3.102.61 \(\int \frac {128-32 x+64 x^2-16 x^3+8 x^4-2 x^5+(40-530 x+280 x^2-545 x^3+258 x^4-128 x^5+48 x^6-6 x^7) \log (x)+(2-296 x+82 x^2-258 x^3+64 x^4-48 x^5+12 x^6) \log ^2(x)+(-49 x+4 x^2-32 x^3-6 x^5) \log ^3(x)-2 x \log ^4(x)+((52-x+88 x^2-16 x^3+19 x^4-4 x^5) \log (x)+(20+24 x^2+5 x^4) \log ^2(x)+\log ^3(x)) \log (\log ^2(x))}{(16-8 x+x^2) \log (x)+(8-2 x) \log ^2(x)+\log ^3(x)} \, dx\)

Optimal. Leaf size=31 \[ x \left (\left (4+x^2\right )^2+\log (x)\right ) \left (-x+\frac {\log \left (\log ^2(x)\right )}{4-x+\log (x)}\right ) \]

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Rubi [F]  time = 9.45, 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*} \int \frac {128-32 x+64 x^2-16 x^3+8 x^4-2 x^5+\left (40-530 x+280 x^2-545 x^3+258 x^4-128 x^5+48 x^6-6 x^7\right ) \log (x)+\left (2-296 x+82 x^2-258 x^3+64 x^4-48 x^5+12 x^6\right ) \log ^2(x)+\left (-49 x+4 x^2-32 x^3-6 x^5\right ) \log ^3(x)-2 x \log ^4(x)+\left (\left (52-x+88 x^2-16 x^3+19 x^4-4 x^5\right ) \log (x)+\left (20+24 x^2+5 x^4\right ) \log ^2(x)+\log ^3(x)\right ) \log \left (\log ^2(x)\right )}{\left (16-8 x+x^2\right ) \log (x)+(8-2 x) \log ^2(x)+\log ^3(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(128 - 32*x + 64*x^2 - 16*x^3 + 8*x^4 - 2*x^5 + (40 - 530*x + 280*x^2 - 545*x^3 + 258*x^4 - 128*x^5 + 48*x
^6 - 6*x^7)*Log[x] + (2 - 296*x + 82*x^2 - 258*x^3 + 64*x^4 - 48*x^5 + 12*x^6)*Log[x]^2 + (-49*x + 4*x^2 - 32*
x^3 - 6*x^5)*Log[x]^3 - 2*x*Log[x]^4 + ((52 - x + 88*x^2 - 16*x^3 + 19*x^4 - 4*x^5)*Log[x] + (20 + 24*x^2 + 5*
x^4)*Log[x]^2 + Log[x]^3)*Log[Log[x]^2])/((16 - 8*x + x^2)*Log[x] + (8 - 2*x)*Log[x]^2 + Log[x]^3),x]

[Out]

-16*x^2 - 8*x^4 - x^6 - x^2*Log[x] - 192*Defer[Int][(-4 + x - Log[x])^(-1), x] - 800*Defer[Int][1/((-4 + x)*(-
4 + x - Log[x])), x] - 48*Defer[Int][x/(-4 + x - Log[x]), x] - 8*Defer[Int][x^2/(-4 + x - Log[x]), x] - 2*Defe
r[Int][x^3/(-4 + x - Log[x]), x] + 128*Defer[Int][1/((-4 + x)^2*Log[x]), x] - 32*Defer[Int][x/((-4 + x)^2*Log[
x]), x] + 64*Defer[Int][x^2/((-4 + x)^2*Log[x]), x] - 16*Defer[Int][x^3/((-4 + x)^2*Log[x]), x] + 8*Defer[Int]
[x^4/((-4 + x)^2*Log[x]), x] - 2*Defer[Int][x^5/((-4 + x)^2*Log[x]), x] + 2*Defer[Int][(4 - x + Log[x])^(-1),
x] + 52*Defer[Int][Log[Log[x]^2]/(-4 + x - Log[x])^2, x] - Defer[Int][(x*Log[Log[x]^2])/(-4 + x - Log[x])^2, x
] + 88*Defer[Int][(x^2*Log[Log[x]^2])/(-4 + x - Log[x])^2, x] - 16*Defer[Int][(x^3*Log[Log[x]^2])/(-4 + x - Lo
g[x])^2, x] + 19*Defer[Int][(x^4*Log[Log[x]^2])/(-4 + x - Log[x])^2, x] - 4*Defer[Int][(x^5*Log[Log[x]^2])/(-4
+ x - Log[x])^2, x] + 24*Defer[Int][(x^2*Log[x]*Log[Log[x]^2])/(-4 + x - Log[x])^2, x] + 5*Defer[Int][(x^4*Lo
g[x]*Log[Log[x]^2])/(-4 + x - Log[x])^2, x] + 20*Defer[Int][(Log[x]*Log[Log[x]^2])/(4 - x + Log[x])^2, x] + De
fer[Int][(Log[x]^2*Log[Log[x]^2])/(4 - x + Log[x])^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {128-32 x+64 x^2-16 x^3+8 x^4-2 x^5+\left (40-530 x+280 x^2-545 x^3+258 x^4-128 x^5+48 x^6-6 x^7\right ) \log (x)+\left (2-296 x+82 x^2-258 x^3+64 x^4-48 x^5+12 x^6\right ) \log ^2(x)+\left (-49 x+4 x^2-32 x^3-6 x^5\right ) \log ^3(x)-2 x \log ^4(x)+\left (\left (52-x+88 x^2-16 x^3+19 x^4-4 x^5\right ) \log (x)+\left (20+24 x^2+5 x^4\right ) \log ^2(x)+\log ^3(x)\right ) \log \left (\log ^2(x)\right )}{\log (x) (4-x+\log (x))^2} \, dx\\ &=\int \left (\frac {40-530 x+280 x^2-545 x^3+258 x^4-128 x^5+48 x^6-6 x^7}{(-4+x-\log (x))^2}-\frac {32 x}{(-4+x-\log (x))^2 \log (x)}+\frac {64 x^2}{(-4+x-\log (x))^2 \log (x)}-\frac {16 x^3}{(-4+x-\log (x))^2 \log (x)}+\frac {8 x^4}{(-4+x-\log (x))^2 \log (x)}-\frac {2 x^5}{(-4+x-\log (x))^2 \log (x)}+\frac {2 \left (1-148 x+41 x^2-129 x^3+32 x^4-24 x^5+6 x^6\right ) \log (x)}{(-4+x-\log (x))^2}-\frac {x \left (49-4 x+32 x^2+6 x^4\right ) \log ^2(x)}{(-4+x-\log (x))^2}-\frac {2 x \log ^3(x)}{(-4+x-\log (x))^2}+\frac {128}{\log (x) (4-x+\log (x))^2}-\frac {\left (-52+x-88 x^2+16 x^3-19 x^4+4 x^5-20 \log (x)-24 x^2 \log (x)-5 x^4 \log (x)-\log ^2(x)\right ) \log \left (\log ^2(x)\right )}{(-4+x-\log (x))^2}\right ) \, dx\\ &=-\left (2 \int \frac {x^5}{(-4+x-\log (x))^2 \log (x)} \, dx\right )+2 \int \frac {\left (1-148 x+41 x^2-129 x^3+32 x^4-24 x^5+6 x^6\right ) \log (x)}{(-4+x-\log (x))^2} \, dx-2 \int \frac {x \log ^3(x)}{(-4+x-\log (x))^2} \, dx+8 \int \frac {x^4}{(-4+x-\log (x))^2 \log (x)} \, dx-16 \int \frac {x^3}{(-4+x-\log (x))^2 \log (x)} \, dx-32 \int \frac {x}{(-4+x-\log (x))^2 \log (x)} \, dx+64 \int \frac {x^2}{(-4+x-\log (x))^2 \log (x)} \, dx+128 \int \frac {1}{\log (x) (4-x+\log (x))^2} \, dx+\int \frac {40-530 x+280 x^2-545 x^3+258 x^4-128 x^5+48 x^6-6 x^7}{(-4+x-\log (x))^2} \, dx-\int \frac {x \left (49-4 x+32 x^2+6 x^4\right ) \log ^2(x)}{(-4+x-\log (x))^2} \, dx-\int \frac {\left (-52+x-88 x^2+16 x^3-19 x^4+4 x^5-20 \log (x)-24 x^2 \log (x)-5 x^4 \log (x)-\log ^2(x)\right ) \log \left (\log ^2(x)\right )}{(-4+x-\log (x))^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.15, size = 38, normalized size = 1.23 \begin {gather*} -\frac {x \left (\left (4+x^2\right )^2+\log (x)\right ) \left ((-4+x) x-x \log (x)+\log \left (\log ^2(x)\right )\right )}{-4+x-\log (x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(128 - 32*x + 64*x^2 - 16*x^3 + 8*x^4 - 2*x^5 + (40 - 530*x + 280*x^2 - 545*x^3 + 258*x^4 - 128*x^5
+ 48*x^6 - 6*x^7)*Log[x] + (2 - 296*x + 82*x^2 - 258*x^3 + 64*x^4 - 48*x^5 + 12*x^6)*Log[x]^2 + (-49*x + 4*x^2
- 32*x^3 - 6*x^5)*Log[x]^3 - 2*x*Log[x]^4 + ((52 - x + 88*x^2 - 16*x^3 + 19*x^4 - 4*x^5)*Log[x] + (20 + 24*x^
2 + 5*x^4)*Log[x]^2 + Log[x]^3)*Log[Log[x]^2])/((16 - 8*x + x^2)*Log[x] + (8 - 2*x)*Log[x]^2 + Log[x]^3),x]

[Out]

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

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fricas [B]  time = 0.68, size = 94, normalized size = 3.03 \begin {gather*} -\frac {x^{7} - 4 \, x^{6} + 8 \, x^{5} - 32 \, x^{4} - x^{2} \log \relax (x)^{2} + 16 \, x^{3} - 64 \, x^{2} + {\left (x^{5} + 8 \, x^{3} + x \log \relax (x) + 16 \, x\right )} \log \left (\log \relax (x)^{2}\right ) - {\left (x^{6} + 8 \, x^{4} - x^{3} + 20 \, x^{2}\right )} \log \relax (x)}{x - \log \relax (x) - 4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((log(x)^3+(5*x^4+24*x^2+20)*log(x)^2+(-4*x^5+19*x^4-16*x^3+88*x^2-x+52)*log(x))*log(log(x)^2)-2*x*l
og(x)^4+(-6*x^5-32*x^3+4*x^2-49*x)*log(x)^3+(12*x^6-48*x^5+64*x^4-258*x^3+82*x^2-296*x+2)*log(x)^2+(-6*x^7+48*
x^6-128*x^5+258*x^4-545*x^3+280*x^2-530*x+40)*log(x)-2*x^5+8*x^4-16*x^3+64*x^2-32*x+128)/(log(x)^3+(-2*x+8)*lo
g(x)^2+(x^2-8*x+16)*log(x)),x, algorithm="fricas")

[Out]

-(x^7 - 4*x^6 + 8*x^5 - 32*x^4 - x^2*log(x)^2 + 16*x^3 - 64*x^2 + (x^5 + 8*x^3 + x*log(x) + 16*x)*log(log(x)^2
) - (x^6 + 8*x^4 - x^3 + 20*x^2)*log(x))/(x - log(x) - 4)

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giac [A]  time = 0.34, size = 57, normalized size = 1.84 \begin {gather*} -x^{6} - 8 \, x^{4} - x^{2} \log \relax (x) - 16 \, x^{2} + {\left (x - \frac {x^{5} + 8 \, x^{3} + x^{2} + 12 \, x}{x - \log \relax (x) - 4}\right )} \log \left (\log \relax (x)^{2}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((log(x)^3+(5*x^4+24*x^2+20)*log(x)^2+(-4*x^5+19*x^4-16*x^3+88*x^2-x+52)*log(x))*log(log(x)^2)-2*x*l
og(x)^4+(-6*x^5-32*x^3+4*x^2-49*x)*log(x)^3+(12*x^6-48*x^5+64*x^4-258*x^3+82*x^2-296*x+2)*log(x)^2+(-6*x^7+48*
x^6-128*x^5+258*x^4-545*x^3+280*x^2-530*x+40)*log(x)-2*x^5+8*x^4-16*x^3+64*x^2-32*x+128)/(log(x)^3+(-2*x+8)*lo
g(x)^2+(x^2-8*x+16)*log(x)),x, algorithm="giac")

[Out]

-x^6 - 8*x^4 - x^2*log(x) - 16*x^2 + (x - (x^5 + 8*x^3 + x^2 + 12*x)/(x - log(x) - 4))*log(log(x)^2)

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maple [C]  time = 0.34, size = 343, normalized size = 11.06

method	result	size
risch	\(-\frac {2 x \left (x^{4}+8 x^{2}+\ln \relax (x )+16\right ) \ln \left (\ln \relax (x )\right )}{-\ln \relax (x )+x -4}-\frac {x \left (-16 i \pi \mathrm {csgn}\left (i \ln \relax (x )\right )^{2} \mathrm {csgn}\left (i \ln \relax (x )^{2}\right )-i \pi \mathrm {csgn}\left (i \ln \relax (x )\right )^{2} \mathrm {csgn}\left (i \ln \relax (x )^{2}\right ) \ln \relax (x )+32 i \pi \,\mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (i \ln \relax (x )^{2}\right )^{2}+16 i \pi \,x^{2} \mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (i \ln \relax (x )^{2}\right )^{2}+2 i \pi \,x^{4} \mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (i \ln \relax (x )^{2}\right )^{2}+2 i \pi \,\mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (i \ln \relax (x )^{2}\right )^{2} \ln \relax (x )-16 i \pi \mathrm {csgn}\left (i \ln \relax (x )^{2}\right )^{3}-8 i \pi \,x^{2} \mathrm {csgn}\left (i \ln \relax (x )^{2}\right )^{3}-i \pi \mathrm {csgn}\left (i \ln \relax (x )^{2}\right )^{3} \ln \relax (x )+2 x^{6}-2 x^{5} \ln \relax (x )-i \pi \,x^{4} \mathrm {csgn}\left (i \ln \relax (x )^{2}\right )^{3}-8 i \pi \,x^{2} \mathrm {csgn}\left (i \ln \relax (x )\right )^{2} \mathrm {csgn}\left (i \ln \relax (x )^{2}\right )-i \pi \,x^{4} \mathrm {csgn}\left (i \ln \relax (x )\right )^{2} \mathrm {csgn}\left (i \ln \relax (x )^{2}\right )-8 x^{5}+16 x^{4}-16 x^{3} \ln \relax (x )-64 x^{3}+2 x^{2} \ln \relax (x )-2 x \ln \relax (x )^{2}+32 x^{2}-40 x \ln \relax (x )-128 x \right )}{2 \left (-\ln \relax (x )+x -4\right )}\)	\(343\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((ln(x)^3+(5*x^4+24*x^2+20)*ln(x)^2+(-4*x^5+19*x^4-16*x^3+88*x^2-x+52)*ln(x))*ln(ln(x)^2)-2*x*ln(x)^4+(-6*
x^5-32*x^3+4*x^2-49*x)*ln(x)^3+(12*x^6-48*x^5+64*x^4-258*x^3+82*x^2-296*x+2)*ln(x)^2+(-6*x^7+48*x^6-128*x^5+25
8*x^4-545*x^3+280*x^2-530*x+40)*ln(x)-2*x^5+8*x^4-16*x^3+64*x^2-32*x+128)/(ln(x)^3+(-2*x+8)*ln(x)^2+(x^2-8*x+1
6)*ln(x)),x,method=_RETURNVERBOSE)

[Out]

-2*x*(x^4+8*x^2+ln(x)+16)/(-ln(x)+x-4)*ln(ln(x))-1/2*x*(-16*I*Pi*csgn(I*ln(x))^2*csgn(I*ln(x)^2)-I*Pi*csgn(I*l
n(x))^2*csgn(I*ln(x)^2)*ln(x)+32*I*Pi*csgn(I*ln(x))*csgn(I*ln(x)^2)^2+16*I*Pi*x^2*csgn(I*ln(x))*csgn(I*ln(x)^2
)^2+2*I*Pi*x^4*csgn(I*ln(x))*csgn(I*ln(x)^2)^2+2*I*Pi*csgn(I*ln(x))*csgn(I*ln(x)^2)^2*ln(x)-16*I*Pi*csgn(I*ln(
x)^2)^3-8*I*Pi*x^2*csgn(I*ln(x)^2)^3-I*Pi*csgn(I*ln(x)^2)^3*ln(x)+2*x^6-2*x^5*ln(x)-I*Pi*x^4*csgn(I*ln(x)^2)^3
-8*I*Pi*x^2*csgn(I*ln(x))^2*csgn(I*ln(x)^2)-I*Pi*x^4*csgn(I*ln(x))^2*csgn(I*ln(x)^2)-8*x^5+16*x^4-16*x^3*ln(x)
-64*x^3+2*x^2*ln(x)-2*x*ln(x)^2+32*x^2-40*x*ln(x)-128*x)/(-ln(x)+x-4)

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maxima [B]  time = 0.40, size = 93, normalized size = 3.00 \begin {gather*} -\frac {x^{7} - 4 \, x^{6} + 8 \, x^{5} - 32 \, x^{4} - x^{2} \log \relax (x)^{2} + 16 \, x^{3} - 64 \, x^{2} - {\left (x^{6} + 8 \, x^{4} - x^{3} + 20 \, x^{2}\right )} \log \relax (x) + 2 \, {\left (x^{5} + 8 \, x^{3} + x \log \relax (x) + 16 \, x\right )} \log \left (\log \relax (x)\right )}{x - \log \relax (x) - 4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((log(x)^3+(5*x^4+24*x^2+20)*log(x)^2+(-4*x^5+19*x^4-16*x^3+88*x^2-x+52)*log(x))*log(log(x)^2)-2*x*l
og(x)^4+(-6*x^5-32*x^3+4*x^2-49*x)*log(x)^3+(12*x^6-48*x^5+64*x^4-258*x^3+82*x^2-296*x+2)*log(x)^2+(-6*x^7+48*
x^6-128*x^5+258*x^4-545*x^3+280*x^2-530*x+40)*log(x)-2*x^5+8*x^4-16*x^3+64*x^2-32*x+128)/(log(x)^3+(-2*x+8)*lo
g(x)^2+(x^2-8*x+16)*log(x)),x, algorithm="maxima")

[Out]

-(x^7 - 4*x^6 + 8*x^5 - 32*x^4 - x^2*log(x)^2 + 16*x^3 - 64*x^2 - (x^6 + 8*x^4 - x^3 + 20*x^2)*log(x) + 2*(x^5
+ 8*x^3 + x*log(x) + 16*x)*log(log(x)))/(x - log(x) - 4)

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mupad [B]  time = 9.55, size = 281, normalized size = 9.06 \begin {gather*} -34\,\ln \left (\ln \relax (x)\right )-x^2\,\ln \relax (x)-16\,x^2-8\,x^4-x^6-\frac {\ln \left ({\ln \relax (x)}^2\right )\,\left ({\ln \relax (x)}^2\,\left (\frac {1}{x-1}-\frac {x}{x-1}+1\right )-\left (x-4\right )\,\left (\frac {1}{x-1}-\frac {20\,x^5-25\,x^4+48\,x^3-72\,x^2+x-18}{x-1}+\frac {x-2}{x-1}-\frac {-25\,x^5+25\,x^4-72\,x^3+72\,x^2}{x-1}\right )-\ln \relax (x)\,\left (\frac {20\,x^5-25\,x^4+48\,x^3-72\,x^2+x-18}{x-1}-\frac {1}{x-1}-\frac {x-2}{x-1}+\left (\frac {1}{x-1}+1\right )\,\left (x-4\right )+\frac {-25\,x^5+25\,x^4-72\,x^3+72\,x^2}{x-1}+\frac {x\,\left (5\,x^4+24\,x^2+20\right )}{x-1}\right )+\frac {x\,\left (4\,x^5-19\,x^4+16\,x^3-88\,x^2+x-52\right )}{x-1}\right )}{\ln \relax (x)-x+4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(32*x - log(log(x)^2)*(log(x)^3 + log(x)^2*(24*x^2 + 5*x^4 + 20) - log(x)*(x - 88*x^2 + 16*x^3 - 19*x^4 +
4*x^5 - 52)) + 2*x*log(x)^4 + log(x)^3*(49*x - 4*x^2 + 32*x^3 + 6*x^5) + log(x)*(530*x - 280*x^2 + 545*x^3 -
258*x^4 + 128*x^5 - 48*x^6 + 6*x^7 - 40) - 64*x^2 + 16*x^3 - 8*x^4 + 2*x^5 - log(x)^2*(82*x^2 - 296*x - 258*x^
3 + 64*x^4 - 48*x^5 + 12*x^6 + 2) - 128)/(log(x)^3 + log(x)*(x^2 - 8*x + 16) - log(x)^2*(2*x - 8)),x)

[Out]

- 34*log(log(x)) - x^2*log(x) - 16*x^2 - 8*x^4 - x^6 - (log(log(x)^2)*(log(x)^2*(1/(x - 1) - x/(x - 1) + 1) -
(x - 4)*(1/(x - 1) - (x - 72*x^2 + 48*x^3 - 25*x^4 + 20*x^5 - 18)/(x - 1) + (x - 2)/(x - 1) - (72*x^2 - 72*x^3
+ 25*x^4 - 25*x^5)/(x - 1)) - log(x)*((x - 72*x^2 + 48*x^3 - 25*x^4 + 20*x^5 - 18)/(x - 1) - 1/(x - 1) - (x -
2)/(x - 1) + (1/(x - 1) + 1)*(x - 4) + (72*x^2 - 72*x^3 + 25*x^4 - 25*x^5)/(x - 1) + (x*(24*x^2 + 5*x^4 + 20)
)/(x - 1)) + (x*(x - 88*x^2 + 16*x^3 - 19*x^4 + 4*x^5 - 52))/(x - 1)))/(log(x) - x + 4)

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sympy [A]  time = 0.62, size = 51, normalized size = 1.65 \begin {gather*} - x^{6} - 8 x^{4} - x^{2} \log {\relax (x )} - 16 x^{2} + \frac {\left (- x^{5} - 8 x^{3} - x \log {\relax (x )} - 16 x\right ) \log {\left (\log {\relax (x )}^{2} \right )}}{x - \log {\relax (x )} - 4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((ln(x)**3+(5*x**4+24*x**2+20)*ln(x)**2+(-4*x**5+19*x**4-16*x**3+88*x**2-x+52)*ln(x))*ln(ln(x)**2)-2
*x*ln(x)**4+(-6*x**5-32*x**3+4*x**2-49*x)*ln(x)**3+(12*x**6-48*x**5+64*x**4-258*x**3+82*x**2-296*x+2)*ln(x)**2
+(-6*x**7+48*x**6-128*x**5+258*x**4-545*x**3+280*x**2-530*x+40)*ln(x)-2*x**5+8*x**4-16*x**3+64*x**2-32*x+128)/
(ln(x)**3+(-2*x+8)*ln(x)**2+(x**2-8*x+16)*ln(x)),x)

[Out]

-x**6 - 8*x**4 - x**2*log(x) - 16*x**2 + (-x**5 - 8*x**3 - x*log(x) - 16*x)*log(log(x)**2)/(x - log(x) - 4)

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