3.8.89 \(\int \frac {e^{-\frac {256 x^2+6561 \log (x)+279936 \log ^3(x)+5225472 \log ^5(x)[phone] \log ^7(x)[phone] \log ^9(x)[phone] \log ^{11}(x)[phone] \log ^{13}(x)[phone] \log ^{15}(x)[phone] \log ^{17}(x)}{6561+279936 \log ^2(x)+5225472 \log ^4(x)[phone] \log ^6(x)[phone] \log ^8(x)[phone] \log ^{10}(x)[phone] \log ^{12}(x)[phone] \log ^{14}(x)[phone] \log ^{16}(x)}} (e^x (-39366+19683 x-1536 x^2)+65536 e^x x^2 \log (x)+e^x (-1889568+944784 x-8192 x^2) \log ^2(x)+e^x (-40310784+20155392 x) \log ^4(x)+e^x (-501645312+250822656 x) \log ^6(x)+e^x (-4013162496+2006581248 x) \log ^8(x)+e^x (-21403533312+10701766656 x) \log ^{10}(x)+e^x (-76101451776+38050725888 x) \log ^{12}(x)+e^x (-173946175488+86973087744 x) \log ^{14}(x)+e^x (-231928233984+115964116992 x) \log ^{16}(x)+e^x (-137438953472+68719476736 x) \log ^{18}(x))}{19683 x^2+944784 x^2 \log ^2(x)[phone] x^2 \log ^4(x)[phone] x^2 \log ^6(x)[phone] x^2 \log ^8(x)[phone] x^2 \log ^{10}(x)[phone] x^2 \log ^{12}(x)[phone] x^2 \log ^{14}(x)[phone] x^2 \log ^{16}(x)[phone] x^2 \log ^{18}(x)} \, dx\) [789]

3.8.89.1 Optimal result

Integrand size = 351, antiderivative size = 23 \[ \int \frac {e^{-\frac {256 x^2+6561 \log (x)+279936 \log ^3(x)+5225472 \log ^5(x)[phone] \log ^7(x)[phone] \log ^9(x)[phone] \log ^{11}(x)[phone] \log ^{13}(x)[phone] \log ^{15}(x)[phone] \log ^{17}(x)}{6561+279936 \log ^2(x)+5225472 \log ^4(x)[phone] \log ^6(x)[phone] \log ^8(x)[phone] \log ^{10}(x)[phone] \log ^{12}(x)[phone] \log ^{14}(x)[phone] \log ^{16}(x)}} \left (e^x \left (-39366+19683 x-1536 x^2\right )+65536 e^x x^2 \log (x)+e^x \left (-1889568+944784 x-8192 x^2\right ) \log ^2(x)+e^x (-40310784+20155392 x) \log ^4(x)+e^x (-501645312+250822656 x) \log ^6(x)+e^x (-4013162496+2006581248 x) \log ^8(x)+e^x (-21403533312+10701766656 x) \log ^{10}(x)+e^x (-76101451776+38050725888 x) \log ^{12}(x)+e^x (-173946175488+86973087744 x) \log ^{14}(x)+e^x (-231928233984+115964116992 x) \log ^{16}(x)+e^x (-137438953472+68719476736 x) \log ^{18}(x)\right )}{19683 x^2+944784 x^2 \log ^2(x)[phone] x^2 \log ^4(x)[phone] x^2 \log ^6(x)[phone] x^2 \log ^8(x)[phone] x^2 \log ^{10}(x)[phone] x^2 \log ^{12}(x)[phone] x^2 \log ^{14}(x)[phone] x^2 \log ^{16}(x)[phone] x^2 \log ^{18}(x)} \, dx=\frac {e^{x-\frac {256 x^2}{\left (3+16 \log ^2(x)\right )^8}}}{x^2} \]

output

exp(x)/x/exp(ln(x)+256*x^2/(3+16*ln(x)^2)^8)
 

3.8.89.2 Mathematica [A] (verified)

Time = 1.54 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.00 \[ \int \frac {e^{-\frac {256 x^2+6561 \log (x)+279936 \log ^3(x)+5225472 \log ^5(x)[phone] \log ^7(x)[phone] \log ^9(x)[phone] \log ^{11}(x)[phone] \log ^{13}(x)[phone] \log ^{15}(x)[phone] \log ^{17}(x)}{6561+279936 \log ^2(x)+5225472 \log ^4(x)[phone] \log ^6(x)[phone] \log ^8(x)[phone] \log ^{10}(x)[phone] \log ^{12}(x)[phone] \log ^{14}(x)[phone] \log ^{16}(x)}} \left (e^x \left (-39366+19683 x-1536 x^2\right )+65536 e^x x^2 \log (x)+e^x \left (-1889568+944784 x-8192 x^2\right ) \log ^2(x)+e^x (-40310784+20155392 x) \log ^4(x)+e^x (-501645312+250822656 x) \log ^6(x)+e^x (-4013162496+2006581248 x) \log ^8(x)+e^x (-21403533312+10701766656 x) \log ^{10}(x)+e^x (-76101451776+38050725888 x) \log ^{12}(x)+e^x (-173946175488+86973087744 x) \log ^{14}(x)+e^x (-231928233984+115964116992 x) \log ^{16}(x)+e^x (-137438953472+68719476736 x) \log ^{18}(x)\right )}{19683 x^2+944784 x^2 \log ^2(x)[phone] x^2 \log ^4(x)[phone] x^2 \log ^6(x)[phone] x^2 \log ^8(x)[phone] x^2 \log ^{10}(x)[phone] x^2 \log ^{12}(x)[phone] x^2 \log ^{14}(x)[phone] x^2 \log ^{16}(x)[phone] x^2 \log ^{18}(x)} \, dx=\frac {e^{x-\frac {256 x^2}{\left (3+16 \log ^2(x)\right )^8}}}{x^2} \]

input

Integrate[(E^x*(-39366 + 19683*x - 1536*x^2) + 65536*E^x*x^2*Log[x] + E^x* 
(-1889568 + 944784*x - 8192*x^2)*Log[x]^2 + E^x*(-40310784 + 20155392*x)*L 
og[x]^4 + E^x*(-501645312 + 250822656*x)*Log[x]^6 + E^x*(-4013162496 + 200 
6581248*x)*Log[x]^8 + E^x*(-21403533312 + 10701766656*x)*Log[x]^10 + E^x*( 
-76101451776 + 38050725888*x)*Log[x]^12 + E^x*(-173946175488 + 86973087744 
*x)*Log[x]^14 + E^x*(-231928233984 + 115964116992*x)*Log[x]^16 + E^x*(-137 
438953472 + 68719476736*x)*Log[x]^18)/(E^((256*x^2 + 6561*Log[x] + 279936* 
Log[x]^3 + 5225472*Log[x]^5 + 55738368*Log[x]^7 + 371589120*Log[x]^9 + 158 
5446912*Log[x]^11 + 4227858432*Log[x]^13 + 6442450944*Log[x]^15 + 42949672 
96*Log[x]^17)/(6561 + 279936*Log[x]^2 + 5225472*Log[x]^4 + 55738368*Log[x] 
^6 + 371589120*Log[x]^8 + 1585446912*Log[x]^10 + 4227858432*Log[x]^12 + 64 
42450944*Log[x]^14 + 4294967296*Log[x]^16))*(19683*x^2 + 944784*x^2*Log[x] 
^2 + 20155392*x^2*Log[x]^4 + 250822656*x^2*Log[x]^6 + 2006581248*x^2*Log[x 
]^8 + 10701766656*x^2*Log[x]^10 + 38050725888*x^2*Log[x]^12 + 86973087744* 
x^2*Log[x]^14 + 115964116992*x^2*Log[x]^16 + 68719476736*x^2*Log[x]^18)),x 
]
 

output

E^(x - (256*x^2)/(3 + 16*Log[x]^2)^8)/x^2
 

3.8.89.3 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.

\(\displaystyle \int \frac {\left (e^x \left (-1536 x^2+19683 x-39366\right )+e^x \left (-8192 x^2+944784 x-1889568\right ) \log ^2(x)+65536 e^x x^2 \log (x)+e^x (68719476736 x-137438953472) \log ^{18}(x)+e^x (115964116992 x-231928233984) \log ^{16}(x)+e^x (86973087744 x-173946175488) \log ^{14}(x)+e^x (38050725888 x-76101451776) \log ^{12}(x)+e^x (10701766656 x-21403533312) \log ^{10}(x)+e^x (2006581248 x-4013162496) \log ^8(x)+e^x (250822656 x-501645312) \log ^6(x)+e^x (20155392 x-40310784) \log ^4(x)\right ) \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)+6561 \log (x)}{4294967296 \log ^{16}(x)[phone] \log ^{14}(x)[phone] \log ^{12}(x)[phone] \log ^{10}(x)[phone] \log ^8(x)[phone] \log ^6(x)+5225472 \log ^4(x)+279936 \log ^2(x)+6561}\right )}{19683 x^2+68719476736 x^2 \log ^{18}(x)[phone] x^2 \log ^{16}(x)[phone] x^2 \log ^{14}(x)[phone] x^2 \log ^{12}(x)[phone] x^2 \log ^{10}(x)[phone] x^2 \log ^8(x)[phone] x^2 \log ^6(x)[phone] x^2 \log ^4(x)+944784 x^2 \log ^2(x)} \, dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-2} \left (-1536 x^2-16 \left (512 x^2-59049 x+118098\right ) \log ^2(x)+65536 x^2 \log (x)+19683 x+68719476736 (x-2) \log ^{18}(x)[phone] (x-2) \log ^{16}(x)[phone] (x-2) \log ^{14}(x)[phone] (x-2) \log ^{12}(x)[phone] (x-2) \log ^{10}(x)[phone] (x-2) \log ^8(x)[phone] (x-2) \log ^6(x)[phone] (x-2) \log ^4(x)-39366\right ) \exp \left (x-\frac {128 \left (2 x^2+33554432 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)+2903040 \log ^9(x)+435456 \log ^7(x)+40824 \log ^5(x)+2187 \log ^3(x)\right )}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^9}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {512 x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}} \exp \left (x-\frac {128 \left (2 x^2+33554432 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)+2903040 \log ^9(x)+435456 \log ^7(x)+40824 \log ^5(x)+2187 \log ^3(x)\right )}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^8}+\frac {65536 \log (x) x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}} \exp \left (x-\frac {128 \left (2 x^2+33554432 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)+2903040 \log ^9(x)+435456 \log ^7(x)+40824 \log ^5(x)+2187 \log ^3(x)\right )}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^9}-2 x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-2} \exp \left (x-\frac {128 \left (2 x^2+33554432 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)+2903040 \log ^9(x)+435456 \log ^7(x)+40824 \log ^5(x)+2187 \log ^3(x)\right )}{\left (16 \log ^2(x)+3\right )^8}\right )+x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-1} \exp \left (x-\frac {128 \left (2 x^2+33554432 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)+2903040 \log ^9(x)+435456 \log ^7(x)+40824 \log ^5(x)+2187 \log ^3(x)\right )}{\left (16 \log ^2(x)+3\right )^8}\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-2} \left (-3 \left (512 x^2-6561 x+13122\right )-16 \left (512 x^2-59049 x+118098\right ) \log ^2(x)+65536 x^2 \log (x)[phone] (x-2) \log ^{18}(x)[phone] (x-2) \log ^{16}(x)[phone] (x-2) \log ^{14}(x)[phone] (x-2) \log ^{12}(x)[phone] (x-2) \log ^{10}(x)[phone] (x-2) \log ^8(x)[phone] (x-2) \log ^6(x)[phone] (x-2) \log ^4(x)\right ) \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^9}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {512 x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^8}+\frac {65536 \log (x) x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^9}-2 x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-2} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )+x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-1} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-2} \left (-3 \left (512 x^2-6561 x+13122\right )-16 \left (512 x^2-59049 x+118098\right ) \log ^2(x)+65536 x^2 \log (x)[phone] (x-2) \log ^{18}(x)[phone] (x-2) \log ^{16}(x)[phone] (x-2) \log ^{14}(x)[phone] (x-2) \log ^{12}(x)[phone] (x-2) \log ^{10}(x)[phone] (x-2) \log ^8(x)[phone] (x-2) \log ^6(x)[phone] (x-2) \log ^4(x)\right ) \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^9}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {512 x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^8}+\frac {65536 \log (x) x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^9}-2 x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-2} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )+x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-1} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-2} \left (-3 \left (512 x^2-6561 x+13122\right )-16 \left (512 x^2-59049 x+118098\right ) \log ^2(x)+65536 x^2 \log (x)[phone] (x-2) \log ^{18}(x)[phone] (x-2) \log ^{16}(x)[phone] (x-2) \log ^{14}(x)[phone] (x-2) \log ^{12}(x)[phone] (x-2) \log ^{10}(x)[phone] (x-2) \log ^8(x)[phone] (x-2) \log ^6(x)[phone] (x-2) \log ^4(x)\right ) \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^9}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {512 x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^8}+\frac {65536 \log (x) x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^9}-2 x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-2} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )+x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-1} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-2} \left (-3 \left (512 x^2-6561 x+13122\right )-16 \left (512 x^2-59049 x+118098\right ) \log ^2(x)+65536 x^2 \log (x)[phone] (x-2) \log ^{18}(x)[phone] (x-2) \log ^{16}(x)[phone] (x-2) \log ^{14}(x)[phone] (x-2) \log ^{12}(x)[phone] (x-2) \log ^{10}(x)[phone] (x-2) \log ^8(x)[phone] (x-2) \log ^6(x)[phone] (x-2) \log ^4(x)\right ) \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^9}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {512 x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^8}+\frac {65536 \log (x) x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^9}-2 x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-2} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )+x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-1} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-2} \left (-3 \left (512 x^2-6561 x+13122\right )-16 \left (512 x^2-59049 x+118098\right ) \log ^2(x)+65536 x^2 \log (x)[phone] (x-2) \log ^{18}(x)[phone] (x-2) \log ^{16}(x)[phone] (x-2) \log ^{14}(x)[phone] (x-2) \log ^{12}(x)[phone] (x-2) \log ^{10}(x)[phone] (x-2) \log ^8(x)[phone] (x-2) \log ^6(x)[phone] (x-2) \log ^4(x)\right ) \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^9}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {512 x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^8}+\frac {65536 \log (x) x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^9}-2 x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-2} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )+x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-1} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-2} \left (-3 \left (512 x^2-6561 x+13122\right )-16 \left (512 x^2-59049 x+118098\right ) \log ^2(x)+65536 x^2 \log (x)[phone] (x-2) \log ^{18}(x)[phone] (x-2) \log ^{16}(x)[phone] (x-2) \log ^{14}(x)[phone] (x-2) \log ^{12}(x)[phone] (x-2) \log ^{10}(x)[phone] (x-2) \log ^8(x)[phone] (x-2) \log ^6(x)[phone] (x-2) \log ^4(x)\right ) \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^9}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {512 x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^8}+\frac {65536 \log (x) x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^9}-2 x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-2} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )+x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-1} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-2} \left (-3 \left (512 x^2-6561 x+13122\right )-16 \left (512 x^2-59049 x+118098\right ) \log ^2(x)+65536 x^2 \log (x)[phone] (x-2) \log ^{18}(x)[phone] (x-2) \log ^{16}(x)[phone] (x-2) \log ^{14}(x)[phone] (x-2) \log ^{12}(x)[phone] (x-2) \log ^{10}(x)[phone] (x-2) \log ^8(x)[phone] (x-2) \log ^6(x)[phone] (x-2) \log ^4(x)\right ) \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^9}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {512 x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^8}+\frac {65536 \log (x) x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^9}-2 x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-2} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )+x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-1} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-2} \left (-3 \left (512 x^2-6561 x+13122\right )-16 \left (512 x^2-59049 x+118098\right ) \log ^2(x)+65536 x^2 \log (x)[phone] (x-2) \log ^{18}(x)[phone] (x-2) \log ^{16}(x)[phone] (x-2) \log ^{14}(x)[phone] (x-2) \log ^{12}(x)[phone] (x-2) \log ^{10}(x)[phone] (x-2) \log ^8(x)[phone] (x-2) \log ^6(x)[phone] (x-2) \log ^4(x)\right ) \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^9}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {512 x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^8}+\frac {65536 \log (x) x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^9}-2 x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-2} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )+x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-1} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-2} \left (-3 \left (512 x^2-6561 x+13122\right )-16 \left (512 x^2-59049 x+118098\right ) \log ^2(x)+65536 x^2 \log (x)[phone] (x-2) \log ^{18}(x)[phone] (x-2) \log ^{16}(x)[phone] (x-2) \log ^{14}(x)[phone] (x-2) \log ^{12}(x)[phone] (x-2) \log ^{10}(x)[phone] (x-2) \log ^8(x)[phone] (x-2) \log ^6(x)[phone] (x-2) \log ^4(x)\right ) \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^9}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {512 x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^8}+\frac {65536 \log (x) x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^9}-2 x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-2} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )+x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-1} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-2} \left (-3 \left (512 x^2-6561 x+13122\right )-16 \left (512 x^2-59049 x+118098\right ) \log ^2(x)+65536 x^2 \log (x)[phone] (x-2) \log ^{18}(x)[phone] (x-2) \log ^{16}(x)[phone] (x-2) \log ^{14}(x)[phone] (x-2) \log ^{12}(x)[phone] (x-2) \log ^{10}(x)[phone] (x-2) \log ^8(x)[phone] (x-2) \log ^6(x)[phone] (x-2) \log ^4(x)\right ) \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^9}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {512 x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^8}+\frac {65536 \log (x) x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^9}-2 x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-2} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )+x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-1} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-2} \left (-3 \left (512 x^2-6561 x+13122\right )-16 \left (512 x^2-59049 x+118098\right ) \log ^2(x)+65536 x^2 \log (x)[phone] (x-2) \log ^{18}(x)[phone] (x-2) \log ^{16}(x)[phone] (x-2) \log ^{14}(x)[phone] (x-2) \log ^{12}(x)[phone] (x-2) \log ^{10}(x)[phone] (x-2) \log ^8(x)[phone] (x-2) \log ^6(x)[phone] (x-2) \log ^4(x)\right ) \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^9}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {512 x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^8}+\frac {65536 \log (x) x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^9}-2 x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-2} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )+x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-1} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-2} \left (-3 \left (512 x^2-6561 x+13122\right )-16 \left (512 x^2-59049 x+118098\right ) \log ^2(x)+65536 x^2 \log (x)[phone] (x-2) \log ^{18}(x)[phone] (x-2) \log ^{16}(x)[phone] (x-2) \log ^{14}(x)[phone] (x-2) \log ^{12}(x)[phone] (x-2) \log ^{10}(x)[phone] (x-2) \log ^8(x)[phone] (x-2) \log ^6(x)[phone] (x-2) \log ^4(x)\right ) \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^9}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {512 x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^8}+\frac {65536 \log (x) x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^9}-2 x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-2} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )+x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-1} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-2} \left (-3 \left (512 x^2-6561 x+13122\right )-16 \left (512 x^2-59049 x+118098\right ) \log ^2(x)+65536 x^2 \log (x)[phone] (x-2) \log ^{18}(x)[phone] (x-2) \log ^{16}(x)[phone] (x-2) \log ^{14}(x)[phone] (x-2) \log ^{12}(x)[phone] (x-2) \log ^{10}(x)[phone] (x-2) \log ^8(x)[phone] (x-2) \log ^6(x)[phone] (x-2) \log ^4(x)\right ) \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^9}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {512 x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^8}+\frac {65536 \log (x) x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^9}-2 x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-2} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )+x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-1} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-2} \left (-3 \left (512 x^2-6561 x+13122\right )-16 \left (512 x^2-59049 x+118098\right ) \log ^2(x)+65536 x^2 \log (x)[phone] (x-2) \log ^{18}(x)[phone] (x-2) \log ^{16}(x)[phone] (x-2) \log ^{14}(x)[phone] (x-2) \log ^{12}(x)[phone] (x-2) \log ^{10}(x)[phone] (x-2) \log ^8(x)[phone] (x-2) \log ^6(x)[phone] (x-2) \log ^4(x)\right ) \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^9}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {512 x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^8}+\frac {65536 \log (x) x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )}{\left (16 \log ^2(x)+3\right )^9}-2 x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-2} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )+x^{-\frac {6561}{\left (16 \log ^2(x)+3\right )^8}-1} \exp \left (-\frac {256 x^2+4294967296 \log ^{17}(x)[phone] \log ^{15}(x)[phone] \log ^{13}(x)[phone] \log ^{11}(x)[phone] \log ^9(x)[phone] \log ^7(x)+5225472 \log ^5(x)+279936 \log ^3(x)-x \left (16 \log ^2(x)+3\right )^8}{\left (16 \log ^2(x)+3\right )^8}\right )\right )dx\)

input

Int[(E^x*(-39366 + 19683*x - 1536*x^2) + 65536*E^x*x^2*Log[x] + E^x*(-1889 
568 + 944784*x - 8192*x^2)*Log[x]^2 + E^x*(-40310784 + 20155392*x)*Log[x]^ 
4 + E^x*(-501645312 + 250822656*x)*Log[x]^6 + E^x*(-4013162496 + 200658124 
8*x)*Log[x]^8 + E^x*(-21403533312 + 10701766656*x)*Log[x]^10 + E^x*(-76101 
451776 + 38050725888*x)*Log[x]^12 + E^x*(-173946175488 + 86973087744*x)*Lo 
g[x]^14 + E^x*(-231928233984 + 115964116992*x)*Log[x]^16 + E^x*(-137438953 
472 + 68719476736*x)*Log[x]^18)/(E^((256*x^2 + 6561*Log[x] + 279936*Log[x] 
^3 + 5225472*Log[x]^5 + 55738368*Log[x]^7 + 371589120*Log[x]^9 + 158544691 
2*Log[x]^11 + 4227858432*Log[x]^13 + 6442450944*Log[x]^15 + 4294967296*Log 
[x]^17)/(6561 + 279936*Log[x]^2 + 5225472*Log[x]^4 + 55738368*Log[x]^6 + 3 
71589120*Log[x]^8 + 1585446912*Log[x]^10 + 4227858432*Log[x]^12 + 64424509 
44*Log[x]^14 + 4294967296*Log[x]^16))*(19683*x^2 + 944784*x^2*Log[x]^2 + 2 
0155392*x^2*Log[x]^4 + 250822656*x^2*Log[x]^6 + 2006581248*x^2*Log[x]^8 + 
10701766656*x^2*Log[x]^10 + 38050725888*x^2*Log[x]^12 + 86973087744*x^2*Lo 
g[x]^14 + 115964116992*x^2*Log[x]^16 + 68719476736*x^2*Log[x]^18)),x]
 

output

$Aborted
 

3.8.89.3.1 Defintions of rubi rules used

rule 7239

Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl 
erIntegrandQ[v, u, x]]
 

rule 7293

Int[u_, x_Symbol] :> With[{v = ExpandIntegrand[u, x]}, Int[v, x] /; SumQ[v] 
]
 

3.8.89.4 Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(146\) vs. \(2(27)=54\).

Time = 0.80 (sec) , antiderivative size = 147, normalized size of antiderivative = 6.39

\[\frac {x^{-\frac {6561}{\left (3+16 \ln \left (x \right )^{2}\right )^{8}}} {\mathrm e}^{-\frac {4294967296 \ln \left (x \right )^{17}-4294967296 x \ln \left (x \right )^{16}[phone] \ln \left (x \right )^{15}-6442450944 x \ln \left (x \right )^{14}[phone] \ln \left (x \right )^{13}-4227858432 x \ln \left (x \right )^{12}[phone] \ln \left (x \right )^{11}-1585446912 x \ln \left (x \right )^{10}[phone] \ln \left (x \right )^{9}-371589120 x \ln \left (x \right )^{8}[phone] \ln \left (x \right )^{7}-55738368 x \ln \left (x \right )^{6}+5225472 \ln \left (x \right )^{5}-5225472 x \ln \left (x \right )^{4}+279936 \ln \left (x \right )^{3}-279936 x \ln \left (x \right )^{2}+256 x^{2}-6561 x}{\left (3+16 \ln \left (x \right )^{2}\right )^{8}}}}{x}\]

input

int(((68719476736*x-137438953472)*exp(x)*ln(x)^18+(115964116992*x-23192823 
3984)*exp(x)*ln(x)^16+(86973087744*x-173946175488)*exp(x)*ln(x)^14+(380507 
25888*x-76101451776)*exp(x)*ln(x)^12+(10701766656*x-21403533312)*exp(x)*ln 
(x)^10+(2006581248*x-4013162496)*exp(x)*ln(x)^8+(250822656*x-501645312)*ex 
p(x)*ln(x)^6+(20155392*x-40310784)*exp(x)*ln(x)^4+(-8192*x^2+944784*x-1889 
568)*exp(x)*ln(x)^2+65536*x^2*exp(x)*ln(x)+(-1536*x^2+19683*x-39366)*exp(x 
))/(68719476736*x^2*ln(x)^18+115964116992*x^2*ln(x)^16+86973087744*x^2*ln( 
x)^14+38050725888*x^2*ln(x)^12+10701766656*x^2*ln(x)^10+2006581248*x^2*ln( 
x)^8+250822656*x^2*ln(x)^6+20155392*x^2*ln(x)^4+944784*x^2*ln(x)^2+19683*x 
^2)/exp((4294967296*ln(x)^17+6442450944*ln(x)^15+4227858432*ln(x)^13+15854 
46912*ln(x)^11+371589120*ln(x)^9+55738368*ln(x)^7+5225472*ln(x)^5+279936*l 
n(x)^3+6561*ln(x)+256*x^2)/(4294967296*ln(x)^16+6442450944*ln(x)^14+422785 
8432*ln(x)^12+1585446912*ln(x)^10+371589120*ln(x)^8+55738368*ln(x)^6+52254 
72*ln(x)^4+279936*ln(x)^2+6561)),x)
 

output

1/(x^(6561/(3+16*ln(x)^2)^8))/x*exp(-(4294967296*ln(x)^17-4294967296*x*ln( 
x)^16+6442450944*ln(x)^15-6442450944*x*ln(x)^14+4227858432*ln(x)^13-422785 
8432*x*ln(x)^12+1585446912*ln(x)^11-1585446912*x*ln(x)^10+371589120*ln(x)^ 
9-371589120*x*ln(x)^8+55738368*ln(x)^7-55738368*x*ln(x)^6+5225472*ln(x)^5- 
5225472*x*ln(x)^4+279936*ln(x)^3-279936*x*ln(x)^2+256*x^2-6561*x)/(3+16*ln 
(x)^2)^8)
 

3.8.89.5 Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 119 vs. \(2 (26) = 52\).

Time = 0.28 (sec) , antiderivative size = 119, normalized size of antiderivative = 5.17 \[ \int \frac {e^{-\frac {256 x^2+6561 \log (x)+279936 \log ^3(x)+5225472 \log ^5(x)[phone] \log ^7(x)[phone] \log ^9(x)[phone] \log ^{11}(x)[phone] \log ^{13}(x)[phone] \log ^{15}(x)[phone] \log ^{17}(x)}{6561+279936 \log ^2(x)+5225472 \log ^4(x)[phone] \log ^6(x)[phone] \log ^8(x)[phone] \log ^{10}(x)[phone] \log ^{12}(x)[phone] \log ^{14}(x)[phone] \log ^{16}(x)}} \left (e^x \left (-39366+19683 x-1536 x^2\right )+65536 e^x x^2 \log (x)+e^x \left (-1889568+944784 x-8192 x^2\right ) \log ^2(x)+e^x (-40310784+20155392 x) \log ^4(x)+e^x (-501645312+250822656 x) \log ^6(x)+e^x (-4013162496+2006581248 x) \log ^8(x)+e^x (-21403533312+10701766656 x) \log ^{10}(x)+e^x (-76101451776+38050725888 x) \log ^{12}(x)+e^x (-173946175488+86973087744 x) \log ^{14}(x)+e^x (-231928233984+115964116992 x) \log ^{16}(x)+e^x (-137438953472+68719476736 x) \log ^{18}(x)\right )}{19683 x^2+944784 x^2 \log ^2(x)[phone] x^2 \log ^4(x)[phone] x^2 \log ^6(x)[phone] x^2 \log ^8(x)[phone] x^2 \log ^{10}(x)[phone] x^2 \log ^{12}(x)[phone] x^2 \log ^{14}(x)[phone] x^2 \log ^{16}(x)[phone] x^2 \log ^{18}(x)} \, dx=\frac {e^{\left (x - \frac {4294967296 \, \log \left (x\right )^{17} + 6442450944 \, \log \left (x\right )^{15} + 4227858432 \, \log \left (x\right )^{13} + 1585446912 \, \log \left (x\right )^{11} + 371589120 \, \log \left (x\right )^{9} + 55738368 \, \log \left (x\right )^{7} + 5225472 \, \log \left (x\right )^{5} + 279936 \, \log \left (x\right )^{3} + 256 \, x^{2} + 6561 \, \log \left (x\right )}{4294967296 \, \log \left (x\right )^{16} + 6442450944 \, \log \left (x\right )^{14} + 4227858432 \, \log \left (x\right )^{12} + 1585446912 \, \log \left (x\right )^{10} + 371589120 \, \log \left (x\right )^{8} + 55738368 \, \log \left (x\right )^{6} + 5225472 \, \log \left (x\right )^{4} + 279936 \, \log \left (x\right )^{2} + 6561}\right )}}{x} \]

input

integrate(((68719476736*x-137438953472)*exp(x)*log(x)^18+(115964116992*x-2 
31928233984)*exp(x)*log(x)^16+(86973087744*x-173946175488)*exp(x)*log(x)^1 
4+(38050725888*x-76101451776)*exp(x)*log(x)^12+(10701766656*x-21403533312) 
*exp(x)*log(x)^10+(2006581248*x-4013162496)*exp(x)*log(x)^8+(250822656*x-5 
01645312)*exp(x)*log(x)^6+(20155392*x-40310784)*exp(x)*log(x)^4+(-8192*x^2 
+944784*x-1889568)*exp(x)*log(x)^2+65536*x^2*exp(x)*log(x)+(-1536*x^2+1968 
3*x-39366)*exp(x))/(68719476736*x^2*log(x)^18+115964116992*x^2*log(x)^16+8 
6973087744*x^2*log(x)^14+38050725888*x^2*log(x)^12+10701766656*x^2*log(x)^ 
10+2006581248*x^2*log(x)^8+250822656*x^2*log(x)^6+20155392*x^2*log(x)^4+94 
4784*x^2*log(x)^2+19683*x^2)/exp((4294967296*log(x)^17+6442450944*log(x)^1 
5+4227858432*log(x)^13+1585446912*log(x)^11+371589120*log(x)^9+55738368*lo 
g(x)^7+5225472*log(x)^5+279936*log(x)^3+6561*log(x)+256*x^2)/(4294967296*l 
og(x)^16+6442450944*log(x)^14+4227858432*log(x)^12+1585446912*log(x)^10+37 
1589120*log(x)^8+55738368*log(x)^6+5225472*log(x)^4+279936*log(x)^2+6561)) 
,x, algorithm=\
 

output

e^(x - (4294967296*log(x)^17 + 6442450944*log(x)^15 + 4227858432*log(x)^13 
 + 1585446912*log(x)^11 + 371589120*log(x)^9 + 55738368*log(x)^7 + 5225472 
*log(x)^5 + 279936*log(x)^3 + 256*x^2 + 6561*log(x))/(4294967296*log(x)^16 
 + 6442450944*log(x)^14 + 4227858432*log(x)^12 + 1585446912*log(x)^10 + 37 
1589120*log(x)^8 + 55738368*log(x)^6 + 5225472*log(x)^4 + 279936*log(x)^2 
+ 6561))/x
 

3.8.89.6 Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 126 vs. \(2 (22) = 44\).

Time = 1.59 (sec) , antiderivative size = 126, normalized size of antiderivative = 5.48 \[ \int \frac {e^{-\frac {256 x^2+6561 \log (x)+279936 \log ^3(x)+5225472 \log ^5(x)[phone] \log ^7(x)[phone] \log ^9(x)[phone] \log ^{11}(x)[phone] \log ^{13}(x)[phone] \log ^{15}(x)[phone] \log ^{17}(x)}{6561+279936 \log ^2(x)+5225472 \log ^4(x)[phone] \log ^6(x)[phone] \log ^8(x)[phone] \log ^{10}(x)[phone] \log ^{12}(x)[phone] \log ^{14}(x)[phone] \log ^{16}(x)}} \left (e^x \left (-39366+19683 x-1536 x^2\right )+65536 e^x x^2 \log (x)+e^x \left (-1889568+944784 x-8192 x^2\right ) \log ^2(x)+e^x (-40310784+20155392 x) \log ^4(x)+e^x (-501645312+250822656 x) \log ^6(x)+e^x (-4013162496+2006581248 x) \log ^8(x)+e^x (-21403533312+10701766656 x) \log ^{10}(x)+e^x (-76101451776+38050725888 x) \log ^{12}(x)+e^x (-173946175488+86973087744 x) \log ^{14}(x)+e^x (-231928233984+115964116992 x) \log ^{16}(x)+e^x (-137438953472+68719476736 x) \log ^{18}(x)\right )}{19683 x^2+944784 x^2 \log ^2(x)[phone] x^2 \log ^4(x)[phone] x^2 \log ^6(x)[phone] x^2 \log ^8(x)[phone] x^2 \log ^{10}(x)[phone] x^2 \log ^{12}(x)[phone] x^2 \log ^{14}(x)[phone] x^2 \log ^{16}(x)[phone] x^2 \log ^{18}(x)} \, dx=\frac {e^{x} e^{- \frac {256 x^{2} + 4294967296 \log {\left (x \right )}^{17} + 6442450944 \log {\left (x \right )}^{15} + 4227858432 \log {\left (x \right )}^{13} + 1585446912 \log {\left (x \right )}^{11} + 371589120 \log {\left (x \right )}^{9} + 55738368 \log {\left (x \right )}^{7} + 5225472 \log {\left (x \right )}^{5} + 279936 \log {\left (x \right )}^{3} + 6561 \log {\left (x \right )}}{4294967296 \log {\left (x \right )}^{16} + 6442450944 \log {\left (x \right )}^{14} + 4227858432 \log {\left (x \right )}^{12} + 1585446912 \log {\left (x \right )}^{10} + 371589120 \log {\left (x \right )}^{8} + 55738368 \log {\left (x \right )}^{6} + 5225472 \log {\left (x \right )}^{4} + 279936 \log {\left (x \right )}^{2} + 6561}}}{x} \]

input

integrate(((68719476736*x-137438953472)*exp(x)*ln(x)**18+(115964116992*x-2 
31928233984)*exp(x)*ln(x)**16+(86973087744*x-173946175488)*exp(x)*ln(x)**1 
4+(38050725888*x-76101451776)*exp(x)*ln(x)**12+(10701766656*x-21403533312) 
*exp(x)*ln(x)**10+(2006581248*x-4013162496)*exp(x)*ln(x)**8+(250822656*x-5 
01645312)*exp(x)*ln(x)**6+(20155392*x-40310784)*exp(x)*ln(x)**4+(-8192*x** 
2+944784*x-1889568)*exp(x)*ln(x)**2+65536*x**2*exp(x)*ln(x)+(-1536*x**2+19 
683*x-39366)*exp(x))/(68719476736*x**2*ln(x)**18+115964116992*x**2*ln(x)** 
16+86973087744*x**2*ln(x)**14+38050725888*x**2*ln(x)**12+10701766656*x**2* 
ln(x)**10+2006581248*x**2*ln(x)**8+250822656*x**2*ln(x)**6+20155392*x**2*l 
n(x)**4+944784*x**2*ln(x)**2+19683*x**2)/exp((4294967296*ln(x)**17+6442450 
944*ln(x)**15+4227858432*ln(x)**13+1585446912*ln(x)**11+371589120*ln(x)**9 
[phone]*ln(x)**7+5225472*ln(x)**5+279936*ln(x)**3+6561*ln(x)+256*x**2)/( 
4294967296*ln(x)**16+6442450944*ln(x)**14+4227858432*ln(x)**12+1585446912* 
ln(x)**10+371589120*ln(x)**8+55738368*ln(x)**6+5225472*ln(x)**4+279936*ln( 
x)**2+6561)),x)
 

output

exp(x)*exp(-(256*x**2 + 4294967296*log(x)**17 + 6442450944*log(x)**15 + 42 
27858432*log(x)**13 + 1585446912*log(x)**11 + 371589120*log(x)**9 + 557383 
68*log(x)**7 + 5225472*log(x)**5 + 279936*log(x)**3 + 6561*log(x))/(429496 
7296*log(x)**16 + 6442450944*log(x)**14 + 4227858432*log(x)**12 + 15854469 
12*log(x)**10 + 371589120*log(x)**8 + 55738368*log(x)**6 + 5225472*log(x)* 
*4 + 279936*log(x)**2 + 6561))/x
 

3.8.89.7 Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 584 vs. \(2 (26) = 52\).

Time = 0.83 (sec) , antiderivative size = 584, normalized size of antiderivative = 25.39 \[ \int \frac {e^{-\frac {256 x^2+6561 \log (x)+279936 \log ^3(x)+5225472 \log ^5(x)[phone] \log ^7(x)[phone] \log ^9(x)[phone] \log ^{11}(x)[phone] \log ^{13}(x)[phone] \log ^{15}(x)[phone] \log ^{17}(x)}{6561+279936 \log ^2(x)+5225472 \log ^4(x)[phone] \log ^6(x)[phone] \log ^8(x)[phone] \log ^{10}(x)[phone] \log ^{12}(x)[phone] \log ^{14}(x)[phone] \log ^{16}(x)}} \left (e^x \left (-39366+19683 x-1536 x^2\right )+65536 e^x x^2 \log (x)+e^x \left (-1889568+944784 x-8192 x^2\right ) \log ^2(x)+e^x (-40310784+20155392 x) \log ^4(x)+e^x (-501645312+250822656 x) \log ^6(x)+e^x (-4013162496+2006581248 x) \log ^8(x)+e^x (-21403533312+10701766656 x) \log ^{10}(x)+e^x (-76101451776+38050725888 x) \log ^{12}(x)+e^x (-173946175488+86973087744 x) \log ^{14}(x)+e^x (-231928233984+115964116992 x) \log ^{16}(x)+e^x (-137438953472+68719476736 x) \log ^{18}(x)\right )}{19683 x^2+944784 x^2 \log ^2(x)[phone] x^2 \log ^4(x)[phone] x^2 \log ^6(x)[phone] x^2 \log ^8(x)[phone] x^2 \log ^{10}(x)[phone] x^2 \log ^{12}(x)[phone] x^2 \log ^{14}(x)[phone] x^2 \log ^{16}(x)[phone] x^2 \log ^{18}(x)} \, dx=\text {Too large to display} \]

input

integrate(((68719476736*x-137438953472)*exp(x)*log(x)^18+(115964116992*x-2 
31928233984)*exp(x)*log(x)^16+(86973087744*x-173946175488)*exp(x)*log(x)^1 
4+(38050725888*x-76101451776)*exp(x)*log(x)^12+(10701766656*x-21403533312) 
*exp(x)*log(x)^10+(2006581248*x-4013162496)*exp(x)*log(x)^8+(250822656*x-5 
01645312)*exp(x)*log(x)^6+(20155392*x-40310784)*exp(x)*log(x)^4+(-8192*x^2 
+944784*x-1889568)*exp(x)*log(x)^2+65536*x^2*exp(x)*log(x)+(-1536*x^2+1968 
3*x-39366)*exp(x))/(68719476736*x^2*log(x)^18+115964116992*x^2*log(x)^16+8 
6973087744*x^2*log(x)^14+38050725888*x^2*log(x)^12+10701766656*x^2*log(x)^ 
10+2006581248*x^2*log(x)^8+250822656*x^2*log(x)^6+20155392*x^2*log(x)^4+94 
4784*x^2*log(x)^2+19683*x^2)/exp((4294967296*log(x)^17+6442450944*log(x)^1 
5+4227858432*log(x)^13+1585446912*log(x)^11+371589120*log(x)^9+55738368*lo 
g(x)^7+5225472*log(x)^5+279936*log(x)^3+6561*log(x)+256*x^2)/(4294967296*l 
og(x)^16+6442450944*log(x)^14+4227858432*log(x)^12+1585446912*log(x)^10+37 
1589120*log(x)^8+55738368*log(x)^6+5225472*log(x)^4+279936*log(x)^2+6561)) 
,x, algorithm=\
 

output

e^(-4294967296*log(x)^17/(4294967296*log(x)^16 + 6442450944*log(x)^14 + 42 
27858432*log(x)^12 + 1585446912*log(x)^10 + 371589120*log(x)^8 + 55738368* 
log(x)^6 + 5225472*log(x)^4 + 279936*log(x)^2 + 6561) - 6442450944*log(x)^ 
15/(4294967296*log(x)^16 + 6442450944*log(x)^14 + 4227858432*log(x)^12 + 1 
585446912*log(x)^10 + 371589120*log(x)^8 + 55738368*log(x)^6 + 5225472*log 
(x)^4 + 279936*log(x)^2 + 6561) - 4227858432*log(x)^13/(4294967296*log(x)^ 
16 + 6442450944*log(x)^14 + 4227858432*log(x)^12 + 1585446912*log(x)^10 + 
371589120*log(x)^8 + 55738368*log(x)^6 + 5225472*log(x)^4 + 279936*log(x)^ 
2 + 6561) - 1585446912*log(x)^11/(4294967296*log(x)^16 + 6442450944*log(x) 
^14 + 4227858432*log(x)^12 + 1585446912*log(x)^10 + 371589120*log(x)^8 + 5 
5738368*log(x)^6 + 5225472*log(x)^4 + 279936*log(x)^2 + 6561) - 371589120* 
log(x)^9/(4294967296*log(x)^16 + 6442450944*log(x)^14 + 4227858432*log(x)^ 
12 + 1585446912*log(x)^10 + 371589120*log(x)^8 + 55738368*log(x)^6 + 52254 
72*log(x)^4 + 279936*log(x)^2 + 6561) - 55738368*log(x)^7/(4294967296*log( 
x)^16 + 6442450944*log(x)^14 + 4227858432*log(x)^12 + 1585446912*log(x)^10 
 + 371589120*log(x)^8 + 55738368*log(x)^6 + 5225472*log(x)^4 + 279936*log( 
x)^2 + 6561) - 5225472*log(x)^5/(4294967296*log(x)^16 + 6442450944*log(x)^ 
14 + 4227858432*log(x)^12 + 1585446912*log(x)^10 + 371589120*log(x)^8 + 55 
738368*log(x)^6 + 5225472*log(x)^4 + 279936*log(x)^2 + 6561) - 279936*log( 
x)^3/(4294967296*log(x)^16 + 6442450944*log(x)^14 + 4227858432*log(x)^1...
 

3.8.89.8 Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 123 vs. \(2 (26) = 52\).

Time = 6.19 (sec) , antiderivative size = 123, normalized size of antiderivative = 5.35 \[ \int \frac {e^{-\frac {256 x^2+6561 \log (x)+279936 \log ^3(x)+5225472 \log ^5(x)[phone] \log ^7(x)[phone] \log ^9(x)[phone] \log ^{11}(x)[phone] \log ^{13}(x)[phone] \log ^{15}(x)[phone] \log ^{17}(x)}{6561+279936 \log ^2(x)+5225472 \log ^4(x)[phone] \log ^6(x)[phone] \log ^8(x)[phone] \log ^{10}(x)[phone] \log ^{12}(x)[phone] \log ^{14}(x)[phone] \log ^{16}(x)}} \left (e^x \left (-39366+19683 x-1536 x^2\right )+65536 e^x x^2 \log (x)+e^x \left (-1889568+944784 x-8192 x^2\right ) \log ^2(x)+e^x (-40310784+20155392 x) \log ^4(x)+e^x (-501645312+250822656 x) \log ^6(x)+e^x (-4013162496+2006581248 x) \log ^8(x)+e^x (-21403533312+10701766656 x) \log ^{10}(x)+e^x (-76101451776+38050725888 x) \log ^{12}(x)+e^x (-173946175488+86973087744 x) \log ^{14}(x)+e^x (-231928233984+115964116992 x) \log ^{16}(x)+e^x (-137438953472+68719476736 x) \log ^{18}(x)\right )}{19683 x^2+944784 x^2 \log ^2(x)[phone] x^2 \log ^4(x)[phone] x^2 \log ^6(x)[phone] x^2 \log ^8(x)[phone] x^2 \log ^{10}(x)[phone] x^2 \log ^{12}(x)[phone] x^2 \log ^{14}(x)[phone] x^2 \log ^{16}(x)[phone] x^2 \log ^{18}(x)} \, dx=\frac {e^{\left (\frac {4294967296 \, x \log \left (x\right )^{16} + 6442450944 \, x \log \left (x\right )^{14} + 4227858432 \, x \log \left (x\right )^{12} + 1585446912 \, x \log \left (x\right )^{10} + 371589120 \, x \log \left (x\right )^{8} + 55738368 \, x \log \left (x\right )^{6} + 5225472 \, x \log \left (x\right )^{4} + 279936 \, x \log \left (x\right )^{2} - 256 \, x^{2} + 6561 \, x}{4294967296 \, \log \left (x\right )^{16} + 6442450944 \, \log \left (x\right )^{14} + 4227858432 \, \log \left (x\right )^{12} + 1585446912 \, \log \left (x\right )^{10} + 371589120 \, \log \left (x\right )^{8} + 55738368 \, \log \left (x\right )^{6} + 5225472 \, \log \left (x\right )^{4} + 279936 \, \log \left (x\right )^{2} + 6561}\right )}}{x^{2}} \]

input

integrate(((68719476736*x-137438953472)*exp(x)*log(x)^18+(115964116992*x-2 
31928233984)*exp(x)*log(x)^16+(86973087744*x-173946175488)*exp(x)*log(x)^1 
4+(38050725888*x-76101451776)*exp(x)*log(x)^12+(10701766656*x-21403533312) 
*exp(x)*log(x)^10+(2006581248*x-4013162496)*exp(x)*log(x)^8+(250822656*x-5 
01645312)*exp(x)*log(x)^6+(20155392*x-40310784)*exp(x)*log(x)^4+(-8192*x^2 
+944784*x-1889568)*exp(x)*log(x)^2+65536*x^2*exp(x)*log(x)+(-1536*x^2+1968 
3*x-39366)*exp(x))/(68719476736*x^2*log(x)^18+115964116992*x^2*log(x)^16+8 
6973087744*x^2*log(x)^14+38050725888*x^2*log(x)^12+10701766656*x^2*log(x)^ 
10+2006581248*x^2*log(x)^8+250822656*x^2*log(x)^6+20155392*x^2*log(x)^4+94 
4784*x^2*log(x)^2+19683*x^2)/exp((4294967296*log(x)^17+6442450944*log(x)^1 
5+4227858432*log(x)^13+1585446912*log(x)^11+371589120*log(x)^9+55738368*lo 
g(x)^7+5225472*log(x)^5+279936*log(x)^3+6561*log(x)+256*x^2)/(4294967296*l 
og(x)^16+6442450944*log(x)^14+4227858432*log(x)^12+1585446912*log(x)^10+37 
1589120*log(x)^8+55738368*log(x)^6+5225472*log(x)^4+279936*log(x)^2+6561)) 
,x, algorithm=\
 

output

e^((4294967296*x*log(x)^16 + 6442450944*x*log(x)^14 + 4227858432*x*log(x)^ 
12 + 1585446912*x*log(x)^10 + 371589120*x*log(x)^8 + 55738368*x*log(x)^6 + 
 5225472*x*log(x)^4 + 279936*x*log(x)^2 - 256*x^2 + 6561*x)/(4294967296*lo 
g(x)^16 + 6442450944*log(x)^14 + 4227858432*log(x)^12 + 1585446912*log(x)^ 
10 + 371589120*log(x)^8 + 55738368*log(x)^6 + 5225472*log(x)^4 + 279936*lo 
g(x)^2 + 6561))/x^2
 

3.8.89.9 Mupad [B] (verification not implemented)

Time = 13.01 (sec) , antiderivative size = 594, normalized size of antiderivative = 25.83 \[ \int \frac {e^{-\frac {256 x^2+6561 \log (x)+279936 \log ^3(x)+5225472 \log ^5(x)[phone] \log ^7(x)[phone] \log ^9(x)[phone] \log ^{11}(x)[phone] \log ^{13}(x)[phone] \log ^{15}(x)[phone] \log ^{17}(x)}{6561+279936 \log ^2(x)+5225472 \log ^4(x)[phone] \log ^6(x)[phone] \log ^8(x)[phone] \log ^{10}(x)[phone] \log ^{12}(x)[phone] \log ^{14}(x)[phone] \log ^{16}(x)}} \left (e^x \left (-39366+19683 x-1536 x^2\right )+65536 e^x x^2 \log (x)+e^x \left (-1889568+944784 x-8192 x^2\right ) \log ^2(x)+e^x (-40310784+20155392 x) \log ^4(x)+e^x (-501645312+250822656 x) \log ^6(x)+e^x (-4013162496+2006581248 x) \log ^8(x)+e^x (-21403533312+10701766656 x) \log ^{10}(x)+e^x (-76101451776+38050725888 x) \log ^{12}(x)+e^x (-173946175488+86973087744 x) \log ^{14}(x)+e^x (-231928233984+115964116992 x) \log ^{16}(x)+e^x (-137438953472+68719476736 x) \log ^{18}(x)\right )}{19683 x^2+944784 x^2 \log ^2(x)[phone] x^2 \log ^4(x)[phone] x^2 \log ^6(x)[phone] x^2 \log ^8(x)[phone] x^2 \log ^{10}(x)[phone] x^2 \log ^{12}(x)[phone] x^2 \log ^{14}(x)[phone] x^2 \log ^{16}(x)[phone] x^2 \log ^{18}(x)} \, dx=\text {Too large to display} \]

input

int((exp(-(6561*log(x) + 279936*log(x)^3 + 5225472*log(x)^5 + 55738368*log 
(x)^7 + 371589120*log(x)^9 + 1585446912*log(x)^11 + 4227858432*log(x)^13 + 
 6442450944*log(x)^15 + 4294967296*log(x)^17 + 256*x^2)/(279936*log(x)^2 + 
 5225472*log(x)^4 + 55738368*log(x)^6 + 371589120*log(x)^8 + 1585446912*lo 
g(x)^10 + 4227858432*log(x)^12 + 6442450944*log(x)^14 + 4294967296*log(x)^ 
16 + 6561))*(exp(x)*log(x)^8*(2006581248*x - 4013162496) - exp(x)*(1536*x^ 
2 - 19683*x + 39366) + exp(x)*log(x)^10*(10701766656*x - 21403533312) + ex 
p(x)*log(x)^12*(38050725888*x - 76101451776) + exp(x)*log(x)^14*(869730877 
44*x - 173946175488) + exp(x)*log(x)^16*(115964116992*x - 231928233984) + 
exp(x)*log(x)^18*(68719476736*x - 137438953472) + exp(x)*log(x)^4*(2015539 
2*x - 40310784) + exp(x)*log(x)^6*(250822656*x - 501645312) - exp(x)*log(x 
)^2*(8192*x^2 - 944784*x + 1889568) + 65536*x^2*exp(x)*log(x)))/(944784*x^ 
2*log(x)^2 + 20155392*x^2*log(x)^4 + 250822656*x^2*log(x)^6 + 2006581248*x 
^2*log(x)^8 + 10701766656*x^2*log(x)^10 + 38050725888*x^2*log(x)^12 + 8697 
3087744*x^2*log(x)^14 + 115964116992*x^2*log(x)^16 + 68719476736*x^2*log(x 
)^18 + 19683*x^2),x)
 

output

(exp(-(1585446912*log(x)^11)/(279936*log(x)^2 + 5225472*log(x)^4 + 5573836 
8*log(x)^6 + 371589120*log(x)^8 + 1585446912*log(x)^10 + 4227858432*log(x) 
^12 + 6442450944*log(x)^14 + 4294967296*log(x)^16 + 6561))*exp(-(644245094 
4*log(x)^15)/(279936*log(x)^2 + 5225472*log(x)^4 + 55738368*log(x)^6 + 371 
589120*log(x)^8 + 1585446912*log(x)^10 + 4227858432*log(x)^12 + 6442450944 
*log(x)^14 + 4294967296*log(x)^16 + 6561))*exp(-(256*x^2)/(279936*log(x)^2 
 + 5225472*log(x)^4 + 55738368*log(x)^6 + 371589120*log(x)^8 + 1585446912* 
log(x)^10 + 4227858432*log(x)^12 + 6442450944*log(x)^14 + 4294967296*log(x 
)^16 + 6561))*exp(-(4227858432*log(x)^13)/(279936*log(x)^2 + 5225472*log(x 
)^4 + 55738368*log(x)^6 + 371589120*log(x)^8 + 1585446912*log(x)^10 + 4227 
858432*log(x)^12 + 6442450944*log(x)^14 + 4294967296*log(x)^16 + 6561))*ex 
p(-(4294967296*log(x)^17)/(279936*log(x)^2 + 5225472*log(x)^4 + 55738368*l 
og(x)^6 + 371589120*log(x)^8 + 1585446912*log(x)^10 + 4227858432*log(x)^12 
 + 6442450944*log(x)^14 + 4294967296*log(x)^16 + 6561))*exp(-(279936*log(x 
)^3)/(279936*log(x)^2 + 5225472*log(x)^4 + 55738368*log(x)^6 + 371589120*l 
og(x)^8 + 1585446912*log(x)^10 + 4227858432*log(x)^12 + 6442450944*log(x)^ 
14 + 4294967296*log(x)^16 + 6561))*exp(-(5225472*log(x)^5)/(279936*log(x)^ 
2 + 5225472*log(x)^4 + 55738368*log(x)^6 + 371589120*log(x)^8 + 1585446912 
*log(x)^10 + 4227858432*log(x)^12 + 6442450944*log(x)^14 + 4294967296*log( 
x)^16 + 6561))*exp(-(55738368*log(x)^7)/(279936*log(x)^2 + 5225472*log(...