3.11.92 \(\int \frac {e^{\frac {25 x^2-40 x^3+6 x^4+8 x^5+x^6+(-110 x+278 x^2-90 x^3-70 x^4-8 x^5) \log ^2(x)+(121-418 x+273 x^2+152 x^3+16 x^4) \log ^4(x)}{x^2-2 x^3+x^4+(-2 x+10 x^2-8 x^3) \log ^2(x)+(1-8 x+16 x^2) \log ^4(x)}} (10 x^3-28 x^4+24 x^5-4 x^6-2 x^7+(-120 x+216 x^2-72 x^3-24 x^4) \log (x)+(60 x-210 x^2+282 x^3-222 x^4+66 x^5+24 x^6) \log ^2(x)+(264-720 x+360 x^2+96 x^3) \log ^3(x)+(-132+786 x-984 x^2+618 x^3-336 x^4-96 x^5) \log ^4(x)+(-550+1126 x-456 x^2+544 x^3+128 x^4) \log ^6(x))}{x^3-3 x^4+3 x^5-x^6+(-3 x^2+18 x^3-27 x^4+12 x^5) \log ^2(x)+(3 x-27 x^2+72 x^3-48 x^4) \log ^4(x)+(-1+12 x-48 x^2+64 x^3) \log ^6(x)} \, dx\)
Optimal. Leaf size=28 \[ e^{\left (5+x+\frac {6}{1-4 x+\frac {-x+x^2}{\log ^2(x)}}\right )^2} \]
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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 {gather*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
[In]
Int[(E^((25*x^2 - 40*x^3 + 6*x^4 + 8*x^5 + x^6 + (-110*x + 278*x^2 - 90*x^3 - 70*x^4 - 8*x^5)*Log[x]^2 + (121
- 418*x + 273*x^2 + 152*x^3 + 16*x^4)*Log[x]^4)/(x^2 - 2*x^3 + x^4 + (-2*x + 10*x^2 - 8*x^3)*Log[x]^2 + (1 - 8
*x + 16*x^2)*Log[x]^4))*(10*x^3 - 28*x^4 + 24*x^5 - 4*x^6 - 2*x^7 + (-120*x + 216*x^2 - 72*x^3 - 24*x^4)*Log[x
] + (60*x - 210*x^2 + 282*x^3 - 222*x^4 + 66*x^5 + 24*x^6)*Log[x]^2 + (264 - 720*x + 360*x^2 + 96*x^3)*Log[x]^
3 + (-132 + 786*x - 984*x^2 + 618*x^3 - 336*x^4 - 96*x^5)*Log[x]^4 + (-550 + 1126*x - 456*x^2 + 544*x^3 + 128*
x^4)*Log[x]^6))/(x^3 - 3*x^4 + 3*x^5 - x^6 + (-3*x^2 + 18*x^3 - 27*x^4 + 12*x^5)*Log[x]^2 + (3*x - 27*x^2 + 72
*x^3 - 48*x^4)*Log[x]^4 + (-1 + 12*x - 48*x^2 + 64*x^3)*Log[x]^6),x]
[Out]
$Aborted
Rubi steps
Aborted
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Mathematica [A] time = 0.33, size = 49, normalized size = 1.75 \begin {gather*} e^{\frac {\left (x \left (-5+4 x+x^2\right )+\left (11-19 x-4 x^2\right ) \log ^2(x)\right )^2}{\left ((-1+x) x+(1-4 x) \log ^2(x)\right )^2}} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(E^((25*x^2 - 40*x^3 + 6*x^4 + 8*x^5 + x^6 + (-110*x + 278*x^2 - 90*x^3 - 70*x^4 - 8*x^5)*Log[x]^2 +
(121 - 418*x + 273*x^2 + 152*x^3 + 16*x^4)*Log[x]^4)/(x^2 - 2*x^3 + x^4 + (-2*x + 10*x^2 - 8*x^3)*Log[x]^2 +
(1 - 8*x + 16*x^2)*Log[x]^4))*(10*x^3 - 28*x^4 + 24*x^5 - 4*x^6 - 2*x^7 + (-120*x + 216*x^2 - 72*x^3 - 24*x^4)
*Log[x] + (60*x - 210*x^2 + 282*x^3 - 222*x^4 + 66*x^5 + 24*x^6)*Log[x]^2 + (264 - 720*x + 360*x^2 + 96*x^3)*L
og[x]^3 + (-132 + 786*x - 984*x^2 + 618*x^3 - 336*x^4 - 96*x^5)*Log[x]^4 + (-550 + 1126*x - 456*x^2 + 544*x^3
+ 128*x^4)*Log[x]^6))/(x^3 - 3*x^4 + 3*x^5 - x^6 + (-3*x^2 + 18*x^3 - 27*x^4 + 12*x^5)*Log[x]^2 + (3*x - 27*x^
2 + 72*x^3 - 48*x^4)*Log[x]^4 + (-1 + 12*x - 48*x^2 + 64*x^3)*Log[x]^6),x]
[Out]
E^((x*(-5 + 4*x + x^2) + (11 - 19*x - 4*x^2)*Log[x]^2)^2/((-1 + x)*x + (1 - 4*x)*Log[x]^2)^2)
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fricas [B] time = 0.73, size = 128, normalized size = 4.57 \begin {gather*} e^{\left (\frac {x^{6} + 8 \, x^{5} + {\left (16 \, x^{4} + 152 \, x^{3} + 273 \, x^{2} - 418 \, x + 121\right )} \log \relax (x)^{4} + 6 \, x^{4} - 40 \, x^{3} - 2 \, {\left (4 \, x^{5} + 35 \, x^{4} + 45 \, x^{3} - 139 \, x^{2} + 55 \, x\right )} \log \relax (x)^{2} + 25 \, x^{2}}{{\left (16 \, x^{2} - 8 \, x + 1\right )} \log \relax (x)^{4} + x^{4} - 2 \, x^{3} - 2 \, {\left (4 \, x^{3} - 5 \, x^{2} + x\right )} \log \relax (x)^{2} + x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((128*x^4+544*x^3-456*x^2+1126*x-550)*log(x)^6+(-96*x^5-336*x^4+618*x^3-984*x^2+786*x-132)*log(x)^4+
(96*x^3+360*x^2-720*x+264)*log(x)^3+(24*x^6+66*x^5-222*x^4+282*x^3-210*x^2+60*x)*log(x)^2+(-24*x^4-72*x^3+216*
x^2-120*x)*log(x)-2*x^7-4*x^6+24*x^5-28*x^4+10*x^3)*exp(((16*x^4+152*x^3+273*x^2-418*x+121)*log(x)^4+(-8*x^5-7
0*x^4-90*x^3+278*x^2-110*x)*log(x)^2+x^6+8*x^5+6*x^4-40*x^3+25*x^2)/((16*x^2-8*x+1)*log(x)^4+(-8*x^3+10*x^2-2*
x)*log(x)^2+x^4-2*x^3+x^2))/((64*x^3-48*x^2+12*x-1)*log(x)^6+(-48*x^4+72*x^3-27*x^2+3*x)*log(x)^4+(12*x^5-27*x
^4+18*x^3-3*x^2)*log(x)^2-x^6+3*x^5-3*x^4+x^3),x, algorithm="fricas")
[Out]
e^((x^6 + 8*x^5 + (16*x^4 + 152*x^3 + 273*x^2 - 418*x + 121)*log(x)^4 + 6*x^4 - 40*x^3 - 2*(4*x^5 + 35*x^4 + 4
5*x^3 - 139*x^2 + 55*x)*log(x)^2 + 25*x^2)/((16*x^2 - 8*x + 1)*log(x)^4 + x^4 - 2*x^3 - 2*(4*x^3 - 5*x^2 + x)*
log(x)^2 + x^2))
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giac [B] time = 15.35, size = 994, normalized size = 35.50 result too large to
display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((128*x^4+544*x^3-456*x^2+1126*x-550)*log(x)^6+(-96*x^5-336*x^4+618*x^3-984*x^2+786*x-132)*log(x)^4+
(96*x^3+360*x^2-720*x+264)*log(x)^3+(24*x^6+66*x^5-222*x^4+282*x^3-210*x^2+60*x)*log(x)^2+(-24*x^4-72*x^3+216*
x^2-120*x)*log(x)-2*x^7-4*x^6+24*x^5-28*x^4+10*x^3)*exp(((16*x^4+152*x^3+273*x^2-418*x+121)*log(x)^4+(-8*x^5-7
0*x^4-90*x^3+278*x^2-110*x)*log(x)^2+x^6+8*x^5+6*x^4-40*x^3+25*x^2)/((16*x^2-8*x+1)*log(x)^4+(-8*x^3+10*x^2-2*
x)*log(x)^2+x^4-2*x^3+x^2))/((64*x^3-48*x^2+12*x-1)*log(x)^6+(-48*x^4+72*x^3-27*x^2+3*x)*log(x)^4+(12*x^5-27*x
^4+18*x^3-3*x^2)*log(x)^2-x^6+3*x^5-3*x^4+x^3),x, algorithm="giac")
[Out]
e^(16*x^4*log(x)^4/(16*x^2*log(x)^4 - 8*x^3*log(x)^2 - 8*x*log(x)^4 + x^4 + 10*x^2*log(x)^2 + log(x)^4 - 2*x^3
- 2*x*log(x)^2 + x^2) - 8*x^5*log(x)^2/(16*x^2*log(x)^4 - 8*x^3*log(x)^2 - 8*x*log(x)^4 + x^4 + 10*x^2*log(x)
^2 + log(x)^4 - 2*x^3 - 2*x*log(x)^2 + x^2) + 152*x^3*log(x)^4/(16*x^2*log(x)^4 - 8*x^3*log(x)^2 - 8*x*log(x)^
4 + x^4 + 10*x^2*log(x)^2 + log(x)^4 - 2*x^3 - 2*x*log(x)^2 + x^2) + x^6/(16*x^2*log(x)^4 - 8*x^3*log(x)^2 - 8
*x*log(x)^4 + x^4 + 10*x^2*log(x)^2 + log(x)^4 - 2*x^3 - 2*x*log(x)^2 + x^2) - 70*x^4*log(x)^2/(16*x^2*log(x)^
4 - 8*x^3*log(x)^2 - 8*x*log(x)^4 + x^4 + 10*x^2*log(x)^2 + log(x)^4 - 2*x^3 - 2*x*log(x)^2 + x^2) + 273*x^2*l
og(x)^4/(16*x^2*log(x)^4 - 8*x^3*log(x)^2 - 8*x*log(x)^4 + x^4 + 10*x^2*log(x)^2 + log(x)^4 - 2*x^3 - 2*x*log(
x)^2 + x^2) + 8*x^5/(16*x^2*log(x)^4 - 8*x^3*log(x)^2 - 8*x*log(x)^4 + x^4 + 10*x^2*log(x)^2 + log(x)^4 - 2*x^
3 - 2*x*log(x)^2 + x^2) - 90*x^3*log(x)^2/(16*x^2*log(x)^4 - 8*x^3*log(x)^2 - 8*x*log(x)^4 + x^4 + 10*x^2*log(
x)^2 + log(x)^4 - 2*x^3 - 2*x*log(x)^2 + x^2) - 418*x*log(x)^4/(16*x^2*log(x)^4 - 8*x^3*log(x)^2 - 8*x*log(x)^
4 + x^4 + 10*x^2*log(x)^2 + log(x)^4 - 2*x^3 - 2*x*log(x)^2 + x^2) + 6*x^4/(16*x^2*log(x)^4 - 8*x^3*log(x)^2 -
8*x*log(x)^4 + x^4 + 10*x^2*log(x)^2 + log(x)^4 - 2*x^3 - 2*x*log(x)^2 + x^2) + 278*x^2*log(x)^2/(16*x^2*log(
x)^4 - 8*x^3*log(x)^2 - 8*x*log(x)^4 + x^4 + 10*x^2*log(x)^2 + log(x)^4 - 2*x^3 - 2*x*log(x)^2 + x^2) + 121*lo
g(x)^4/(16*x^2*log(x)^4 - 8*x^3*log(x)^2 - 8*x*log(x)^4 + x^4 + 10*x^2*log(x)^2 + log(x)^4 - 2*x^3 - 2*x*log(x
)^2 + x^2) - 40*x^3/(16*x^2*log(x)^4 - 8*x^3*log(x)^2 - 8*x*log(x)^4 + x^4 + 10*x^2*log(x)^2 + log(x)^4 - 2*x^
3 - 2*x*log(x)^2 + x^2) - 110*x*log(x)^2/(16*x^2*log(x)^4 - 8*x^3*log(x)^2 - 8*x*log(x)^4 + x^4 + 10*x^2*log(x
)^2 + log(x)^4 - 2*x^3 - 2*x*log(x)^2 + x^2) + 25*x^2/(16*x^2*log(x)^4 - 8*x^3*log(x)^2 - 8*x*log(x)^4 + x^4 +
10*x^2*log(x)^2 + log(x)^4 - 2*x^3 - 2*x*log(x)^2 + x^2))
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maple [B] time = 0.06, size = 63, normalized size = 2.25
|
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| method |
result |
size |
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| risch |
\({\mathrm e}^{\frac {\left (4 x^{2} \ln \relax (x )^{2}+19 x \ln \relax (x )^{2}-x^{3}-11 \ln \relax (x )^{2}-4 x^{2}+5 x \right )^{2}}{\left (4 x \ln \relax (x )^{2}-\ln \relax (x )^{2}-x^{2}+x \right )^{2}}}\) |
\(63\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((128*x^4+544*x^3-456*x^2+1126*x-550)*ln(x)^6+(-96*x^5-336*x^4+618*x^3-984*x^2+786*x-132)*ln(x)^4+(96*x^3+
360*x^2-720*x+264)*ln(x)^3+(24*x^6+66*x^5-222*x^4+282*x^3-210*x^2+60*x)*ln(x)^2+(-24*x^4-72*x^3+216*x^2-120*x)
*ln(x)-2*x^7-4*x^6+24*x^5-28*x^4+10*x^3)*exp(((16*x^4+152*x^3+273*x^2-418*x+121)*ln(x)^4+(-8*x^5-70*x^4-90*x^3
+278*x^2-110*x)*ln(x)^2+x^6+8*x^5+6*x^4-40*x^3+25*x^2)/((16*x^2-8*x+1)*ln(x)^4+(-8*x^3+10*x^2-2*x)*ln(x)^2+x^4
-2*x^3+x^2))/((64*x^3-48*x^2+12*x-1)*ln(x)^6+(-48*x^4+72*x^3-27*x^2+3*x)*ln(x)^4+(12*x^5-27*x^4+18*x^3-3*x^2)*
ln(x)^2-x^6+3*x^5-3*x^4+x^3),x,method=_RETURNVERBOSE)
[Out]
exp((4*x^2*ln(x)^2+19*x*ln(x)^2-x^3-11*ln(x)^2-4*x^2+5*x)^2/(4*x*ln(x)^2-ln(x)^2-x^2+x)^2)
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maxima [B] time = 12.60, size = 113, normalized size = 4.04 \begin {gather*} e^{\left (\frac {36 \, \log \relax (x)^{4}}{{\left (16 \, x^{2} - 8 \, x + 1\right )} \log \relax (x)^{4} + x^{4} - 2 \, x^{3} - 2 \, {\left (4 \, x^{3} - 5 \, x^{2} + x\right )} \log \relax (x)^{2} + x^{2}} + x^{2} - \frac {12 \, x \log \relax (x)^{2}}{{\left (4 \, x - 1\right )} \log \relax (x)^{2} - x^{2} + x} + 10 \, x - \frac {60 \, \log \relax (x)^{2}}{{\left (4 \, x - 1\right )} \log \relax (x)^{2} - x^{2} + x} + 25\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((128*x^4+544*x^3-456*x^2+1126*x-550)*log(x)^6+(-96*x^5-336*x^4+618*x^3-984*x^2+786*x-132)*log(x)^4+
(96*x^3+360*x^2-720*x+264)*log(x)^3+(24*x^6+66*x^5-222*x^4+282*x^3-210*x^2+60*x)*log(x)^2+(-24*x^4-72*x^3+216*
x^2-120*x)*log(x)-2*x^7-4*x^6+24*x^5-28*x^4+10*x^3)*exp(((16*x^4+152*x^3+273*x^2-418*x+121)*log(x)^4+(-8*x^5-7
0*x^4-90*x^3+278*x^2-110*x)*log(x)^2+x^6+8*x^5+6*x^4-40*x^3+25*x^2)/((16*x^2-8*x+1)*log(x)^4+(-8*x^3+10*x^2-2*
x)*log(x)^2+x^4-2*x^3+x^2))/((64*x^3-48*x^2+12*x-1)*log(x)^6+(-48*x^4+72*x^3-27*x^2+3*x)*log(x)^4+(12*x^5-27*x
^4+18*x^3-3*x^2)*log(x)^2-x^6+3*x^5-3*x^4+x^3),x, algorithm="maxima")
[Out]
e^(36*log(x)^4/((16*x^2 - 8*x + 1)*log(x)^4 + x^4 - 2*x^3 - 2*(4*x^3 - 5*x^2 + x)*log(x)^2 + x^2) + x^2 - 12*x
*log(x)^2/((4*x - 1)*log(x)^2 - x^2 + x) + 10*x - 60*log(x)^2/((4*x - 1)*log(x)^2 - x^2 + x) + 25)
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mupad [B] time = 1.99, size = 1008, normalized size = 36.00 result too large to
display
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(-(exp((log(x)^4*(273*x^2 - 418*x + 152*x^3 + 16*x^4 + 121) - log(x)^2*(110*x - 278*x^2 + 90*x^3 + 70*x^4 +
8*x^5) + 25*x^2 - 40*x^3 + 6*x^4 + 8*x^5 + x^6)/(log(x)^4*(16*x^2 - 8*x + 1) - log(x)^2*(2*x - 10*x^2 + 8*x^3
) + x^2 - 2*x^3 + x^4))*(log(x)*(120*x - 216*x^2 + 72*x^3 + 24*x^4) - log(x)^3*(360*x^2 - 720*x + 96*x^3 + 264
) - log(x)^6*(1126*x - 456*x^2 + 544*x^3 + 128*x^4 - 550) + log(x)^4*(984*x^2 - 786*x - 618*x^3 + 336*x^4 + 96
*x^5 + 132) - 10*x^3 + 28*x^4 - 24*x^5 + 4*x^6 + 2*x^7 - log(x)^2*(60*x - 210*x^2 + 282*x^3 - 222*x^4 + 66*x^5
+ 24*x^6)))/(log(x)^6*(12*x - 48*x^2 + 64*x^3 - 1) + log(x)^4*(3*x - 27*x^2 + 72*x^3 - 48*x^4) + x^3 - 3*x^4
+ 3*x^5 - x^6 - log(x)^2*(3*x^2 - 18*x^3 + 27*x^4 - 12*x^5)),x)
[Out]
exp(-(110*x*log(x)^2)/(log(x)^4 - 8*x*log(x)^4 - 2*x*log(x)^2 + 10*x^2*log(x)^2 - 8*x^3*log(x)^2 + 16*x^2*log(
x)^4 + x^2 - 2*x^3 + x^4))*exp(-(418*x*log(x)^4)/(log(x)^4 - 8*x*log(x)^4 - 2*x*log(x)^2 + 10*x^2*log(x)^2 - 8
*x^3*log(x)^2 + 16*x^2*log(x)^4 + x^2 - 2*x^3 + x^4))*exp(x^6/(log(x)^4 - 8*x*log(x)^4 - 2*x*log(x)^2 + 10*x^2
*log(x)^2 - 8*x^3*log(x)^2 + 16*x^2*log(x)^4 + x^2 - 2*x^3 + x^4))*exp((6*x^4)/(log(x)^4 - 8*x*log(x)^4 - 2*x*
log(x)^2 + 10*x^2*log(x)^2 - 8*x^3*log(x)^2 + 16*x^2*log(x)^4 + x^2 - 2*x^3 + x^4))*exp((8*x^5)/(log(x)^4 - 8*
x*log(x)^4 - 2*x*log(x)^2 + 10*x^2*log(x)^2 - 8*x^3*log(x)^2 + 16*x^2*log(x)^4 + x^2 - 2*x^3 + x^4))*exp((25*x
^2)/(log(x)^4 - 8*x*log(x)^4 - 2*x*log(x)^2 + 10*x^2*log(x)^2 - 8*x^3*log(x)^2 + 16*x^2*log(x)^4 + x^2 - 2*x^3
+ x^4))*exp(-(40*x^3)/(log(x)^4 - 8*x*log(x)^4 - 2*x*log(x)^2 + 10*x^2*log(x)^2 - 8*x^3*log(x)^2 + 16*x^2*log
(x)^4 + x^2 - 2*x^3 + x^4))*exp(-(8*x^5*log(x)^2)/(log(x)^4 - 8*x*log(x)^4 - 2*x*log(x)^2 + 10*x^2*log(x)^2 -
8*x^3*log(x)^2 + 16*x^2*log(x)^4 + x^2 - 2*x^3 + x^4))*exp((16*x^4*log(x)^4)/(log(x)^4 - 8*x*log(x)^4 - 2*x*lo
g(x)^2 + 10*x^2*log(x)^2 - 8*x^3*log(x)^2 + 16*x^2*log(x)^4 + x^2 - 2*x^3 + x^4))*exp(-(70*x^4*log(x)^2)/(log(
x)^4 - 8*x*log(x)^4 - 2*x*log(x)^2 + 10*x^2*log(x)^2 - 8*x^3*log(x)^2 + 16*x^2*log(x)^4 + x^2 - 2*x^3 + x^4))*
exp(-(90*x^3*log(x)^2)/(log(x)^4 - 8*x*log(x)^4 - 2*x*log(x)^2 + 10*x^2*log(x)^2 - 8*x^3*log(x)^2 + 16*x^2*log
(x)^4 + x^2 - 2*x^3 + x^4))*exp((152*x^3*log(x)^4)/(log(x)^4 - 8*x*log(x)^4 - 2*x*log(x)^2 + 10*x^2*log(x)^2 -
8*x^3*log(x)^2 + 16*x^2*log(x)^4 + x^2 - 2*x^3 + x^4))*exp((273*x^2*log(x)^4)/(log(x)^4 - 8*x*log(x)^4 - 2*x*
log(x)^2 + 10*x^2*log(x)^2 - 8*x^3*log(x)^2 + 16*x^2*log(x)^4 + x^2 - 2*x^3 + x^4))*exp((278*x^2*log(x)^2)/(lo
g(x)^4 - 8*x*log(x)^4 - 2*x*log(x)^2 + 10*x^2*log(x)^2 - 8*x^3*log(x)^2 + 16*x^2*log(x)^4 + x^2 - 2*x^3 + x^4)
)*exp((121*log(x)^4)/(log(x)^4 - 8*x*log(x)^4 - 2*x*log(x)^2 + 10*x^2*log(x)^2 - 8*x^3*log(x)^2 + 16*x^2*log(x
)^4 + x^2 - 2*x^3 + x^4))
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sympy [B] time = 5.60, size = 124, normalized size = 4.43 \begin {gather*} e^{\frac {x^{6} + 8 x^{5} + 6 x^{4} - 40 x^{3} + 25 x^{2} + \left (16 x^{4} + 152 x^{3} + 273 x^{2} - 418 x + 121\right ) \log {\relax (x )}^{4} + \left (- 8 x^{5} - 70 x^{4} - 90 x^{3} + 278 x^{2} - 110 x\right ) \log {\relax (x )}^{2}}{x^{4} - 2 x^{3} + x^{2} + \left (16 x^{2} - 8 x + 1\right ) \log {\relax (x )}^{4} + \left (- 8 x^{3} + 10 x^{2} - 2 x\right ) \log {\relax (x )}^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((128*x**4+544*x**3-456*x**2+1126*x-550)*ln(x)**6+(-96*x**5-336*x**4+618*x**3-984*x**2+786*x-132)*ln
(x)**4+(96*x**3+360*x**2-720*x+264)*ln(x)**3+(24*x**6+66*x**5-222*x**4+282*x**3-210*x**2+60*x)*ln(x)**2+(-24*x
**4-72*x**3+216*x**2-120*x)*ln(x)-2*x**7-4*x**6+24*x**5-28*x**4+10*x**3)*exp(((16*x**4+152*x**3+273*x**2-418*x
+121)*ln(x)**4+(-8*x**5-70*x**4-90*x**3+278*x**2-110*x)*ln(x)**2+x**6+8*x**5+6*x**4-40*x**3+25*x**2)/((16*x**2
-8*x+1)*ln(x)**4+(-8*x**3+10*x**2-2*x)*ln(x)**2+x**4-2*x**3+x**2))/((64*x**3-48*x**2+12*x-1)*ln(x)**6+(-48*x**
4+72*x**3-27*x**2+3*x)*ln(x)**4+(12*x**5-27*x**4+18*x**3-3*x**2)*ln(x)**2-x**6+3*x**5-3*x**4+x**3),x)
[Out]
exp((x**6 + 8*x**5 + 6*x**4 - 40*x**3 + 25*x**2 + (16*x**4 + 152*x**3 + 273*x**2 - 418*x + 121)*log(x)**4 + (-
8*x**5 - 70*x**4 - 90*x**3 + 278*x**2 - 110*x)*log(x)**2)/(x**4 - 2*x**3 + x**2 + (16*x**2 - 8*x + 1)*log(x)**
4 + (-8*x**3 + 10*x**2 - 2*x)*log(x)**2))
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