\(\int \frac {(4-12 x) \log (4)+x^{x^2} ((2-8 x^2) \log (4)-16 x^2 \log (4) \log (x))}{32+160 x+320 x^2+320 x^3+160 x^4+32 x^5+x^{5 x^2}+x^{4 x^2} (10+10 x)+x^{3 x^2} (40+80 x+40 x^2)+x^{2 x^2} (80+240 x+240 x^2+80 x^3)+x^{x^2} (80+320 x+480 x^2+320 x^3+80 x^4)} \, dx\) [641]

Optimal result

Integrand size = 150, antiderivative size = 17 \[ \int \frac {(4-12 x) \log (4)+x^{x^2} \left (\left (2-8 x^2\right ) \log (4)-16 x^2 \log (4) \log (x)\right )}{32+160 x+320 x^2+320 x^3+160 x^4+32 x^5+x^{5 x^2}+x^{4 x^2} (10+10 x)+x^{3 x^2} \left (40+80 x+40 x^2\right )+x^{2 x^2} \left (80+240 x+240 x^2+80 x^3\right )+x^{x^2} \left (80+320 x+480 x^2+320 x^3+80 x^4\right )} \, dx=\frac {2 x \log (4)}{\left (2+2 x+x^{x^2}\right )^4} \]

[Out]

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

Rubi [F]

\[ \int \frac {(4-12 x) \log (4)+x^{x^2} \left (\left (2-8 x^2\right ) \log (4)-16 x^2 \log (4) \log (x)\right )}{32+160 x+320 x^2+320 x^3+160 x^4+32 x^5+x^{5 x^2}+x^{4 x^2} (10+10 x)+x^{3 x^2} \left (40+80 x+40 x^2\right )+x^{2 x^2} \left (80+240 x+240 x^2+80 x^3\right )+x^{x^2} \left (80+320 x+480 x^2+320 x^3+80 x^4\right )} \, dx=\int \frac {(4-12 x) \log (4)+x^{x^2} \left (\left (2-8 x^2\right ) \log (4)-16 x^2 \log (4) \log (x)\right )}{32+160 x+320 x^2+320 x^3+160 x^4+32 x^5+x^{5 x^2}+x^{4 x^2} (10+10 x)+x^{3 x^2} \left (40+80 x+40 x^2\right )+x^{2 x^2} \left (80+240 x+240 x^2+80 x^3\right )+x^{x^2} \left (80+320 x+480 x^2+320 x^3+80 x^4\right )} \, dx \]

[In]

Int[((4 - 12*x)*Log[4] + x^x^2*((2 - 8*x^2)*Log[4] - 16*x^2*Log[4]*Log[x]))/(32 + 160*x + 320*x^2 + 320*x^3 +
160*x^4 + 32*x^5 + x^(5*x^2) + x^(4*x^2)*(10 + 10*x) + x^(3*x^2)*(40 + 80*x + 40*x^2) + x^(2*x^2)*(80 + 240*x
+ 240*x^2 + 80*x^3) + x^x^2*(80 + 320*x + 480*x^2 + 320*x^3 + 80*x^4)),x]

[Out]

-16*Log[4]*Defer[Int][x/(2 + 2*x + x^x^2)^5, x] + 16*Log[4]*Defer[Int][x^2/(2 + 2*x + x^x^2)^5, x] + 32*Log[4]
*Log[x]*Defer[Int][x^2/(2 + 2*x + x^x^2)^5, x] + 16*Log[4]*Defer[Int][x^3/(2 + 2*x + x^x^2)^5, x] + 32*Log[4]*
Log[x]*Defer[Int][x^3/(2 + 2*x + x^x^2)^5, x] + 2*Log[4]*Defer[Int][(2 + 2*x + x^x^2)^(-4), x] - 8*Log[4]*Defe
r[Int][x^2/(2 + 2*x + x^x^2)^4, x] - 16*Log[4]*Log[x]*Defer[Int][x^2/(2 + 2*x + x^x^2)^4, x] - 32*Log[4]*Defer
[Int][Defer[Int][x^2/(2 + 2*x + x^x^2)^5, x]/x, x] - 32*Log[4]*Defer[Int][Defer[Int][x^3/(2 + 2*x + x^x^2)^5,
x]/x, x] + 16*Log[4]*Defer[Int][Defer[Int][x^2/(2 + 2*x + x^x^2)^4, x]/x, x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {2 \log (4) \left (2-6 x+x^{x^2}-4 x^{2+x^2}-8 x^{2+x^2} \log (x)\right )}{\left (2+2 x+x^{x^2}\right )^5} \, dx \\ & = (2 \log (4)) \int \frac {2-6 x+x^{x^2}-4 x^{2+x^2}-8 x^{2+x^2} \log (x)}{\left (2+2 x+x^{x^2}\right )^5} \, dx \\ & = (2 \log (4)) \int \left (\frac {8 x \left (-1+x+x^2+2 x \log (x)+2 x^2 \log (x)\right )}{\left (2+2 x+x^{x^2}\right )^5}-\frac {-1+4 x^2+8 x^2 \log (x)}{\left (2+2 x+x^{x^2}\right )^4}\right ) \, dx \\ & = -\left ((2 \log (4)) \int \frac {-1+4 x^2+8 x^2 \log (x)}{\left (2+2 x+x^{x^2}\right )^4} \, dx\right )+(16 \log (4)) \int \frac {x \left (-1+x+x^2+2 x \log (x)+2 x^2 \log (x)\right )}{\left (2+2 x+x^{x^2}\right )^5} \, dx \\ & = -\left ((2 \log (4)) \int \left (-\frac {1}{\left (2+2 x+x^{x^2}\right )^4}+\frac {4 x^2}{\left (2+2 x+x^{x^2}\right )^4}+\frac {8 x^2 \log (x)}{\left (2+2 x+x^{x^2}\right )^4}\right ) \, dx\right )+(16 \log (4)) \int \left (-\frac {x}{\left (2+2 x+x^{x^2}\right )^5}+\frac {x^2}{\left (2+2 x+x^{x^2}\right )^5}+\frac {x^3}{\left (2+2 x+x^{x^2}\right )^5}+\frac {2 x^2 \log (x)}{\left (2+2 x+x^{x^2}\right )^5}+\frac {2 x^3 \log (x)}{\left (2+2 x+x^{x^2}\right )^5}\right ) \, dx \\ & = (2 \log (4)) \int \frac {1}{\left (2+2 x+x^{x^2}\right )^4} \, dx-(8 \log (4)) \int \frac {x^2}{\left (2+2 x+x^{x^2}\right )^4} \, dx-(16 \log (4)) \int \frac {x}{\left (2+2 x+x^{x^2}\right )^5} \, dx+(16 \log (4)) \int \frac {x^2}{\left (2+2 x+x^{x^2}\right )^5} \, dx+(16 \log (4)) \int \frac {x^3}{\left (2+2 x+x^{x^2}\right )^5} \, dx-(16 \log (4)) \int \frac {x^2 \log (x)}{\left (2+2 x+x^{x^2}\right )^4} \, dx+(32 \log (4)) \int \frac {x^2 \log (x)}{\left (2+2 x+x^{x^2}\right )^5} \, dx+(32 \log (4)) \int \frac {x^3 \log (x)}{\left (2+2 x+x^{x^2}\right )^5} \, dx \\ & = (2 \log (4)) \int \frac {1}{\left (2+2 x+x^{x^2}\right )^4} \, dx-(8 \log (4)) \int \frac {x^2}{\left (2+2 x+x^{x^2}\right )^4} \, dx-(16 \log (4)) \int \frac {x}{\left (2+2 x+x^{x^2}\right )^5} \, dx+(16 \log (4)) \int \frac {x^2}{\left (2+2 x+x^{x^2}\right )^5} \, dx+(16 \log (4)) \int \frac {x^3}{\left (2+2 x+x^{x^2}\right )^5} \, dx+(16 \log (4)) \int \frac {\int \frac {x^2}{\left (2+2 x+x^{x^2}\right )^4} \, dx}{x} \, dx-(32 \log (4)) \int \frac {\int \frac {x^2}{\left (2+2 x+x^{x^2}\right )^5} \, dx}{x} \, dx-(32 \log (4)) \int \frac {\int \frac {x^3}{\left (2+2 x+x^{x^2}\right )^5} \, dx}{x} \, dx-(16 \log (4) \log (x)) \int \frac {x^2}{\left (2+2 x+x^{x^2}\right )^4} \, dx+(32 \log (4) \log (x)) \int \frac {x^2}{\left (2+2 x+x^{x^2}\right )^5} \, dx+(32 \log (4) \log (x)) \int \frac {x^3}{\left (2+2 x+x^{x^2}\right )^5} \, dx \\ \end{align*}

Mathematica [A] (verified)

Time = 0.16 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00 \[ \int \frac {(4-12 x) \log (4)+x^{x^2} \left (\left (2-8 x^2\right ) \log (4)-16 x^2 \log (4) \log (x)\right )}{32+160 x+320 x^2+320 x^3+160 x^4+32 x^5+x^{5 x^2}+x^{4 x^2} (10+10 x)+x^{3 x^2} \left (40+80 x+40 x^2\right )+x^{2 x^2} \left (80+240 x+240 x^2+80 x^3\right )+x^{x^2} \left (80+320 x+480 x^2+320 x^3+80 x^4\right )} \, dx=\frac {2 x \log (4)}{\left (2+2 x+x^{x^2}\right )^4} \]

[In]

Integrate[((4 - 12*x)*Log[4] + x^x^2*((2 - 8*x^2)*Log[4] - 16*x^2*Log[4]*Log[x]))/(32 + 160*x + 320*x^2 + 320*
x^3 + 160*x^4 + 32*x^5 + x^(5*x^2) + x^(4*x^2)*(10 + 10*x) + x^(3*x^2)*(40 + 80*x + 40*x^2) + x^(2*x^2)*(80 +
240*x + 240*x^2 + 80*x^3) + x^x^2*(80 + 320*x + 480*x^2 + 320*x^3 + 80*x^4)),x]

[Out]

(2*x*Log[4])/(2 + 2*x + x^x^2)^4

Maple [A] (verified)

Time = 0.65 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.06

method	result	size
risch	\(\frac {4 x \ln \left (2\right )}{\left (2 x +2+x^{x^{2}}\right )^{4}}\)	\(18\)
parallelrisch	\(\frac {4 x \ln \left (2\right )}{16 x^{4}+32 \,{\mathrm e}^{x^{2} \ln \left (x \right )} x^{3}+24 \,{\mathrm e}^{2 x^{2} \ln \left (x \right )} x^{2}+8 \,{\mathrm e}^{3 x^{2} \ln \left (x \right )} x +{\mathrm e}^{4 x^{2} \ln \left (x \right )}+64 x^{3}+96 \,{\mathrm e}^{x^{2} \ln \left (x \right )} x^{2}+48 \,{\mathrm e}^{2 x^{2} \ln \left (x \right )} x +8 \,{\mathrm e}^{3 x^{2} \ln \left (x \right )}+96 x^{2}+96 \,{\mathrm e}^{x^{2} \ln \left (x \right )} x +24 \,{\mathrm e}^{2 x^{2} \ln \left (x \right )}+64 x +32 \,{\mathrm e}^{x^{2} \ln \left (x \right )}+16}\)	\(140\)

[In]

int(((-32*x^2*ln(2)*ln(x)+2*(-8*x^2+2)*ln(2))*exp(x^2*ln(x))+2*(-12*x+4)*ln(2))/(exp(x^2*ln(x))^5+(10*x+10)*ex
p(x^2*ln(x))^4+(40*x^2+80*x+40)*exp(x^2*ln(x))^3+(80*x^3+240*x^2+240*x+80)*exp(x^2*ln(x))^2+(80*x^4+320*x^3+48
0*x^2+320*x+80)*exp(x^2*ln(x))+32*x^5+160*x^4+320*x^3+320*x^2+160*x+32),x,method=_RETURNVERBOSE)

[Out]

4*x*ln(2)/(2*x+2+x^(x^2))^4

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 83 vs. \(2 (17) = 34\).

Time = 0.26 (sec) , antiderivative size = 83, normalized size of antiderivative = 4.88 \[ \int \frac {(4-12 x) \log (4)+x^{x^2} \left (\left (2-8 x^2\right ) \log (4)-16 x^2 \log (4) \log (x)\right )}{32+160 x+320 x^2+320 x^3+160 x^4+32 x^5+x^{5 x^2}+x^{4 x^2} (10+10 x)+x^{3 x^2} \left (40+80 x+40 x^2\right )+x^{2 x^2} \left (80+240 x+240 x^2+80 x^3\right )+x^{x^2} \left (80+320 x+480 x^2+320 x^3+80 x^4\right )} \, dx=\frac {4 \, x \log \left (2\right )}{16 \, x^{4} + 64 \, x^{3} + 8 \, {\left (x + 1\right )} x^{3 \, x^{2}} + 24 \, {\left (x^{2} + 2 \, x + 1\right )} x^{2 \, x^{2}} + 32 \, {\left (x^{3} + 3 \, x^{2} + 3 \, x + 1\right )} x^{\left (x^{2}\right )} + 96 \, x^{2} + 64 \, x + x^{4 \, x^{2}} + 16} \]

[In]

integrate(((-32*x^2*log(2)*log(x)+2*(-8*x^2+2)*log(2))*exp(x^2*log(x))+2*(-12*x+4)*log(2))/(exp(x^2*log(x))^5+
(10*x+10)*exp(x^2*log(x))^4+(40*x^2+80*x+40)*exp(x^2*log(x))^3+(80*x^3+240*x^2+240*x+80)*exp(x^2*log(x))^2+(80
*x^4+320*x^3+480*x^2+320*x+80)*exp(x^2*log(x))+32*x^5+160*x^4+320*x^3+320*x^2+160*x+32),x, algorithm="fricas")

[Out]

4*x*log(2)/(16*x^4 + 64*x^3 + 8*(x + 1)*x^(3*x^2) + 24*(x^2 + 2*x + 1)*x^(2*x^2) + 32*(x^3 + 3*x^2 + 3*x + 1)*
x^(x^2) + 96*x^2 + 64*x + x^(4*x^2) + 16)

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 95 vs. \(2 (20) = 40\).

Time = 0.17 (sec) , antiderivative size = 95, normalized size of antiderivative = 5.59 \[ \int \frac {(4-12 x) \log (4)+x^{x^2} \left (\left (2-8 x^2\right ) \log (4)-16 x^2 \log (4) \log (x)\right )}{32+160 x+320 x^2+320 x^3+160 x^4+32 x^5+x^{5 x^2}+x^{4 x^2} (10+10 x)+x^{3 x^2} \left (40+80 x+40 x^2\right )+x^{2 x^2} \left (80+240 x+240 x^2+80 x^3\right )+x^{x^2} \left (80+320 x+480 x^2+320 x^3+80 x^4\right )} \, dx=\frac {4 x \log {\left (2 \right )}}{16 x^{4} + 64 x^{3} + 96 x^{2} + 64 x + \left (8 x + 8\right ) e^{3 x^{2} \log {\left (x \right )}} + \left (24 x^{2} + 48 x + 24\right ) e^{2 x^{2} \log {\left (x \right )}} + \left (32 x^{3} + 96 x^{2} + 96 x + 32\right ) e^{x^{2} \log {\left (x \right )}} + e^{4 x^{2} \log {\left (x \right )}} + 16} \]

[In]

integrate(((-32*x**2*ln(2)*ln(x)+2*(-8*x**2+2)*ln(2))*exp(x**2*ln(x))+2*(-12*x+4)*ln(2))/(exp(x**2*ln(x))**5+(
10*x+10)*exp(x**2*ln(x))**4+(40*x**2+80*x+40)*exp(x**2*ln(x))**3+(80*x**3+240*x**2+240*x+80)*exp(x**2*ln(x))**
2+(80*x**4+320*x**3+480*x**2+320*x+80)*exp(x**2*ln(x))+32*x**5+160*x**4+320*x**3+320*x**2+160*x+32),x)

[Out]

4*x*log(2)/(16*x**4 + 64*x**3 + 96*x**2 + 64*x + (8*x + 8)*exp(3*x**2*log(x)) + (24*x**2 + 48*x + 24)*exp(2*x*
*2*log(x)) + (32*x**3 + 96*x**2 + 96*x + 32)*exp(x**2*log(x)) + exp(4*x**2*log(x)) + 16)

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 83 vs. \(2 (17) = 34\).

Time = 0.61 (sec) , antiderivative size = 83, normalized size of antiderivative = 4.88 \[ \int \frac {(4-12 x) \log (4)+x^{x^2} \left (\left (2-8 x^2\right ) \log (4)-16 x^2 \log (4) \log (x)\right )}{32+160 x+320 x^2+320 x^3+160 x^4+32 x^5+x^{5 x^2}+x^{4 x^2} (10+10 x)+x^{3 x^2} \left (40+80 x+40 x^2\right )+x^{2 x^2} \left (80+240 x+240 x^2+80 x^3\right )+x^{x^2} \left (80+320 x+480 x^2+320 x^3+80 x^4\right )} \, dx=\frac {4 \, x \log \left (2\right )}{16 \, x^{4} + 64 \, x^{3} + 8 \, {\left (x + 1\right )} x^{3 \, x^{2}} + 24 \, {\left (x^{2} + 2 \, x + 1\right )} x^{2 \, x^{2}} + 32 \, {\left (x^{3} + 3 \, x^{2} + 3 \, x + 1\right )} x^{\left (x^{2}\right )} + 96 \, x^{2} + 64 \, x + x^{4 \, x^{2}} + 16} \]

[In]

integrate(((-32*x^2*log(2)*log(x)+2*(-8*x^2+2)*log(2))*exp(x^2*log(x))+2*(-12*x+4)*log(2))/(exp(x^2*log(x))^5+
(10*x+10)*exp(x^2*log(x))^4+(40*x^2+80*x+40)*exp(x^2*log(x))^3+(80*x^3+240*x^2+240*x+80)*exp(x^2*log(x))^2+(80
*x^4+320*x^3+480*x^2+320*x+80)*exp(x^2*log(x))+32*x^5+160*x^4+320*x^3+320*x^2+160*x+32),x, algorithm="maxima")

[Out]

4*x*log(2)/(16*x^4 + 64*x^3 + 8*(x + 1)*x^(3*x^2) + 24*(x^2 + 2*x + 1)*x^(2*x^2) + 32*(x^3 + 3*x^2 + 3*x + 1)*
x^(x^2) + 96*x^2 + 64*x + x^(4*x^2) + 16)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 7896 vs. \(2 (17) = 34\).

Time = 3.14 (sec) , antiderivative size = 7896, normalized size of antiderivative = 464.47 \[ \int \frac {(4-12 x) \log (4)+x^{x^2} \left (\left (2-8 x^2\right ) \log (4)-16 x^2 \log (4) \log (x)\right )}{32+160 x+320 x^2+320 x^3+160 x^4+32 x^5+x^{5 x^2}+x^{4 x^2} (10+10 x)+x^{3 x^2} \left (40+80 x+40 x^2\right )+x^{2 x^2} \left (80+240 x+240 x^2+80 x^3\right )+x^{x^2} \left (80+320 x+480 x^2+320 x^3+80 x^4\right )} \, dx=\text {Too large to display} \]

[In]

integrate(((-32*x^2*log(2)*log(x)+2*(-8*x^2+2)*log(2))*exp(x^2*log(x))+2*(-12*x+4)*log(2))/(exp(x^2*log(x))^5+
(10*x+10)*exp(x^2*log(x))^4+(40*x^2+80*x+40)*exp(x^2*log(x))^3+(80*x^3+240*x^2+240*x+80)*exp(x^2*log(x))^2+(80
*x^4+320*x^3+480*x^2+320*x+80)*exp(x^2*log(x))+32*x^5+160*x^4+320*x^3+320*x^2+160*x+32),x, algorithm="giac")

[Out]

4*(128*x^34*log(2)*log(x)^7 + 448*x^34*log(2)*log(x)^6 + 896*x^33*log(2)*log(x)^7 + 672*x^34*log(2)*log(x)^5 +
3136*x^33*log(2)*log(x)^6 + 2688*x^32*log(2)*log(x)^7 + 560*x^34*log(2)*log(x)^4 + 4704*x^33*log(2)*log(x)^5
+ 8960*x^32*log(2)*log(x)^6 + 4480*x^31*log(2)*log(x)^7 + 280*x^34*log(2)*log(x)^3 + 3920*x^33*log(2)*log(x)^4
+ 12768*x^32*log(2)*log(x)^5 + 12992*x^31*log(2)*log(x)^6 + 4480*x^30*log(2)*log(x)^7 + 84*x^34*log(2)*log(x)
^2 + 1960*x^33*log(2)*log(x)^3 + 10080*x^32*log(2)*log(x)^4 + 15456*x^31*log(2)*log(x)^5 + 8960*x^30*log(2)*lo
g(x)^6 + 2688*x^29*log(2)*log(x)^7 + 14*x^34*log(2)*log(x) + 588*x^33*log(2)*log(x)^2 + 4760*x^32*log(2)*log(x
)^3 + 9520*x^31*log(2)*log(x)^4 + 4032*x^30*log(2)*log(x)^5 + 448*x^29*log(2)*log(x)^6 + 896*x^28*log(2)*log(x
)^7 + x^34*log(2) + 98*x^33*log(2)*log(x) + 1344*x^32*log(2)*log(x)^2 + 3080*x^31*log(2)*log(x)^3 - 3920*x^30*
log(2)*log(x)^4 - 9408*x^29*log(2)*log(x)^5 - 3584*x^28*log(2)*log(x)^6 + 128*x^27*log(2)*log(x)^7 + 7*x^33*lo
g(2) + 210*x^32*log(2)*log(x) + 420*x^31*log(2)*log(x)^2 - 5320*x^30*log(2)*log(x)^3 - 13440*x^29*log(2)*log(x
)^4 - 8736*x^28*log(2)*log(x)^5 - 2240*x^27*log(2)*log(x)^6 + 14*x^32*log(2) - 14*x^31*log(2)*log(x) - 2520*x^
30*log(2)*log(x)^2 - 8120*x^29*log(2)*log(x)^3 - 5040*x^28*log(2)*log(x)^4 - 672*x^27*log(2)*log(x)^5 - 448*x^
26*log(2)*log(x)^6 - 7*x^31*log(2) - 560*x^30*log(2)*log(x) - 2436*x^29*log(2)*log(x)^2 + 840*x^28*log(2)*log(
x)^3 + 5040*x^27*log(2)*log(x)^4 + 2016*x^26*log(2)*log(x)^5 - 49*x^30*log(2) - 336*x^29*log(2)*log(x) + 1848*
x^28*log(2)*log(x)^2 + 5880*x^27*log(2)*log(x)^3 + 3360*x^26*log(2)*log(x)^4 + 672*x^25*log(2)*log(x)^5 - 14*x
^29*log(2) + 658*x^28*log(2)*log(x) + 2604*x^27*log(2)*log(x)^2 + 840*x^26*log(2)*log(x)^3 - 560*x^25*log(2)*l
og(x)^4 + 77*x^28*log(2) + 490*x^27*log(2)*log(x) - 840*x^26*log(2)*log(x)^2 - 1960*x^25*log(2)*log(x)^3 - 560
*x^24*log(2)*log(x)^4 + 29*x^27*log(2) - 504*x^26*log(2)*log(x) - 1260*x^25*log(2)*log(x)^2 - 280*x^24*log(2)*
log(x)^3 - 77*x^26*log(2) - 280*x^25*log(2)*log(x) + 336*x^24*log(2)*log(x)^2 + 280*x^23*log(2)*log(x)^3 - 14*
x^25*log(2) + 266*x^24*log(2)*log(x) + 252*x^23*log(2)*log(x)^2 + 49*x^24*log(2) + 42*x^23*log(2)*log(x) - 84*
x^22*log(2)*log(x)^2 - 7*x^23*log(2) - 70*x^22*log(2)*log(x) - 14*x^22*log(2) + 14*x^21*log(2)*log(x) + 7*x^21
*log(2) - x^20*log(2))/(4096*x^36*x^(x^2)*log(x)^7 + 2048*x^37*log(x)^7 + 14336*x^36*x^(x^2)*log(x)^6 + 7168*x
^37*log(x)^6 + 3072*x^35*x^(2*x^2)*log(x)^7 + 40960*x^35*x^(x^2)*log(x)^7 + 22528*x^36*log(x)^7 + 21504*x^36*x
^(x^2)*log(x)^5 + 10752*x^37*log(x)^5 + 10752*x^35*x^(2*x^2)*log(x)^6 + 143360*x^35*x^(x^2)*log(x)^6 + 78848*x
^36*log(x)^6 + 1024*x^34*x^(3*x^2)*log(x)^7 + 27648*x^34*x^(2*x^2)*log(x)^7 + 184320*x^34*x^(x^2)*log(x)^7 + 1
12640*x^35*log(x)^7 + 17920*x^36*x^(x^2)*log(x)^4 + 8960*x^37*log(x)^4 + 16128*x^35*x^(2*x^2)*log(x)^5 + 21504
0*x^35*x^(x^2)*log(x)^5 + 118272*x^36*log(x)^5 + 3584*x^34*x^(3*x^2)*log(x)^6 + 96768*x^34*x^(2*x^2)*log(x)^6
+ 630784*x^34*x^(x^2)*log(x)^6 + 387072*x^35*log(x)^6 + 128*x^33*x^(4*x^2)*log(x)^7 + 8192*x^33*x^(3*x^2)*log(
x)^7 + 110592*x^33*x^(2*x^2)*log(x)^7 + 491520*x^33*x^(x^2)*log(x)^7 + 337920*x^34*log(x)^7 + 8960*x^36*x^(x^2
)*log(x)^3 + 4480*x^37*log(x)^3 + 13440*x^35*x^(2*x^2)*log(x)^4 + 179200*x^35*x^(x^2)*log(x)^4 + 98560*x^36*lo
g(x)^4 + 5376*x^34*x^(3*x^2)*log(x)^5 + 145152*x^34*x^(2*x^2)*log(x)^5 + 924672*x^34*x^(x^2)*log(x)^5 + 569856
*x^35*log(x)^5 + 448*x^33*x^(4*x^2)*log(x)^6 + 28672*x^33*x^(3*x^2)*log(x)^6 + 376320*x^33*x^(2*x^2)*log(x)^6
+ 1591296*x^33*x^(x^2)*log(x)^6 + 1111040*x^34*log(x)^6 + 896*x^32*x^(4*x^2)*log(x)^7 + 28672*x^32*x^(3*x^2)*l
og(x)^7 + 258048*x^32*x^(2*x^2)*log(x)^7 + 860160*x^32*x^(x^2)*log(x)^7 + 675840*x^33*log(x)^7 + 2688*x^36*x^(
x^2)*log(x)^2 + 1344*x^37*log(x)^2 + 6720*x^35*x^(2*x^2)*log(x)^3 + 89600*x^35*x^(x^2)*log(x)^3 + 49280*x^36*l
og(x)^3 + 4480*x^34*x^(3*x^2)*log(x)^4 + 120960*x^34*x^(2*x^2)*log(x)^4 + 752640*x^34*x^(x^2)*log(x)^4 + 46592
0*x^35*log(x)^4 + 672*x^33*x^(4*x^2)*log(x)^5 + 43008*x^33*x^(3*x^2)*log(x)^5 + 548352*x^33*x^(2*x^2)*log(x)^5
+ 2193408*x^33*x^(x^2)*log(x)^5 + 1559040*x^34*log(x)^5 + 3136*x^32*x^(4*x^2)*log(x)^6 + 96768*x^32*x^(3*x^2)
*log(x)^6 + 817152*x^32*x^(2*x^2)*log(x)^6 + 2494464*x^32*x^(x^2)*log(x)^6 + 2042880*x^33*log(x)^6 + 2688*x^31
*x^(4*x^2)*log(x)^7 + 57344*x^31*x^(3*x^2)*log(x)^7 + 387072*x^31*x^(2*x^2)*log(x)^7 + 1032192*x^31*x^(x^2)*lo
g(x)^7 + 946176*x^32*log(x)^7 + 448*x^36*x^(x^2)*log(x) + 224*x^37*log(x) + 2016*x^35*x^(2*x^2)*log(x)^2 + 268
80*x^35*x^(x^2)*log(x)^2 + 14784*x^36*log(x)^2 + 2240*x^34*x^(3*x^2)*log(x)^3 + 60480*x^34*x^(2*x^2)*log(x)^3
+ 367360*x^34*x^(x^2)*log(x)^3 + 228480*x^35*log(x)^3 + 560*x^33*x^(4*x^2)*log(x)^4 + 35840*x^33*x^(3*x^2)*log
(x)^4 + 443520*x^33*x^(2*x^2)*log(x)^4 + 1666560*x^33*x^(x^2)*log(x)^4 + 1209600*x^34*log(x)^4 + 4704*x^32*x^(
4*x^2)*log(x)^5 + 139776*x^32*x^(3*x^2)*log(x)^5 + 1096704*x^32*x^(2*x^2)*log(x)^5 + 2989056*x^32*x^(x^2)*log(
x)^5 + 2591232*x^33*log(x)^5 + 8960*x^31*x^(4*x^2)*log(x)^6 + 175616*x^31*x^(3*x^2)*log(x)^6 + 1053696*x^31*x^
(2*x^2)*log(x)^6 + 2408448*x^31*x^(x^2)*log(x)^6 + 2451456*x^32*log(x)^6 + 4480*x^30*x^(4*x^2)*log(x)^7 + 7168
0*x^30*x^(3*x^2)*log(x)^7 + 387072*x^30*x^(2*x^2)*log(x)^7 + 860160*x^30*x^(x^2)*log(x)^7 + 946176*x^31*log(x)
^7 + 32*x^36*x^(x^2) + 16*x^37 + 336*x^35*x^(2*x^2)*log(x) + 4480*x^35*x^(x^2)*log(x) + 2464*x^36*log(x) + 672
*x^34*x^(3*x^2)*log(x)^2 + 18144*x^34*x^(2*x^2)*log(x)^2 + 107520*x^34*x^(x^2)*log(x)^2 + 67200*x^35*log(x)^2
+ 280*x^33*x^(4*x^2)*log(x)^3 + 17920*x^33*x^(3*x^2)*log(x)^3 + 215040*x^33*x^(2*x^2)*log(x)^3 + 752640*x^33*x
^(x^2)*log(x)^3 + 560000*x^34*log(x)^3 + 3920*x^32*x^(4*x^2)*log(x)^4 + 112000*x^32*x^(3*x^2)*log(x)^4 + 80640
0*x^32*x^(2*x^2)*log(x)^4 + 1881600*x^32*x^(x^2)*log(x)^4 + 1774080*x^33*log(x)^4 + 12768*x^31*x^(4*x^2)*log(x
)^5 + 225792*x^31*x^(3*x^2)*log(x)^5 + 1145088*x^31*x^(2*x^2)*log(x)^5 + 1978368*x^31*x^(x^2)*log(x)^5 + 24837
12*x^32*log(x)^5 + 12992*x^30*x^(4*x^2)*log(x)^6 + 175616*x^30*x^(3*x^2)*log(x)^6 + 752640*x^30*x^(2*x^2)*log(
x)^6 + 1204224*x^30*x^(x^2)*log(x)^6 + 1806336*x^31*log(x)^6 + 4480*x^29*x^(4*x^2)*log(x)^7 + 57344*x^29*x^(3*
x^2)*log(x)^7 + 258048*x^29*x^(2*x^2)*log(x)^7 + 491520*x^29*x^(x^2)*log(x)^7 + 675840*x^30*log(x)^7 + 24*x^35
*x^(2*x^2) + 320*x^35*x^(x^2) + 176*x^36 + 112*x^34*x^(3*x^2)*log(x) + 3024*x^34*x^(2*x^2)*log(x) + 17472*x^34
*x^(x^2)*log(x) + 10976*x^35*log(x) + 84*x^33*x^(4*x^2)*log(x)^2 + 5376*x^33*x^(3*x^2)*log(x)^2 + 62496*x^33*x
^(2*x^2)*log(x)^2 + 201600*x^33*x^(x^2)*log(x)^2 + 154560*x^34*log(x)^2 + 1960*x^32*x^(4*x^2)*log(x)^3 + 53760
*x^32*x^(3*x^2)*log(x)^3 + 349440*x^32*x^(2*x^2)*log(x)^3 + 645120*x^32*x^(x^2)*log(x)^3 + 698880*x^33*log(x)^
3 + 10080*x^31*x^(4*x^2)*log(x)^4 + 156800*x^31*x^(3*x^2)*log(x)^4 + 604800*x^31*x^(2*x^2)*log(x)^4 + 430080*x
^31*x^(x^2)*log(x)^4 + 1155840*x^32*log(x)^4 + 15456*x^30*x^(4*x^2)*log(x)^5 + 155904*x^30*x^(3*x^2)*log(x)^5
+ 338688*x^30*x^(2*x^2)*log(x)^5 - 301056*x^30*x^(x^2)*log(x)^5 + 838656*x^31*log(x)^5 + 8960*x^29*x^(4*x^2)*l
og(x)^6 + 75264*x^29*x^(3*x^2)*log(x)^6 + 150528*x^29*x^(2*x^2)*log(x)^6 - 86016*x^29*x^(x^2)*log(x)^6 + 55910
4*x^30*log(x)^6 + 2688*x^28*x^(4*x^2)*log(x)^7 + 28672*x^28*x^(3*x^2)*log(x)^7 + 110592*x^28*x^(2*x^2)*log(x)^
7 + 184320*x^28*x^(x^2)*log(x)^7 + 337920*x^29*log(x)^7 + 8*x^34*x^(3*x^2) + 216*x^34*x^(2*x^2) + 1216*x^34*x^
(x^2) + 768*x^35 + 14*x^33*x^(4*x^2)*log(x) + 896*x^33*x^(3*x^2)*log(x) + 10080*x^33*x^(2*x^2)*log(x) + 29568*
x^33*x^(x^2)*log(x) + 23520*x^34*log(x) + 588*x^32*x^(4*x^2)*log(x)^2 + 15456*x^32*x^(3*x^2)*log(x)^2 + 88704*
x^32*x^(2*x^2)*log(x)^2 + 107520*x^32*x^(x^2)*log(x)^2 + 154560*x^33*log(x)^2 + 4760*x^31*x^(4*x^2)*log(x)^3 +
62720*x^31*x^(3*x^2)*log(x)^3 + 134400*x^31*x^(2*x^2)*log(x)^3 - 322560*x^31*x^(x^2)*log(x)^3 + 161280*x^32*l
og(x)^3 + 9520*x^30*x^(4*x^2)*log(x)^4 + 44800*x^30*x^(3*x^2)*log(x)^4 - 282240*x^30*x^(2*x^2)*log(x)^4 - 1523
200*x^30*x^(x^2)*log(x)^4 - 546560*x^31*log(x)^4 + 4032*x^29*x^(4*x^2)*log(x)^5 - 43008*x^29*x^(3*x^2)*log(x)^
5 - 564480*x^29*x^(2*x^2)*log(x)^5 - 1634304*x^29*x^(x^2)*log(x)^5 - 967680*x^30*log(x)^5 + 448*x^28*x^(4*x^2)
*log(x)^6 - 25088*x^28*x^(3*x^2)*log(x)^6 - 215040*x^28*x^(2*x^2)*log(x)^6 - 559104*x^28*x^(x^2)*log(x)^6 - 32
2560*x^29*log(x)^6 + 896*x^27*x^(4*x^2)*log(x)^7 + 8192*x^27*x^(3*x^2)*log(x)^7 + 27648*x^27*x^(2*x^2)*log(x)^
7 + 40960*x^27*x^(x^2)*log(x)^7 + 112640*x^28*log(x)^7 + x^33*x^(4*x^2) + 64*x^33*x^(3*x^2) + 696*x^33*x^(2*x^
2) + 1824*x^33*x^(x^2) + 1520*x^34 + 98*x^32*x^(4*x^2)*log(x) + 2464*x^32*x^(3*x^2)*log(x) + 12096*x^32*x^(2*x
^2)*log(x) + 4032*x^32*x^(x^2)*log(x) + 16800*x^33*log(x) + 1344*x^31*x^(4*x^2)*log(x)^2 + 14112*x^31*x^(3*x^2
)*log(x)^2 - 8064*x^31*x^(2*x^2)*log(x)^2 - 236544*x^31*x^(x^2)*log(x)^2 - 64512*x^32*log(x)^2 + 3080*x^30*x^(
4*x^2)*log(x)^3 - 17920*x^30*x^(3*x^2)*log(x)^3 - 376320*x^30*x^(2*x^2)*log(x)^3 - 1164800*x^30*x^(x^2)*log(x)
^3 - 743680*x^31*log(x)^3 - 3920*x^29*x^(4*x^2)*log(x)^4 - 138880*x^29*x^(3*x^2)*log(x)^4 - 860160*x^29*x^(2*x
^2)*log(x)^4 - 1738240*x^29*x^(x^2)*log(x)^4 - 1630720*x^30*log(x)^4 - 9408*x^28*x^(4*x^2)*log(x)^5 - 145152*x
^28*x^(3*x^2)*log(x)^5 - 661248*x^28*x^(2*x^2)*log(x)^5 - 1139712*x^28*x^(x^2)*log(x)^5 - 1387008*x^29*log(x)^
5 - 3584*x^27*x^(4*x^2)*log(x)^6 - 46592*x^27*x^(3*x^2)*log(x)^6 - 204288*x^27*x^(2*x^2)*log(x)^6 - 372736*x^2
7*x^(x^2)*log(x)^6 - 465920*x^28*log(x)^6 + 128*x^26*x^(4*x^2)*log(x)^7 + 1024*x^26*x^(3*x^2)*log(x)^7 + 3072*
x^26*x^(2*x^2)*log(x)^7 + 4096*x^26*x^(x^2)*log(x)^7 + 22528*x^27*log(x)^7 + 7*x^32*x^(4*x^2) + 168*x^32*x^(3*
x^2) + 672*x^32*x^(2*x^2) - 672*x^32*x^(x^2) + 576*x^33 + 210*x^31*x^(4*x^2)*log(x) + 1568*x^31*x^(3*x^2)*log(
x) - 9072*x^31*x^(2*x^2)*log(x) - 59136*x^31*x^(x^2)*log(x) - 27552*x^32*log(x) + 420*x^30*x^(4*x^2)*log(x)^2
- 16800*x^30*x^(3*x^2)*log(x)^2 - 169344*x^30*x^(2*x^2)*log(x)^2 - 403200*x^30*x^(x^2)*log(x)^2 - 319872*x^31*
log(x)^2 - 5320*x^29*x^(4*x^2)*log(x)^3 - 107520*x^29*x^(3*x^2)*log(x)^3 - 497280*x^29*x^(2*x^2)*log(x)^3 - 68
0960*x^29*x^(x^2)*log(x)^3 - 922880*x^30*log(x)^3 - 13440*x^28*x^(4*x^2)*log(x)^4 - 147840*x^28*x^(3*x^2)*log(
x)^4 - 443520*x^28*x^(2*x^2)*log(x)^4 - 322560*x^28*x^(x^2)*log(x)^4 - 1030400*x^29*log(x)^4 - 8736*x^27*x^(4*
x^2)*log(x)^5 - 75264*x^27*x^(3*x^2)*log(x)^5 - 193536*x^27*x^(2*x^2)*log(x)^5 - 129024*x^27*x^(x^2)*log(x)^5
- 634368*x^28*log(x)^5 - 2240*x^26*x^(4*x^2)*log(x)^6 - 21504*x^26*x^(3*x^2)*log(x)^6 - 75264*x^26*x^(2*x^2)*l
og(x)^6 - 114688*x^26*x^(x^2)*log(x)^6 - 243712*x^27*log(x)^6 + 2048*x^26*log(x)^7 + 14*x^31*x^(4*x^2) + 56*x^
31*x^(3*x^2) - 1176*x^31*x^(2*x^2) - 5376*x^31*x^(x^2) - 3024*x^32 - 14*x^30*x^(4*x^2)*log(x) - 4592*x^30*x^(3
*x^2)*log(x) - 35280*x^30*x^(2*x^2)*log(x) - 65408*x^30*x^(x^2)*log(x) - 62272*x^31*log(x) - 2520*x^29*x^(4*x^
2)*log(x)^2 - 39648*x^29*x^(3*x^2)*log(x)^2 - 133056*x^29*x^(2*x^2)*log(x)^2 - 53760*x^29*x^(x^2)*log(x)^2 - 2
28480*x^30*log(x)^2 - 8120*x^28*x^(4*x^2)*log(x)^3 - 58240*x^28*x^(3*x^2)*log(x)^3 - 13440*x^28*x^(2*x^2)*log(
x)^3 + 412160*x^28*x^(x^2)*log(x)^3 - 134400*x^29*log(x)^3 - 5040*x^27*x^(4*x^2)*log(x)^4 + 201600*x^27*x^(2*x
^2)*log(x)^4 + 627200*x^27*x^(x^2)*log(x)^4 + 152320*x^28*log(x)^4 - 672*x^26*x^(4*x^2)*log(x)^5 + 10752*x^26*
x^(3*x^2)*log(x)^5 + 96768*x^26*x^(2*x^2)*log(x)^5 + 236544*x^26*x^(x^2)*log(x)^5 + 53760*x^27*log(x)^5 - 448*
x^25*x^(4*x^2)*log(x)^6 - 3584*x^25*x^(3*x^2)*log(x)^6 - 10752*x^25*x^(2*x^2)*log(x)^6 - 14336*x^25*x^(x^2)*lo
g(x)^6 - 64512*x^26*log(x)^6 - 7*x^30*x^(4*x^2) - 448*x^30*x^(3*x^2) - 2856*x^30*x^(2*x^2) - 3808*x^30*x^(x^2)
- 4592*x^31 - 560*x^29*x^(4*x^2)*log(x) - 7168*x^29*x^(3*x^2)*log(x) - 13776*x^29*x^(2*x^2)*log(x) + 28672*x^
29*x^(x^2)*log(x) - 18368*x^30*log(x) - 2436*x^28*x^(4*x^2)*log(x)^2 - 4704*x^28*x^(3*x^2)*log(x)^2 + 92736*x^
28*x^(2*x^2)*log(x)^2 + 322560*x^28*x^(x^2)*log(x)^2 + 134400*x^29*log(x)^2 + 840*x^27*x^(4*x^2)*log(x)^3 + 53
760*x^27*x^(3*x^2)*log(x)^3 + 322560*x^27*x^(2*x^2)*log(x)^3 + 609280*x^27*x^(x^2)*log(x)^3 + 510720*x^28*log(
x)^3 + 5040*x^26*x^(4*x^2)*log(x)^4 + 67200*x^26*x^(3*x^2)*log(x)^4 + 268800*x^26*x^(2*x^2)*log(x)^4 + 412160*
x^26*x^(x^2)*log(x)^4 + 519680*x^27*log(x)^4 + 2016*x^25*x^(4*x^2)*log(x)^5 + 21504*x^25*x^(3*x^2)*log(x)^5 +
80640*x^25*x^(2*x^2)*log(x)^5 + 129024*x^25*x^(x^2)*log(x)^5 + 182784*x^26*log(x)^5 - 7168*x^25*log(x)^6 - 49*
x^29*x^(4*x^2) - 504*x^29*x^(3*x^2) + 5408*x^29*x^(x^2) + 800*x^30 - 336*x^28*x^(4*x^2)*log(x) + 2576*x^28*x^(
3*x^2)*log(x) + 35280*x^28*x^(2*x^2)*log(x) + 83328*x^28*x^(x^2)*log(x) + 56000*x^29*log(x) + 1848*x^27*x^(4*x
^2)*log(x)^2 + 35616*x^27*x^(3*x^2)*log(x)^2 + 149184*x^27*x^(2*x^2)*log(x)^2 + 188160*x^27*x^(x^2)*log(x)^2 +
255360*x^28*log(x)^2 + 5880*x^26*x^(4*x^2)*log(x)^3 + 53760*x^26*x^(3*x^2)*log(x)^3 + 134400*x^26*x^(2*x^2)*l
og(x)^3 + 71680*x^26*x^(x^2)*log(x)^3 + 340480*x^27*log(x)^3 + 3360*x^25*x^(4*x^2)*log(x)^4 + 22400*x^25*x^(3*
x^2)*log(x)^4 + 40320*x^25*x^(2*x^2)*log(x)^4 + 206080*x^26*log(x)^4 + 672*x^24*x^(4*x^2)*log(x)^5 + 5376*x^24
*x^(3*x^2)*log(x)^5 + 16128*x^24*x^(2*x^2)*log(x)^5 + 21504*x^24*x^(x^2)*log(x)^5 + 75264*x^25*log(x)^5 - 14*x
^28*x^(4*x^2) + 504*x^28*x^(3*x^2) + 4056*x^28*x^(2*x^2) + 7264*x^28*x^(x^2) + 6336*x^29 + 658*x^27*x^(4*x^2)*
log(x) + 9184*x^27*x^(3*x^2)*log(x) + 27216*x^27*x^(2*x^2)*log(x) + 10752*x^27*x^(x^2)*log(x) + 47040*x^28*log
(x) + 2604*x^26*x^(4*x^2)*log(x)^2 + 14112*x^26*x^(3*x^2)*log(x)^2 - 8064*x^26*x^(2*x^2)*log(x)^2 - 107520*x^2
6*x^(x^2)*log(x)^2 + 40320*x^27*log(x)^2 + 840*x^25*x^(4*x^2)*log(x)^3 - 8960*x^25*x^(3*x^2)*log(x)^3 - 80640*
x^25*x^(2*x^2)*log(x)^3 - 179200*x^25*x^(x^2)*log(x)^3 - 53760*x^26*log(x)^3 - 560*x^24*x^(4*x^2)*log(x)^4 - 8
960*x^24*x^(3*x^2)*log(x)^4 - 40320*x^24*x^(2*x^2)*log(x)^4 - 71680*x^24*x^(x^2)*log(x)^4 - 35840*x^25*log(x)^
4 + 10752*x^24*log(x)^5 + 77*x^27*x^(4*x^2) + 848*x^27*x^(3*x^2) + 1392*x^27*x^(2*x^2) - 2592*x^27*x^(x^2) + 2
336*x^28 + 490*x^26*x^(4*x^2)*log(x) - 112*x^26*x^(3*x^2)*log(x) - 19152*x^26*x^(2*x^2)*log(x) - 51072*x^26*x^
(x^2)*log(x) - 20160*x^27*log(x) - 840*x^25*x^(4*x^2)*log(x)^2 - 16800*x^25*x^(3*x^2)*log(x)^2 - 72576*x^25*x^
(2*x^2)*log(x)^2 - 107520*x^25*x^(x^2)*log(x)^2 - 107520*x^26*log(x)^2 - 1960*x^24*x^(4*x^2)*log(x)^3 - 17920*
x^24*x^(3*x^2)*log(x)^3 - 53760*x^24*x^(2*x^2)*log(x)^3 - 62720*x^24*x^(x^2)*log(x)^3 - 120960*x^25*log(x)^3 -
560*x^23*x^(4*x^2)*log(x)^4 - 4480*x^23*x^(3*x^2)*log(x)^4 - 13440*x^23*x^(2*x^2)*log(x)^4 - 17920*x^23*x^(x^
2)*log(x)^4 - 44800*x^24*log(x)^4 + 29*x^26*x^(4*x^2) - 384*x^26*x^(3*x^2) - 3336*x^26*x^(2*x^2) - 6240*x^26*x
^(x^2) - 4416*x^27 - 504*x^25*x^(4*x^2)*log(x) - 6272*x^25*x^(3*x^2)*log(x) - 19152*x^25*x^(2*x^2)*log(x) - 16
128*x^25*x^(x^2)*log(x) - 33600*x^26*log(x) - 1260*x^24*x^(4*x^2)*log(x)^2 - 7392*x^24*x^(3*x^2)*log(x)^2 - 80
64*x^24*x^(2*x^2)*log(x)^2 + 13440*x^24*x^(x^2)*log(x)^2 - 47040*x^25*log(x)^2 - 280*x^23*x^(4*x^2)*log(x)^3 +
6720*x^23*x^(2*x^2)*log(x)^3 + 17920*x^23*x^(x^2)*log(x)^3 - 22400*x^24*log(x)^3 - 8960*x^23*log(x)^4 - 77*x^
25*x^(4*x^2) - 728*x^25*x^(3*x^2) - 1344*x^25*x^(2*x^2) + 672*x^25*x^(x^2) - 2784*x^26 - 280*x^24*x^(4*x^2)*lo
g(x) - 112*x^24*x^(3*x^2)*log(x) + 7056*x^24*x^(2*x^2)*log(x) + 18368*x^24*x^(x^2)*log(x) + 1120*x^25*log(x) +
336*x^23*x^(4*x^2)*log(x)^2 + 4704*x^23*x^(3*x^2)*log(x)^2 + 18144*x^23*x^(2*x^2)*log(x)^2 + 26880*x^23*x^(x^
2)*log(x)^2 + 20160*x^24*log(x)^2 + 280*x^22*x^(4*x^2)*log(x)^3 + 2240*x^22*x^(3*x^2)*log(x)^3 + 6720*x^22*x^(
2*x^2)*log(x)^3 + 8960*x^22*x^(x^2)*log(x)^3 + 13440*x^23*log(x)^3 - 14*x^24*x^(4*x^2) + 280*x^24*x^(3*x^2) +
1848*x^24*x^(2*x^2) + 3136*x^24*x^(x^2) + 1904*x^25 + 266*x^23*x^(4*x^2)*log(x) + 2464*x^23*x^(3*x^2)*log(x) +
6720*x^23*x^(2*x^2)*log(x) + 6272*x^23*x^(x^2)*log(x) + 12320*x^24*log(x) + 252*x^22*x^(4*x^2)*log(x)^2 + 134
4*x^22*x^(3*x^2)*log(x)^2 + 2016*x^22*x^(2*x^2)*log(x)^2 + 13440*x^23*log(x)^2 + 4480*x^22*log(x)^3 + 49*x^23*
x^(4*x^2) + 336*x^23*x^(3*x^2) + 504*x^23*x^(2*x^2) - 224*x^23*x^(x^2) + 1456*x^24 + 42*x^22*x^(4*x^2)*log(x)
- 224*x^22*x^(3*x^2)*log(x) - 2016*x^22*x^(2*x^2)*log(x) - 4032*x^22*x^(x^2)*log(x) + 1120*x^23*log(x) - 84*x^
21*x^(4*x^2)*log(x)^2 - 672*x^21*x^(3*x^2)*log(x)^2 - 2016*x^21*x^(2*x^2)*log(x)^2 - 2688*x^21*x^(x^2)*log(x)^
2 - 1344*x^22*log(x)^2 - 7*x^22*x^(4*x^2) - 168*x^22*x^(3*x^2) - 672*x^22*x^(2*x^2) - 928*x^22*x^(x^2) - 576*x
^23 - 70*x^21*x^(4*x^2)*log(x) - 448*x^21*x^(3*x^2)*log(x) - 1008*x^21*x^(2*x^2)*log(x) - 896*x^21*x^(x^2)*log
(x) - 2464*x^22*log(x) - 1344*x^21*log(x)^2 - 14*x^21*x^(4*x^2) - 56*x^21*x^(3*x^2) - 24*x^21*x^(2*x^2) + 128*
x^21*x^(x^2) - 400*x^22 + 14*x^20*x^(4*x^2)*log(x) + 112*x^20*x^(3*x^2)*log(x) + 336*x^20*x^(2*x^2)*log(x) + 4
48*x^20*x^(x^2)*log(x) - 224*x^21*log(x) + 7*x^20*x^(4*x^2) + 48*x^20*x^(3*x^2) + 120*x^20*x^(2*x^2) + 128*x^2
0*x^(x^2) + 128*x^21 + 224*x^20*log(x) - x^19*x^(4*x^2) - 8*x^19*x^(3*x^2) - 24*x^19*x^(2*x^2) - 32*x^19*x^(x^
2) + 48*x^20 - 16*x^19)

Mupad [F(-1)]

Timed out. \[ \int \frac {(4-12 x) \log (4)+x^{x^2} \left (\left (2-8 x^2\right ) \log (4)-16 x^2 \log (4) \log (x)\right )}{32+160 x+320 x^2+320 x^3+160 x^4+32 x^5+x^{5 x^2}+x^{4 x^2} (10+10 x)+x^{3 x^2} \left (40+80 x+40 x^2\right )+x^{2 x^2} \left (80+240 x+240 x^2+80 x^3\right )+x^{x^2} \left (80+320 x+480 x^2+320 x^3+80 x^4\right )} \, dx=\int -\frac {2\,\ln \left (2\right )\,\left (12\,x-4\right )+{\mathrm {e}}^{x^2\,\ln \left (x\right )}\,\left (2\,\ln \left (2\right )\,\left (8\,x^2-2\right )+32\,x^2\,\ln \left (2\right )\,\ln \left (x\right )\right )}{160\,x+{\mathrm {e}}^{5\,x^2\,\ln \left (x\right )}+{\mathrm {e}}^{4\,x^2\,\ln \left (x\right )}\,\left (10\,x+10\right )+{\mathrm {e}}^{3\,x^2\,\ln \left (x\right )}\,\left (40\,x^2+80\,x+40\right )+{\mathrm {e}}^{2\,x^2\,\ln \left (x\right )}\,\left (80\,x^3+240\,x^2+240\,x+80\right )+{\mathrm {e}}^{x^2\,\ln \left (x\right )}\,\left (80\,x^4+320\,x^3+480\,x^2+320\,x+80\right )+320\,x^2+320\,x^3+160\,x^4+32\,x^5+32} \,d x \]

[In]

int(-(2*log(2)*(12*x - 4) + exp(x^2*log(x))*(2*log(2)*(8*x^2 - 2) + 32*x^2*log(2)*log(x)))/(160*x + exp(5*x^2*
log(x)) + exp(4*x^2*log(x))*(10*x + 10) + exp(3*x^2*log(x))*(80*x + 40*x^2 + 40) + exp(2*x^2*log(x))*(240*x +
240*x^2 + 80*x^3 + 80) + exp(x^2*log(x))*(320*x + 480*x^2 + 320*x^3 + 80*x^4 + 80) + 320*x^2 + 320*x^3 + 160*x
^4 + 32*x^5 + 32),x)

[Out]

int(-(2*log(2)*(12*x - 4) + exp(x^2*log(x))*(2*log(2)*(8*x^2 - 2) + 32*x^2*log(2)*log(x)))/(160*x + exp(5*x^2*
log(x)) + exp(4*x^2*log(x))*(10*x + 10) + exp(3*x^2*log(x))*(80*x + 40*x^2 + 40) + exp(2*x^2*log(x))*(240*x +
240*x^2 + 80*x^3 + 80) + exp(x^2*log(x))*(320*x + 480*x^2 + 320*x^3 + 80*x^4 + 80) + 320*x^2 + 320*x^3 + 160*x
^4 + 32*x^5 + 32), x)