5} x-36 e^{x+5} (3 x+2) x+4 e^x (3 x+2) \left (9 x^3+12 x^2+4 x+9 \log (3)\right ) x-6 e^{2 x} \left (9 x^3+12 x^2+4 x+\log (27)\right ) x-9 (-9+8 \log (3)) x+18 e^5 \left (9 x^3+12 x^2+4 x+9 \log (3)\right )-81 e^{10} \left (1+\frac {-2+\log ^2(3)}{e^{10}}\right )\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 162 \int \left (\frac {4 x+3}{x^2 \left (81 x^6-108 e^x x^5+216 x^5-216 e^x x^4+54 e^{2 x} x^4+216 x^4-144 e^x x^3+72 e^{2 x} x^3-12 e^{3 x} x^3+96 \left (1-\frac {27}{16} \left (e^5-\log (3)\right )\right ) x^3+24 e^{2 x} x^2-8 e^{3 x} x^2+e^{4 x} x^2-32 e^x \left (1-\frac {27}{8} \left (e^5-\log (3)\right )\right ) x^2+16 \left (1-\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^2-18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+72 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x-81 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x-162 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )\right )}+\frac {-324 x^7+324 e^x x^6-540 x^6+324 e^x x^5-108 e^{2 x} x^5-216 x^5-36 e^{2 x} x^4+12 e^{3 x} x^4+48 \left (1+\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^4+24 e^{2 x} x^3-4 e^{3 x} x^3+32 \left (1+\frac {351}{16} \left (e^5-\log (3)\right )\right ) x^3-48 e^x \left (1+\frac {27}{4} \left (e^5-\log (3)\right )\right ) x^3+36 e^{2 x+5} \left (1-\frac {\log (729)}{6 e^5}\right ) x^2-216 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x^2+324 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x^2+729 \left (1+\frac {1}{81} \left (-36 e^{10}-36 \log ^2(3)+8 e^5 (1+9 \log (3))-\log (6561)\right )\right ) x-72 e^{x+5} \left (1-\frac {\log (729)}{6 e^5}\right ) x+18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+324 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )}{x^2 \left (81 x^6-108 e^x x^5+216 x^5-216 e^x x^4+54 e^{2 x} x^4+216 x^4-144 e^x x^3+72 e^{2 x} x^3-12 e^{3 x} x^3+96 \left (1-\frac {27}{16} \left (e^5-\log (3)\right )\right ) x^3+24 e^{2 x} x^2-8 e^{3 x} x^2+e^{4 x} x^2-32 e^x \left (1-\frac {27}{8} \left (e^5-\log (3)\right )\right ) x^2+16 \left (1-\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^2-18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+72 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x-81 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x-162 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 162 \int \frac {e^{4 x} (4 x+3) x^2-12 e^{3 x} \left (3 x^2+6 x+2\right ) x^2-36 e^{2 x+5} (x+1) x+36 e^{x+5} \left (3 x^2+11 x+4\right ) x-4 e^x \left (27 x^5+216 x^4+306 x^3+(152+27 \log (3)) x^2+3 (8+33 \log (3)) x-3 \log (729)+54 \log (3)\right ) x+6 e^{2 x} \left (18 x^4+69 x^3+56 x^2+(12+\log (729)) x+\log (729)\right ) x-18 e^5 \left (36 x^3+36 x^2+8 x+9 \log (3)\right )+3 \left (189 x^6+432 x^5+360 x^4+8 (16+27 \log (3)) x^3+8 (2+27 \log (3)) x^2-3 (18+\log (6561)) x+72 \log (3) x+27 \left (-2+\log ^2(3)\right )\right )+81 e^{10}}{x^2 \left (-81 x^6-216 x^5-216 x^4-6 (16+27 \log (3)) x^3-e^{4 x} x^2+4 e^{3 x} (3 x+2) x^2-8 (2+27 \log (3)) x^2+18 e^{2 x+5} x-36 e^{x+5} (3 x+2) x+4 e^x (3 x+2) \left (9 x^3+12 x^2+4 x+9 \log (3)\right ) x-6 e^{2 x} \left (9 x^3+12 x^2+4 x+\log (27)\right ) x-9 (-9+8 \log (3)) x+18 e^5 \left (9 x^3+12 x^2+4 x+9 \log (3)\right )-81 e^{10} \left (1+\frac {-2+\log ^2(3)}{e^{10}}\right )\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 162 \int \left (\frac {4 x+3}{x^2 \left (81 x^6-108 e^x x^5+216 x^5-216 e^x x^4+54 e^{2 x} x^4+216 x^4-144 e^x x^3+72 e^{2 x} x^3-12 e^{3 x} x^3+96 \left (1-\frac {27}{16} \left (e^5-\log (3)\right )\right ) x^3+24 e^{2 x} x^2-8 e^{3 x} x^2+e^{4 x} x^2-32 e^x \left (1-\frac {27}{8} \left (e^5-\log (3)\right )\right ) x^2+16 \left (1-\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^2-18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+72 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x-81 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x-162 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )\right )}+\frac {-324 x^7+324 e^x x^6-540 x^6+324 e^x x^5-108 e^{2 x} x^5-216 x^5-36 e^{2 x} x^4+12 e^{3 x} x^4+48 \left (1+\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^4+24 e^{2 x} x^3-4 e^{3 x} x^3+32 \left (1+\frac {351}{16} \left (e^5-\log (3)\right )\right ) x^3-48 e^x \left (1+\frac {27}{4} \left (e^5-\log (3)\right )\right ) x^3+36 e^{2 x+5} \left (1-\frac {\log (729)}{6 e^5}\right ) x^2-216 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x^2+324 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x^2+729 \left (1+\frac {1}{81} \left (-36 e^{10}-36 \log ^2(3)+8 e^5 (1+9 \log (3))-\log (6561)\right )\right ) x-72 e^{x+5} \left (1-\frac {\log (729)}{6 e^5}\right ) x+18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+324 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )}{x^2 \left (81 x^6-108 e^x x^5+216 x^5-216 e^x x^4+54 e^{2 x} x^4+216 x^4-144 e^x x^3+72 e^{2 x} x^3-12 e^{3 x} x^3+96 \left (1-\frac {27}{16} \left (e^5-\log (3)\right )\right ) x^3+24 e^{2 x} x^2-8 e^{3 x} x^2+e^{4 x} x^2-32 e^x \left (1-\frac {27}{8} \left (e^5-\log (3)\right )\right ) x^2+16 \left (1-\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^2-18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+72 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x-81 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x-162 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 162 \int \frac {e^{4 x} (4 x+3) x^2-12 e^{3 x} \left (3 x^2+6 x+2\right ) x^2-36 e^{2 x+5} (x+1) x+36 e^{x+5} \left (3 x^2+11 x+4\right ) x-4 e^x \left (27 x^5+216 x^4+306 x^3+(152+27 \log (3)) x^2+3 (8+33 \log (3)) x-3 \log (729)+54 \log (3)\right ) x+6 e^{2 x} \left (18 x^4+69 x^3+56 x^2+(12+\log (729)) x+\log (729)\right ) x-18 e^5 \left (36 x^3+36 x^2+8 x+9 \log (3)\right )+3 \left (189 x^6+432 x^5+360 x^4+8 (16+27 \log (3)) x^3+8 (2+27 \log (3)) x^2-3 (18+\log (6561)) x+72 \log (3) x+27 \left (-2+\log ^2(3)\right )\right )+81 e^{10}}{x^2 \left (-81 x^6-216 x^5-216 x^4-6 (16+27 \log (3)) x^3-e^{4 x} x^2+4 e^{3 x} (3 x+2) x^2-8 (2+27 \log (3)) x^2+18 e^{2 x+5} x-36 e^{x+5} (3 x+2) x+4 e^x (3 x+2) \left (9 x^3+12 x^2+4 x+9 \log (3)\right ) x-6 e^{2 x} \left (9 x^3+12 x^2+4 x+\log (27)\right ) x-9 (-9+8 \log (3)) x+18 e^5 \left (9 x^3+12 x^2+4 x+9 \log (3)\right )-81 e^{10} \left (1+\frac {-2+\log ^2(3)}{e^{10}}\right )\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 162 \int \left (\frac {4 x+3}{x^2 \left (81 x^6-108 e^x x^5+216 x^5-216 e^x x^4+54 e^{2 x} x^4+216 x^4-144 e^x x^3+72 e^{2 x} x^3-12 e^{3 x} x^3+96 \left (1-\frac {27}{16} \left (e^5-\log (3)\right )\right ) x^3+24 e^{2 x} x^2-8 e^{3 x} x^2+e^{4 x} x^2-32 e^x \left (1-\frac {27}{8} \left (e^5-\log (3)\right )\right ) x^2+16 \left (1-\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^2-18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+72 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x-81 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x-162 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )\right )}+\frac {-324 x^7+324 e^x x^6-540 x^6+324 e^x x^5-108 e^{2 x} x^5-216 x^5-36 e^{2 x} x^4+12 e^{3 x} x^4+48 \left (1+\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^4+24 e^{2 x} x^3-4 e^{3 x} x^3+32 \left (1+\frac {351}{16} \left (e^5-\log (3)\right )\right ) x^3-48 e^x \left (1+\frac {27}{4} \left (e^5-\log (3)\right )\right ) x^3+36 e^{2 x+5} \left (1-\frac {\log (729)}{6 e^5}\right ) x^2-216 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x^2+324 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x^2+729 \left (1+\frac {1}{81} \left (-36 e^{10}-36 \log ^2(3)+8 e^5 (1+9 \log (3))-\log (6561)\right )\right ) x-72 e^{x+5} \left (1-\frac {\log (729)}{6 e^5}\right ) x+18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+324 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )}{x^2 \left (81 x^6-108 e^x x^5+216 x^5-216 e^x x^4+54 e^{2 x} x^4+216 x^4-144 e^x x^3+72 e^{2 x} x^3-12 e^{3 x} x^3+96 \left (1-\frac {27}{16} \left (e^5-\log (3)\right )\right ) x^3+24 e^{2 x} x^2-8 e^{3 x} x^2+e^{4 x} x^2-32 e^x \left (1-\frac {27}{8} \left (e^5-\log (3)\right )\right ) x^2+16 \left (1-\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^2-18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+72 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x-81 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x-162 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 162 \int \frac {e^{4 x} (4 x+3) x^2-12 e^{3 x} \left (3 x^2+6 x+2\right ) x^2-36 e^{2 x+5} (x+1) x+36 e^{x+5} \left (3 x^2+11 x+4\right ) x-4 e^x \left (27 x^5+216 x^4+306 x^3+(152+27 \log (3)) x^2+3 (8+33 \log (3)) x-3 \log (729)+54 \log (3)\right ) x+6 e^{2 x} \left (18 x^4+69 x^3+56 x^2+(12+\log (729)) x+\log (729)\right ) x-18 e^5 \left (36 x^3+36 x^2+8 x+9 \log (3)\right )+3 \left (189 x^6+432 x^5+360 x^4+8 (16+27 \log (3)) x^3+8 (2+27 \log (3)) x^2-3 (18+\log (6561)) x+72 \log (3) x+27 \left (-2+\log ^2(3)\right )\right )+81 e^{10}}{x^2 \left (-81 x^6-216 x^5-216 x^4-6 (16+27 \log (3)) x^3-e^{4 x} x^2+4 e^{3 x} (3 x+2) x^2-8 (2+27 \log (3)) x^2+18 e^{2 x+5} x-36 e^{x+5} (3 x+2) x+4 e^x (3 x+2) \left (9 x^3+12 x^2+4 x+9 \log (3)\right ) x-6 e^{2 x} \left (9 x^3+12 x^2+4 x+\log (27)\right ) x-9 (-9+8 \log (3)) x+18 e^5 \left (9 x^3+12 x^2+4 x+9 \log (3)\right )-81 e^{10} \left (1+\frac {-2+\log ^2(3)}{e^{10}}\right )\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 162 \int \left (\frac {4 x+3}{x^2 \left (81 x^6-108 e^x x^5+216 x^5-216 e^x x^4+54 e^{2 x} x^4+216 x^4-144 e^x x^3+72 e^{2 x} x^3-12 e^{3 x} x^3+96 \left (1-\frac {27}{16} \left (e^5-\log (3)\right )\right ) x^3+24 e^{2 x} x^2-8 e^{3 x} x^2+e^{4 x} x^2-32 e^x \left (1-\frac {27}{8} \left (e^5-\log (3)\right )\right ) x^2+16 \left (1-\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^2-18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+72 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x-81 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x-162 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )\right )}+\frac {-324 x^7+324 e^x x^6-540 x^6+324 e^x x^5-108 e^{2 x} x^5-216 x^5-36 e^{2 x} x^4+12 e^{3 x} x^4+48 \left (1+\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^4+24 e^{2 x} x^3-4 e^{3 x} x^3+32 \left (1+\frac {351}{16} \left (e^5-\log (3)\right )\right ) x^3-48 e^x \left (1+\frac {27}{4} \left (e^5-\log (3)\right )\right ) x^3+36 e^{2 x+5} \left (1-\frac {\log (729)}{6 e^5}\right ) x^2-216 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x^2+324 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x^2+729 \left (1+\frac {1}{81} \left (-36 e^{10}-36 \log ^2(3)+8 e^5 (1+9 \log (3))-\log (6561)\right )\right ) x-72 e^{x+5} \left (1-\frac {\log (729)}{6 e^5}\right ) x+18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+324 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )}{x^2 \left (81 x^6-108 e^x x^5+216 x^5-216 e^x x^4+54 e^{2 x} x^4+216 x^4-144 e^x x^3+72 e^{2 x} x^3-12 e^{3 x} x^3+96 \left (1-\frac {27}{16} \left (e^5-\log (3)\right )\right ) x^3+24 e^{2 x} x^2-8 e^{3 x} x^2+e^{4 x} x^2-32 e^x \left (1-\frac {27}{8} \left (e^5-\log (3)\right )\right ) x^2+16 \left (1-\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^2-18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+72 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x-81 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x-162 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 162 \int \frac {e^{4 x} (4 x+3) x^2-12 e^{3 x} \left (3 x^2+6 x+2\right ) x^2-36 e^{2 x+5} (x+1) x+36 e^{x+5} \left (3 x^2+11 x+4\right ) x-4 e^x \left (27 x^5+216 x^4+306 x^3+(152+27 \log (3)) x^2+3 (8+33 \log (3)) x-3 \log (729)+54 \log (3)\right ) x+6 e^{2 x} \left (18 x^4+69 x^3+56 x^2+(12+\log (729)) x+\log (729)\right ) x-18 e^5 \left (36 x^3+36 x^2+8 x+9 \log (3)\right )+3 \left (189 x^6+432 x^5+360 x^4+8 (16+27 \log (3)) x^3+8 (2+27 \log (3)) x^2-3 (18+\log (6561)) x+72 \log (3) x+27 \left (-2+\log ^2(3)\right )\right )+81 e^{10}}{x^2 \left (-81 x^6-216 x^5-216 x^4-6 (16+27 \log (3)) x^3-e^{4 x} x^2+4 e^{3 x} (3 x+2) x^2-8 (2+27 \log (3)) x^2+18 e^{2 x+5} x-36 e^{x+5} (3 x+2) x+4 e^x (3 x+2) \left (9 x^3+12 x^2+4 x+9 \log (3)\right ) x-6 e^{2 x} \left (9 x^3+12 x^2+4 x+\log (27)\right ) x-9 (-9+8 \log (3)) x+18 e^5 \left (9 x^3+12 x^2+4 x+9 \log (3)\right )-81 e^{10} \left (1+\frac {-2+\log ^2(3)}{e^{10}}\right )\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 162 \int \left (\frac {4 x+3}{x^2 \left (81 x^6-108 e^x x^5+216 x^5-216 e^x x^4+54 e^{2 x} x^4+216 x^4-144 e^x x^3+72 e^{2 x} x^3-12 e^{3 x} x^3+96 \left (1-\frac {27}{16} \left (e^5-\log (3)\right )\right ) x^3+24 e^{2 x} x^2-8 e^{3 x} x^2+e^{4 x} x^2-32 e^x \left (1-\frac {27}{8} \left (e^5-\log (3)\right )\right ) x^2+16 \left (1-\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^2-18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+72 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x-81 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x-162 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )\right )}+\frac {-324 x^7+324 e^x x^6-540 x^6+324 e^x x^5-108 e^{2 x} x^5-216 x^5-36 e^{2 x} x^4+12 e^{3 x} x^4+48 \left (1+\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^4+24 e^{2 x} x^3-4 e^{3 x} x^3+32 \left (1+\frac {351}{16} \left (e^5-\log (3)\right )\right ) x^3-48 e^x \left (1+\frac {27}{4} \left (e^5-\log (3)\right )\right ) x^3+36 e^{2 x+5} \left (1-\frac {\log (729)}{6 e^5}\right ) x^2-216 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x^2+324 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x^2+729 \left (1+\frac {1}{81} \left (-36 e^{10}-36 \log ^2(3)+8 e^5 (1+9 \log (3))-\log (6561)\right )\right ) x-72 e^{x+5} \left (1-\frac {\log (729)}{6 e^5}\right ) x+18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+324 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )}{x^2 \left (81 x^6-108 e^x x^5+216 x^5-216 e^x x^4+54 e^{2 x} x^4+216 x^4-144 e^x x^3+72 e^{2 x} x^3-12 e^{3 x} x^3+96 \left (1-\frac {27}{16} \left (e^5-\log (3)\right )\right ) x^3+24 e^{2 x} x^2-8 e^{3 x} x^2+e^{4 x} x^2-32 e^x \left (1-\frac {27}{8} \left (e^5-\log (3)\right )\right ) x^2+16 \left (1-\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^2-18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+72 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x-81 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x-162 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 162 \int \frac {e^{4 x} (4 x+3) x^2-12 e^{3 x} \left (3 x^2+6 x+2\right ) x^2-36 e^{2 x+5} (x+1) x+36 e^{x+5} \left (3 x^2+11 x+4\right ) x-4 e^x \left (27 x^5+216 x^4+306 x^3+(152+27 \log (3)) x^2+3 (8+33 \log (3)) x-3 \log (729)+54 \log (3)\right ) x+6 e^{2 x} \left (18 x^4+69 x^3+56 x^2+(12+\log (729)) x+\log (729)\right ) x-18 e^5 \left (36 x^3+36 x^2+8 x+9 \log (3)\right )+3 \left (189 x^6+432 x^5+360 x^4+8 (16+27 \log (3)) x^3+8 (2+27 \log (3)) x^2-3 (18+\log (6561)) x+72 \log (3) x+27 \left (-2+\log ^2(3)\right )\right )+81 e^{10}}{x^2 \left (-81 x^6-216 x^5-216 x^4-6 (16+27 \log (3)) x^3-e^{4 x} x^2+4 e^{3 x} (3 x+2) x^2-8 (2+27 \log (3)) x^2+18 e^{2 x+5} x-36 e^{x+5} (3 x+2) x+4 e^x (3 x+2) \left (9 x^3+12 x^2+4 x+9 \log (3)\right ) x-6 e^{2 x} \left (9 x^3+12 x^2+4 x+\log (27)\right ) x-9 (-9+8 \log (3)) x+18 e^5 \left (9 x^3+12 x^2+4 x+9 \log (3)\right )-81 e^{10} \left (1+\frac {-2+\log ^2(3)}{e^{10}}\right )\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 162 \int \left (\frac {4 x+3}{x^2 \left (81 x^6-108 e^x x^5+216 x^5-216 e^x x^4+54 e^{2 x} x^4+216 x^4-144 e^x x^3+72 e^{2 x} x^3-12 e^{3 x} x^3+96 \left (1-\frac {27}{16} \left (e^5-\log (3)\right )\right ) x^3+24 e^{2 x} x^2-8 e^{3 x} x^2+e^{4 x} x^2-32 e^x \left (1-\frac {27}{8} \left (e^5-\log (3)\right )\right ) x^2+16 \left (1-\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^2-18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+72 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x-81 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x-162 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )\right )}+\frac {-324 x^7+324 e^x x^6-540 x^6+324 e^x x^5-108 e^{2 x} x^5-216 x^5-36 e^{2 x} x^4+12 e^{3 x} x^4+48 \left (1+\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^4+24 e^{2 x} x^3-4 e^{3 x} x^3+32 \left (1+\frac {351}{16} \left (e^5-\log (3)\right )\right ) x^3-48 e^x \left (1+\frac {27}{4} \left (e^5-\log (3)\right )\right ) x^3+36 e^{2 x+5} \left (1-\frac {\log (729)}{6 e^5}\right ) x^2-216 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x^2+324 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x^2+729 \left (1+\frac {1}{81} \left (-36 e^{10}-36 \log ^2(3)+8 e^5 (1+9 \log (3))-\log (6561)\right )\right ) x-72 e^{x+5} \left (1-\frac {\log (729)}{6 e^5}\right ) x+18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+324 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )}{x^2 \left (81 x^6-108 e^x x^5+216 x^5-216 e^x x^4+54 e^{2 x} x^4+216 x^4-144 e^x x^3+72 e^{2 x} x^3-12 e^{3 x} x^3+96 \left (1-\frac {27}{16} \left (e^5-\log (3)\right )\right ) x^3+24 e^{2 x} x^2-8 e^{3 x} x^2+e^{4 x} x^2-32 e^x \left (1-\frac {27}{8} \left (e^5-\log (3)\right )\right ) x^2+16 \left (1-\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^2-18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+72 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x-81 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x-162 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 162 \int \frac {e^{4 x} (4 x+3) x^2-12 e^{3 x} \left (3 x^2+6 x+2\right ) x^2-36 e^{2 x+5} (x+1) x+36 e^{x+5} \left (3 x^2+11 x+4\right ) x-4 e^x \left (27 x^5+216 x^4+306 x^3+(152+27 \log (3)) x^2+3 (8+33 \log (3)) x-3 \log (729)+54 \log (3)\right ) x+6 e^{2 x} \left (18 x^4+69 x^3+56 x^2+(12+\log (729)) x+\log (729)\right ) x-18 e^5 \left (36 x^3+36 x^2+8 x+9 \log (3)\right )+3 \left (189 x^6+432 x^5+360 x^4+8 (16+27 \log (3)) x^3+8 (2+27 \log (3)) x^2-3 (18+\log (6561)) x+72 \log (3) x+27 \left (-2+\log ^2(3)\right )\right )+81 e^{10}}{x^2 \left (-81 x^6-216 x^5-216 x^4-6 (16+27 \log (3)) x^3-e^{4 x} x^2+4 e^{3 x} (3 x+2) x^2-8 (2+27 \log (3)) x^2+18 e^{2 x+5} x-36 e^{x+5} (3 x+2) x+4 e^x (3 x+2) \left (9 x^3+12 x^2+4 x+9 \log (3)\right ) x-6 e^{2 x} \left (9 x^3+12 x^2+4 x+\log (27)\right ) x-9 (-9+8 \log (3)) x+18 e^5 \left (9 x^3+12 x^2+4 x+9 \log (3)\right )-81 e^{10} \left (1+\frac {-2+\log ^2(3)}{e^{10}}\right )\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 162 \int \left (\frac {4 x+3}{x^2 \left (81 x^6-108 e^x x^5+216 x^5-216 e^x x^4+54 e^{2 x} x^4+216 x^4-144 e^x x^3+72 e^{2 x} x^3-12 e^{3 x} x^3+96 \left (1-\frac {27}{16} \left (e^5-\log (3)\right )\right ) x^3+24 e^{2 x} x^2-8 e^{3 x} x^2+e^{4 x} x^2-32 e^x \left (1-\frac {27}{8} \left (e^5-\log (3)\right )\right ) x^2+16 \left (1-\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^2-18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+72 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x-81 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x-162 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )\right )}+\frac {-324 x^7+324 e^x x^6-540 x^6+324 e^x x^5-108 e^{2 x} x^5-216 x^5-36 e^{2 x} x^4+12 e^{3 x} x^4+48 \left (1+\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^4+24 e^{2 x} x^3-4 e^{3 x} x^3+32 \left (1+\frac {351}{16} \left (e^5-\log (3)\right )\right ) x^3-48 e^x \left (1+\frac {27}{4} \left (e^5-\log (3)\right )\right ) x^3+36 e^{2 x+5} \left (1-\frac {\log (729)}{6 e^5}\right ) x^2-216 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x^2+324 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x^2+729 \left (1+\frac {1}{81} \left (-36 e^{10}-36 \log ^2(3)+8 e^5 (1+9 \log (3))-\log (6561)\right )\right ) x-72 e^{x+5} \left (1-\frac {\log (729)}{6 e^5}\right ) x+18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+324 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )}{x^2 \left (81 x^6-108 e^x x^5+216 x^5-216 e^x x^4+54 e^{2 x} x^4+216 x^4-144 e^x x^3+72 e^{2 x} x^3-12 e^{3 x} x^3+96 \left (1-\frac {27}{16} \left (e^5-\log (3)\right )\right ) x^3+24 e^{2 x} x^2-8 e^{3 x} x^2+e^{4 x} x^2-32 e^x \left (1-\frac {27}{8} \left (e^5-\log (3)\right )\right ) x^2+16 \left (1-\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^2-18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+72 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x-81 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x-162 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 162 \int \frac {e^{4 x} (4 x+3) x^2-12 e^{3 x} \left (3 x^2+6 x+2\right ) x^2-36 e^{2 x+5} (x+1) x+36 e^{x+5} \left (3 x^2+11 x+4\right ) x-4 e^x \left (27 x^5+216 x^4+306 x^3+(152+27 \log (3)) x^2+3 (8+33 \log (3)) x-3 \log (729)+54 \log (3)\right ) x+6 e^{2 x} \left (18 x^4+69 x^3+56 x^2+(12+\log (729)) x+\log (729)\right ) x-18 e^5 \left (36 x^3+36 x^2+8 x+9 \log (3)\right )+3 \left (189 x^6+432 x^5+360 x^4+8 (16+27 \log (3)) x^3+8 (2+27 \log (3)) x^2-3 (18+\log (6561)) x+72 \log (3) x+27 \left (-2+\log ^2(3)\right )\right )+81 e^{10}}{x^2 \left (-81 x^6-216 x^5-216 x^4-6 (16+27 \log (3)) x^3-e^{4 x} x^2+4 e^{3 x} (3 x+2) x^2-8 (2+27 \log (3)) x^2+18 e^{2 x+5} x-36 e^{x+5} (3 x+2) x+4 e^x (3 x+2) \left (9 x^3+12 x^2+4 x+9 \log (3)\right ) x-6 e^{2 x} \left (9 x^3+12 x^2+4 x+\log (27)\right ) x-9 (-9+8 \log (3)) x+18 e^5 \left (9 x^3+12 x^2+4 x+9 \log (3)\right )-81 e^{10} \left (1+\frac {-2+\log ^2(3)}{e^{10}}\right )\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 162 \int \left (\frac {4 x+3}{x^2 \left (81 x^6-108 e^x x^5+216 x^5-216 e^x x^4+54 e^{2 x} x^4+216 x^4-144 e^x x^3+72 e^{2 x} x^3-12 e^{3 x} x^3+96 \left (1-\frac {27}{16} \left (e^5-\log (3)\right )\right ) x^3+24 e^{2 x} x^2-8 e^{3 x} x^2+e^{4 x} x^2-32 e^x \left (1-\frac {27}{8} \left (e^5-\log (3)\right )\right ) x^2+16 \left (1-\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^2-18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+72 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x-81 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x-162 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )\right )}+\frac {-324 x^7+324 e^x x^6-540 x^6+324 e^x x^5-108 e^{2 x} x^5-216 x^5-36 e^{2 x} x^4+12 e^{3 x} x^4+48 \left (1+\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^4+24 e^{2 x} x^3-4 e^{3 x} x^3+32 \left (1+\frac {351}{16} \left (e^5-\log (3)\right )\right ) x^3-48 e^x \left (1+\frac {27}{4} \left (e^5-\log (3)\right )\right ) x^3+36 e^{2 x+5} \left (1-\frac {\log (729)}{6 e^5}\right ) x^2-216 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x^2+324 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x^2+729 \left (1+\frac {1}{81} \left (-36 e^{10}-36 \log ^2(3)+8 e^5 (1+9 \log (3))-\log (6561)\right )\right ) x-72 e^{x+5} \left (1-\frac {\log (729)}{6 e^5}\right ) x+18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+324 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )}{x^2 \left (81 x^6-108 e^x x^5+216 x^5-216 e^x x^4+54 e^{2 x} x^4+216 x^4-144 e^x x^3+72 e^{2 x} x^3-12 e^{3 x} x^3+96 \left (1-\frac {27}{16} \left (e^5-\log (3)\right )\right ) x^3+24 e^{2 x} x^2-8 e^{3 x} x^2+e^{4 x} x^2-32 e^x \left (1-\frac {27}{8} \left (e^5-\log (3)\right )\right ) x^2+16 \left (1-\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^2-18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+72 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x-81 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x-162 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 162 \int \frac {e^{4 x} (4 x+3) x^2-12 e^{3 x} \left (3 x^2+6 x+2\right ) x^2-36 e^{2 x+5} (x+1) x+36 e^{x+5} \left (3 x^2+11 x+4\right ) x-4 e^x \left (27 x^5+216 x^4+306 x^3+(152+27 \log (3)) x^2+3 (8+33 \log (3)) x-3 \log (729)+54 \log (3)\right ) x+6 e^{2 x} \left (18 x^4+69 x^3+56 x^2+(12+\log (729)) x+\log (729)\right ) x-18 e^5 \left (36 x^3+36 x^2+8 x+9 \log (3)\right )+3 \left (189 x^6+432 x^5+360 x^4+8 (16+27 \log (3)) x^3+8 (2+27 \log (3)) x^2-3 (18+\log (6561)) x+72 \log (3) x+27 \left (-2+\log ^2(3)\right )\right )+81 e^{10}}{x^2 \left (-81 x^6-216 x^5-216 x^4-6 (16+27 \log (3)) x^3-e^{4 x} x^2+4 e^{3 x} (3 x+2) x^2-8 (2+27 \log (3)) x^2+18 e^{2 x+5} x-36 e^{x+5} (3 x+2) x+4 e^x (3 x+2) \left (9 x^3+12 x^2+4 x+9 \log (3)\right ) x-6 e^{2 x} \left (9 x^3+12 x^2+4 x+\log (27)\right ) x-9 (-9+8 \log (3)) x+18 e^5 \left (9 x^3+12 x^2+4 x+9 \log (3)\right )-81 e^{10} \left (1+\frac {-2+\log ^2(3)}{e^{10}}\right )\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 162 \int \left (\frac {4 x+3}{x^2 \left (81 x^6-108 e^x x^5+216 x^5-216 e^x x^4+54 e^{2 x} x^4+216 x^4-144 e^x x^3+72 e^{2 x} x^3-12 e^{3 x} x^3+96 \left (1-\frac {27}{16} \left (e^5-\log (3)\right )\right ) x^3+24 e^{2 x} x^2-8 e^{3 x} x^2+e^{4 x} x^2-32 e^x \left (1-\frac {27}{8} \left (e^5-\log (3)\right )\right ) x^2+16 \left (1-\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^2-18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+72 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x-81 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x-162 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )\right )}+\frac {-324 x^7+324 e^x x^6-540 x^6+324 e^x x^5-108 e^{2 x} x^5-216 x^5-36 e^{2 x} x^4+12 e^{3 x} x^4+48 \left (1+\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^4+24 e^{2 x} x^3-4 e^{3 x} x^3+32 \left (1+\frac {351}{16} \left (e^5-\log (3)\right )\right ) x^3-48 e^x \left (1+\frac {27}{4} \left (e^5-\log (3)\right )\right ) x^3+36 e^{2 x+5} \left (1-\frac {\log (729)}{6 e^5}\right ) x^2-216 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x^2+324 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x^2+729 \left (1+\frac {1}{81} \left (-36 e^{10}-36 \log ^2(3)+8 e^5 (1+9 \log (3))-\log (6561)\right )\right ) x-72 e^{x+5} \left (1-\frac {\log (729)}{6 e^5}\right ) x+18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+324 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )}{x^2 \left (81 x^6-108 e^x x^5+216 x^5-216 e^x x^4+54 e^{2 x} x^4+216 x^4-144 e^x x^3+72 e^{2 x} x^3-12 e^{3 x} x^3+96 \left (1-\frac {27}{16} \left (e^5-\log (3)\right )\right ) x^3+24 e^{2 x} x^2-8 e^{3 x} x^2+e^{4 x} x^2-32 e^x \left (1-\frac {27}{8} \left (e^5-\log (3)\right )\right ) x^2+16 \left (1-\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^2-18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+72 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x-81 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x-162 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 162 \int \frac {e^{4 x} (4 x+3) x^2-12 e^{3 x} \left (3 x^2+6 x+2\right ) x^2-36 e^{2 x+5} (x+1) x+36 e^{x+5} \left (3 x^2+11 x+4\right ) x-4 e^x \left (27 x^5+216 x^4+306 x^3+(152+27 \log (3)) x^2+3 (8+33 \log (3)) x-3 \log (729)+54 \log (3)\right ) x+6 e^{2 x} \left (18 x^4+69 x^3+56 x^2+(12+\log (729)) x+\log (729)\right ) x-18 e^5 \left (36 x^3+36 x^2+8 x+9 \log (3)\right )+3 \left (189 x^6+432 x^5+360 x^4+8 (16+27 \log (3)) x^3+8 (2+27 \log (3)) x^2-3 (18+\log (6561)) x+72 \log (3) x+27 \left (-2+\log ^2(3)\right )\right )+81 e^{10}}{x^2 \left (-81 x^6-216 x^5-216 x^4-6 (16+27 \log (3)) x^3-e^{4 x} x^2+4 e^{3 x} (3 x+2) x^2-8 (2+27 \log (3)) x^2+18 e^{2 x+5} x-36 e^{x+5} (3 x+2) x+4 e^x (3 x+2) \left (9 x^3+12 x^2+4 x+9 \log (3)\right ) x-6 e^{2 x} \left (9 x^3+12 x^2+4 x+\log (27)\right ) x-9 (-9+8 \log (3)) x+18 e^5 \left (9 x^3+12 x^2+4 x+9 \log (3)\right )-81 e^{10} \left (1+\frac {-2+\log ^2(3)}{e^{10}}\right )\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 162 \int \left (\frac {4 x+3}{x^2 \left (81 x^6-108 e^x x^5+216 x^5-216 e^x x^4+54 e^{2 x} x^4+216 x^4-144 e^x x^3+72 e^{2 x} x^3-12 e^{3 x} x^3+96 \left (1-\frac {27}{16} \left (e^5-\log (3)\right )\right ) x^3+24 e^{2 x} x^2-8 e^{3 x} x^2+e^{4 x} x^2-32 e^x \left (1-\frac {27}{8} \left (e^5-\log (3)\right )\right ) x^2+16 \left (1-\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^2-18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+72 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x-81 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x-162 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )\right )}+\frac {-324 x^7+324 e^x x^6-540 x^6+324 e^x x^5-108 e^{2 x} x^5-216 x^5-36 e^{2 x} x^4+12 e^{3 x} x^4+48 \left (1+\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^4+24 e^{2 x} x^3-4 e^{3 x} x^3+32 \left (1+\frac {351}{16} \left (e^5-\log (3)\right )\right ) x^3-48 e^x \left (1+\frac {27}{4} \left (e^5-\log (3)\right )\right ) x^3+36 e^{2 x+5} \left (1-\frac {\log (729)}{6 e^5}\right ) x^2-216 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x^2+324 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x^2+729 \left (1+\frac {1}{81} \left (-36 e^{10}-36 \log ^2(3)+8 e^5 (1+9 \log (3))-\log (6561)\right )\right ) x-72 e^{x+5} \left (1-\frac {\log (729)}{6 e^5}\right ) x+18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+324 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )}{x^2 \left (81 x^6-108 e^x x^5+216 x^5-216 e^x x^4+54 e^{2 x} x^4+216 x^4-144 e^x x^3+72 e^{2 x} x^3-12 e^{3 x} x^3+96 \left (1-\frac {27}{16} \left (e^5-\log (3)\right )\right ) x^3+24 e^{2 x} x^2-8 e^{3 x} x^2+e^{4 x} x^2-32 e^x \left (1-\frac {27}{8} \left (e^5-\log (3)\right )\right ) x^2+16 \left (1-\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^2-18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+72 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x-81 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x-162 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 162 \int \frac {e^{4 x} (4 x+3) x^2-12 e^{3 x} \left (3 x^2+6 x+2\right ) x^2-36 e^{2 x+5} (x+1) x+36 e^{x+5} \left (3 x^2+11 x+4\right ) x-4 e^x \left (27 x^5+216 x^4+306 x^3+(152+27 \log (3)) x^2+3 (8+33 \log (3)) x-3 \log (729)+54 \log (3)\right ) x+6 e^{2 x} \left (18 x^4+69 x^3+56 x^2+(12+\log (729)) x+\log (729)\right ) x-18 e^5 \left (36 x^3+36 x^2+8 x+9 \log (3)\right )+3 \left (189 x^6+432 x^5+360 x^4+8 (16+27 \log (3)) x^3+8 (2+27 \log (3)) x^2-3 (18+\log (6561)) x+72 \log (3) x+27 \left (-2+\log ^2(3)\right )\right )+81 e^{10}}{x^2 \left (-81 x^6-216 x^5-216 x^4-6 (16+27 \log (3)) x^3-e^{4 x} x^2+4 e^{3 x} (3 x+2) x^2-8 (2+27 \log (3)) x^2+18 e^{2 x+5} x-36 e^{x+5} (3 x+2) x+4 e^x (3 x+2) \left (9 x^3+12 x^2+4 x+9 \log (3)\right ) x-6 e^{2 x} \left (9 x^3+12 x^2+4 x+\log (27)\right ) x-9 (-9+8 \log (3)) x+18 e^5 \left (9 x^3+12 x^2+4 x+9 \log (3)\right )-81 e^{10} \left (1+\frac {-2+\log ^2(3)}{e^{10}}\right )\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 162 \int \left (\frac {4 x+3}{x^2 \left (81 x^6-108 e^x x^5+216 x^5-216 e^x x^4+54 e^{2 x} x^4+216 x^4-144 e^x x^3+72 e^{2 x} x^3-12 e^{3 x} x^3+96 \left (1-\frac {27}{16} \left (e^5-\log (3)\right )\right ) x^3+24 e^{2 x} x^2-8 e^{3 x} x^2+e^{4 x} x^2-32 e^x \left (1-\frac {27}{8} \left (e^5-\log (3)\right )\right ) x^2+16 \left (1-\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^2-18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+72 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x-81 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x-162 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )\right )}+\frac {-324 x^7+324 e^x x^6-540 x^6+324 e^x x^5-108 e^{2 x} x^5-216 x^5-36 e^{2 x} x^4+12 e^{3 x} x^4+48 \left (1+\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^4+24 e^{2 x} x^3-4 e^{3 x} x^3+32 \left (1+\frac {351}{16} \left (e^5-\log (3)\right )\right ) x^3-48 e^x \left (1+\frac {27}{4} \left (e^5-\log (3)\right )\right ) x^3+36 e^{2 x+5} \left (1-\frac {\log (729)}{6 e^5}\right ) x^2-216 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x^2+324 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x^2+729 \left (1+\frac {1}{81} \left (-36 e^{10}-36 \log ^2(3)+8 e^5 (1+9 \log (3))-\log (6561)\right )\right ) x-72 e^{x+5} \left (1-\frac {\log (729)}{6 e^5}\right ) x+18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+324 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )}{x^2 \left (81 x^6-108 e^x x^5+216 x^5-216 e^x x^4+54 e^{2 x} x^4+216 x^4-144 e^x x^3+72 e^{2 x} x^3-12 e^{3 x} x^3+96 \left (1-\frac {27}{16} \left (e^5-\log (3)\right )\right ) x^3+24 e^{2 x} x^2-8 e^{3 x} x^2+e^{4 x} x^2-32 e^x \left (1-\frac {27}{8} \left (e^5-\log (3)\right )\right ) x^2+16 \left (1-\frac {27}{2} \left (e^5-\log (3)\right )\right ) x^2-18 e^{2 x+5} \left (1-\frac {\log (27)}{3 e^5}\right ) x+72 e^{x+5} \left (1-\frac {\log (3)}{e^5}\right ) x-81 \left (1+\frac {8}{9} \left (e^5-\log (3)\right )\right ) x-162 \left (1-\frac {1}{2} \left (e^5-\log (3)\right )^2\right )\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 162 \int \frac {e^{4 x} (4 x+3) x^2-12 e^{3 x} \left (3 x^2+6 x+2\right ) x^2-36 e^{2 x+5} (x+1) x+36 e^{x+5} \left (3 x^2+11 x+4\right ) x-4 e^x \left (27 x^5+216 x^4+306 x^3+(152+27 \log (3)) x^2+3 (8+33 \log (3)) x-3 \log (729)+54 \log (3)\right ) x+6 e^{2 x} \left (18 x^4+69 x^3+56 x^2+(12+\log (729)) x+\log (729)\right ) x-18 e^5 \left (36 x^3+36 x^2+8 x+9 \log (3)\right )+3 \left (189 x^6+432 x^5+360 x^4+8 (16+27 \log (3)) x^3+8 (2+27 \log (3)) x^2-3 (18+\log (6561)) x+72 \log (3) x+27 \left (-2+\log ^2(3)\right )\right )+81 e^{10}}{x^2 \left (-81 x^6-216 x^5-216 x^4-6 (16+27 \log (3)) x^3-e^{4 x} x^2+4 e^{3 x} (3 x+2) x^2-8 (2+27 \log (3)) x^2+18 e^{2 x+5} x-36 e^{x+5} (3 x+2) x+4 e^x (3 x+2) \left (9 x^3+12 x^2+4 x+9 \log (3)\right ) x-6 e^{2 x} \left (9 x^3+12 x^2+4 x+\log (27)\right ) x-9 (-9+8 \log (3)) x+18 e^5 \left (9 x^3+12 x^2+4 x+9 \log (3)\right )-81 e^{10} \left (1+\frac {-2+\log ^2(3)}{e^{10}}\right )\right )^2}dx\)

Input:

Int[(-26244 + 13122*E^10 - 26244*x + 7776*x^2 + 62208*x^3 + 174960*x^4 + 2 
09952*x^5 + 91854*x^6 + E^5*(-23328*x - 104976*x^2 - 104976*x^3) + E^(4*x) 
*(486*x^2 + 648*x^3) + E^(3*x)*(-3888*x^2 - 11664*x^3 - 5832*x^4) + (-2624 
4*E^5 + 23328*x + 104976*x^2 + 104976*x^3)*Log[3] + 13122*Log[3]^2 + E^(2* 
x)*(11664*x^2 + 54432*x^3 + 67068*x^4 + 17496*x^5 + E^5*(-5832*x - 5832*x^ 
2) + (5832*x + 5832*x^2)*Log[3]) + E^x*(-15552*x^2 - 98496*x^3 - 198288*x^ 
4 - 139968*x^5 - 17496*x^6 + E^5*(23328*x + 64152*x^2 + 17496*x^3) + (-233 
28*x - 64152*x^2 - 17496*x^3)*Log[3]))/(26244*x^2 + 6561*E^20*x^2 + 26244* 
x^3 + 1377*x^4 - 33696*x^5 - 85280*x^6 + E^(8*x)*x^6 - 101904*x^7 - 45108* 
x^8 + 35262*x^9 + 90720*x^10 + 108864*x^11 + 81648*x^12 + 34992*x^13 + 656 
1*x^14 + E^15*(-11664*x^3 - 34992*x^4 - 26244*x^5) + E^(7*x)*(-16*x^6 - 24 
*x^7) + E^10*(-26244*x^2 - 13122*x^3 + 7776*x^4 + 46656*x^5 + 104976*x^6 + 
 104976*x^7 + 39366*x^8) + E^5*(23328*x^3 + 81648*x^4 + 85176*x^5 + 5508*x 
^6 - 77760*x^7 - 155520*x^8 - 174960*x^9 - 104976*x^10 - 26244*x^11) + (-2 
6244*E^15*x^2 - 23328*x^3 - 81648*x^4 - 85176*x^5 - 5508*x^6 + 77760*x^7 + 
 155520*x^8 + 174960*x^9 + 104976*x^10 + 26244*x^11 + E^10*(34992*x^3 + 10 
4976*x^4 + 78732*x^5) + E^5*(52488*x^2 + 26244*x^3 - 15552*x^4 - 93312*x^5 
 - 209952*x^6 - 209952*x^7 - 78732*x^8))*Log[3] + (-26244*x^2 + 39366*E^10 
*x^2 - 13122*x^3 + 7776*x^4 + 46656*x^5 + 104976*x^6 + 104976*x^7 + 39366* 
x^8 + E^5*(-34992*x^3 - 104976*x^4 - 78732*x^5))*Log[3]^2 + (-26244*E^5*x^ 
2 + 11664*x^3 + 34992*x^4 + 26244*x^5)*Log[3]^3 + 6561*x^2*Log[3]^4 + E^(6 
*x)*(-36*E^5*x^5 + 112*x^6 + 336*x^7 + 252*x^8 + 36*x^5*Log[3]) + E^(5*x)* 
(-448*x^6 - 2016*x^7 - 3024*x^8 - 1512*x^9 + E^5*(432*x^5 + 648*x^6) + (-4 
32*x^5 - 648*x^6)*Log[3]) + E^(4*x)*(-324*x^4 + 486*E^10*x^4 - 162*x^5 + 1 
120*x^6 + 6720*x^7 + 15120*x^8 + 15120*x^9 + 5670*x^10 + E^5*(-2160*x^5 - 
6480*x^6 - 4860*x^7) + (-972*E^5*x^4 + 2160*x^5 + 6480*x^6 + 4860*x^7)*Log 
[3] + 486*x^4*Log[3]^2) + E^(3*x)*(2592*x^4 + 5184*x^5 + 152*x^6 - 13440*x 
^7 - 40320*x^8 - 60480*x^9 - 45360*x^10 - 13608*x^11 + E^10*(-3888*x^4 - 5 
832*x^5) + E^5*(5760*x^5 + 25920*x^6 + 38880*x^7 + 19440*x^8) + (-5760*x^5 
 - 25920*x^6 - 38880*x^7 - 19440*x^8 + E^5*(7776*x^4 + 11664*x^5))*Log[3] 
+ (-3888*x^4 - 5832*x^5)*Log[3]^2) + E^(2*x)*(-2916*E^15*x^3 - 7776*x^4 - 
27216*x^5 - 27368*x^6 + 7380*x^7 + 60480*x^8 + 120960*x^9 + 136080*x^10 + 
81648*x^11 + 20412*x^12 + E^10*(11664*x^4 + 34992*x^5 + 26244*x^6) + E^5*( 
5832*x^3 + 2916*x^4 - 8640*x^5 - 51840*x^6 - 116640*x^7 - 116640*x^8 - 437 
40*x^9) + (-5832*x^3 + 8748*E^10*x^3 - 2916*x^4 + 8640*x^5 + 51840*x^6 + 1 
16640*x^7 + 116640*x^8 + 43740*x^9 + E^5*(-23328*x^4 - 69984*x^5 - 52488*x 
^6))*Log[3] + (-8748*E^5*x^3 + 11664*x^4 + 34992*x^5 + 26244*x^6)*Log[3]^2 
 + 2916*x^3*Log[3]^3) + E^x*(10368*x^4 + 51840*x^5 + 92288*x^6 + 59232*x^7 
 - 30888*x^8 - 120960*x^9 - 181440*x^10 - 163296*x^11 - 81648*x^12 - 17496 
*x^13 + E^15*(11664*x^3 + 17496*x^4) + E^10*(-15552*x^4 - 69984*x^5 - 1049 
76*x^6 - 52488*x^7) + E^5*(-23328*x^3 - 46656*x^4 - 10584*x^5 + 51840*x^6 
+ 155520*x^7 + 233280*x^8 + 174960*x^9 + 52488*x^10) + (23328*x^3 + 46656* 
x^4 + 10584*x^5 - 51840*x^6 - 155520*x^7 - 233280*x^8 - 174960*x^9 - 52488 
*x^10 + E^10*(-34992*x^3 - 52488*x^4) + E^5*(31104*x^4 + 139968*x^5 + 2099 
52*x^6 + 104976*x^7))*Log[3] + (-15552*x^4 - 69984*x^5 - 104976*x^6 - 5248 
8*x^7 + E^5*(34992*x^3 + 52488*x^4))*Log[3]^2 + (-11664*x^3 - 17496*x^4)*L 
og[3]^3)),x]
 

Output:

$Aborted
 

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(224\) vs. \(2(34)=68\).

Time = 21.82 (sec) , antiderivative size = 225, normalized size of antiderivative = 5.77

method	result	size
risch	\(-\frac {162}{x \left (-162-81 x -108 \,{\mathrm e}^{x} \ln \left (3\right ) x^{2}+108 \,{\mathrm e}^{x} {\mathrm e}^{5} x^{2}-108 x^{5} {\mathrm e}^{x}-162 \,{\mathrm e}^{5} \ln \left (3\right )+72 \,{\mathrm e}^{2 x} x^{3}-216 \,{\mathrm e}^{x} x^{4}-162 x^{3} {\mathrm e}^{5}+162 x^{3} \ln \left (3\right )+24 \,{\mathrm e}^{2 x} x^{2}-72 x \,{\mathrm e}^{5}+x^{2} {\mathrm e}^{4 x}-216 x^{2} {\mathrm e}^{5}+216 x^{2} \ln \left (3\right )+72 x \ln \left (3\right )+81 \,{\mathrm e}^{10}-144 \,{\mathrm e}^{x} x^{3}-32 \,{\mathrm e}^{x} x^{2}+81 \ln \left (3\right )^{2}+81 x^{6}+16 x^{2}+96 x^{3}+216 x^{4}+216 x^{5}-72 x \ln \left (3\right ) {\mathrm e}^{x}+72 x \,{\mathrm e}^{5} {\mathrm e}^{x}+54 \,{\mathrm e}^{2 x} x^{4}+18 \ln \left (3\right ) {\mathrm e}^{2 x} x -18 \,{\mathrm e}^{5} {\mathrm e}^{2 x} x -12 \,{\mathrm e}^{3 x} x^{3}-8 \,{\mathrm e}^{3 x} x^{2}\right )}\)	\(225\)
parallelrisch	\(-\frac {162}{x \left (-162-81 x -108 \,{\mathrm e}^{x} \ln \left (3\right ) x^{2}+108 \,{\mathrm e}^{x} {\mathrm e}^{5} x^{2}-108 x^{5} {\mathrm e}^{x}-162 \,{\mathrm e}^{5} \ln \left (3\right )+72 \,{\mathrm e}^{2 x} x^{3}-216 \,{\mathrm e}^{x} x^{4}-162 x^{3} {\mathrm e}^{5}+162 x^{3} \ln \left (3\right )+24 \,{\mathrm e}^{2 x} x^{2}-72 x \,{\mathrm e}^{5}+x^{2} {\mathrm e}^{4 x}-216 x^{2} {\mathrm e}^{5}+216 x^{2} \ln \left (3\right )+72 x \ln \left (3\right )+81 \,{\mathrm e}^{10}-144 \,{\mathrm e}^{x} x^{3}-32 \,{\mathrm e}^{x} x^{2}+81 \ln \left (3\right )^{2}+81 x^{6}+16 x^{2}+96 x^{3}+216 x^{4}+216 x^{5}-72 x \ln \left (3\right ) {\mathrm e}^{x}+72 x \,{\mathrm e}^{5} {\mathrm e}^{x}+54 \,{\mathrm e}^{2 x} x^{4}+18 \ln \left (3\right ) {\mathrm e}^{2 x} x -18 \,{\mathrm e}^{5} {\mathrm e}^{2 x} x -12 \,{\mathrm e}^{3 x} x^{3}-8 \,{\mathrm e}^{3 x} x^{2}\right )}\)	\(225\)

Input:

int(((648*x^3+486*x^2)*exp(x)^4+(-5832*x^4-11664*x^3-3888*x^2)*exp(x)^3+(( 
5832*x^2+5832*x)*ln(3)+(-5832*x^2-5832*x)*exp(5)+17496*x^5+67068*x^4+54432 
*x^3+11664*x^2)*exp(x)^2+((-17496*x^3-64152*x^2-23328*x)*ln(3)+(17496*x^3+ 
64152*x^2+23328*x)*exp(5)-17496*x^6-139968*x^5-198288*x^4-98496*x^3-15552* 
x^2)*exp(x)+13122*ln(3)^2+(-26244*exp(5)+104976*x^3+104976*x^2+23328*x)*ln 
(3)+13122*exp(5)^2+(-104976*x^3-104976*x^2-23328*x)*exp(5)+91854*x^6+20995 
2*x^5+174960*x^4+62208*x^3+7776*x^2-26244*x-26244)/(6561*x^2*ln(3)^4+6561* 
x^2*exp(5)^4+(39366*x^2*exp(5)^2+(-78732*x^5-104976*x^4-34992*x^3)*exp(5)+ 
39366*x^8+104976*x^7+104976*x^6+46656*x^5+7776*x^4-13122*x^3-26244*x^2)*ln 
(3)^2+((-5832*x^5-3888*x^4)*ln(3)^2+((11664*x^5+7776*x^4)*exp(5)-19440*x^8 
-38880*x^7-25920*x^6-5760*x^5)*ln(3)+(-5832*x^5-3888*x^4)*exp(5)^2+(19440* 
x^8+38880*x^7+25920*x^6+5760*x^5)*exp(5)-13608*x^11-45360*x^10-60480*x^9-4 
0320*x^8-13440*x^7+152*x^6+5184*x^5+2592*x^4)*exp(x)^3+((-17496*x^4-11664* 
x^3)*ln(3)^3+((52488*x^4+34992*x^3)*exp(5)-52488*x^7-104976*x^6-69984*x^5- 
15552*x^4)*ln(3)^2+((-52488*x^4-34992*x^3)*exp(5)^2+(104976*x^7+209952*x^6 
+139968*x^5+31104*x^4)*exp(5)-52488*x^10-174960*x^9-233280*x^8-155520*x^7- 
51840*x^6+10584*x^5+46656*x^4+23328*x^3)*ln(3)+(17496*x^4+11664*x^3)*exp(5 
)^3+(-52488*x^7-104976*x^6-69984*x^5-15552*x^4)*exp(5)^2+(52488*x^10+17496 
0*x^9+233280*x^8+155520*x^7+51840*x^6-10584*x^5-46656*x^4-23328*x^3)*exp(5 
)-17496*x^13-81648*x^12-163296*x^11-181440*x^10-120960*x^9-30888*x^8+59232 
*x^7+92288*x^6+51840*x^5+10368*x^4)*exp(x)+(-26244*x^2*exp(5)+26244*x^5+34 
992*x^4+11664*x^3)*ln(3)^3+(2916*x^3*ln(3)^3+(-8748*x^3*exp(5)+26244*x^6+3 
4992*x^5+11664*x^4)*ln(3)^2+(8748*x^3*exp(5)^2+(-52488*x^6-69984*x^5-23328 
*x^4)*exp(5)+43740*x^9+116640*x^8+116640*x^7+51840*x^6+8640*x^5-2916*x^4-5 
832*x^3)*ln(3)-2916*x^3*exp(5)^3+(26244*x^6+34992*x^5+11664*x^4)*exp(5)^2+ 
(-43740*x^9-116640*x^8-116640*x^7-51840*x^6-8640*x^5+2916*x^4+5832*x^3)*ex 
p(5)+20412*x^12+81648*x^11+136080*x^10+120960*x^9+60480*x^8+7380*x^7-27368 
*x^6-27216*x^5-7776*x^4)*exp(x)^2+x^6*exp(x)^8+(-24*x^7-16*x^6)*exp(x)^7+( 
36*x^5*ln(3)-36*x^5*exp(5)+252*x^8+336*x^7+112*x^6)*exp(x)^6+((-648*x^6-43 
2*x^5)*ln(3)+(648*x^6+432*x^5)*exp(5)-1512*x^9-3024*x^8-2016*x^7-448*x^6)* 
exp(x)^5+(486*x^4*ln(3)^2+(-972*x^4*exp(5)+4860*x^7+6480*x^6+2160*x^5)*ln( 
3)+486*x^4*exp(5)^2+(-4860*x^7-6480*x^6-2160*x^5)*exp(5)+5670*x^10+15120*x 
^9+15120*x^8+6720*x^7+1120*x^6-162*x^5-324*x^4)*exp(x)^4+(-26244*x^2*exp(5 
)^3+(78732*x^5+104976*x^4+34992*x^3)*exp(5)^2+(-78732*x^8-209952*x^7-20995 
2*x^6-93312*x^5-15552*x^4+26244*x^3+52488*x^2)*exp(5)+26244*x^11+104976*x^ 
10+174960*x^9+155520*x^8+77760*x^7-5508*x^6-85176*x^5-81648*x^4-23328*x^3) 
*ln(3)+(-26244*x^5-34992*x^4-11664*x^3)*exp(5)^3+(39366*x^8+104976*x^7+104 
976*x^6+46656*x^5+7776*x^4-13122*x^3-26244*x^2)*exp(5)^2+(-26244*x^11-1049 
76*x^10-174960*x^9-155520*x^8-77760*x^7+5508*x^6+85176*x^5+81648*x^4+23328 
*x^3)*exp(5)+6561*x^14+34992*x^13+108864*x^11+90720*x^10+81648*x^12-45108* 
x^8+35262*x^9-85280*x^6-101904*x^7+26244*x^2+26244*x^3+1377*x^4-33696*x^5) 
,x,method=_RETURNVERBOSE)
 

Output:

-162/x/(-162-81*x+18*exp(x)^2*ln(3)*x-18*exp(x)^2*exp(5)*x-108*exp(x)*ln(3 
)*x^2+108*exp(x)*exp(5)*x^2-108*x^5*exp(x)-162*exp(5)*ln(3)+x^2*exp(x)^4-2 
16*exp(x)*x^4-162*x^3*exp(5)-12*x^3*exp(x)^3+72*exp(x)^2*x^3+162*x^3*ln(3) 
+24*exp(x)^2*x^2-72*x*exp(5)-216*x^2*exp(5)+216*x^2*ln(3)+72*x*ln(3)+54*ex 
p(x)^2*x^4-8*exp(x)^3*x^2-144*exp(x)*x^3-32*exp(x)*x^2+81*ln(3)^2+81*exp(5 
)^2+81*x^6+16*x^2+96*x^3+216*x^4+216*x^5-72*x*ln(3)*exp(x)+72*x*exp(5)*exp 
(x))
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 211 vs. \(2 (36) = 72\).

Time = 0.28 (sec) , antiderivative size = 211, normalized size of antiderivative = 5.41 \[ \text {the integral} =-\frac {162}{81 \, x^{7} + 216 \, x^{6} + 216 \, x^{5} + 96 \, x^{4} + x^{3} e^{\left (4 \, x\right )} + 16 \, x^{3} + 81 \, x \log \left (3\right )^{2} - 81 \, x^{2} + 81 \, x e^{10} - 18 \, {\left (9 \, x^{4} + 12 \, x^{3} + 4 \, x^{2}\right )} e^{5} - 4 \, {\left (3 \, x^{4} + 2 \, x^{3}\right )} e^{\left (3 \, x\right )} + 6 \, {\left (9 \, x^{5} + 12 \, x^{4} + 4 \, x^{3} - 3 \, x^{2} e^{5} + 3 \, x^{2} \log \left (3\right )\right )} e^{\left (2 \, x\right )} - 4 \, {\left (27 \, x^{6} + 54 \, x^{5} + 36 \, x^{4} + 8 \, x^{3} - 9 \, {\left (3 \, x^{3} + 2 \, x^{2}\right )} e^{5} + 9 \, {\left (3 \, x^{3} + 2 \, x^{2}\right )} \log \left (3\right )\right )} e^{x} + 18 \, {\left (9 \, x^{4} + 12 \, x^{3} + 4 \, x^{2} - 9 \, x e^{5}\right )} \log \left (3\right ) - 162 \, x} \] Input:

integrate(((648*x^3+486*x^2)*exp(x)^4+(-5832*x^4-11664*x^3-3888*x^2)*exp(x 
)^3+((5832*x^2+5832*x)*log(3)+(-5832*x^2-5832*x)*exp(5)+17496*x^5+67068*x^ 
4+54432*x^3+11664*x^2)*exp(x)^2+((-17496*x^3-64152*x^2-23328*x)*log(3)+(17 
496*x^3+64152*x^2+23328*x)*exp(5)-17496*x^6-139968*x^5-198288*x^4-98496*x^ 
3-15552*x^2)*exp(x)+13122*log(3)^2+(-26244*exp(5)+104976*x^3+104976*x^2+23 
328*x)*log(3)+13122*exp(5)^2+(-104976*x^3-104976*x^2-23328*x)*exp(5)+91854 
*x^6+209952*x^5+174960*x^4+62208*x^3+7776*x^2-26244*x-26244)/(6561*x^14-33 
696*x^5+26244*x^2+6561*x^2*exp(5)^4-85280*x^6-101904*x^7+81648*x^12+1377*x 
^4+26244*x^3+6561*x^2*log(3)^4+((-17496*x^4-11664*x^3)*log(3)^3+((52488*x^ 
4+34992*x^3)*exp(5)-52488*x^7-104976*x^6-69984*x^5-15552*x^4)*log(3)^2+((- 
52488*x^4-34992*x^3)*exp(5)^2+(104976*x^7+209952*x^6+139968*x^5+31104*x^4) 
*exp(5)-52488*x^10-174960*x^9-233280*x^8-155520*x^7-51840*x^6+10584*x^5+46 
656*x^4+23328*x^3)*log(3)+(17496*x^4+11664*x^3)*exp(5)^3+(-52488*x^7-10497 
6*x^6-69984*x^5-15552*x^4)*exp(5)^2+(52488*x^10+174960*x^9+233280*x^8+1555 
20*x^7+51840*x^6-10584*x^5-46656*x^4-23328*x^3)*exp(5)-17496*x^13-81648*x^ 
12-163296*x^11-181440*x^10-120960*x^9-30888*x^8+59232*x^7+92288*x^6+51840* 
x^5+10368*x^4)*exp(x)+(-26244*x^2*exp(5)+26244*x^5+34992*x^4+11664*x^3)*lo 
g(3)^3+(39366*x^2*exp(5)^2+(-78732*x^5-104976*x^4-34992*x^3)*exp(5)+39366* 
x^8+104976*x^7+104976*x^6+46656*x^5+7776*x^4-13122*x^3-26244*x^2)*log(3)^2 
+(-26244*x^2*exp(5)^3+(78732*x^5+104976*x^4+34992*x^3)*exp(5)^2+(-78732*x^ 
8-209952*x^7-209952*x^6-93312*x^5-15552*x^4+26244*x^3+52488*x^2)*exp(5)+26 
244*x^11+104976*x^10+174960*x^9+155520*x^8+77760*x^7-5508*x^6-85176*x^5-81 
648*x^4-23328*x^3)*log(3)+(-26244*x^5-34992*x^4-11664*x^3)*exp(5)^3+(39366 
*x^8+104976*x^7+104976*x^6+46656*x^5+7776*x^4-13122*x^3-26244*x^2)*exp(5)^ 
2+(-26244*x^11-104976*x^10-174960*x^9-155520*x^8-77760*x^7+5508*x^6+85176* 
x^5+81648*x^4+23328*x^3)*exp(5)+((-5832*x^5-3888*x^4)*log(3)^2+((11664*x^5 
+7776*x^4)*exp(5)-19440*x^8-38880*x^7-25920*x^6-5760*x^5)*log(3)+(-5832*x^ 
5-3888*x^4)*exp(5)^2+(19440*x^8+38880*x^7+25920*x^6+5760*x^5)*exp(5)-13608 
*x^11-45360*x^10-60480*x^9-40320*x^8-13440*x^7+152*x^6+5184*x^5+2592*x^4)* 
exp(x)^3+(2916*x^3*log(3)^3+(-8748*x^3*exp(5)+26244*x^6+34992*x^5+11664*x^ 
4)*log(3)^2+(8748*x^3*exp(5)^2+(-52488*x^6-69984*x^5-23328*x^4)*exp(5)+437 
40*x^9+116640*x^8+116640*x^7+51840*x^6+8640*x^5-2916*x^4-5832*x^3)*log(3)- 
2916*x^3*exp(5)^3+(26244*x^6+34992*x^5+11664*x^4)*exp(5)^2+(-43740*x^9-116 
640*x^8-116640*x^7-51840*x^6-8640*x^5+2916*x^4+5832*x^3)*exp(5)+20412*x^12 
+81648*x^11+136080*x^10+120960*x^9+60480*x^8+7380*x^7-27368*x^6-27216*x^5- 
7776*x^4)*exp(x)^2+x^6*exp(x)^8+(-24*x^7-16*x^6)*exp(x)^7+(36*x^5*log(3)-3 
6*x^5*exp(5)+252*x^8+336*x^7+112*x^6)*exp(x)^6+((-648*x^6-432*x^5)*log(3)+ 
(648*x^6+432*x^5)*exp(5)-1512*x^9-3024*x^8-2016*x^7-448*x^6)*exp(x)^5+(486 
*x^4*log(3)^2+(-972*x^4*exp(5)+4860*x^7+6480*x^6+2160*x^5)*log(3)+486*x^4* 
exp(5)^2+(-4860*x^7-6480*x^6-2160*x^5)*exp(5)+5670*x^10+15120*x^9+15120*x^ 
8+6720*x^7+1120*x^6-162*x^5-324*x^4)*exp(x)^4+108864*x^11+90720*x^10+35262 
*x^9-45108*x^8+34992*x^13),x, algorithm="fricas")
 

Output:

-162/(81*x^7 + 216*x^6 + 216*x^5 + 96*x^4 + x^3*e^(4*x) + 16*x^3 + 81*x*lo 
g(3)^2 - 81*x^2 + 81*x*e^10 - 18*(9*x^4 + 12*x^3 + 4*x^2)*e^5 - 4*(3*x^4 + 
 2*x^3)*e^(3*x) + 6*(9*x^5 + 12*x^4 + 4*x^3 - 3*x^2*e^5 + 3*x^2*log(3))*e^ 
(2*x) - 4*(27*x^6 + 54*x^5 + 36*x^4 + 8*x^3 - 9*(3*x^3 + 2*x^2)*e^5 + 9*(3 
*x^3 + 2*x^2)*log(3))*e^x + 18*(9*x^4 + 12*x^3 + 4*x^2 - 9*x*e^5)*log(3) - 
 162*x)
 

Sympy [F(-1)]

Timed out. \[ \text {the integral} =\text {Timed out} \] Input:

integrate(((648*x**3+486*x**2)*exp(x)**4+(-5832*x**4-11664*x**3-3888*x**2) 
*exp(x)**3+((5832*x**2+5832*x)*ln(3)+(-5832*x**2-5832*x)*exp(5)+17496*x**5 
+67068*x**4+54432*x**3+11664*x**2)*exp(x)**2+((-17496*x**3-64152*x**2-2332 
8*x)*ln(3)+(17496*x**3+64152*x**2+23328*x)*exp(5)-17496*x**6-139968*x**5-1 
98288*x**4-98496*x**3-15552*x**2)*exp(x)+13122*ln(3)**2+(-26244*exp(5)+104 
976*x**3+104976*x**2+23328*x)*ln(3)+13122*exp(5)**2+(-104976*x**3-104976*x 
**2-23328*x)*exp(5)+91854*x**6+209952*x**5+174960*x**4+62208*x**3+7776*x** 
2-26244*x-26244)/(26244*x**2+108864*x**11+34992*x**13+90720*x**10+35262*x* 
*9+81648*x**12-101904*x**7+(-26244*x**2*exp(5)**3+(78732*x**5+104976*x**4+ 
34992*x**3)*exp(5)**2+(-78732*x**8-209952*x**7-209952*x**6-93312*x**5-1555 
2*x**4+26244*x**3+52488*x**2)*exp(5)+26244*x**11+104976*x**10+174960*x**9+ 
155520*x**8+77760*x**7-5508*x**6-85176*x**5-81648*x**4-23328*x**3)*ln(3)+( 
-26244*x**5-34992*x**4-11664*x**3)*exp(5)**3+(39366*x**8+104976*x**7+10497 
6*x**6+46656*x**5+7776*x**4-13122*x**3-26244*x**2)*exp(5)**2+(-26244*x**11 
-104976*x**10-174960*x**9-155520*x**8-77760*x**7+5508*x**6+85176*x**5+8164 
8*x**4+23328*x**3)*exp(5)-33696*x**5+26244*x**3+6561*x**2*ln(3)**4+((-1749 
6*x**4-11664*x**3)*ln(3)**3+((52488*x**4+34992*x**3)*exp(5)-52488*x**7-104 
976*x**6-69984*x**5-15552*x**4)*ln(3)**2+((-52488*x**4-34992*x**3)*exp(5)* 
*2+(104976*x**7+209952*x**6+139968*x**5+31104*x**4)*exp(5)-52488*x**10-174 
960*x**9-233280*x**8-155520*x**7-51840*x**6+10584*x**5+46656*x**4+23328*x* 
*3)*ln(3)+(17496*x**4+11664*x**3)*exp(5)**3+(-52488*x**7-104976*x**6-69984 
*x**5-15552*x**4)*exp(5)**2+(52488*x**10+174960*x**9+233280*x**8+155520*x* 
*7+51840*x**6-10584*x**5-46656*x**4-23328*x**3)*exp(5)-17496*x**13-81648*x 
**12-163296*x**11-181440*x**10-120960*x**9-30888*x**8+59232*x**7+92288*x** 
6+51840*x**5+10368*x**4)*exp(x)+(-26244*x**2*exp(5)+26244*x**5+34992*x**4+ 
11664*x**3)*ln(3)**3+(39366*x**2*exp(5)**2+(-78732*x**5-104976*x**4-34992* 
x**3)*exp(5)+39366*x**8+104976*x**7+104976*x**6+46656*x**5+7776*x**4-13122 
*x**3-26244*x**2)*ln(3)**2+6561*x**2*exp(5)**4+((-5832*x**5-3888*x**4)*ln( 
3)**2+((11664*x**5+7776*x**4)*exp(5)-19440*x**8-38880*x**7-25920*x**6-5760 
*x**5)*ln(3)+(-5832*x**5-3888*x**4)*exp(5)**2+(19440*x**8+38880*x**7+25920 
*x**6+5760*x**5)*exp(5)-13608*x**11-45360*x**10-60480*x**9-40320*x**8-1344 
0*x**7+152*x**6+5184*x**5+2592*x**4)*exp(x)**3+6561*x**14-45108*x**8+1377* 
x**4+(2916*x**3*ln(3)**3+(-8748*x**3*exp(5)+26244*x**6+34992*x**5+11664*x* 
*4)*ln(3)**2+(8748*x**3*exp(5)**2+(-52488*x**6-69984*x**5-23328*x**4)*exp( 
5)+43740*x**9+116640*x**8+116640*x**7+51840*x**6+8640*x**5-2916*x**4-5832* 
x**3)*ln(3)-2916*x**3*exp(5)**3+(26244*x**6+34992*x**5+11664*x**4)*exp(5)* 
*2+(-43740*x**9-116640*x**8-116640*x**7-51840*x**6-8640*x**5+2916*x**4+583 
2*x**3)*exp(5)+20412*x**12+81648*x**11+136080*x**10+120960*x**9+60480*x**8 
+7380*x**7-27368*x**6-27216*x**5-7776*x**4)*exp(x)**2+x**6*exp(x)**8+(-24* 
x**7-16*x**6)*exp(x)**7+(36*x**5*ln(3)-36*x**5*exp(5)+252*x**8+336*x**7+11 
2*x**6)*exp(x)**6+((-648*x**6-432*x**5)*ln(3)+(648*x**6+432*x**5)*exp(5)-1 
512*x**9-3024*x**8-2016*x**7-448*x**6)*exp(x)**5+(486*x**4*ln(3)**2+(-972* 
x**4*exp(5)+4860*x**7+6480*x**6+2160*x**5)*ln(3)+486*x**4*exp(5)**2+(-4860 
*x**7-6480*x**6-2160*x**5)*exp(5)+5670*x**10+15120*x**9+15120*x**8+6720*x* 
*7+1120*x**6-162*x**5-324*x**4)*exp(x)**4-85280*x**6),x)
 

Output:

Timed out
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 192 vs. \(2 (36) = 72\).

Time = 24.97 (sec) , antiderivative size = 192, normalized size of antiderivative = 4.92 \[ \text {the integral} =-\frac {162}{81 \, x^{7} + 216 \, x^{6} + 216 \, x^{5} - 6 \, x^{4} {\left (27 \, e^{5} - 27 \, \log \left (3\right ) - 16\right )} - 8 \, x^{3} {\left (27 \, e^{5} - 27 \, \log \left (3\right ) - 2\right )} + x^{3} e^{\left (4 \, x\right )} - 9 \, x^{2} {\left (8 \, e^{5} - 8 \, \log \left (3\right ) + 9\right )} - 81 \, {\left (2 \, e^{5} \log \left (3\right ) - \log \left (3\right )^{2} - e^{10} + 2\right )} x - 4 \, {\left (3 \, x^{4} + 2 \, x^{3}\right )} e^{\left (3 \, x\right )} + 6 \, {\left (9 \, x^{5} + 12 \, x^{4} + 4 \, x^{3} - 3 \, x^{2} {\left (e^{5} - \log \left (3\right )\right )}\right )} e^{\left (2 \, x\right )} - 4 \, {\left (27 \, x^{6} + 54 \, x^{5} + 36 \, x^{4} - x^{3} {\left (27 \, e^{5} - 27 \, \log \left (3\right ) - 8\right )} - 18 \, x^{2} {\left (e^{5} - \log \left (3\right )\right )}\right )} e^{x}} \] Input:

integrate(((648*x^3+486*x^2)*exp(x)^4+(-5832*x^4-11664*x^3-3888*x^2)*exp(x 
)^3+((5832*x^2+5832*x)*log(3)+(-5832*x^2-5832*x)*exp(5)+17496*x^5+67068*x^ 
4+54432*x^3+11664*x^2)*exp(x)^2+((-17496*x^3-64152*x^2-23328*x)*log(3)+(17 
496*x^3+64152*x^2+23328*x)*exp(5)-17496*x^6-139968*x^5-198288*x^4-98496*x^ 
3-15552*x^2)*exp(x)+13122*log(3)^2+(-26244*exp(5)+104976*x^3+104976*x^2+23 
328*x)*log(3)+13122*exp(5)^2+(-104976*x^3-104976*x^2-23328*x)*exp(5)+91854 
*x^6+209952*x^5+174960*x^4+62208*x^3+7776*x^2-26244*x-26244)/(6561*x^14-33 
696*x^5+26244*x^2+6561*x^2*exp(5)^4-85280*x^6-101904*x^7+81648*x^12+1377*x 
^4+26244*x^3+6561*x^2*log(3)^4+((-17496*x^4-11664*x^3)*log(3)^3+((52488*x^ 
4+34992*x^3)*exp(5)-52488*x^7-104976*x^6-69984*x^5-15552*x^4)*log(3)^2+((- 
52488*x^4-34992*x^3)*exp(5)^2+(104976*x^7+209952*x^6+139968*x^5+31104*x^4) 
*exp(5)-52488*x^10-174960*x^9-233280*x^8-155520*x^7-51840*x^6+10584*x^5+46 
656*x^4+23328*x^3)*log(3)+(17496*x^4+11664*x^3)*exp(5)^3+(-52488*x^7-10497 
6*x^6-69984*x^5-15552*x^4)*exp(5)^2+(52488*x^10+174960*x^9+233280*x^8+1555 
20*x^7+51840*x^6-10584*x^5-46656*x^4-23328*x^3)*exp(5)-17496*x^13-81648*x^ 
12-163296*x^11-181440*x^10-120960*x^9-30888*x^8+59232*x^7+92288*x^6+51840* 
x^5+10368*x^4)*exp(x)+(-26244*x^2*exp(5)+26244*x^5+34992*x^4+11664*x^3)*lo 
g(3)^3+(39366*x^2*exp(5)^2+(-78732*x^5-104976*x^4-34992*x^3)*exp(5)+39366* 
x^8+104976*x^7+104976*x^6+46656*x^5+7776*x^4-13122*x^3-26244*x^2)*log(3)^2 
+(-26244*x^2*exp(5)^3+(78732*x^5+104976*x^4+34992*x^3)*exp(5)^2+(-78732*x^ 
8-209952*x^7-209952*x^6-93312*x^5-15552*x^4+26244*x^3+52488*x^2)*exp(5)+26 
244*x^11+104976*x^10+174960*x^9+155520*x^8+77760*x^7-5508*x^6-85176*x^5-81 
648*x^4-23328*x^3)*log(3)+(-26244*x^5-34992*x^4-11664*x^3)*exp(5)^3+(39366 
*x^8+104976*x^7+104976*x^6+46656*x^5+7776*x^4-13122*x^3-26244*x^2)*exp(5)^ 
2+(-26244*x^11-104976*x^10-174960*x^9-155520*x^8-77760*x^7+5508*x^6+85176* 
x^5+81648*x^4+23328*x^3)*exp(5)+((-5832*x^5-3888*x^4)*log(3)^2+((11664*x^5 
+7776*x^4)*exp(5)-19440*x^8-38880*x^7-25920*x^6-5760*x^5)*log(3)+(-5832*x^ 
5-3888*x^4)*exp(5)^2+(19440*x^8+38880*x^7+25920*x^6+5760*x^5)*exp(5)-13608 
*x^11-45360*x^10-60480*x^9-40320*x^8-13440*x^7+152*x^6+5184*x^5+2592*x^4)* 
exp(x)^3+(2916*x^3*log(3)^3+(-8748*x^3*exp(5)+26244*x^6+34992*x^5+11664*x^ 
4)*log(3)^2+(8748*x^3*exp(5)^2+(-52488*x^6-69984*x^5-23328*x^4)*exp(5)+437 
40*x^9+116640*x^8+116640*x^7+51840*x^6+8640*x^5-2916*x^4-5832*x^3)*log(3)- 
2916*x^3*exp(5)^3+(26244*x^6+34992*x^5+11664*x^4)*exp(5)^2+(-43740*x^9-116 
640*x^8-116640*x^7-51840*x^6-8640*x^5+2916*x^4+5832*x^3)*exp(5)+20412*x^12 
+81648*x^11+136080*x^10+120960*x^9+60480*x^8+7380*x^7-27368*x^6-27216*x^5- 
7776*x^4)*exp(x)^2+x^6*exp(x)^8+(-24*x^7-16*x^6)*exp(x)^7+(36*x^5*log(3)-3 
6*x^5*exp(5)+252*x^8+336*x^7+112*x^6)*exp(x)^6+((-648*x^6-432*x^5)*log(3)+ 
(648*x^6+432*x^5)*exp(5)-1512*x^9-3024*x^8-2016*x^7-448*x^6)*exp(x)^5+(486 
*x^4*log(3)^2+(-972*x^4*exp(5)+4860*x^7+6480*x^6+2160*x^5)*log(3)+486*x^4* 
exp(5)^2+(-4860*x^7-6480*x^6-2160*x^5)*exp(5)+5670*x^10+15120*x^9+15120*x^ 
8+6720*x^7+1120*x^6-162*x^5-324*x^4)*exp(x)^4+108864*x^11+90720*x^10+35262 
*x^9-45108*x^8+34992*x^13),x, algorithm="maxima")
 

Output:

-162/(81*x^7 + 216*x^6 + 216*x^5 - 6*x^4*(27*e^5 - 27*log(3) - 16) - 8*x^3 
*(27*e^5 - 27*log(3) - 2) + x^3*e^(4*x) - 9*x^2*(8*e^5 - 8*log(3) + 9) - 8 
1*(2*e^5*log(3) - log(3)^2 - e^10 + 2)*x - 4*(3*x^4 + 2*x^3)*e^(3*x) + 6*( 
9*x^5 + 12*x^4 + 4*x^3 - 3*x^2*(e^5 - log(3)))*e^(2*x) - 4*(27*x^6 + 54*x^ 
5 + 36*x^4 - x^3*(27*e^5 - 27*log(3) - 8) - 18*x^2*(e^5 - log(3)))*e^x)
 

Giac [F(-1)]

Timed out. \[ \text {the integral} =\text {Timed out} \] Input:

integrate(((648*x^3+486*x^2)*exp(x)^4+(-5832*x^4-11664*x^3-3888*x^2)*exp(x 
)^3+((5832*x^2+5832*x)*log(3)+(-5832*x^2-5832*x)*exp(5)+17496*x^5+67068*x^ 
4+54432*x^3+11664*x^2)*exp(x)^2+((-17496*x^3-64152*x^2-23328*x)*log(3)+(17 
496*x^3+64152*x^2+23328*x)*exp(5)-17496*x^6-139968*x^5-198288*x^4-98496*x^ 
3-15552*x^2)*exp(x)+13122*log(3)^2+(-26244*exp(5)+104976*x^3+104976*x^2+23 
328*x)*log(3)+13122*exp(5)^2+(-104976*x^3-104976*x^2-23328*x)*exp(5)+91854 
*x^6+209952*x^5+174960*x^4+62208*x^3+7776*x^2-26244*x-26244)/(6561*x^14-33 
696*x^5+26244*x^2+6561*x^2*exp(5)^4-85280*x^6-101904*x^7+81648*x^12+1377*x 
^4+26244*x^3+6561*x^2*log(3)^4+((-17496*x^4-11664*x^3)*log(3)^3+((52488*x^ 
4+34992*x^3)*exp(5)-52488*x^7-104976*x^6-69984*x^5-15552*x^4)*log(3)^2+((- 
52488*x^4-34992*x^3)*exp(5)^2+(104976*x^7+209952*x^6+139968*x^5+31104*x^4) 
*exp(5)-52488*x^10-174960*x^9-233280*x^8-155520*x^7-51840*x^6+10584*x^5+46 
656*x^4+23328*x^3)*log(3)+(17496*x^4+11664*x^3)*exp(5)^3+(-52488*x^7-10497 
6*x^6-69984*x^5-15552*x^4)*exp(5)^2+(52488*x^10+174960*x^9+233280*x^8+1555 
20*x^7+51840*x^6-10584*x^5-46656*x^4-23328*x^3)*exp(5)-17496*x^13-81648*x^ 
12-163296*x^11-181440*x^10-120960*x^9-30888*x^8+59232*x^7+92288*x^6+51840* 
x^5+10368*x^4)*exp(x)+(-26244*x^2*exp(5)+26244*x^5+34992*x^4+11664*x^3)*lo 
g(3)^3+(39366*x^2*exp(5)^2+(-78732*x^5-104976*x^4-34992*x^3)*exp(5)+39366* 
x^8+104976*x^7+104976*x^6+46656*x^5+7776*x^4-13122*x^3-26244*x^2)*log(3)^2 
+(-26244*x^2*exp(5)^3+(78732*x^5+104976*x^4+34992*x^3)*exp(5)^2+(-78732*x^ 
8-209952*x^7-209952*x^6-93312*x^5-15552*x^4+26244*x^3+52488*x^2)*exp(5)+26 
244*x^11+104976*x^10+174960*x^9+155520*x^8+77760*x^7-5508*x^6-85176*x^5-81 
648*x^4-23328*x^3)*log(3)+(-26244*x^5-34992*x^4-11664*x^3)*exp(5)^3+(39366 
*x^8+104976*x^7+104976*x^6+46656*x^5+7776*x^4-13122*x^3-26244*x^2)*exp(5)^ 
2+(-26244*x^11-104976*x^10-174960*x^9-155520*x^8-77760*x^7+5508*x^6+85176* 
x^5+81648*x^4+23328*x^3)*exp(5)+((-5832*x^5-3888*x^4)*log(3)^2+((11664*x^5 
+7776*x^4)*exp(5)-19440*x^8-38880*x^7-25920*x^6-5760*x^5)*log(3)+(-5832*x^ 
5-3888*x^4)*exp(5)^2+(19440*x^8+38880*x^7+25920*x^6+5760*x^5)*exp(5)-13608 
*x^11-45360*x^10-60480*x^9-40320*x^8-13440*x^7+152*x^6+5184*x^5+2592*x^4)* 
exp(x)^3+(2916*x^3*log(3)^3+(-8748*x^3*exp(5)+26244*x^6+34992*x^5+11664*x^ 
4)*log(3)^2+(8748*x^3*exp(5)^2+(-52488*x^6-69984*x^5-23328*x^4)*exp(5)+437 
40*x^9+116640*x^8+116640*x^7+51840*x^6+8640*x^5-2916*x^4-5832*x^3)*log(3)- 
2916*x^3*exp(5)^3+(26244*x^6+34992*x^5+11664*x^4)*exp(5)^2+(-43740*x^9-116 
640*x^8-116640*x^7-51840*x^6-8640*x^5+2916*x^4+5832*x^3)*exp(5)+20412*x^12 
+81648*x^11+136080*x^10+120960*x^9+60480*x^8+7380*x^7-27368*x^6-27216*x^5- 
7776*x^4)*exp(x)^2+x^6*exp(x)^8+(-24*x^7-16*x^6)*exp(x)^7+(36*x^5*log(3)-3 
6*x^5*exp(5)+252*x^8+336*x^7+112*x^6)*exp(x)^6+((-648*x^6-432*x^5)*log(3)+ 
(648*x^6+432*x^5)*exp(5)-1512*x^9-3024*x^8-2016*x^7-448*x^6)*exp(x)^5+(486 
*x^4*log(3)^2+(-972*x^4*exp(5)+4860*x^7+6480*x^6+2160*x^5)*log(3)+486*x^4* 
exp(5)^2+(-4860*x^7-6480*x^6-2160*x^5)*exp(5)+5670*x^10+15120*x^9+15120*x^ 
8+6720*x^7+1120*x^6-162*x^5-324*x^4)*exp(x)^4+108864*x^11+90720*x^10+35262 
*x^9-45108*x^8+34992*x^13),x, algorithm="giac")
 

Output:

Timed out
 

Mupad [F(-1)]

Timed out. \[ \text {the integral} =\text {Too large to display} \] Input:

int((13122*exp(10) - 26244*x + log(3)*(23328*x - 26244*exp(5) + 104976*x^2 
 + 104976*x^3) + exp(2*x)*(log(3)*(5832*x + 5832*x^2) - exp(5)*(5832*x + 5 
832*x^2) + 11664*x^2 + 54432*x^3 + 67068*x^4 + 17496*x^5) + exp(4*x)*(486* 
x^2 + 648*x^3) - exp(5)*(23328*x + 104976*x^2 + 104976*x^3) - exp(x)*(log( 
3)*(23328*x + 64152*x^2 + 17496*x^3) - exp(5)*(23328*x + 64152*x^2 + 17496 
*x^3) + 15552*x^2 + 98496*x^3 + 198288*x^4 + 139968*x^5 + 17496*x^6) - exp 
(3*x)*(3888*x^2 + 11664*x^3 + 5832*x^4) + 13122*log(3)^2 + 7776*x^2 + 6220 
8*x^3 + 174960*x^4 + 209952*x^5 + 91854*x^6 - 26244)/(6561*x^2*log(3)^4 - 
exp(5*x)*(log(3)*(432*x^5 + 648*x^6) - exp(5)*(432*x^5 + 648*x^6) + 448*x^ 
6 + 2016*x^7 + 3024*x^8 + 1512*x^9) - exp(5)*(77760*x^7 - 81648*x^4 - 8517 
6*x^5 - 5508*x^6 - 23328*x^3 + 155520*x^8 + 174960*x^9 + 104976*x^10 + 262 
44*x^11) - log(3)*(26244*x^2*exp(15) + exp(5)*(15552*x^4 - 26244*x^3 - 524 
88*x^2 + 93312*x^5 + 209952*x^6 + 209952*x^7 + 78732*x^8) - exp(10)*(34992 
*x^3 + 104976*x^4 + 78732*x^5) + 23328*x^3 + 81648*x^4 + 85176*x^5 + 5508* 
x^6 - 77760*x^7 - 155520*x^8 - 174960*x^9 - 104976*x^10 - 26244*x^11) + ex 
p(4*x)*(486*x^4*log(3)^2 + log(3)*(2160*x^5 - 972*x^4*exp(5) + 6480*x^6 + 
4860*x^7) + 486*x^4*exp(10) - exp(5)*(2160*x^5 + 6480*x^6 + 4860*x^7) - 32 
4*x^4 - 162*x^5 + 1120*x^6 + 6720*x^7 + 15120*x^8 + 15120*x^9 + 5670*x^10) 
 - exp(7*x)*(16*x^6 + 24*x^7) + log(3)^2*(39366*x^2*exp(10) - exp(5)*(3499 
2*x^3 + 104976*x^4 + 78732*x^5) - 26244*x^2 - 13122*x^3 + 7776*x^4 + 46656 
*x^5 + 104976*x^6 + 104976*x^7 + 39366*x^8) + x^6*exp(8*x) - exp(x)*(log(3 
)*(exp(10)*(34992*x^3 + 52488*x^4) - 23328*x^3 - 46656*x^4 - 10584*x^5 + 5 
1840*x^6 + 155520*x^7 + 233280*x^8 + 174960*x^9 + 52488*x^10 - exp(5)*(311 
04*x^4 + 139968*x^5 + 209952*x^6 + 104976*x^7)) - exp(15)*(11664*x^3 + 174 
96*x^4) - 10368*x^4 - 51840*x^5 - 92288*x^6 - 59232*x^7 + 30888*x^8 + 1209 
60*x^9 + 181440*x^10 + 163296*x^11 + 81648*x^12 + 17496*x^13 - exp(5)*(518 
40*x^6 - 46656*x^4 - 10584*x^5 - 23328*x^3 + 155520*x^7 + 233280*x^8 + 174 
960*x^9 + 52488*x^10) + log(3)^2*(15552*x^4 - exp(5)*(34992*x^3 + 52488*x^ 
4) + 69984*x^5 + 104976*x^6 + 52488*x^7) + log(3)^3*(11664*x^3 + 17496*x^4 
) + exp(10)*(15552*x^4 + 69984*x^5 + 104976*x^6 + 52488*x^7)) + 6561*x^2*e 
xp(20) + exp(10)*(7776*x^4 - 13122*x^3 - 26244*x^2 + 46656*x^5 + 104976*x^ 
6 + 104976*x^7 + 39366*x^8) - exp(15)*(11664*x^3 + 34992*x^4 + 26244*x^5) 
+ log(3)^3*(11664*x^3 - 26244*x^2*exp(5) + 34992*x^4 + 26244*x^5) + exp(2* 
x)*(2916*x^3*log(3)^3 + log(3)*(8748*x^3*exp(10) - exp(5)*(23328*x^4 + 699 
84*x^5 + 52488*x^6) - 5832*x^3 - 2916*x^4 + 8640*x^5 + 51840*x^6 + 116640* 
x^7 + 116640*x^8 + 43740*x^9) - 2916*x^3*exp(15) - exp(5)*(8640*x^5 - 2916 
*x^4 - 5832*x^3 + 51840*x^6 + 116640*x^7 + 116640*x^8 + 43740*x^9) + exp(1 
0)*(11664*x^4 + 34992*x^5 + 26244*x^6) + log(3)^2*(11664*x^4 - 8748*x^3*ex 
p(5) + 34992*x^5 + 26244*x^6) - 7776*x^4 - 27216*x^5 - 27368*x^6 + 7380*x^ 
7 + 60480*x^8 + 120960*x^9 + 136080*x^10 + 81648*x^11 + 20412*x^12) - exp( 
3*x)*(exp(10)*(3888*x^4 + 5832*x^5) + log(3)*(5760*x^5 - exp(5)*(7776*x^4 
+ 11664*x^5) + 25920*x^6 + 38880*x^7 + 19440*x^8) - 2592*x^4 - 5184*x^5 - 
152*x^6 + 13440*x^7 + 40320*x^8 + 60480*x^9 + 45360*x^10 + 13608*x^11 + lo 
g(3)^2*(3888*x^4 + 5832*x^5) - exp(5)*(5760*x^5 + 25920*x^6 + 38880*x^7 + 
19440*x^8)) + 26244*x^2 + 26244*x^3 + 1377*x^4 - 33696*x^5 - 85280*x^6 - 1 
01904*x^7 - 45108*x^8 + 35262*x^9 + 90720*x^10 + 108864*x^11 + 81648*x^12 
+ 34992*x^13 + 6561*x^14 + exp(6*x)*(36*x^5*log(3) - 36*x^5*exp(5) + 112*x 
^6 + 336*x^7 + 252*x^8)),x)
 

Output:

int((13122*exp(10) - 26244*x + log(3)*(23328*x - 26244*exp(5) + 104976*x^2 
 + 104976*x^3) + exp(2*x)*(log(3)*(5832*x + 5832*x^2) - exp(5)*(5832*x + 5 
832*x^2) + 11664*x^2 + 54432*x^3 + 67068*x^4 + 17496*x^5) + exp(4*x)*(486* 
x^2 + 648*x^3) - exp(5)*(23328*x + 104976*x^2 + 104976*x^3) - exp(x)*(log( 
3)*(23328*x + 64152*x^2 + 17496*x^3) - exp(5)*(23328*x + 64152*x^2 + 17496 
*x^3) + 15552*x^2 + 98496*x^3 + 198288*x^4 + 139968*x^5 + 17496*x^6) - exp 
(3*x)*(3888*x^2 + 11664*x^3 + 5832*x^4) + 13122*log(3)^2 + 7776*x^2 + 6220 
8*x^3 + 174960*x^4 + 209952*x^5 + 91854*x^6 - 26244)/(6561*x^2*log(3)^4 - 
exp(5*x)*(log(3)*(432*x^5 + 648*x^6) - exp(5)*(432*x^5 + 648*x^6) + 448*x^ 
6 + 2016*x^7 + 3024*x^8 + 1512*x^9) - exp(5)*(77760*x^7 - 81648*x^4 - 8517 
6*x^5 - 5508*x^6 - 23328*x^3 + 155520*x^8 + 174960*x^9 + 104976*x^10 + 262 
44*x^11) - log(3)*(26244*x^2*exp(15) + exp(5)*(15552*x^4 - 26244*x^3 - 524 
88*x^2 + 93312*x^5 + 209952*x^6 + 209952*x^7 + 78732*x^8) - exp(10)*(34992 
*x^3 + 104976*x^4 + 78732*x^5) + 23328*x^3 + 81648*x^4 + 85176*x^5 + 5508* 
x^6 - 77760*x^7 - 155520*x^8 - 174960*x^9 - 104976*x^10 - 26244*x^11) + ex 
p(4*x)*(486*x^4*log(3)^2 + log(3)*(2160*x^5 - 972*x^4*exp(5) + 6480*x^6 + 
4860*x^7) + 486*x^4*exp(10) - exp(5)*(2160*x^5 + 6480*x^6 + 4860*x^7) - 32 
4*x^4 - 162*x^5 + 1120*x^6 + 6720*x^7 + 15120*x^8 + 15120*x^9 + 5670*x^10) 
 - exp(7*x)*(16*x^6 + 24*x^7) + log(3)^2*(39366*x^2*exp(10) - exp(5)*(3499 
2*x^3 + 104976*x^4 + 78732*x^5) - 26244*x^2 - 13122*x^3 + 7776*x^4 + 46...
 

Reduce [F]

\[ \text {the integral} =\text {too large to display} \] Input:

int(((648*x^3+486*x^2)*exp(x)^4+(-5832*x^4-11664*x^3-3888*x^2)*exp(x)^3+(( 
5832*x^2+5832*x)*log(3)+(-5832*x^2-5832*x)*exp(5)+17496*x^5+67068*x^4+5443 
2*x^3+11664*x^2)*exp(x)^2+((-17496*x^3-64152*x^2-23328*x)*log(3)+(17496*x^ 
3+64152*x^2+23328*x)*exp(5)-17496*x^6-139968*x^5-198288*x^4-98496*x^3-1555 
2*x^2)*exp(x)+13122*log(3)^2+(-26244*exp(5)+104976*x^3+104976*x^2+23328*x) 
*log(3)+13122*exp(5)^2+(-104976*x^3-104976*x^2-23328*x)*exp(5)+91854*x^6+2 
09952*x^5+174960*x^4+62208*x^3+7776*x^2-26244*x-26244)/((39366*x^2*exp(5)^ 
2+(-78732*x^5-104976*x^4-34992*x^3)*exp(5)+39366*x^8+104976*x^7+104976*x^6 
+46656*x^5+7776*x^4-13122*x^3-26244*x^2)*log(3)^2+((-5832*x^5-3888*x^4)*lo 
g(3)^2+((11664*x^5+7776*x^4)*exp(5)-19440*x^8-38880*x^7-25920*x^6-5760*x^5 
)*log(3)+(-5832*x^5-3888*x^4)*exp(5)^2+(19440*x^8+38880*x^7+25920*x^6+5760 
*x^5)*exp(5)-13608*x^11-45360*x^10-60480*x^9-40320*x^8-13440*x^7+152*x^6+5 
184*x^5+2592*x^4)*exp(x)^3+((-17496*x^4-11664*x^3)*log(3)^3+((52488*x^4+34 
992*x^3)*exp(5)-52488*x^7-104976*x^6-69984*x^5-15552*x^4)*log(3)^2+((-5248 
8*x^4-34992*x^3)*exp(5)^2+(104976*x^7+209952*x^6+139968*x^5+31104*x^4)*exp 
(5)-52488*x^10-174960*x^9-233280*x^8-155520*x^7-51840*x^6+10584*x^5+46656* 
x^4+23328*x^3)*log(3)+(17496*x^4+11664*x^3)*exp(5)^3+(-52488*x^7-104976*x^ 
6-69984*x^5-15552*x^4)*exp(5)^2+(52488*x^10+174960*x^9+233280*x^8+155520*x 
^7+51840*x^6-10584*x^5-46656*x^4-23328*x^3)*exp(5)-17496*x^13-81648*x^12-1 
63296*x^11-181440*x^10-120960*x^9-30888*x^8+59232*x^7+92288*x^6+51840*x^5+ 
10368*x^4)*exp(x)+(-26244*x^2*exp(5)+26244*x^5+34992*x^4+11664*x^3)*log(3) 
^3+(36*x^5*log(3)-36*x^5*exp(5)+252*x^8+336*x^7+112*x^6)*exp(x)^6+((-648*x 
^6-432*x^5)*log(3)+(648*x^6+432*x^5)*exp(5)-1512*x^9-3024*x^8-2016*x^7-448 
*x^6)*exp(x)^5+(486*x^4*log(3)^2+(-972*x^4*exp(5)+4860*x^7+6480*x^6+2160*x 
^5)*log(3)+486*x^4*exp(5)^2+(-4860*x^7-6480*x^6-2160*x^5)*exp(5)+5670*x^10 
+15120*x^9+15120*x^8+6720*x^7+1120*x^6-162*x^5-324*x^4)*exp(x)^4+(-26244*x 
^2*exp(5)^3+(78732*x^5+104976*x^4+34992*x^3)*exp(5)^2+(-78732*x^8-209952*x 
^7-209952*x^6-93312*x^5-15552*x^4+26244*x^3+52488*x^2)*exp(5)+26244*x^11+1 
04976*x^10+174960*x^9+155520*x^8+77760*x^7-5508*x^6-85176*x^5-81648*x^4-23 
328*x^3)*log(3)+(-26244*x^5-34992*x^4-11664*x^3)*exp(5)^3+(39366*x^8+10497 
6*x^7+104976*x^6+46656*x^5+7776*x^4-13122*x^3-26244*x^2)*exp(5)^2+(-26244* 
x^11-104976*x^10-174960*x^9-155520*x^8-77760*x^7+5508*x^6+85176*x^5+81648* 
x^4+23328*x^3)*exp(5)+(2916*x^3*log(3)^3+(-8748*x^3*exp(5)+26244*x^6+34992 
*x^5+11664*x^4)*log(3)^2+(8748*x^3*exp(5)^2+(-52488*x^6-69984*x^5-23328*x^ 
4)*exp(5)+43740*x^9+116640*x^8+116640*x^7+51840*x^6+8640*x^5-2916*x^4-5832 
*x^3)*log(3)-2916*x^3*exp(5)^3+(26244*x^6+34992*x^5+11664*x^4)*exp(5)^2+(- 
43740*x^9-116640*x^8-116640*x^7-51840*x^6-8640*x^5+2916*x^4+5832*x^3)*exp( 
5)+20412*x^12+81648*x^11+136080*x^10+120960*x^9+60480*x^8+7380*x^7-27368*x 
^6-27216*x^5-7776*x^4)*exp(x)^2+x^6*exp(x)^8+(-24*x^7-16*x^6)*exp(x)^7+656 
1*x^14-33696*x^5+26244*x^2+6561*x^2*log(3)^4+6561*x^2*exp(5)^4-85280*x^6-4 
5108*x^8+108864*x^11+90720*x^10+81648*x^12-101904*x^7+1377*x^4+26244*x^3+3 
4992*x^13+35262*x^9),x)
 

Output:

int(((648*x^3+486*x^2)*exp(x)^4+(-5832*x^4-11664*x^3-3888*x^2)*exp(x)^3+(( 
5832*x^2+5832*x)*log(3)+(-5832*x^2-5832*x)*exp(5)+17496*x^5+67068*x^4+5443 
2*x^3+11664*x^2)*exp(x)^2+((-17496*x^3-64152*x^2-23328*x)*log(3)+(17496*x^ 
3+64152*x^2+23328*x)*exp(5)-17496*x^6-139968*x^5-198288*x^4-98496*x^3-1555 
2*x^2)*exp(x)+13122*log(3)^2+(-26244*exp(5)+104976*x^3+104976*x^2+23328*x) 
*log(3)+13122*exp(5)^2+(-104976*x^3-104976*x^2-23328*x)*exp(5)+91854*x^6+2 
09952*x^5+174960*x^4+62208*x^3+7776*x^2-26244*x-26244)/((39366*x^2*exp(5)^ 
2+(-78732*x^5-104976*x^4-34992*x^3)*exp(5)+39366*x^8+104976*x^7+104976*x^6 
+46656*x^5+7776*x^4-13122*x^3-26244*x^2)*log(3)^2+((-5832*x^5-3888*x^4)*lo 
g(3)^2+((11664*x^5+7776*x^4)*exp(5)-19440*x^8-38880*x^7-25920*x^6-5760*x^5 
)*log(3)+(-5832*x^5-3888*x^4)*exp(5)^2+(19440*x^8+38880*x^7+25920*x^6+5760 
*x^5)*exp(5)-13608*x^11-45360*x^10-60480*x^9-40320*x^8-13440*x^7+152*x^6+5 
184*x^5+2592*x^4)*exp(x)^3+((-17496*x^4-11664*x^3)*log(3)^3+((52488*x^4+34 
992*x^3)*exp(5)-52488*x^7-104976*x^6-69984*x^5-15552*x^4)*log(3)^2+((-5248 
8*x^4-34992*x^3)*exp(5)^2+(104976*x^7+209952*x^6+139968*x^5+31104*x^4)*exp 
(5)-52488*x^10-174960*x^9-233280*x^8-155520*x^7-51840*x^6+10584*x^5+46656* 
x^4+23328*x^3)*log(3)+(17496*x^4+11664*x^3)*exp(5)^3+(-52488*x^7-104976*x^ 
6-69984*x^5-15552*x^4)*exp(5)^2+(52488*x^10+174960*x^9+233280*x^8+155520*x 
^7+51840*x^6-10584*x^5-46656*x^4-23328*x^3)*exp(5)-17496*x^13-81648*x^12-1 
63296*x^11-181440*x^10-120960*x^9-30888*x^8+59232*x^7+92288*x^6+51840*x...