Integrand size = 1521, antiderivative size = 39 \begin {dmath*} \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 )} \end {dmath*}
Timed out. \begin {dmath*} \text {the integral} =\text {\$Aborted} \end {dmath*}
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]
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 |
\(\displaystyle 162 \int \frac {e^{4 x} (4 x+3) x^2-12 e^{3 x} \left (3 x^2+6 x+2\right ) x^2-36 e^{2 x+5} (x+1) x+36 e^{x+5} \left (3 x^2+11 x+4\right ) x-4 e^x \left (27 x^5+216 x^4+306 x^3+(152+27 \log (3)) x^2+3 (8+33 \log (3)) x-3 \log (729)+54 \log (3)\right ) x+6 e^{2 x} \left (18 x^4+69 x^3+56 x^2+(12+\log (729)) x+\log (729)\right ) x-18 e^5 \left (36 x^3+36 x^2+8 x+9 \log (3)\right )+3 \left (189 x^6+432 x^5+360 x^4+8 (16+27 \log (3)) x^3+8 (2+27 \log (3)) x^2-3 (18+\log (6561)) x+72 \log (3) x+27 \left (-2+\log ^2(3)\right )\right )+81 e^{10}}{x^2 \left (-81 x^6-216 x^5-216 x^4-6 (16+27 \log (3)) x^3-e^{4 x} x^2+4 e^{3 x} (3 x+2) x^2-8 (2+27 \log (3)) x^2+18 e^{2 x+5} x-36 e^{x+5} (3 x+2) x+4 e^x (3 x+2) \left (9 x^3+12 x^2+4 x+9 \log (3)\right ) x-6 e^{2 x} \left (9 x^3+12 x^2+4 x+\log (27)\right ) x-9 (-9+8 \log (3)) x+18 e^5 \left (9 x^3+12 x^2+4 x+9 \log (3)\right )-81 e^{10} \left (1+\frac {-2+\log ^2(3)}{e^{10}}\right )\right )^2}dx\) |
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]
3.8.10.3.1 Defintions of rubi rules used
Int[(u_.)*((v_.) + (a_.)*(Fx_) + (b_.)*(Fx_))^(p_.), x_Symbol] :> Int[u*(v + (a + b)*Fx)^p, x] /; FreeQ[{a, b}, x] && !FreeQ[Fx, x]
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(224\) vs. \(2(34)=68\).
Time = 4.20 (sec) , antiderivative size = 225, normalized size of antiderivative = 5.77
method | result | size |
risch | \(-\frac {162}{x \left (-162+54 \,{\mathrm e}^{2 x} x^{4}-81 x +18 \ln \left (3\right ) {\mathrm e}^{2 x} x -8 x^{2} {\mathrm e}^{3 x}+72 \,{\mathrm e}^{2 x} x^{3}-216 x^{2} {\mathrm e}^{5}+24 \,{\mathrm e}^{2 x} x^{2}+162 x^{3} \ln \left (3\right )-216 \,{\mathrm e}^{x} x^{4}-32 \,{\mathrm e}^{x} x^{2}+72 x \ln \left (3\right )-144 \,{\mathrm e}^{x} x^{3}-162 x^{3} {\mathrm e}^{5}-108 x^{2} \ln \left (3\right ) {\mathrm e}^{x}-72 x \ln \left (3\right ) {\mathrm e}^{x}-162 \,{\mathrm e}^{5} \ln \left (3\right )+108 x^{2} {\mathrm e}^{5} {\mathrm e}^{x}+x^{2} {\mathrm e}^{4 x}-12 x^{3} {\mathrm e}^{3 x}-108 x^{5} {\mathrm e}^{x}+81 \,{\mathrm e}^{10}+216 x^{2} \ln \left (3\right )-72 x \,{\mathrm e}^{5}+81 \ln \left (3\right )^{2}+72 x \,{\mathrm e}^{5} {\mathrm e}^{x}+81 x^{6}+216 x^{5}+216 x^{4}+96 x^{3}+16 x^{2}-18 \,{\mathrm e}^{5} {\mathrm e}^{2 x} x \right )}\) | \(225\) |
parallelrisch | \(-\frac {162}{x \left (-162+54 \,{\mathrm e}^{2 x} x^{4}-81 x +18 \ln \left (3\right ) {\mathrm e}^{2 x} x -8 x^{2} {\mathrm e}^{3 x}+72 \,{\mathrm e}^{2 x} x^{3}-216 x^{2} {\mathrm e}^{5}+24 \,{\mathrm e}^{2 x} x^{2}+162 x^{3} \ln \left (3\right )-216 \,{\mathrm e}^{x} x^{4}-32 \,{\mathrm e}^{x} x^{2}+72 x \ln \left (3\right )-144 \,{\mathrm e}^{x} x^{3}-162 x^{3} {\mathrm e}^{5}-108 x^{2} \ln \left (3\right ) {\mathrm e}^{x}-72 x \ln \left (3\right ) {\mathrm e}^{x}-162 \,{\mathrm e}^{5} \ln \left (3\right )+108 x^{2} {\mathrm e}^{5} {\mathrm e}^{x}+x^{2} {\mathrm e}^{4 x}-12 x^{3} {\mathrm e}^{3 x}-108 x^{5} {\mathrm e}^{x}+81 \,{\mathrm e}^{10}+216 x^{2} \ln \left (3\right )-72 x \,{\mathrm e}^{5}+81 \ln \left (3\right )^{2}+72 x \,{\mathrm e}^{5} {\mathrm e}^{x}+81 x^{6}+216 x^{5}+216 x^{4}+96 x^{3}+16 x^{2}-18 \,{\mathrm e}^{5} {\mathrm e}^{2 x} x \right )}\) | \(225\) |
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*exp(5)^4+((-1 7496*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+1 1664*x^3)*exp(5)^3+(-52488*x^7-104976*x^6-69984*x^5-15552*x^4)*exp(5)^2+(5 2488*x^10+174960*x^9+233280*x^8+155520*x^7+51840*x^6-10584*x^5-46656*x^4-2 3328*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+777 6*x^4-13122*x^3-26244*x^2)*ln(3)^2+(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^7-209952*x^6-93312*x^5-15552*x^4+26244*x^3+52488*x^2)*e xp(5)+26244*x^11+104976*x^10+174960*x^9+155520*x^8+77760*x^7-5508*x^6-8517 6*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+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)*ln(3)^2+((116 64*x^5+7776*x^4)*exp(5)-19440*x^8-38880*x^7-25920*x^6-5760*x^5)*ln(3)+(-58 32*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*ln(3)^3+(-8748*x^3*exp(5)+26244*x^6+34992*x^5+1166 4*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^9-1 16640*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*ln(3)- 36*x^5*exp(5)+252*x^8+336*x^7+112*x^6)*exp(x)^6+((-648*x^6-432*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+6561 *x^2*ln(3)^4+108864*x^11+81648*x^12+34992*x^13+6561*x^14-101904*x^7-45108* x^8+90720*x^10+35262*x^9-85280*x^6-33696*x^5+1377*x^4+26244*x^3+26244*x^2) ,x,method=_RETURNVERBOSE)
-162/x/(-162-81*x-8*x^2*exp(x)^3-216*x^2*exp(5)+54*exp(x)^2*x^4+162*x^3*ln (3)-216*exp(x)*x^4+24*exp(x)^2*x^2-32*exp(x)*x^2+72*x*ln(3)-144*exp(x)*x^3 -162*x^3*exp(5)-108*x^2*ln(3)*exp(x)-18*x*exp(5)*exp(x)^2-72*x*ln(3)*exp(x )-162*exp(5)*ln(3)+108*x^2*exp(5)*exp(x)+x^2*exp(x)^4-12*x^3*exp(x)^3-108* x^5*exp(x)+216*x^2*ln(3)+72*exp(x)^2*x^3-72*x*exp(5)+81*ln(3)^2+72*x*exp(5 )*exp(x)+81*x^6+216*x^5+81*exp(5)^2+216*x^4+96*x^3+16*x^2+18*exp(x)^2*ln(3 )*x)
Leaf count of result is larger than twice the leaf count of optimal. 211 vs. \(2 (36) = 72\).
Time = 0.44 (sec) , antiderivative size = 211, normalized size of antiderivative = 5.41 \begin {dmath*} \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} \end {dmath*}
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)/(-33696*x^5+1 377*x^4+26244*x^2+6561*x^2*exp(5)^4+(2916*x^3*log(3)^3+(-8748*x^3*exp(5)+2 6244*x^6+34992*x^5+11664*x^4)*log(3)^2+(8748*x^3*exp(5)^2+(-52488*x^6-6998 4*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+73 80*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)-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+81648*x^12-85280*x^6+6561*x^2*log(3)^4+26244*x^3+35 262*x^9+90720*x^10-101904*x^7-45108*x^8+(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^6-2 160*x^5)*exp(5)+5670*x^10+15120*x^9+15120*x^8+6720*x^7+1120*x^6-162*x^5-32 4*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+104976*x^10+174960*x^9+155520*x^8+77760*x^7-5508*x ^6-85176*x^5-81648*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^3-262 44*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)*l og(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+6561*x^14+34992*x^13+108864*x^11+((-17496*x^4-1166 4*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+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^12-163296*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)*log(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^4-131 22*x^3-26244*x^2)*log(3)^2),x, algorithm=\
-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)
Timed out. \begin {dmath*} \text {the integral} =\text {Timed out} \end {dmath*}
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+1377*x**4+35262*x**9+(2916*x**3*ln(3)**3+(-87 48*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+116 640*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**8-1 16640*x**7-51840*x**6-8640*x**5+2916*x**4+5832*x**3)*exp(5)+20412*x**12+81 648*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 -432*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)*ex p(5)+5670*x**10+15120*x**9+15120*x**8+6720*x**7+1120*x**6-162*x**5-324*x** 4)*exp(x)**4-33696*x**5-85280*x**6+6561*x**14+34992*x**13+108864*x**11+816 48*x**12+((-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**4-349 92*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+466 56*x**4+23328*x**3)*ln(3)+(17496*x**4+11664*x**3)*exp(5)**3+(-52488*x**7-1 04976*x**6-69984*x**5-15552*x**4)*exp(5)**2+(52488*x**10+174960*x**9+23328 0*x**8+155520*x**7+51840*x**6-10584*x**5-46656*x**4-23328*x**3)*exp(5)-174 96*x**13-81648*x**12-163296*x**11-181440*x**10-120960*x**9-30888*x**8+5923 2*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**5-10 4976*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+26244*x**3+(-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**1 1+104976*x**10+174960*x**9+155520*x**8+77760*x**7-5508*x**6-85176*x**5-816 48*x**4-23328*x**3)*ln(3)+(-26244*x**5-34992*x**4-11664*x**3)*exp(5)**3+(3 9366*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)*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** 8-13440*x**7+152*x**6+5184*x**5+2592*x**4)*exp(x)**3+6561*x**2*exp(5)**4-1 01904*x**7-45108*x**8+6561*x**2*ln(3)**4+90720*x**10),x)
Leaf count of result is larger than twice the leaf count of optimal. 192 vs. \(2 (36) = 72\).
Time = 22.65 (sec) , antiderivative size = 192, normalized size of antiderivative = 4.92 \begin {dmath*} \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}} \end {dmath*}
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)/(-33696*x^5+1 377*x^4+26244*x^2+6561*x^2*exp(5)^4+(2916*x^3*log(3)^3+(-8748*x^3*exp(5)+2 6244*x^6+34992*x^5+11664*x^4)*log(3)^2+(8748*x^3*exp(5)^2+(-52488*x^6-6998 4*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+73 80*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)-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+81648*x^12-85280*x^6+6561*x^2*log(3)^4+26244*x^3+35 262*x^9+90720*x^10-101904*x^7-45108*x^8+(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^6-2 160*x^5)*exp(5)+5670*x^10+15120*x^9+15120*x^8+6720*x^7+1120*x^6-162*x^5-32 4*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+104976*x^10+174960*x^9+155520*x^8+77760*x^7-5508*x ^6-85176*x^5-81648*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^3-262 44*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)*l og(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+6561*x^14+34992*x^13+108864*x^11+((-17496*x^4-1166 4*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+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^12-163296*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)*log(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^4-131 22*x^3-26244*x^2)*log(3)^2),x, algorithm=\
-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)
Timed out. \begin {dmath*} \text {the integral} =\text {Timed out} \end {dmath*}
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)/(-33696*x^5+1 377*x^4+26244*x^2+6561*x^2*exp(5)^4+(2916*x^3*log(3)^3+(-8748*x^3*exp(5)+2 6244*x^6+34992*x^5+11664*x^4)*log(3)^2+(8748*x^3*exp(5)^2+(-52488*x^6-6998 4*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+73 80*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)-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+81648*x^12-85280*x^6+6561*x^2*log(3)^4+26244*x^3+35 262*x^9+90720*x^10-101904*x^7-45108*x^8+(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^6-2 160*x^5)*exp(5)+5670*x^10+15120*x^9+15120*x^8+6720*x^7+1120*x^6-162*x^5-32 4*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+104976*x^10+174960*x^9+155520*x^8+77760*x^7-5508*x ^6-85176*x^5-81648*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^3-262 44*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)*l og(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+6561*x^14+34992*x^13+108864*x^11+((-17496*x^4-1166 4*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+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^12-163296*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)*log(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^4-131 22*x^3-26244*x^2)*log(3)^2),x, algorithm=\
Timed out. \begin {dmath*} \text {the integral} =\text {Too large to display} \end {dmath*}
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)
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...