3.38.89 $\int \frac{e^{-\frac{256x^2+6561\log (x)+279936{\log }^3(x)+5225472{\log }^5(x)[phone]\mathrm{}{\log }^7(x)[phone]\mathrm{}{\log }^9(x)[phone]\mathrm{}{\log }^{11}(x)[phone]\mathrm{}{\log }^{13}(x)[phone]\mathrm{}{\log }^{15}(x)[phone]\mathrm{}{\log }^{17}(x)}{6561+279936{\log }^2(x)+5225472{\log }^4(x)[phone]\mathrm{}{\log }^6(x)[phone]\mathrm{}{\log }^8(x)[phone]\mathrm{}{\log }^{10}(x)[phone]\mathrm{}{\log }^{12}(x)[phone]\mathrm{}{\log }^{14}(x)[phone]\mathrm{}{\log }^{16}(x)}}(e^x(-39366+19683x-1536x^2)+65536e^x{x}^2\log (x)+e^x(-1889568+944784x-8192x^2){\log }^2(x)+e^x(-40310784+20155392x){\log }^4(x)+e^x(-501645312+250822656x){\log }^6(x)+e^x(-4013162496+2006581248x){\log }^8(x)+e^x(-21403533312+10701766656x){\log }^{10}(x)+e^x(-76101451776+38050725888x){\log }^{12}(x)+e^x(-173946175488+86973087744x){\log }^{14}(x)+e^x(-231928233984+115964116992x){\log }^{16}(x)+e^x(-137438953472+68719476736x){\log }^{18}(x))}{19683x^2+944784x^2{\log }^2(x)[phone]\mathrm{}{x}^2{\log }^4(x)[phone]\mathrm{}{x}^2{\log }^6(x)[phone]\mathrm{}{x}^2{\log }^8(x)[phone]\mathrm{}{x}^2{\log }^{10}(x)[phone]\mathrm{}{x}^2{\log }^{12}(x)[phone]\mathrm{}{x}^2{\log }^{14}(x)[phone]\mathrm{}{x}^2{\log }^{16}(x)[phone]\mathrm{}{x}^2{\log }^{18}(x)}dx$

Optimal. Leaf size=23 $$\frac{e^{x-\frac{256x^2}{{(3+16{\log }^2(x))}^8}}}{x^2}$$

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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 = {} $$\begin{array}{c}\text{\$Aborted}\end{array}$$

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

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Mathematica [A]  time = 1.46, size = 23, normalized size = 1.00 $$\begin{array}{c}\frac{e^{x-\frac{256x^2}{{(3+16{\log }^2(x))}^8}}}{x^2}\end{array}$$

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

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fricas [B]  time = 0.64, size = 119, normalized size = 5.17 $$\begin{array}{c}\frac{e^{(x-\frac{4294967296\log (x{)}^{17}+6442450944\log (x{)}^{15}+4227858432\log (x{)}^{13}+1585446912\log (x{)}^{11}+371589120\log (x{)}^9+55738368\log (x{)}^7+5225472\log (x{)}^5+279936\log (x{)}^3+256x^2+6561\log (x)}{4294967296\log (x{)}^{16}+6442450944\log (x{)}^{14}+4227858432\log (x{)}^{12}+1585446912\log (x{)}^{10}+371589120\log (x{)}^8+55738368\log (x{)}^6+5225472\log (x{)}^4+279936\log (x{)}^2+6561})}}{x}\end{array}$$

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 $$\begin{array}{c}\frac{e^{\left(\frac{4294967296x\log (x{)}^{16}+6442450944x\log (x{)}^{14}+4227858432x\log (x{)}^{12}+1585446912x\log (x{)}^{10}+371589120x\log (x{)}^8+55738368x\log (x{)}^6+5225472x\log (x{)}^4+279936x\log (x{)}^2-256x^2+6561x}{4294967296\log (x{)}^{16}+6442450944\log (x{)}^{14}+4227858432\log (x{)}^{12}+1585446912\log (x{)}^{10}+371589120\log (x{)}^8+55738368\log (x{)}^6+5225472\log (x{)}^4+279936\log (x{)}^2+6561}\right)}}{x^2}\end{array}$$

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

method	result	size
risch	$\frac{{\mathrm{e}}^{-\frac{4294967296\ln (x{)}^{17}-4294967296x\ln (x{)}^{16}+6442450944\ln (x{)}^{15}-6442450944x\ln (x{)}^{14}+4227858432\ln (x{)}^{13}-4227858432x\ln (x{)}^{12}+1585446912\ln (x{)}^{11}-1585446912x\ln (x{)}^{10}+371589120\ln (x{)}^9-371589120x\ln (x{)}^8+55738368\ln (x{)}^7-55738368x\ln (x{)}^6+5225472\ln (x{)}^5-5225472x\ln (x{)}^4+279936\ln (x{)}^3-279936x\ln (x{)}^2+256x^2+6561\ln (x)-6561x}{{(3+16\ln (x{)}^2)}^8}}}{x}$	$135$

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

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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 $$\begin{array}{c}\frac{e^x{e}^{-\frac{256x^2+4294967296\log {(x)}^{17}+6442450944\log {(x)}^{15}+4227858432\log {(x)}^{13}+1585446912\log {(x)}^{11}+371589120\log {(x)}^9+55738368\log {(x)}^7+5225472\log {(x)}^5+279936\log {(x)}^3+6561\log (x)}{4294967296\log {(x)}^{16}+6442450944\log {(x)}^{14}+4227858432\log {(x)}^{12}+1585446912\log {(x)}^{10}+371589120\log {(x)}^8+55738368\log {(x)}^6+5225472\log {(x)}^4+279936\log {(x)}^2+6561}}}{x}\end{array}$$

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
[phone]*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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