\(\int \frac {(-4-6 x^2+3 x^4) \log ^2(x)+e^{\frac {8 x}{\log (x)}} (-8 x+8 x \log (x)-\log ^2(x))+e^{\frac {4 x}{\log (x)}} (24 x-8 x^3+(-24 x+8 x^3) \log (x)+(6+2 x^2) \log ^2(x))}{e^{\frac {8 x}{\log (x)}} x \log ^2(x)+e^{\frac {4 x}{\log (x)}} (-6 x+2 x^3) \log ^2(x)+(4 x-6 x^3+x^5) \log ^2(x)} \, dx\) [587]

Optimal result

Integrand size = 145, antiderivative size = 36 \[ \int \frac {\left (-4-6 x^2+3 x^4\right ) \log ^2(x)+e^{\frac {8 x}{\log (x)}} \left (-8 x+8 x \log (x)-\log ^2(x)\right )+e^{\frac {4 x}{\log (x)}} \left (24 x-8 x^3+\left (-24 x+8 x^3\right ) \log (x)+\left (6+2 x^2\right ) \log ^2(x)\right )}{e^{\frac {8 x}{\log (x)}} x \log ^2(x)+e^{\frac {4 x}{\log (x)}} \left (-6 x+2 x^3\right ) \log ^2(x)+\left (4 x-6 x^3+x^5\right ) \log ^2(x)} \, dx=3+\log \left (\frac {5-x^2 \left (-\frac {3-e^{\frac {4 x}{\log (x)}}}{x}+x\right )^2}{x}\right ) \] Output:

ln((-(x-(3-exp(4*x/ln(x)))/x)^2*x^2+5)/x)+3
 

Mathematica [A] (verified)

Time = 0.11 (sec) , antiderivative size = 50, normalized size of antiderivative = 1.39 \[ \int \frac {\left (-4-6 x^2+3 x^4\right ) \log ^2(x)+e^{\frac {8 x}{\log (x)}} \left (-8 x+8 x \log (x)-\log ^2(x)\right )+e^{\frac {4 x}{\log (x)}} \left (24 x-8 x^3+\left (-24 x+8 x^3\right ) \log (x)+\left (6+2 x^2\right ) \log ^2(x)\right )}{e^{\frac {8 x}{\log (x)}} x \log ^2(x)+e^{\frac {4 x}{\log (x)}} \left (-6 x+2 x^3\right ) \log ^2(x)+\left (4 x-6 x^3+x^5\right ) \log ^2(x)} \, dx=-\log (x)+\log \left (4-6 e^{\frac {4 x}{\log (x)}}+e^{\frac {8 x}{\log (x)}}-6 x^2+2 e^{\frac {4 x}{\log (x)}} x^2+x^4\right ) \] Input:

Integrate[((-4 - 6*x^2 + 3*x^4)*Log[x]^2 + E^((8*x)/Log[x])*(-8*x + 8*x*Lo 
g[x] - Log[x]^2) + E^((4*x)/Log[x])*(24*x - 8*x^3 + (-24*x + 8*x^3)*Log[x] 
 + (6 + 2*x^2)*Log[x]^2))/(E^((8*x)/Log[x])*x*Log[x]^2 + E^((4*x)/Log[x])* 
(-6*x + 2*x^3)*Log[x]^2 + (4*x - 6*x^3 + x^5)*Log[x]^2),x]
 

Output:

-Log[x] + Log[4 - 6*E^((4*x)/Log[x]) + E^((8*x)/Log[x]) - 6*x^2 + 2*E^((4* 
x)/Log[x])*x^2 + x^4]
 

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.

\(\displaystyle \int \frac {\left (3 x^4-6 x^2-4\right ) \log ^2(x)+e^{\frac {4 x}{\log (x)}} \left (-8 x^3+\left (8 x^3-24 x\right ) \log (x)+\left (2 x^2+6\right ) \log ^2(x)+24 x\right )+e^{\frac {8 x}{\log (x)}} \left (-8 x-\log ^2(x)+8 x \log (x)\right )}{\left (2 x^3-6 x\right ) e^{\frac {4 x}{\log (x)}} \log ^2(x)+\left (x^5-6 x^3+4 x\right ) \log ^2(x)+x e^{\frac {8 x}{\log (x)}} \log ^2(x)} \, dx\)

\(\Big \downarrow \) 7292

\(\displaystyle \int \frac {\left (3 x^4-6 x^2-4\right ) \log ^2(x)+e^{\frac {4 x}{\log (x)}} \left (-8 x^3+\left (8 x^3-24 x\right ) \log (x)+\left (2 x^2+6\right ) \log ^2(x)+24 x\right )+e^{\frac {8 x}{\log (x)}} \left (-8 x-\log ^2(x)+8 x \log (x)\right )}{x \left (x^4-6 x^2+2 x^2 e^{\frac {4 x}{\log (x)}}-6 e^{\frac {4 x}{\log (x)}}+e^{\frac {8 x}{\log (x)}}+4\right ) \log ^2(x)}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {-8 x-\log ^2(x)+8 x \log (x)}{x \log ^2(x)}-\frac {4 \left (-2 x^4+2 x^4 \log (x)-x^3 \log ^2(x)+12 x^2-2 x^2 e^{\frac {4 x}{\log (x)}}+2 x^2 e^{\frac {4 x}{\log (x)}} \log (x)-12 x^2 \log (x)-x e^{\frac {4 x}{\log (x)}} \log ^2(x)+3 x \log ^2(x)+6 e^{\frac {4 x}{\log (x)}}-6 e^{\frac {4 x}{\log (x)}} \log (x)+8 \log (x)-8\right )}{\left (x^4-6 x^2+2 x^2 e^{\frac {4 x}{\log (x)}}-6 e^{\frac {4 x}{\log (x)}}+e^{\frac {8 x}{\log (x)}}+4\right ) \log ^2(x)}\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle \frac {8 x}{\log (x)}-\log (x)-12 \int \frac {x}{x^4+2 e^{\frac {4 x}{\log (x)}} x^2-6 x^2-6 e^{\frac {4 x}{\log (x)}}+e^{\frac {8 x}{\log (x)}}+4}dx+4 \int \frac {e^{\frac {4 x}{\log (x)}} x}{x^4+2 e^{\frac {4 x}{\log (x)}} x^2-6 x^2-6 e^{\frac {4 x}{\log (x)}}+e^{\frac {8 x}{\log (x)}}+4}dx+4 \int \frac {x^3}{x^4+2 e^{\frac {4 x}{\log (x)}} x^2-6 x^2-6 e^{\frac {4 x}{\log (x)}}+e^{\frac {8 x}{\log (x)}}+4}dx+32 \int \frac {1}{\left (x^4+2 e^{\frac {4 x}{\log (x)}} x^2-6 x^2-6 e^{\frac {4 x}{\log (x)}}+e^{\frac {8 x}{\log (x)}}+4\right ) \log ^2(x)}dx-24 \int \frac {e^{\frac {4 x}{\log (x)}}}{\left (x^4+2 e^{\frac {4 x}{\log (x)}} x^2-6 x^2-6 e^{\frac {4 x}{\log (x)}}+e^{\frac {8 x}{\log (x)}}+4\right ) \log ^2(x)}dx-48 \int \frac {x^2}{\left (x^4+2 e^{\frac {4 x}{\log (x)}} x^2-6 x^2-6 e^{\frac {4 x}{\log (x)}}+e^{\frac {8 x}{\log (x)}}+4\right ) \log ^2(x)}dx+8 \int \frac {e^{\frac {4 x}{\log (x)}} x^2}{\left (x^4+2 e^{\frac {4 x}{\log (x)}} x^2-6 x^2-6 e^{\frac {4 x}{\log (x)}}+e^{\frac {8 x}{\log (x)}}+4\right ) \log ^2(x)}dx+8 \int \frac {x^4}{\left (x^4+2 e^{\frac {4 x}{\log (x)}} x^2-6 x^2-6 e^{\frac {4 x}{\log (x)}}+e^{\frac {8 x}{\log (x)}}+4\right ) \log ^2(x)}dx-32 \int \frac {1}{\left (x^4+2 e^{\frac {4 x}{\log (x)}} x^2-6 x^2-6 e^{\frac {4 x}{\log (x)}}+e^{\frac {8 x}{\log (x)}}+4\right ) \log (x)}dx+24 \int \frac {e^{\frac {4 x}{\log (x)}}}{\left (x^4+2 e^{\frac {4 x}{\log (x)}} x^2-6 x^2-6 e^{\frac {4 x}{\log (x)}}+e^{\frac {8 x}{\log (x)}}+4\right ) \log (x)}dx+48 \int \frac {x^2}{\left (x^4+2 e^{\frac {4 x}{\log (x)}} x^2-6 x^2-6 e^{\frac {4 x}{\log (x)}}+e^{\frac {8 x}{\log (x)}}+4\right ) \log (x)}dx-8 \int \frac {e^{\frac {4 x}{\log (x)}} x^2}{\left (x^4+2 e^{\frac {4 x}{\log (x)}} x^2-6 x^2-6 e^{\frac {4 x}{\log (x)}}+e^{\frac {8 x}{\log (x)}}+4\right ) \log (x)}dx-8 \int \frac {x^4}{\left (x^4+2 e^{\frac {4 x}{\log (x)}} x^2-6 x^2-6 e^{\frac {4 x}{\log (x)}}+e^{\frac {8 x}{\log (x)}}+4\right ) \log (x)}dx\)

Input:

Int[((-4 - 6*x^2 + 3*x^4)*Log[x]^2 + E^((8*x)/Log[x])*(-8*x + 8*x*Log[x] - 
 Log[x]^2) + E^((4*x)/Log[x])*(24*x - 8*x^3 + (-24*x + 8*x^3)*Log[x] + (6 
+ 2*x^2)*Log[x]^2))/(E^((8*x)/Log[x])*x*Log[x]^2 + E^((4*x)/Log[x])*(-6*x 
+ 2*x^3)*Log[x]^2 + (4*x - 6*x^3 + x^5)*Log[x]^2),x]
 

Output:

$Aborted
 

Maple [A] (verified)

Time = 1.02 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.14

method	result	size
risch	\(-\ln \left (x \right )+\ln \left ({\mathrm e}^{\frac {8 x}{\ln \left (x \right )}}+\left (2 x^{2}-6\right ) {\mathrm e}^{\frac {4 x}{\ln \left (x \right )}}+x^{4}-6 x^{2}+4\right )\)	\(41\)
parallelrisch	\(\ln \left (x^{4}+2 \,{\mathrm e}^{\frac {4 x}{\ln \left (x \right )}} x^{2}-6 x^{2}+{\mathrm e}^{\frac {8 x}{\ln \left (x \right )}}-6 \,{\mathrm e}^{\frac {4 x}{\ln \left (x \right )}}+4\right )-\ln \left (x \right )\)	\(50\)

Input:

int(((-ln(x)^2+8*x*ln(x)-8*x)*exp(4*x/ln(x))^2+((2*x^2+6)*ln(x)^2+(8*x^3-2 
4*x)*ln(x)-8*x^3+24*x)*exp(4*x/ln(x))+(3*x^4-6*x^2-4)*ln(x)^2)/(x*ln(x)^2* 
exp(4*x/ln(x))^2+(2*x^3-6*x)*ln(x)^2*exp(4*x/ln(x))+(x^5-6*x^3+4*x)*ln(x)^ 
2),x,method=_RETURNVERBOSE)
 

Output:

-ln(x)+ln(exp(8*x/ln(x))+(2*x^2-6)*exp(4*x/ln(x))+x^4-6*x^2+4)
 

Fricas [A] (verification not implemented)

Time = 0.09 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.08 \[ \int \frac {\left (-4-6 x^2+3 x^4\right ) \log ^2(x)+e^{\frac {8 x}{\log (x)}} \left (-8 x+8 x \log (x)-\log ^2(x)\right )+e^{\frac {4 x}{\log (x)}} \left (24 x-8 x^3+\left (-24 x+8 x^3\right ) \log (x)+\left (6+2 x^2\right ) \log ^2(x)\right )}{e^{\frac {8 x}{\log (x)}} x \log ^2(x)+e^{\frac {4 x}{\log (x)}} \left (-6 x+2 x^3\right ) \log ^2(x)+\left (4 x-6 x^3+x^5\right ) \log ^2(x)} \, dx=\log \left (x^{4} - 6 \, x^{2} + 2 \, {\left (x^{2} - 3\right )} e^{\left (\frac {4 \, x}{\log \left (x\right )}\right )} + e^{\left (\frac {8 \, x}{\log \left (x\right )}\right )} + 4\right ) - \log \left (x\right ) \] Input:

integrate(((-log(x)^2+8*x*log(x)-8*x)*exp(4*x/log(x))^2+((2*x^2+6)*log(x)^ 
2+(8*x^3-24*x)*log(x)-8*x^3+24*x)*exp(4*x/log(x))+(3*x^4-6*x^2-4)*log(x)^2 
)/(x*log(x)^2*exp(4*x/log(x))^2+(2*x^3-6*x)*log(x)^2*exp(4*x/log(x))+(x^5- 
6*x^3+4*x)*log(x)^2),x, algorithm="fricas")
 

Output:

log(x^4 - 6*x^2 + 2*(x^2 - 3)*e^(4*x/log(x)) + e^(8*x/log(x)) + 4) - log(x 
)
 

Sympy [A] (verification not implemented)

Time = 0.27 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.03 \[ \int \frac {\left (-4-6 x^2+3 x^4\right ) \log ^2(x)+e^{\frac {8 x}{\log (x)}} \left (-8 x+8 x \log (x)-\log ^2(x)\right )+e^{\frac {4 x}{\log (x)}} \left (24 x-8 x^3+\left (-24 x+8 x^3\right ) \log (x)+\left (6+2 x^2\right ) \log ^2(x)\right )}{e^{\frac {8 x}{\log (x)}} x \log ^2(x)+e^{\frac {4 x}{\log (x)}} \left (-6 x+2 x^3\right ) \log ^2(x)+\left (4 x-6 x^3+x^5\right ) \log ^2(x)} \, dx=- \log {\left (x \right )} + \log {\left (x^{4} - 6 x^{2} + \left (2 x^{2} - 6\right ) e^{\frac {4 x}{\log {\left (x \right )}}} + e^{\frac {8 x}{\log {\left (x \right )}}} + 4 \right )} \] Input:

integrate(((-ln(x)**2+8*x*ln(x)-8*x)*exp(4*x/ln(x))**2+((2*x**2+6)*ln(x)** 
2+(8*x**3-24*x)*ln(x)-8*x**3+24*x)*exp(4*x/ln(x))+(3*x**4-6*x**2-4)*ln(x)* 
*2)/(x*ln(x)**2*exp(4*x/ln(x))**2+(2*x**3-6*x)*ln(x)**2*exp(4*x/ln(x))+(x* 
*5-6*x**3+4*x)*ln(x)**2),x)
 

Output:

-log(x) + log(x**4 - 6*x**2 + (2*x**2 - 6)*exp(4*x/log(x)) + exp(8*x/log(x 
)) + 4)
 

Maxima [A] (verification not implemented)

Time = 0.09 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.08 \[ \int \frac {\left (-4-6 x^2+3 x^4\right ) \log ^2(x)+e^{\frac {8 x}{\log (x)}} \left (-8 x+8 x \log (x)-\log ^2(x)\right )+e^{\frac {4 x}{\log (x)}} \left (24 x-8 x^3+\left (-24 x+8 x^3\right ) \log (x)+\left (6+2 x^2\right ) \log ^2(x)\right )}{e^{\frac {8 x}{\log (x)}} x \log ^2(x)+e^{\frac {4 x}{\log (x)}} \left (-6 x+2 x^3\right ) \log ^2(x)+\left (4 x-6 x^3+x^5\right ) \log ^2(x)} \, dx=\log \left (x^{4} - 6 \, x^{2} + 2 \, {\left (x^{2} - 3\right )} e^{\left (\frac {4 \, x}{\log \left (x\right )}\right )} + e^{\left (\frac {8 \, x}{\log \left (x\right )}\right )} + 4\right ) - \log \left (x\right ) \] Input:

integrate(((-log(x)^2+8*x*log(x)-8*x)*exp(4*x/log(x))^2+((2*x^2+6)*log(x)^ 
2+(8*x^3-24*x)*log(x)-8*x^3+24*x)*exp(4*x/log(x))+(3*x^4-6*x^2-4)*log(x)^2 
)/(x*log(x)^2*exp(4*x/log(x))^2+(2*x^3-6*x)*log(x)^2*exp(4*x/log(x))+(x^5- 
6*x^3+4*x)*log(x)^2),x, algorithm="maxima")
 

Output:

log(x^4 - 6*x^2 + 2*(x^2 - 3)*e^(4*x/log(x)) + e^(8*x/log(x)) + 4) - log(x 
)
 

Giac [A] (verification not implemented)

Time = 0.15 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.31 \[ \int \frac {\left (-4-6 x^2+3 x^4\right ) \log ^2(x)+e^{\frac {8 x}{\log (x)}} \left (-8 x+8 x \log (x)-\log ^2(x)\right )+e^{\frac {4 x}{\log (x)}} \left (24 x-8 x^3+\left (-24 x+8 x^3\right ) \log (x)+\left (6+2 x^2\right ) \log ^2(x)\right )}{e^{\frac {8 x}{\log (x)}} x \log ^2(x)+e^{\frac {4 x}{\log (x)}} \left (-6 x+2 x^3\right ) \log ^2(x)+\left (4 x-6 x^3+x^5\right ) \log ^2(x)} \, dx=\log \left (x^{4} + 2 \, x^{2} e^{\left (\frac {4 \, x}{\log \left (x\right )}\right )} - 6 \, x^{2} + e^{\left (\frac {8 \, x}{\log \left (x\right )}\right )} - 6 \, e^{\left (\frac {4 \, x}{\log \left (x\right )}\right )} + 4\right ) - \log \left (x\right ) \] Input:

integrate(((-log(x)^2+8*x*log(x)-8*x)*exp(4*x/log(x))^2+((2*x^2+6)*log(x)^ 
2+(8*x^3-24*x)*log(x)-8*x^3+24*x)*exp(4*x/log(x))+(3*x^4-6*x^2-4)*log(x)^2 
)/(x*log(x)^2*exp(4*x/log(x))^2+(2*x^3-6*x)*log(x)^2*exp(4*x/log(x))+(x^5- 
6*x^3+4*x)*log(x)^2),x, algorithm="giac")
 

Output:

log(x^4 + 2*x^2*e^(4*x/log(x)) - 6*x^2 + e^(8*x/log(x)) - 6*e^(4*x/log(x)) 
 + 4) - log(x)
 

Mupad [B] (verification not implemented)

Time = 3.08 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.31 \[ \int \frac {\left (-4-6 x^2+3 x^4\right ) \log ^2(x)+e^{\frac {8 x}{\log (x)}} \left (-8 x+8 x \log (x)-\log ^2(x)\right )+e^{\frac {4 x}{\log (x)}} \left (24 x-8 x^3+\left (-24 x+8 x^3\right ) \log (x)+\left (6+2 x^2\right ) \log ^2(x)\right )}{e^{\frac {8 x}{\log (x)}} x \log ^2(x)+e^{\frac {4 x}{\log (x)}} \left (-6 x+2 x^3\right ) \log ^2(x)+\left (4 x-6 x^3+x^5\right ) \log ^2(x)} \, dx=\ln \left ({\mathrm {e}}^{\frac {8\,x}{\ln \left (x\right )}}-6\,{\mathrm {e}}^{\frac {4\,x}{\ln \left (x\right )}}+2\,x^2\,{\mathrm {e}}^{\frac {4\,x}{\ln \left (x\right )}}-6\,x^2+x^4+4\right )-\ln \left (x\right ) \] Input:

int(-(exp((8*x)/log(x))*(8*x + log(x)^2 - 8*x*log(x)) - exp((4*x)/log(x))* 
(24*x + log(x)^2*(2*x^2 + 6) - log(x)*(24*x - 8*x^3) - 8*x^3) + log(x)^2*( 
6*x^2 - 3*x^4 + 4))/(log(x)^2*(4*x - 6*x^3 + x^5) - exp((4*x)/log(x))*log( 
x)^2*(6*x - 2*x^3) + x*exp((8*x)/log(x))*log(x)^2),x)
 

Output:

log(exp((8*x)/log(x)) - 6*exp((4*x)/log(x)) + 2*x^2*exp((4*x)/log(x)) - 6* 
x^2 + x^4 + 4) - log(x)
 

Reduce [F]

\[ \int \frac {\left (-4-6 x^2+3 x^4\right ) \log ^2(x)+e^{\frac {8 x}{\log (x)}} \left (-8 x+8 x \log (x)-\log ^2(x)\right )+e^{\frac {4 x}{\log (x)}} \left (24 x-8 x^3+\left (-24 x+8 x^3\right ) \log (x)+\left (6+2 x^2\right ) \log ^2(x)\right )}{e^{\frac {8 x}{\log (x)}} x \log ^2(x)+e^{\frac {4 x}{\log (x)}} \left (-6 x+2 x^3\right ) \log ^2(x)+\left (4 x-6 x^3+x^5\right ) \log ^2(x)} \, dx =\text {Too large to display} \] Input:

int(((-log(x)^2+8*x*log(x)-8*x)*exp(4*x/log(x))^2+((2*x^2+6)*log(x)^2+(8*x 
^3-24*x)*log(x)-8*x^3+24*x)*exp(4*x/log(x))+(3*x^4-6*x^2-4)*log(x)^2)/(x*l 
og(x)^2*exp(4*x/log(x))^2+(2*x^3-6*x)*log(x)^2*exp(4*x/log(x))+(x^5-6*x^3+ 
4*x)*log(x)^2),x)
 

Output:

 - 8*int(e**((8*x)/log(x))/(e**((8*x)/log(x))*log(x)**2 + 2*e**((4*x)/log( 
x))*log(x)**2*x**2 - 6*e**((4*x)/log(x))*log(x)**2 + log(x)**2*x**4 - 6*lo 
g(x)**2*x**2 + 4*log(x)**2),x) + 8*int(e**((8*x)/log(x))/(e**((8*x)/log(x) 
)*log(x) + 2*e**((4*x)/log(x))*log(x)*x**2 - 6*e**((4*x)/log(x))*log(x) + 
log(x)*x**4 - 6*log(x)*x**2 + 4*log(x)),x) - int(e**((8*x)/log(x))/(e**((8 
*x)/log(x))*x + 2*e**((4*x)/log(x))*x**3 - 6*e**((4*x)/log(x))*x + x**5 - 
6*x**3 + 4*x),x) + 24*int(e**((4*x)/log(x))/(e**((8*x)/log(x))*log(x)**2 + 
 2*e**((4*x)/log(x))*log(x)**2*x**2 - 6*e**((4*x)/log(x))*log(x)**2 + log( 
x)**2*x**4 - 6*log(x)**2*x**2 + 4*log(x)**2),x) - 24*int(e**((4*x)/log(x)) 
/(e**((8*x)/log(x))*log(x) + 2*e**((4*x)/log(x))*log(x)*x**2 - 6*e**((4*x) 
/log(x))*log(x) + log(x)*x**4 - 6*log(x)*x**2 + 4*log(x)),x) + 6*int(e**(( 
4*x)/log(x))/(e**((8*x)/log(x))*x + 2*e**((4*x)/log(x))*x**3 - 6*e**((4*x) 
/log(x))*x + x**5 - 6*x**3 + 4*x),x) + 3*int(x**3/(e**((8*x)/log(x)) + 2*e 
**((4*x)/log(x))*x**2 - 6*e**((4*x)/log(x)) + x**4 - 6*x**2 + 4),x) - 8*in 
t((e**((4*x)/log(x))*x**2)/(e**((8*x)/log(x))*log(x)**2 + 2*e**((4*x)/log( 
x))*log(x)**2*x**2 - 6*e**((4*x)/log(x))*log(x)**2 + log(x)**2*x**4 - 6*lo 
g(x)**2*x**2 + 4*log(x)**2),x) + 8*int((e**((4*x)/log(x))*x**2)/(e**((8*x) 
/log(x))*log(x) + 2*e**((4*x)/log(x))*log(x)*x**2 - 6*e**((4*x)/log(x))*lo 
g(x) + log(x)*x**4 - 6*log(x)*x**2 + 4*log(x)),x) + 2*int((e**((4*x)/log(x 
))*x)/(e**((8*x)/log(x)) + 2*e**((4*x)/log(x))*x**2 - 6*e**((4*x)/log(x...