3.38.89 \(\int \frac {e^{-\frac {256 x^2+6561 \log (x)+279936 \log ^3(x)+5225472 \log ^5(x)+55738368 \log ^7(x)+371589120 \log ^9(x)+1585446912 \log ^{11}(x)+4227858432 \log ^{13}(x)+6442450944 \log ^{15}(x)+4294967296 \log ^{17}(x)}{6561+279936 \log ^2(x)+5225472 \log ^4(x)+55738368 \log ^6(x)+371589120 \log ^8(x)+1585446912 \log ^{10}(x)+4227858432 \log ^{12}(x)+6442450944 \log ^{14}(x)+4294967296 \log ^{16}(x)}} (e^x (-39366+19683 x-1536 x^2)+65536 e^x x^2 \log (x)+e^x (-1889568+944784 x-8192 x^2) \log ^2(x)+e^x (-40310784+20155392 x) \log ^4(x)+e^x (-501645312+250822656 x) \log ^6(x)+e^x (-4013162496+2006581248 x) \log ^8(x)+e^x (-21403533312+10701766656 x) \log ^{10}(x)+e^x (-76101451776+38050725888 x) \log ^{12}(x)+e^x (-173946175488+86973087744 x) \log ^{14}(x)+e^x (-231928233984+115964116992 x) \log ^{16}(x)+e^x (-137438953472+68719476736 x) \log ^{18}(x))}{19683 x^2+944784 x^2 \log ^2(x)+20155392 x^2 \log ^4(x)+250822656 x^2 \log ^6(x)+2006581248 x^2 \log ^8(x)+10701766656 x^2 \log ^{10}(x)+38050725888 x^2 \log ^{12}(x)+86973087744 x^2 \log ^{14}(x)+115964116992 x^2 \log ^{16}(x)+68719476736 x^2 \log ^{18}(x)} \, dx\)
Optimal. Leaf size=23 \[ \frac {e^{x-\frac {256 x^2}{\left (3+16 \log ^2(x)\right )^8}}}{x^2} \]
________________________________________________________________________________________
Rubi [F] time = 180.00, antiderivative size = 0, normalized size of antiderivative = 0.00,
number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used =
{} \begin {gather*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
[In]
Int[(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)*Log[x]^4 + E^x*(-501645312 + 250822656*x)*Log[x]^6 + E^x*(-4013162496 + 2006581
248*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*(-13743
8953472 + 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 + 1585446912*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 + 6442450944*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]
[Out]
$Aborted
Rubi steps
Aborted
________________________________________________________________________________________
Mathematica [A] time = 1.46, size = 23, normalized size = 1.00 \begin {gather*} \frac {e^{x-\frac {256 x^2}{\left (3+16 \log ^2(x)\right )^8}}}{x^2} \end {gather*}
Antiderivative was successfully verified.
[In]
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)*Log[x]^4 + E^x*(-501645312 + 250822656*x)*Log[x]^6 + E^x*(-4013162496 + 2
006581248*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*(
-137438953472 + 68719476736*x)*Log[x]^18)/(E^((256*x^2 + 6561*Log[x] + 279936*Log[x]^3 + 5225472*Log[x]^5 + 55
738368*Log[x]^7 + 371589120*Log[x]^9 + 1585446912*Log[x]^11 + 4227858432*Log[x]^13 + 6442450944*Log[x]^15 + 42
94967296*Log[x]^17)/(6561 + 279936*Log[x]^2 + 5225472*Log[x]^4 + 55738368*Log[x]^6 + 371589120*Log[x]^8 + 1585
446912*Log[x]^10 + 4227858432*Log[x]^12 + 6442450944*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]
[Out]
E^(x - (256*x^2)/(3 + 16*Log[x]^2)^8)/x^2
________________________________________________________________________________________
fricas [B] time = 0.64, size = 119, normalized size = 5.17 \begin {gather*} \frac {e^{\left (x - \frac {4294967296 \, \log \relax (x)^{17} + 6442450944 \, \log \relax (x)^{15} + 4227858432 \, \log \relax (x)^{13} + 1585446912 \, \log \relax (x)^{11} + 371589120 \, \log \relax (x)^{9} + 55738368 \, \log \relax (x)^{7} + 5225472 \, \log \relax (x)^{5} + 279936 \, \log \relax (x)^{3} + 256 \, x^{2} + 6561 \, \log \relax (x)}{4294967296 \, \log \relax (x)^{16} + 6442450944 \, \log \relax (x)^{14} + 4227858432 \, \log \relax (x)^{12} + 1585446912 \, \log \relax (x)^{10} + 371589120 \, \log \relax (x)^{8} + 55738368 \, \log \relax (x)^{6} + 5225472 \, \log \relax (x)^{4} + 279936 \, \log \relax (x)^{2} + 6561}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((68719476736*x-137438953472)*exp(x)*log(x)^18+(115964116992*x-231928233984)*exp(x)*log(x)^16+(86973
087744*x-173946175488)*exp(x)*log(x)^14+(38050725888*x-76101451776)*exp(x)*log(x)^12+(10701766656*x-2140353331
2)*exp(x)*log(x)^10+(2006581248*x-4013162496)*exp(x)*log(x)^8+(250822656*x-501645312)*exp(x)*log(x)^6+(2015539
2*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+
19683*x-39366)*exp(x))/(68719476736*x^2*log(x)^18+115964116992*x^2*log(x)^16+86973087744*x^2*log(x)^14+3805072
5888*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+944784*x^2*log(x)^2+19683*x^2)/exp((4294967296*log(x)^17+6442450944*log(x)^15+4227858432*log(x)^13+1585446
912*log(x)^11+371589120*log(x)^9+55738368*log(x)^7+5225472*log(x)^5+279936*log(x)^3+6561*log(x)+256*x^2)/(4294
967296*log(x)^16+6442450944*log(x)^14+4227858432*log(x)^12+1585446912*log(x)^10+371589120*log(x)^8+55738368*lo
g(x)^6+5225472*log(x)^4+279936*log(x)^2+6561)),x, algorithm="fricas")
[Out]
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 + 371589120*log(x)^8 + 55738368*log(x)
^6 + 5225472*log(x)^4 + 279936*log(x)^2 + 6561))/x
________________________________________________________________________________________
giac [B] time = 37.76, size = 123, normalized size = 5.35 \begin {gather*} \frac {e^{\left (\frac {4294967296 \, x \log \relax (x)^{16} + 6442450944 \, x \log \relax (x)^{14} + 4227858432 \, x \log \relax (x)^{12} + 1585446912 \, x \log \relax (x)^{10} + 371589120 \, x \log \relax (x)^{8} + 55738368 \, x \log \relax (x)^{6} + 5225472 \, x \log \relax (x)^{4} + 279936 \, x \log \relax (x)^{2} - 256 \, x^{2} + 6561 \, x}{4294967296 \, \log \relax (x)^{16} + 6442450944 \, \log \relax (x)^{14} + 4227858432 \, \log \relax (x)^{12} + 1585446912 \, \log \relax (x)^{10} + 371589120 \, \log \relax (x)^{8} + 55738368 \, \log \relax (x)^{6} + 5225472 \, \log \relax (x)^{4} + 279936 \, \log \relax (x)^{2} + 6561}\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((68719476736*x-137438953472)*exp(x)*log(x)^18+(115964116992*x-231928233984)*exp(x)*log(x)^16+(86973
087744*x-173946175488)*exp(x)*log(x)^14+(38050725888*x-76101451776)*exp(x)*log(x)^12+(10701766656*x-2140353331
2)*exp(x)*log(x)^10+(2006581248*x-4013162496)*exp(x)*log(x)^8+(250822656*x-501645312)*exp(x)*log(x)^6+(2015539
2*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+
19683*x-39366)*exp(x))/(68719476736*x^2*log(x)^18+115964116992*x^2*log(x)^16+86973087744*x^2*log(x)^14+3805072
5888*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+944784*x^2*log(x)^2+19683*x^2)/exp((4294967296*log(x)^17+6442450944*log(x)^15+4227858432*log(x)^13+1585446
912*log(x)^11+371589120*log(x)^9+55738368*log(x)^7+5225472*log(x)^5+279936*log(x)^3+6561*log(x)+256*x^2)/(4294
967296*log(x)^16+6442450944*log(x)^14+4227858432*log(x)^12+1585446912*log(x)^10+371589120*log(x)^8+55738368*lo
g(x)^6+5225472*log(x)^4+279936*log(x)^2+6561)),x, algorithm="giac")
[Out]
e^((4294967296*x*log(x)^16 + 6442450944*x*log(x)^14 + 4227858432*x*log(x)^12 + 1585446912*x*log(x)^10 + 371589
120*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*
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))/x^2
________________________________________________________________________________________
maple [B] time = 0.09, size = 135, normalized size = 5.87
|
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| method |
result |
size |
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| risch |
\(\frac {{\mathrm e}^{-\frac {4294967296 \ln \relax (x )^{17}-4294967296 x \ln \relax (x )^{16}+6442450944 \ln \relax (x )^{15}-6442450944 x \ln \relax (x )^{14}+4227858432 \ln \relax (x )^{13}-4227858432 x \ln \relax (x )^{12}+1585446912 \ln \relax (x )^{11}-1585446912 x \ln \relax (x )^{10}+371589120 \ln \relax (x )^{9}-371589120 x \ln \relax (x )^{8}+55738368 \ln \relax (x )^{7}-55738368 x \ln \relax (x )^{6}+5225472 \ln \relax (x )^{5}-5225472 x \ln \relax (x )^{4}+279936 \ln \relax (x )^{3}-279936 x \ln \relax (x )^{2}+256 x^{2}+6561 \ln \relax (x )-6561 x}{\left (3+16 \ln \relax (x )^{2}\right )^{8}}}}{x}\) |
\(135\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((68719476736*x-137438953472)*exp(x)*ln(x)^18+(115964116992*x-231928233984)*exp(x)*ln(x)^16+(86973087744*x
-173946175488)*exp(x)*ln(x)^14+(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-501645312)*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+19683*x-39366)*e
xp(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+1
0701766656*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+1
9683*x^2)/exp((4294967296*ln(x)^17+6442450944*ln(x)^15+4227858432*ln(x)^13+1585446912*ln(x)^11+371589120*ln(x)
^9+55738368*ln(x)^7+5225472*ln(x)^5+279936*ln(x)^3+6561*ln(x)+256*x^2)/(4294967296*ln(x)^16+6442450944*ln(x)^1
4+4227858432*ln(x)^12+1585446912*ln(x)^10+371589120*ln(x)^8+55738368*ln(x)^6+5225472*ln(x)^4+279936*ln(x)^2+65
61)),x,method=_RETURNVERBOSE)
[Out]
1/x*exp(-(4294967296*ln(x)^17-4294967296*x*ln(x)^16+6442450944*ln(x)^15-6442450944*x*ln(x)^14+4227858432*ln(x)
^13-4227858432*x*ln(x)^12+1585446912*ln(x)^11-1585446912*x*ln(x)^10+371589120*ln(x)^9-371589120*x*ln(x)^8+5573
8368*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
*ln(x)-6561*x)/(3+16*ln(x)^2)^8)
________________________________________________________________________________________
maxima [B] time = 1.17, size = 584, normalized size = 25.39 result too large to
display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((68719476736*x-137438953472)*exp(x)*log(x)^18+(115964116992*x-231928233984)*exp(x)*log(x)^16+(86973
087744*x-173946175488)*exp(x)*log(x)^14+(38050725888*x-76101451776)*exp(x)*log(x)^12+(10701766656*x-2140353331
2)*exp(x)*log(x)^10+(2006581248*x-4013162496)*exp(x)*log(x)^8+(250822656*x-501645312)*exp(x)*log(x)^6+(2015539
2*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+
19683*x-39366)*exp(x))/(68719476736*x^2*log(x)^18+115964116992*x^2*log(x)^16+86973087744*x^2*log(x)^14+3805072
5888*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+944784*x^2*log(x)^2+19683*x^2)/exp((4294967296*log(x)^17+6442450944*log(x)^15+4227858432*log(x)^13+1585446
912*log(x)^11+371589120*log(x)^9+55738368*log(x)^7+5225472*log(x)^5+279936*log(x)^3+6561*log(x)+256*x^2)/(4294
967296*log(x)^16+6442450944*log(x)^14+4227858432*log(x)^12+1585446912*log(x)^10+371589120*log(x)^8+55738368*lo
g(x)^6+5225472*log(x)^4+279936*log(x)^2+6561)),x, algorithm="maxima")
[Out]
e^(-4294967296*log(x)^17/(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) - 6442450944*log(x
)^15/(4294967296*log(x)^16 + 6442450944*log(x)^14 + 4227858432*log(x)^12 + 1585446912*log(x)^10 + 371589120*lo
g(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*lo
g(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 + 55738368*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 + 5225472*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*l
og(x)^8 + 55738368*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)^12 + 1585446912*log(x)^10 + 371589120*log(x)^8 + 55738368*log(x)
^6 + 5225472*log(x)^4 + 279936*log(x)^2 + 6561) + x - 256*x^2/(4294967296*log(x)^16 + 6442450944*log(x)^14 + 4
227858432*log(x)^12 + 1585446912*log(x)^10 + 371589120*log(x)^8 + 55738368*log(x)^6 + 5225472*log(x)^4 + 27993
6*log(x)^2 + 6561) - 6561*log(x)/(4294967296*log(x)^16 + 6442450944*log(x)^14 + 4227858432*log(x)^12 + 1585446
912*log(x)^10 + 371589120*log(x)^8 + 55738368*log(x)^6 + 5225472*log(x)^4 + 279936*log(x)^2 + 6561))/x
________________________________________________________________________________________
mupad [B] time = 5.24, size = 594, normalized size = 25.83 result too large to
display
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((exp(-(6561*log(x) + 279936*log(x)^3 + 5225472*log(x)^5 + 55738368*log(x)^7 + 371589120*log(x)^9 + 1585446
912*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*log(x)^10 + 4227858432*log(x)^12 + 6
442450944*log(x)^14 + 4294967296*log(x)^16 + 6561))*(exp(x)*log(x)^8*(2006581248*x - 4013162496) - exp(x)*(153
6*x^2 - 19683*x + 39366) + exp(x)*log(x)^10*(10701766656*x - 21403533312) + exp(x)*log(x)^12*(38050725888*x -
76101451776) + exp(x)*log(x)^14*(86973087744*x - 173946175488) + exp(x)*log(x)^16*(115964116992*x - 2319282339
84) + exp(x)*log(x)^18*(68719476736*x - 137438953472) + exp(x)*log(x)^4*(20155392*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)))/(9
44784*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 + 19683*x^2),x)
[Out]
(exp(-(1585446912*log(x)^11)/(279936*log(x)^2 + 5225472*log(x)^4 + 55738368*log(x)^6 + 371589120*log(x)^8 + 15
85446912*log(x)^10 + 4227858432*log(x)^12 + 6442450944*log(x)^14 + 4294967296*log(x)^16 + 6561))*exp(-(6442450
944*log(x)^15)/(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(-(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 + 4227858432*log(x)^12 + 6442450944*
log(x)^14 + 4294967296*log(x)^16 + 6561))*exp(-(4294967296*log(x)^17)/(279936*log(x)^2 + 5225472*log(x)^4 + 55
738368*log(x)^6 + 371589120*log(x)^8 + 1585446912*log(x)^10 + 4227858432*log(x)^12 + 6442450944*log(x)^14 + 42
94967296*log(x)^16 + 6561))*exp(-(279936*log(x)^3)/(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 + 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(-(557
38368*log(x)^7)/(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(x)*exp(-(371589120*log
(x)^9)/(279936*log(x)^2 + 5225472*log(x)^4 + 55738368*log(x)^6 + 371589120*log(x)^8 + 1585446912*log(x)^10 + 4
227858432*log(x)^12 + 6442450944*log(x)^14 + 4294967296*log(x)^16 + 6561)))/(x^(6561/(279936*log(x)^2 + 522547
2*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))*x)
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sympy [B] time = 3.05, size = 126, normalized size = 5.48 \begin {gather*} \frac {e^{x} e^{- \frac {256 x^{2} + 4294967296 \log {\relax (x )}^{17} + 6442450944 \log {\relax (x )}^{15} + 4227858432 \log {\relax (x )}^{13} + 1585446912 \log {\relax (x )}^{11} + 371589120 \log {\relax (x )}^{9} + 55738368 \log {\relax (x )}^{7} + 5225472 \log {\relax (x )}^{5} + 279936 \log {\relax (x )}^{3} + 6561 \log {\relax (x )}}{4294967296 \log {\relax (x )}^{16} + 6442450944 \log {\relax (x )}^{14} + 4227858432 \log {\relax (x )}^{12} + 1585446912 \log {\relax (x )}^{10} + 371589120 \log {\relax (x )}^{8} + 55738368 \log {\relax (x )}^{6} + 5225472 \log {\relax (x )}^{4} + 279936 \log {\relax (x )}^{2} + 6561}}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((68719476736*x-137438953472)*exp(x)*ln(x)**18+(115964116992*x-231928233984)*exp(x)*ln(x)**16+(86973
087744*x-173946175488)*exp(x)*ln(x)**14+(38050725888*x-76101451776)*exp(x)*ln(x)**12+(10701766656*x-2140353331
2)*exp(x)*ln(x)**10+(2006581248*x-4013162496)*exp(x)*ln(x)**8+(250822656*x-501645312)*exp(x)*ln(x)**6+(2015539
2*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+19683*x-39366)*exp(x))/(68719476736*x**2*ln(x)**18+115964116992*x**2*ln(x)**16+86973087744*x**2*ln(x)**14+38
050725888*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+1585446912*ln(x)**11+371589120*ln(x)**9+55738368*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)
[Out]
exp(x)*exp(-(256*x**2 + 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 + 6561*log(x))/(4294
967296*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))/x
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