Integrand size = 190, antiderivative size = 28 \[ \int \frac {\left (4624+272 x^2-96 e^{3/x} x^3+4 x^4+4 e^{4/x} x^4+e^{\frac {1}{x}} \left (-3264 x-96 x^3\right )+e^{2/x} \left (848 x^2+8 x^4\right )\right ) \log ^3\left (\frac {x}{16}\right )+\left (136 x^2+4 x^4+e^{\frac {1}{x}} \left (816-816 x+24 x^2-72 x^3\right )+e^{3/x} \left (72 x^2-72 x^3\right )+e^{4/x} \left (-4 x^3+4 x^4\right )+e^{2/x} \left (-424 x+424 x^2-4 x^3+8 x^4\right )\right ) \log ^4\left (\frac {x}{16}\right )}{x} \, dx=\left (-2+x^2+\left (6-e^{\frac {1}{x}} x\right )^2\right )^2 \log ^4\left (\frac {x}{16}\right ) \]
Time = 0.12 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.25 \[ \int \frac {\left (4624+272 x^2-96 e^{3/x} x^3+4 x^4+4 e^{4/x} x^4+e^{\frac {1}{x}} \left (-3264 x-96 x^3\right )+e^{2/x} \left (848 x^2+8 x^4\right )\right ) \log ^3\left (\frac {x}{16}\right )+\left (136 x^2+4 x^4+e^{\frac {1}{x}} \left (816-816 x+24 x^2-72 x^3\right )+e^{3/x} \left (72 x^2-72 x^3\right )+e^{4/x} \left (-4 x^3+4 x^4\right )+e^{2/x} \left (-424 x+424 x^2-4 x^3+8 x^4\right )\right ) \log ^4\left (\frac {x}{16}\right )}{x} \, dx=\left (34-12 e^{\frac {1}{x}} x+x^2+e^{2/x} x^2\right )^2 \log ^4\left (\frac {x}{16}\right ) \]
Integrate[((4624 + 272*x^2 - 96*E^(3/x)*x^3 + 4*x^4 + 4*E^(4/x)*x^4 + E^x^ (-1)*(-3264*x - 96*x^3) + E^(2/x)*(848*x^2 + 8*x^4))*Log[x/16]^3 + (136*x^ 2 + 4*x^4 + E^x^(-1)*(816 - 816*x + 24*x^2 - 72*x^3) + E^(3/x)*(72*x^2 - 7 2*x^3) + E^(4/x)*(-4*x^3 + 4*x^4) + E^(2/x)*(-424*x + 424*x^2 - 4*x^3 + 8* x^4))*Log[x/16]^4)/x,x]
Leaf count is larger than twice the leaf count of optimal. \(138\) vs. \(2(28)=56\).
Time = 1.07 (sec) , antiderivative size = 138, normalized size of antiderivative = 4.93, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.011, Rules used = {2010, 2009}
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.
| \(\displaystyle \int \frac {\left (4 x^4+136 x^2+e^{4/x} \left (4 x^4-4 x^3\right )+e^{\frac {1}{x}} \left (-72 x^3+24 x^2-816 x+816\right )+e^{3/x} \left (72 x^2-72 x^3\right )+e^{2/x} \left (8 x^4-4 x^3+424 x^2-424 x\right )\right ) \log ^4\left (\frac {x}{16}\right )+\left (4 e^{4/x} x^4+4 x^4-96 e^{3/x} x^3+e^{\frac {1}{x}} \left (-96 x^3-3264 x\right )+272 x^2+e^{2/x} \left (8 x^4+848 x^2\right )+4624\right ) \log ^3\left (\frac {x}{16}\right )}{x} \, dx\) |
| \(\Big \downarrow \) 2010 |
| \(\displaystyle \int \left (\frac {4 \left (x^2+34\right ) \left (x^2+x^2 \log \left (\frac {x}{16}\right )+34\right ) \log ^3\left (\frac {x}{16}\right )}{x}+4 e^{4/x} x^2 \left (x+x \log \left (\frac {x}{16}\right )-\log (x)+\log (16)\right ) \log ^3\left (\frac {x}{16}\right )+4 e^{2/x} \left (2 x^3+2 x^3 \log \left (\frac {x}{16}\right )-x^2 \log \left (\frac {x}{16}\right )+212 x+106 x \log \left (\frac {x}{16}\right )-106 \log \left (\frac {x}{16}\right )\right ) \log ^3\left (\frac {x}{16}\right )-\frac {24 e^{\frac {1}{x}} \left (4 x^3+3 x^3 \log \left (\frac {x}{16}\right )-x^2 \log \left (\frac {x}{16}\right )+136 x+34 x \log \left (\frac {x}{16}\right )-34 \log \left (\frac {x}{16}\right )\right ) \log ^3\left (\frac {x}{16}\right )}{x}-24 e^{3/x} x \left (4 x+3 x \log \left (\frac {x}{16}\right )-3 \log \left (\frac {x}{16}\right )\right ) \log ^3\left (\frac {x}{16}\right )\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -e^{4/x} x^4 \log ^3\left (\frac {x}{16}\right ) (\log (16)-\log (x))-24 e^{3/x} x^3 \log ^4\left (\frac {x}{16}\right )+\left (x^2+34\right )^2 \log ^4\left (\frac {x}{16}\right )+2 e^{2/x} x^2 \log ^3\left (\frac {x}{16}\right ) \left (x^2 \log \left (\frac {x}{16}\right )+106 \log \left (\frac {x}{16}\right )\right )-24 e^{\frac {1}{x}} x \log ^3\left (\frac {x}{16}\right ) \left (x^2 \log \left (\frac {x}{16}\right )+34 \log \left (\frac {x}{16}\right )\right )\) |
Int[((4624 + 272*x^2 - 96*E^(3/x)*x^3 + 4*x^4 + 4*E^(4/x)*x^4 + E^x^(-1)*( -3264*x - 96*x^3) + E^(2/x)*(848*x^2 + 8*x^4))*Log[x/16]^3 + (136*x^2 + 4* x^4 + E^x^(-1)*(816 - 816*x + 24*x^2 - 72*x^3) + E^(3/x)*(72*x^2 - 72*x^3) + E^(4/x)*(-4*x^3 + 4*x^4) + E^(2/x)*(-424*x + 424*x^2 - 4*x^3 + 8*x^4))* Log[x/16]^4)/x,x]
-24*E^(3/x)*x^3*Log[x/16]^4 + (34 + x^2)^2*Log[x/16]^4 - 24*E^x^(-1)*x*Log [x/16]^3*(34*Log[x/16] + x^2*Log[x/16]) + 2*E^(2/x)*x^2*Log[x/16]^3*(106*L og[x/16] + x^2*Log[x/16]) - E^(4/x)*x^4*Log[x/16]^3*(Log[16] - Log[x])
3.2.65.3.1 Defintions of rubi rules used
Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x] , x] /; FreeQ[{c, m}, x] && SumQ[u] && !LinearQ[u, x] && !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]
Leaf count of result is larger than twice the leaf count of optimal. \(76\) vs. \(2(25)=50\).
Time = 2.70 (sec) , antiderivative size = 77, normalized size of antiderivative = 2.75
| method | result | size |
| risch | \(\left ({\mathrm e}^{\frac {4}{x}} x^{4}+2 \,{\mathrm e}^{\frac {2}{x}} x^{4}-24 \,{\mathrm e}^{\frac {3}{x}} x^{3}+x^{4}-24 x^{3} {\mathrm e}^{\frac {1}{x}}+212 x^{2} {\mathrm e}^{\frac {2}{x}}+68 x^{2}-816 x \,{\mathrm e}^{\frac {1}{x}}+1156\right ) \ln \left (\frac {x}{16}\right )^{4}\) | \(77\) |
| parallelrisch | \(\ln \left (\frac {x}{16}\right )^{4} {\mathrm e}^{\frac {4}{x}} x^{4}+2 \ln \left (\frac {x}{16}\right )^{4} {\mathrm e}^{\frac {2}{x}} x^{4}-24 \ln \left (\frac {x}{16}\right )^{4} {\mathrm e}^{\frac {3}{x}} x^{3}+\ln \left (\frac {x}{16}\right )^{4} x^{4}-24 \,{\mathrm e}^{\frac {1}{x}} \ln \left (\frac {x}{16}\right )^{4} x^{3}+212 \ln \left (\frac {x}{16}\right )^{4} {\mathrm e}^{\frac {2}{x}} x^{2}+68 \ln \left (\frac {x}{16}\right )^{4} x^{2}-816 \,{\mathrm e}^{\frac {1}{x}} \ln \left (\frac {x}{16}\right )^{4} x +1156 \ln \left (\frac {x}{16}\right )^{4}\) | \(126\) |
int((((4*x^4-4*x^3)*exp(1/x)^4+(-72*x^3+72*x^2)*exp(1/x)^3+(8*x^4-4*x^3+42 4*x^2-424*x)*exp(1/x)^2+(-72*x^3+24*x^2-816*x+816)*exp(1/x)+4*x^4+136*x^2) *ln(1/16*x)^4+(4*x^4*exp(1/x)^4-96*x^3*exp(1/x)^3+(8*x^4+848*x^2)*exp(1/x) ^2+(-96*x^3-3264*x)*exp(1/x)+4*x^4+272*x^2+4624)*ln(1/16*x)^3)/x,x,method= _RETURNVERBOSE)
(x^4*exp(1/x)^4+2*exp(1/x)^2*x^4-24*x^3*exp(1/x)^3+x^4-24*x^3*exp(1/x)+212 *x^2*exp(1/x)^2+68*x^2-816*x*exp(1/x)+1156)*ln(1/16*x)^4
Leaf count of result is larger than twice the leaf count of optimal. 68 vs. \(2 (24) = 48\).
Time = 0.26 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.43 \[ \int \frac {\left (4624+272 x^2-96 e^{3/x} x^3+4 x^4+4 e^{4/x} x^4+e^{\frac {1}{x}} \left (-3264 x-96 x^3\right )+e^{2/x} \left (848 x^2+8 x^4\right )\right ) \log ^3\left (\frac {x}{16}\right )+\left (136 x^2+4 x^4+e^{\frac {1}{x}} \left (816-816 x+24 x^2-72 x^3\right )+e^{3/x} \left (72 x^2-72 x^3\right )+e^{4/x} \left (-4 x^3+4 x^4\right )+e^{2/x} \left (-424 x+424 x^2-4 x^3+8 x^4\right )\right ) \log ^4\left (\frac {x}{16}\right )}{x} \, dx={\left (x^{4} e^{\frac {4}{x}} + x^{4} - 24 \, x^{3} e^{\frac {3}{x}} + 68 \, x^{2} + 2 \, {\left (x^{4} + 106 \, x^{2}\right )} e^{\frac {2}{x}} - 24 \, {\left (x^{3} + 34 \, x\right )} e^{\frac {1}{x}} + 1156\right )} \log \left (\frac {1}{16} \, x\right )^{4} \]
integrate((((4*x^4-4*x^3)*exp(1/x)^4+(-72*x^3+72*x^2)*exp(1/x)^3+(8*x^4-4* x^3+424*x^2-424*x)*exp(1/x)^2+(-72*x^3+24*x^2-816*x+816)*exp(1/x)+4*x^4+13 6*x^2)*log(1/16*x)^4+(4*x^4*exp(1/x)^4-96*x^3*exp(1/x)^3+(8*x^4+848*x^2)*e xp(1/x)^2+(-96*x^3-3264*x)*exp(1/x)+4*x^4+272*x^2+4624)*log(1/16*x)^3)/x,x , algorithm=\
(x^4*e^(4/x) + x^4 - 24*x^3*e^(3/x) + 68*x^2 + 2*(x^4 + 106*x^2)*e^(2/x) - 24*(x^3 + 34*x)*e^(1/x) + 1156)*log(1/16*x)^4
Leaf count of result is larger than twice the leaf count of optimal. 105 vs. \(2 (22) = 44\).
Time = 0.60 (sec) , antiderivative size = 105, normalized size of antiderivative = 3.75 \[ \int \frac {\left (4624+272 x^2-96 e^{3/x} x^3+4 x^4+4 e^{4/x} x^4+e^{\frac {1}{x}} \left (-3264 x-96 x^3\right )+e^{2/x} \left (848 x^2+8 x^4\right )\right ) \log ^3\left (\frac {x}{16}\right )+\left (136 x^2+4 x^4+e^{\frac {1}{x}} \left (816-816 x+24 x^2-72 x^3\right )+e^{3/x} \left (72 x^2-72 x^3\right )+e^{4/x} \left (-4 x^3+4 x^4\right )+e^{2/x} \left (-424 x+424 x^2-4 x^3+8 x^4\right )\right ) \log ^4\left (\frac {x}{16}\right )}{x} \, dx=x^{4} e^{\frac {4}{x}} \log {\left (\frac {x}{16} \right )}^{4} - 24 x^{3} e^{\frac {3}{x}} \log {\left (\frac {x}{16} \right )}^{4} + \left (- 24 x^{3} \log {\left (\frac {x}{16} \right )}^{4} - 816 x \log {\left (\frac {x}{16} \right )}^{4}\right ) e^{\frac {1}{x}} + \left (2 x^{4} \log {\left (\frac {x}{16} \right )}^{4} + 212 x^{2} \log {\left (\frac {x}{16} \right )}^{4}\right ) e^{\frac {2}{x}} + \left (x^{4} + 68 x^{2} + 1156\right ) \log {\left (\frac {x}{16} \right )}^{4} \]
integrate((((4*x**4-4*x**3)*exp(1/x)**4+(-72*x**3+72*x**2)*exp(1/x)**3+(8* x**4-4*x**3+424*x**2-424*x)*exp(1/x)**2+(-72*x**3+24*x**2-816*x+816)*exp(1 /x)+4*x**4+136*x**2)*ln(1/16*x)**4+(4*x**4*exp(1/x)**4-96*x**3*exp(1/x)**3 +(8*x**4+848*x**2)*exp(1/x)**2+(-96*x**3-3264*x)*exp(1/x)+4*x**4+272*x**2+ 4624)*ln(1/16*x)**3)/x,x)
x**4*exp(4/x)*log(x/16)**4 - 24*x**3*exp(3/x)*log(x/16)**4 + (-24*x**3*log (x/16)**4 - 816*x*log(x/16)**4)*exp(1/x) + (2*x**4*log(x/16)**4 + 212*x**2 *log(x/16)**4)*exp(2/x) + (x**4 + 68*x**2 + 1156)*log(x/16)**4
Leaf count of result is larger than twice the leaf count of optimal. 464 vs. \(2 (24) = 48\).
Time = 0.32 (sec) , antiderivative size = 464, normalized size of antiderivative = 16.57 \[ \int \frac {\left (4624+272 x^2-96 e^{3/x} x^3+4 x^4+4 e^{4/x} x^4+e^{\frac {1}{x}} \left (-3264 x-96 x^3\right )+e^{2/x} \left (848 x^2+8 x^4\right )\right ) \log ^3\left (\frac {x}{16}\right )+\left (136 x^2+4 x^4+e^{\frac {1}{x}} \left (816-816 x+24 x^2-72 x^3\right )+e^{3/x} \left (72 x^2-72 x^3\right )+e^{4/x} \left (-4 x^3+4 x^4\right )+e^{2/x} \left (-424 x+424 x^2-4 x^3+8 x^4\right )\right ) \log ^4\left (\frac {x}{16}\right )}{x} \, dx =\text {Too large to display} \]
integrate((((4*x^4-4*x^3)*exp(1/x)^4+(-72*x^3+72*x^2)*exp(1/x)^3+(8*x^4-4* x^3+424*x^2-424*x)*exp(1/x)^2+(-72*x^3+24*x^2-816*x+816)*exp(1/x)+4*x^4+13 6*x^2)*log(1/16*x)^4+(4*x^4*exp(1/x)^4-96*x^3*exp(1/x)^3+(8*x^4+848*x^2)*e xp(1/x)^2+(-96*x^3-3264*x)*exp(1/x)+4*x^4+272*x^2+4624)*log(1/16*x)^3)/x,x , algorithm=\
1/32*(32*log(1/16*x)^4 - 32*log(1/16*x)^3 + 24*log(1/16*x)^2 - 12*log(1/16 *x) + 3)*x^4 + 1/32*(32*log(1/16*x)^3 - 24*log(1/16*x)^2 + 12*log(1/16*x) - 3)*x^4 + 1156*log(1/16*x)^4 + 34*(2*log(1/16*x)^4 - 4*log(1/16*x)^3 + 6* log(1/16*x)^2 - 6*log(1/16*x) + 3)*x^2 + 34*(4*log(1/16*x)^3 - 6*log(1/16* x)^2 + 6*log(1/16*x) - 3)*x^2 + (256*x^4*log(2)^4 - 256*x^4*log(2)^3*log(x ) + 96*x^4*log(2)^2*log(x)^2 - 16*x^4*log(2)*log(x)^3 + x^4*log(x)^4)*e^(4 /x) - 24*(256*x^3*log(2)^4 - 256*x^3*log(2)^3*log(x) + 96*x^3*log(2)^2*log (x)^2 - 16*x^3*log(2)*log(x)^3 + x^3*log(x)^4)*e^(3/x) + 2*(256*x^4*log(2) ^4 + 27136*x^2*log(2)^4 + (x^4 + 106*x^2)*log(x)^4 - 16*(x^4*log(2) + 106* x^2*log(2))*log(x)^3 + 96*(x^4*log(2)^2 + 106*x^2*log(2)^2)*log(x)^2 - 256 *(x^4*log(2)^3 + 106*x^2*log(2)^3)*log(x))*e^(2/x) - 24*(256*x^3*log(2)^4 + 8704*x*log(2)^4 + (x^3 + 34*x)*log(x)^4 - 16*(x^3*log(2) + 34*x*log(2))* log(x)^3 + 96*(x^3*log(2)^2 + 34*x*log(2)^2)*log(x)^2 - 256*(x^3*log(2)^3 + 34*x*log(2)^3)*log(x))*e^(1/x)
Leaf count of result is larger than twice the leaf count of optimal. 605 vs. \(2 (24) = 48\).
Time = 0.33 (sec) , antiderivative size = 605, normalized size of antiderivative = 21.61 \[ \int \frac {\left (4624+272 x^2-96 e^{3/x} x^3+4 x^4+4 e^{4/x} x^4+e^{\frac {1}{x}} \left (-3264 x-96 x^3\right )+e^{2/x} \left (848 x^2+8 x^4\right )\right ) \log ^3\left (\frac {x}{16}\right )+\left (136 x^2+4 x^4+e^{\frac {1}{x}} \left (816-816 x+24 x^2-72 x^3\right )+e^{3/x} \left (72 x^2-72 x^3\right )+e^{4/x} \left (-4 x^3+4 x^4\right )+e^{2/x} \left (-424 x+424 x^2-4 x^3+8 x^4\right )\right ) \log ^4\left (\frac {x}{16}\right )}{x} \, dx =\text {Too large to display} \]
integrate((((4*x^4-4*x^3)*exp(1/x)^4+(-72*x^3+72*x^2)*exp(1/x)^3+(8*x^4-4* x^3+424*x^2-424*x)*exp(1/x)^2+(-72*x^3+24*x^2-816*x+816)*exp(1/x)+4*x^4+13 6*x^2)*log(1/16*x)^4+(4*x^4*exp(1/x)^4-96*x^3*exp(1/x)^3+(8*x^4+848*x^2)*e xp(1/x)^2+(-96*x^3-3264*x)*exp(1/x)+4*x^4+272*x^2+4624)*log(1/16*x)^3)/x,x , algorithm=\
256*x^4*e^(4/x)*log(2)^4 + 512*x^4*e^(2/x)*log(2)^4 - 256*x^4*e^(4/x)*log( 2)^3*log(x) - 512*x^4*e^(2/x)*log(2)^3*log(x) + 96*x^4*e^(4/x)*log(2)^2*lo g(x)^2 + 192*x^4*e^(2/x)*log(2)^2*log(x)^2 - 16*x^4*e^(4/x)*log(2)*log(x)^ 3 - 32*x^4*e^(2/x)*log(2)*log(x)^3 + x^4*e^(4/x)*log(x)^4 + 2*x^4*e^(2/x)* log(x)^4 + 256*x^4*log(2)^4 - 6144*x^3*e^(3/x)*log(2)^4 - 6144*x^3*e^(1/x) *log(2)^4 - 256*x^4*log(2)^3*log(x) + 6144*x^3*e^(3/x)*log(2)^3*log(x) + 6 144*x^3*e^(1/x)*log(2)^3*log(x) + 96*x^4*log(2)^2*log(x)^2 - 2304*x^3*e^(3 /x)*log(2)^2*log(x)^2 - 2304*x^3*e^(1/x)*log(2)^2*log(x)^2 - 16*x^4*log(2) *log(x)^3 + 384*x^3*e^(3/x)*log(2)*log(x)^3 + 384*x^3*e^(1/x)*log(2)*log(x )^3 + x^4*log(x)^4 - 24*x^3*e^(3/x)*log(x)^4 - 24*x^3*e^(1/x)*log(x)^4 + 5 4272*x^2*e^(2/x)*log(2)^4 - 54272*x^2*e^(2/x)*log(2)^3*log(x) + 20352*x^2* e^(2/x)*log(2)^2*log(x)^2 - 3392*x^2*e^(2/x)*log(2)*log(x)^3 + 212*x^2*e^( 2/x)*log(x)^4 + 17408*x^2*log(2)^4 - 208896*x*e^(1/x)*log(2)^4 - 17408*x^2 *log(2)^3*log(x) + 208896*x*e^(1/x)*log(2)^3*log(x) + 6528*x^2*log(2)^2*lo g(x)^2 - 78336*x*e^(1/x)*log(2)^2*log(x)^2 - 1088*x^2*log(2)*log(x)^3 + 13 056*x*e^(1/x)*log(2)*log(x)^3 + 68*x^2*log(x)^4 - 816*x*e^(1/x)*log(x)^4 - 295936*log(2)^3*log(x) + 110976*log(2)^2*log(x)^2 - 18496*log(2)*log(x)^3 + 1156*log(x)^4
Timed out. \[ \int \frac {\left (4624+272 x^2-96 e^{3/x} x^3+4 x^4+4 e^{4/x} x^4+e^{\frac {1}{x}} \left (-3264 x-96 x^3\right )+e^{2/x} \left (848 x^2+8 x^4\right )\right ) \log ^3\left (\frac {x}{16}\right )+\left (136 x^2+4 x^4+e^{\frac {1}{x}} \left (816-816 x+24 x^2-72 x^3\right )+e^{3/x} \left (72 x^2-72 x^3\right )+e^{4/x} \left (-4 x^3+4 x^4\right )+e^{2/x} \left (-424 x+424 x^2-4 x^3+8 x^4\right )\right ) \log ^4\left (\frac {x}{16}\right )}{x} \, dx=\int \frac {{\ln \left (\frac {x}{16}\right )}^3\,\left ({\mathrm {e}}^{2/x}\,\left (8\,x^4+848\,x^2\right )-{\mathrm {e}}^{1/x}\,\left (96\,x^3+3264\,x\right )-96\,x^3\,{\mathrm {e}}^{3/x}+4\,x^4\,{\mathrm {e}}^{4/x}+272\,x^2+4\,x^4+4624\right )-{\ln \left (\frac {x}{16}\right )}^4\,\left ({\mathrm {e}}^{1/x}\,\left (72\,x^3-24\,x^2+816\,x-816\right )+{\mathrm {e}}^{4/x}\,\left (4\,x^3-4\,x^4\right )-{\mathrm {e}}^{3/x}\,\left (72\,x^2-72\,x^3\right )+{\mathrm {e}}^{2/x}\,\left (-8\,x^4+4\,x^3-424\,x^2+424\,x\right )-136\,x^2-4\,x^4\right )}{x} \,d x \]
int((log(x/16)^3*(exp(2/x)*(848*x^2 + 8*x^4) - exp(1/x)*(3264*x + 96*x^3) - 96*x^3*exp(3/x) + 4*x^4*exp(4/x) + 272*x^2 + 4*x^4 + 4624) - log(x/16)^4 *(exp(1/x)*(816*x - 24*x^2 + 72*x^3 - 816) + exp(4/x)*(4*x^3 - 4*x^4) - ex p(3/x)*(72*x^2 - 72*x^3) + exp(2/x)*(424*x - 424*x^2 + 4*x^3 - 8*x^4) - 13 6*x^2 - 4*x^4))/x,x)
int((log(x/16)^3*(exp(2/x)*(848*x^2 + 8*x^4) - exp(1/x)*(3264*x + 96*x^3) - 96*x^3*exp(3/x) + 4*x^4*exp(4/x) + 272*x^2 + 4*x^4 + 4624) - log(x/16)^4 *(exp(1/x)*(816*x - 24*x^2 + 72*x^3 - 816) + exp(4/x)*(4*x^3 - 4*x^4) - ex p(3/x)*(72*x^2 - 72*x^3) + exp(2/x)*(424*x - 424*x^2 + 4*x^3 - 8*x^4) - 13 6*x^2 - 4*x^4))/x, x)