\(\int \frac {2 x^2 \log ^2(4)+e^x (-6 x^4+(6 x^3-18 x^4-6 x^5) \log (4))+(-4 x^2 \log (4)+4 x \log ^2(4)+e^x (18 x^4+6 x^5+(-24 x^3-6 x^4) \log (4))) \log (x)+(2 x^2-4 x \log (4)+2 \log ^2(4)) \log ^2(x)}{3 x^2 \log ^2(4)+(-6 x^2 \log (4)+6 x \log ^2(4)) \log (x)+(3 x^2-6 x \log (4)+3 \log ^2(4)) \log ^2(x)} \, dx\) [9039]

Optimal result

Integrand size = 161, antiderivative size = 30 \[ \int \frac {2 x^2 \log ^2(4)+e^x \left (-6 x^4+\left (6 x^3-18 x^4-6 x^5\right ) \log (4)\right )+\left (-4 x^2 \log (4)+4 x \log ^2(4)+e^x \left (18 x^4+6 x^5+\left (-24 x^3-6 x^4\right ) \log (4)\right )\right ) \log (x)+\left (2 x^2-4 x \log (4)+2 \log ^2(4)\right ) \log ^2(x)}{3 x^2 \log ^2(4)+\left (-6 x^2 \log (4)+6 x \log ^2(4)\right ) \log (x)+\left (3 x^2-6 x \log (4)+3 \log ^2(4)\right ) \log ^2(x)} \, dx=x \left (\frac {2}{3}+\frac {2 e^x x^2}{\log (x)-\frac {\log (4) (x+\log (x))}{x}}\right ) \]

[Out]

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

Rubi [F]

\[ \int \frac {2 x^2 \log ^2(4)+e^x \left (-6 x^4+\left (6 x^3-18 x^4-6 x^5\right ) \log (4)\right )+\left (-4 x^2 \log (4)+4 x \log ^2(4)+e^x \left (18 x^4+6 x^5+\left (-24 x^3-6 x^4\right ) \log (4)\right )\right ) \log (x)+\left (2 x^2-4 x \log (4)+2 \log ^2(4)\right ) \log ^2(x)}{3 x^2 \log ^2(4)+\left (-6 x^2 \log (4)+6 x \log ^2(4)\right ) \log (x)+\left (3 x^2-6 x \log (4)+3 \log ^2(4)\right ) \log ^2(x)} \, dx=\int \frac {2 x^2 \log ^2(4)+e^x \left (-6 x^4+\left (6 x^3-18 x^4-6 x^5\right ) \log (4)\right )+\left (-4 x^2 \log (4)+4 x \log ^2(4)+e^x \left (18 x^4+6 x^5+\left (-24 x^3-6 x^4\right ) \log (4)\right )\right ) \log (x)+\left (2 x^2-4 x \log (4)+2 \log ^2(4)\right ) \log ^2(x)}{3 x^2 \log ^2(4)+\left (-6 x^2 \log (4)+6 x \log ^2(4)\right ) \log (x)+\left (3 x^2-6 x \log (4)+3 \log ^2(4)\right ) \log ^2(x)} \, dx \]

[In]

Int[(2*x^2*Log[4]^2 + E^x*(-6*x^4 + (6*x^3 - 18*x^4 - 6*x^5)*Log[4]) + (-4*x^2*Log[4] + 4*x*Log[4]^2 + E^x*(18
*x^4 + 6*x^5 + (-24*x^3 - 6*x^4)*Log[4]))*Log[x] + (2*x^2 - 4*x*Log[4] + 2*Log[4]^2)*Log[x]^2)/(3*x^2*Log[4]^2
+ (-6*x^2*Log[4] + 6*x*Log[4]^2)*Log[x] + (3*x^2 - 6*x*Log[4] + 3*Log[4]^2)*Log[x]^2),x]

[Out]

(2*x)/3 - 2*Log[4]^5*Defer[Int][E^x/(x*Log[4] - x*Log[x] + Log[4]*Log[x])^2, x] - 2*Log[4]^4*Defer[Int][(E^x*x
)/(x*Log[4] - x*Log[x] + Log[4]*Log[x])^2, x] - 2*Log[4]^3*Defer[Int][(E^x*x^2)/(x*Log[4] - x*Log[x] + Log[4]*
Log[x])^2, x] + 2*(1 - Log[4])*Log[4]*Defer[Int][(E^x*x^3)/(x*Log[4] - x*Log[x] + Log[4]*Log[x])^2, x] - 2*Def
er[Int][(E^x*x^4)/(x*Log[4] - x*Log[x] + Log[4]*Log[x])^2, x] - 2*Log[4]^6*Defer[Int][E^x/((x - Log[4])*(x*Log
[4] - x*Log[x] + Log[4]*Log[x])^2), x] + 2*Log[4]^3*Defer[Int][E^x/(x*Log[4] - x*Log[x] + Log[4]*Log[x]), x] +
2*Log[4]^2*Defer[Int][(E^x*x)/(x*Log[4] - x*Log[x] + Log[4]*Log[x]), x] + 2*Log[4]*Defer[Int][(E^x*x^2)/(x*Lo
g[4] - x*Log[x] + Log[4]*Log[x]), x] - 6*Defer[Int][(E^x*x^3)/(x*Log[4] - x*Log[x] + Log[4]*Log[x]), x] - 2*De
fer[Int][(E^x*x^4)/(x*Log[4] - x*Log[x] + Log[4]*Log[x]), x] + 2*Log[4]^4*Defer[Int][E^x/((x - Log[4])*(x*Log[
4] - x*Log[x] + Log[4]*Log[x])), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {2 \left (x^2 \left (\log ^2(4)-3 e^x x \left (x-\log (4)+x^2 \log (4)+x \log (64)\right )\right )+x \left (2 \log (4) (-x+\log (4))+3 e^x x^2 \left (3 x+x^2-4 \log (4)-x \log (4)\right )\right ) \log (x)+(x-\log (4))^2 \log ^2(x)\right )}{3 (x \log (4)+(-x+\log (4)) \log (x))^2} \, dx \\ & = \frac {2}{3} \int \frac {x^2 \left (\log ^2(4)-3 e^x x \left (x-\log (4)+x^2 \log (4)+x \log (64)\right )\right )+x \left (2 \log (4) (-x+\log (4))+3 e^x x^2 \left (3 x+x^2-4 \log (4)-x \log (4)\right )\right ) \log (x)+(x-\log (4))^2 \log ^2(x)}{(x \log (4)+(-x+\log (4)) \log (x))^2} \, dx \\ & = \frac {2}{3} \int \left (1+\frac {3 e^x x^3 \left (\log (4)-x^2 \log (4)-x (1+\log (64))+x^2 \log (x)+3 x \left (1-\frac {2 \log (2)}{3}\right ) \log (x)-\log (256) \log (x)\right )}{(x \log (4)-x \log (x)+\log (4) \log (x))^2}\right ) \, dx \\ & = \frac {2 x}{3}+2 \int \frac {e^x x^3 \left (\log (4)-x^2 \log (4)-x (1+\log (64))+x^2 \log (x)+3 x \left (1-\frac {2 \log (2)}{3}\right ) \log (x)-\log (256) \log (x)\right )}{(x \log (4)-x \log (x)+\log (4) \log (x))^2} \, dx \\ & = \frac {2 x}{3}+2 \int \left (\frac {e^x x^3 \left (-x^2-\log ^2(4)-x \left (\log ^2(4)-\log (16)\right )\right )}{(x-\log (4)) (x \log (4)-x \log (x)+\log (4) \log (x))^2}+\frac {e^x x^3 \left (-x^2-x (3-\log (4))+\log (256)\right )}{(x-\log (4)) (x \log (4)-x \log (x)+\log (4) \log (x))}\right ) \, dx \\ & = \frac {2 x}{3}+2 \int \frac {e^x x^3 \left (-x^2-\log ^2(4)-x \left (\log ^2(4)-\log (16)\right )\right )}{(x-\log (4)) (x \log (4)-x \log (x)+\log (4) \log (x))^2} \, dx+2 \int \frac {e^x x^3 \left (-x^2-x (3-\log (4))+\log (256)\right )}{(x-\log (4)) (x \log (4)-x \log (x)+\log (4) \log (x))} \, dx \\ & = \frac {2 x}{3}+2 \int \left (-\frac {e^x x^4}{(x \log (4)-x \log (x)+\log (4) \log (x))^2}-\frac {e^x x^3 (-1+\log (4)) \log (4)}{(x \log (4)-x \log (x)+\log (4) \log (x))^2}-\frac {e^x x^2 \log ^3(4)}{(x \log (4)-x \log (x)+\log (4) \log (x))^2}-\frac {e^x x \log ^4(4)}{(x \log (4)-x \log (x)+\log (4) \log (x))^2}-\frac {e^x \log ^5(4)}{(x \log (4)-x \log (x)+\log (4) \log (x))^2}-\frac {e^x \log ^6(4)}{(x-\log (4)) (x \log (4)-x \log (x)+\log (4) \log (x))^2}\right ) \, dx+2 \int \left (-\frac {3 e^x x^3}{x \log (4)-x \log (x)+\log (4) \log (x)}-\frac {e^x x^4}{x \log (4)-x \log (x)+\log (4) \log (x)}+\frac {e^x x^2 \log (4)}{x \log (4)-x \log (x)+\log (4) \log (x)}+\frac {e^x x \log ^2(4)}{x \log (4)-x \log (x)+\log (4) \log (x)}+\frac {e^x \log ^3(4)}{x \log (4)-x \log (x)+\log (4) \log (x)}+\frac {e^x \log ^4(4)}{(x-\log (4)) (x \log (4)-x \log (x)+\log (4) \log (x))}\right ) \, dx \\ & = \frac {2 x}{3}-2 \int \frac {e^x x^4}{(x \log (4)-x \log (x)+\log (4) \log (x))^2} \, dx-2 \int \frac {e^x x^4}{x \log (4)-x \log (x)+\log (4) \log (x)} \, dx-6 \int \frac {e^x x^3}{x \log (4)-x \log (x)+\log (4) \log (x)} \, dx+(2 \log (4)) \int \frac {e^x x^2}{x \log (4)-x \log (x)+\log (4) \log (x)} \, dx+(2 (1-\log (4)) \log (4)) \int \frac {e^x x^3}{(x \log (4)-x \log (x)+\log (4) \log (x))^2} \, dx+\left (2 \log ^2(4)\right ) \int \frac {e^x x}{x \log (4)-x \log (x)+\log (4) \log (x)} \, dx-\left (2 \log ^3(4)\right ) \int \frac {e^x x^2}{(x \log (4)-x \log (x)+\log (4) \log (x))^2} \, dx+\left (2 \log ^3(4)\right ) \int \frac {e^x}{x \log (4)-x \log (x)+\log (4) \log (x)} \, dx-\left (2 \log ^4(4)\right ) \int \frac {e^x x}{(x \log (4)-x \log (x)+\log (4) \log (x))^2} \, dx+\left (2 \log ^4(4)\right ) \int \frac {e^x}{(x-\log (4)) (x \log (4)-x \log (x)+\log (4) \log (x))} \, dx-\left (2 \log ^5(4)\right ) \int \frac {e^x}{(x \log (4)-x \log (x)+\log (4) \log (x))^2} \, dx-\left (2 \log ^6(4)\right ) \int \frac {e^x}{(x-\log (4)) (x \log (4)-x \log (x)+\log (4) \log (x))^2} \, dx \\ \end{align*}

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(75\) vs. \(2(30)=60\).

Time = 0.28 (sec) , antiderivative size = 75, normalized size of antiderivative = 2.50 \[ \int \frac {2 x^2 \log ^2(4)+e^x \left (-6 x^4+\left (6 x^3-18 x^4-6 x^5\right ) \log (4)\right )+\left (-4 x^2 \log (4)+4 x \log ^2(4)+e^x \left (18 x^4+6 x^5+\left (-24 x^3-6 x^4\right ) \log (4)\right )\right ) \log (x)+\left (2 x^2-4 x \log (4)+2 \log ^2(4)\right ) \log ^2(x)}{3 x^2 \log ^2(4)+\left (-6 x^2 \log (4)+6 x \log ^2(4)\right ) \log (x)+\left (3 x^2-6 x \log (4)+3 \log ^2(4)\right ) \log ^2(x)} \, dx=\frac {2}{3} \left (x-\frac {3 e^x x^4 \left (x^2+\log ^2(4)+x \left (4 \log ^2(4)-\log (16)-\log (4) \log (64)\right )\right )}{\left (x^2+x (-2+\log (4)) \log (4)+\log ^2(4)\right ) (x \log (4)+(-x+\log (4)) \log (x))}\right ) \]

[In]

Integrate[(2*x^2*Log[4]^2 + E^x*(-6*x^4 + (6*x^3 - 18*x^4 - 6*x^5)*Log[4]) + (-4*x^2*Log[4] + 4*x*Log[4]^2 + E
^x*(18*x^4 + 6*x^5 + (-24*x^3 - 6*x^4)*Log[4]))*Log[x] + (2*x^2 - 4*x*Log[4] + 2*Log[4]^2)*Log[x]^2)/(3*x^2*Lo
g[4]^2 + (-6*x^2*Log[4] + 6*x*Log[4]^2)*Log[x] + (3*x^2 - 6*x*Log[4] + 3*Log[4]^2)*Log[x]^2),x]

[Out]

(2*(x - (3*E^x*x^4*(x^2 + Log[4]^2 + x*(4*Log[4]^2 - Log[16] - Log[4]*Log[64])))/((x^2 + x*(-2 + Log[4])*Log[4
] + Log[4]^2)*(x*Log[4] + (-x + Log[4])*Log[x]))))/3

Maple [A] (verified)

Time = 2.06 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.03

method	result	size
risch	\(\frac {2 x}{3}-\frac {2 x^{4} {\mathrm e}^{x}}{2 \ln \left (2\right ) \ln \left (x \right )-x \ln \left (x \right )+2 x \ln \left (2\right )}\)	\(31\)
parallelrisch	\(-\frac {6 \,{\mathrm e}^{x} x^{4}-8 x \ln \left (2\right )^{2}-8 \ln \left (2\right )^{2} \ln \left (x \right )-4 x^{2} \ln \left (2\right )+2 x^{2} \ln \left (x \right )}{3 \left (2 \ln \left (2\right ) \ln \left (x \right )-x \ln \left (x \right )+2 x \ln \left (2\right )\right )}\)	\(59\)

[In]

int(((8*ln(2)^2-8*x*ln(2)+2*x^2)*ln(x)^2+((2*(-6*x^4-24*x^3)*ln(2)+6*x^5+18*x^4)*exp(x)+16*x*ln(2)^2-8*x^2*ln(
2))*ln(x)+(2*(-6*x^5-18*x^4+6*x^3)*ln(2)-6*x^4)*exp(x)+8*x^2*ln(2)^2)/((12*ln(2)^2-12*x*ln(2)+3*x^2)*ln(x)^2+(
24*x*ln(2)^2-12*x^2*ln(2))*ln(x)+12*x^2*ln(2)^2),x,method=_RETURNVERBOSE)

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.57 \[ \int \frac {2 x^2 \log ^2(4)+e^x \left (-6 x^4+\left (6 x^3-18 x^4-6 x^5\right ) \log (4)\right )+\left (-4 x^2 \log (4)+4 x \log ^2(4)+e^x \left (18 x^4+6 x^5+\left (-24 x^3-6 x^4\right ) \log (4)\right )\right ) \log (x)+\left (2 x^2-4 x \log (4)+2 \log ^2(4)\right ) \log ^2(x)}{3 x^2 \log ^2(4)+\left (-6 x^2 \log (4)+6 x \log ^2(4)\right ) \log (x)+\left (3 x^2-6 x \log (4)+3 \log ^2(4)\right ) \log ^2(x)} \, dx=-\frac {2 \, {\left (3 \, x^{4} e^{x} - 2 \, x^{2} \log \left (2\right ) + {\left (x^{2} - 2 \, x \log \left (2\right )\right )} \log \left (x\right )\right )}}{3 \, {\left (2 \, x \log \left (2\right ) - {\left (x - 2 \, \log \left (2\right )\right )} \log \left (x\right )\right )}} \]

[In]

integrate(((8*log(2)^2-8*x*log(2)+2*x^2)*log(x)^2+((2*(-6*x^4-24*x^3)*log(2)+6*x^5+18*x^4)*exp(x)+16*x*log(2)^
2-8*x^2*log(2))*log(x)+(2*(-6*x^5-18*x^4+6*x^3)*log(2)-6*x^4)*exp(x)+8*x^2*log(2)^2)/((12*log(2)^2-12*x*log(2)
+3*x^2)*log(x)^2+(24*x*log(2)^2-12*x^2*log(2))*log(x)+12*x^2*log(2)^2),x, algorithm="fricas")

[Out]

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

Sympy [A] (verification not implemented)

Time = 0.15 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.07 \[ \int \frac {2 x^2 \log ^2(4)+e^x \left (-6 x^4+\left (6 x^3-18 x^4-6 x^5\right ) \log (4)\right )+\left (-4 x^2 \log (4)+4 x \log ^2(4)+e^x \left (18 x^4+6 x^5+\left (-24 x^3-6 x^4\right ) \log (4)\right )\right ) \log (x)+\left (2 x^2-4 x \log (4)+2 \log ^2(4)\right ) \log ^2(x)}{3 x^2 \log ^2(4)+\left (-6 x^2 \log (4)+6 x \log ^2(4)\right ) \log (x)+\left (3 x^2-6 x \log (4)+3 \log ^2(4)\right ) \log ^2(x)} \, dx=\frac {2 x^{4} e^{x}}{x \log {\left (x \right )} - 2 x \log {\left (2 \right )} - 2 \log {\left (2 \right )} \log {\left (x \right )}} + \frac {2 x}{3} \]

[In]

integrate(((8*ln(2)**2-8*x*ln(2)+2*x**2)*ln(x)**2+((2*(-6*x**4-24*x**3)*ln(2)+6*x**5+18*x**4)*exp(x)+16*x*ln(2
)**2-8*x**2*ln(2))*ln(x)+(2*(-6*x**5-18*x**4+6*x**3)*ln(2)-6*x**4)*exp(x)+8*x**2*ln(2)**2)/((12*ln(2)**2-12*x*
ln(2)+3*x**2)*ln(x)**2+(24*x*ln(2)**2-12*x**2*ln(2))*ln(x)+12*x**2*ln(2)**2),x)

[Out]

2*x**4*exp(x)/(x*log(x) - 2*x*log(2) - 2*log(2)*log(x)) + 2*x/3

Maxima [A] (verification not implemented)

none

Time = 0.31 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.57 \[ \int \frac {2 x^2 \log ^2(4)+e^x \left (-6 x^4+\left (6 x^3-18 x^4-6 x^5\right ) \log (4)\right )+\left (-4 x^2 \log (4)+4 x \log ^2(4)+e^x \left (18 x^4+6 x^5+\left (-24 x^3-6 x^4\right ) \log (4)\right )\right ) \log (x)+\left (2 x^2-4 x \log (4)+2 \log ^2(4)\right ) \log ^2(x)}{3 x^2 \log ^2(4)+\left (-6 x^2 \log (4)+6 x \log ^2(4)\right ) \log (x)+\left (3 x^2-6 x \log (4)+3 \log ^2(4)\right ) \log ^2(x)} \, dx=-\frac {2 \, {\left (3 \, x^{4} e^{x} - 2 \, x^{2} \log \left (2\right ) + {\left (x^{2} - 2 \, x \log \left (2\right )\right )} \log \left (x\right )\right )}}{3 \, {\left (2 \, x \log \left (2\right ) - {\left (x - 2 \, \log \left (2\right )\right )} \log \left (x\right )\right )}} \]

[In]

integrate(((8*log(2)^2-8*x*log(2)+2*x^2)*log(x)^2+((2*(-6*x^4-24*x^3)*log(2)+6*x^5+18*x^4)*exp(x)+16*x*log(2)^
2-8*x^2*log(2))*log(x)+(2*(-6*x^5-18*x^4+6*x^3)*log(2)-6*x^4)*exp(x)+8*x^2*log(2)^2)/((12*log(2)^2-12*x*log(2)
+3*x^2)*log(x)^2+(24*x*log(2)^2-12*x^2*log(2))*log(x)+12*x^2*log(2)^2),x, algorithm="maxima")

[Out]

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

Giac [A] (verification not implemented)

none

Time = 0.31 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.63 \[ \int \frac {2 x^2 \log ^2(4)+e^x \left (-6 x^4+\left (6 x^3-18 x^4-6 x^5\right ) \log (4)\right )+\left (-4 x^2 \log (4)+4 x \log ^2(4)+e^x \left (18 x^4+6 x^5+\left (-24 x^3-6 x^4\right ) \log (4)\right )\right ) \log (x)+\left (2 x^2-4 x \log (4)+2 \log ^2(4)\right ) \log ^2(x)}{3 x^2 \log ^2(4)+\left (-6 x^2 \log (4)+6 x \log ^2(4)\right ) \log (x)+\left (3 x^2-6 x \log (4)+3 \log ^2(4)\right ) \log ^2(x)} \, dx=-\frac {2 \, {\left (3 \, x^{4} e^{x} - 2 \, x^{2} \log \left (2\right ) + x^{2} \log \left (x\right ) - 2 \, x \log \left (2\right ) \log \left (x\right )\right )}}{3 \, {\left (2 \, x \log \left (2\right ) - x \log \left (x\right ) + 2 \, \log \left (2\right ) \log \left (x\right )\right )}} \]

[In]

integrate(((8*log(2)^2-8*x*log(2)+2*x^2)*log(x)^2+((2*(-6*x^4-24*x^3)*log(2)+6*x^5+18*x^4)*exp(x)+16*x*log(2)^
2-8*x^2*log(2))*log(x)+(2*(-6*x^5-18*x^4+6*x^3)*log(2)-6*x^4)*exp(x)+8*x^2*log(2)^2)/((12*log(2)^2-12*x*log(2)
+3*x^2)*log(x)^2+(24*x*log(2)^2-12*x^2*log(2))*log(x)+12*x^2*log(2)^2),x, algorithm="giac")

[Out]

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

Mupad [F(-1)]

Timed out. \[ \int \frac {2 x^2 \log ^2(4)+e^x \left (-6 x^4+\left (6 x^3-18 x^4-6 x^5\right ) \log (4)\right )+\left (-4 x^2 \log (4)+4 x \log ^2(4)+e^x \left (18 x^4+6 x^5+\left (-24 x^3-6 x^4\right ) \log (4)\right )\right ) \log (x)+\left (2 x^2-4 x \log (4)+2 \log ^2(4)\right ) \log ^2(x)}{3 x^2 \log ^2(4)+\left (-6 x^2 \log (4)+6 x \log ^2(4)\right ) \log (x)+\left (3 x^2-6 x \log (4)+3 \log ^2(4)\right ) \log ^2(x)} \, dx=\int \frac {8\,x^2\,{\ln \left (2\right )}^2+\ln \left (x\right )\,\left ({\mathrm {e}}^x\,\left (18\,x^4-2\,\ln \left (2\right )\,\left (6\,x^4+24\,x^3\right )+6\,x^5\right )+16\,x\,{\ln \left (2\right )}^2-8\,x^2\,\ln \left (2\right )\right )-{\mathrm {e}}^x\,\left (2\,\ln \left (2\right )\,\left (6\,x^5+18\,x^4-6\,x^3\right )+6\,x^4\right )+{\ln \left (x\right )}^2\,\left (2\,x^2-8\,\ln \left (2\right )\,x+8\,{\ln \left (2\right )}^2\right )}{12\,x^2\,{\ln \left (2\right )}^2+{\ln \left (x\right )}^2\,\left (3\,x^2-12\,\ln \left (2\right )\,x+12\,{\ln \left (2\right )}^2\right )+\ln \left (x\right )\,\left (24\,x\,{\ln \left (2\right )}^2-12\,x^2\,\ln \left (2\right )\right )} \,d x \]

[In]

int((8*x^2*log(2)^2 + log(x)*(exp(x)*(18*x^4 - 2*log(2)*(24*x^3 + 6*x^4) + 6*x^5) + 16*x*log(2)^2 - 8*x^2*log(
2)) - exp(x)*(2*log(2)*(18*x^4 - 6*x^3 + 6*x^5) + 6*x^4) + log(x)^2*(8*log(2)^2 - 8*x*log(2) + 2*x^2))/(12*x^2
*log(2)^2 + log(x)^2*(12*log(2)^2 - 12*x*log(2) + 3*x^2) + log(x)*(24*x*log(2)^2 - 12*x^2*log(2))),x)

[Out]

int((8*x^2*log(2)^2 + log(x)*(exp(x)*(18*x^4 - 2*log(2)*(24*x^3 + 6*x^4) + 6*x^5) + 16*x*log(2)^2 - 8*x^2*log(
2)) - exp(x)*(2*log(2)*(18*x^4 - 6*x^3 + 6*x^5) + 6*x^4) + log(x)^2*(8*log(2)^2 - 8*x*log(2) + 2*x^2))/(12*x^2
*log(2)^2 + log(x)^2*(12*log(2)^2 - 12*x*log(2) + 3*x^2) + log(x)*(24*x*log(2)^2 - 12*x^2*log(2))), x)