\(\int \frac {-32+(32-2 x) \log (x)+(2 x \log (x)-32 \log (x) \log (\frac {x}{\log (x)})) \log (-x+16 \log (\frac {x}{\log (x)}))}{-x^3 \log (x)+16 x^2 \log (x) \log (\frac {x}{\log (x)})+(-2 x^2 \log (x)+32 x \log (x) \log (\frac {x}{\log (x)})) \log (-x+16 \log (\frac {x}{\log (x)}))+(-x \log (x)+16 \log (x) \log (\frac {x}{\log (x)})) \log ^2(-x+16 \log (\frac {x}{\log (x)}))} \, dx\) [7406]

Optimal result

Integrand size = 136, antiderivative size = 25 \[ \int \frac {-32+(32-2 x) \log (x)+\left (2 x \log (x)-32 \log (x) \log \left (\frac {x}{\log (x)}\right )\right ) \log \left (-x+16 \log \left (\frac {x}{\log (x)}\right )\right )}{-x^3 \log (x)+16 x^2 \log (x) \log \left (\frac {x}{\log (x)}\right )+\left (-2 x^2 \log (x)+32 x \log (x) \log \left (\frac {x}{\log (x)}\right )\right ) \log \left (-x+16 \log \left (\frac {x}{\log (x)}\right )\right )+\left (-x \log (x)+16 \log (x) \log \left (\frac {x}{\log (x)}\right )\right ) \log ^2\left (-x+16 \log \left (\frac {x}{\log (x)}\right )\right )} \, dx=-5+\log (5)-\frac {2 x}{x+\log \left (-x+16 \log \left (\frac {x}{\log (x)}\right )\right )} \]

[Out]

ln(5)-2*x/(x+ln(16*ln(x/ln(x))-x))-5

Rubi [A] (verified)

Time = 0.25 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.96, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.022, Rules used = {6820, 6843, 32} \[ \int \frac {-32+(32-2 x) \log (x)+\left (2 x \log (x)-32 \log (x) \log \left (\frac {x}{\log (x)}\right )\right ) \log \left (-x+16 \log \left (\frac {x}{\log (x)}\right )\right )}{-x^3 \log (x)+16 x^2 \log (x) \log \left (\frac {x}{\log (x)}\right )+\left (-2 x^2 \log (x)+32 x \log (x) \log \left (\frac {x}{\log (x)}\right )\right ) \log \left (-x+16 \log \left (\frac {x}{\log (x)}\right )\right )+\left (-x \log (x)+16 \log (x) \log \left (\frac {x}{\log (x)}\right )\right ) \log ^2\left (-x+16 \log \left (\frac {x}{\log (x)}\right )\right )} \, dx=\frac {2}{\frac {x}{\log \left (16 \log \left (\frac {x}{\log (x)}\right )-x\right )}+1} \]

[In]

Int[(-32 + (32 - 2*x)*Log[x] + (2*x*Log[x] - 32*Log[x]*Log[x/Log[x]])*Log[-x + 16*Log[x/Log[x]]])/(-(x^3*Log[x
]) + 16*x^2*Log[x]*Log[x/Log[x]] + (-2*x^2*Log[x] + 32*x*Log[x]*Log[x/Log[x]])*Log[-x + 16*Log[x/Log[x]]] + (-
(x*Log[x]) + 16*Log[x]*Log[x/Log[x]])*Log[-x + 16*Log[x/Log[x]]]^2),x]

[Out]

2/(1 + x/Log[-x + 16*Log[x/Log[x]]])

Rule 32

Int[((a_.) + (b_.)*(x_))^(m_), x_Symbol] :> Simp[(a + b*x)^(m + 1)/(b*(m + 1)), x] /; FreeQ[{a, b, m}, x] && N
eQ[m, -1]

Rule 6820

Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; SimplerIntegrandQ[v, u, x]]

Rule 6843

Int[(u_)*((a_.)*(v_)^(p_.) + (b_.)*(w_)^(q_.))^(m_.), x_Symbol] :> With[{c = Simplify[u/(p*w*D[v, x] - q*v*D[w
, x])]}, Dist[c*p, Subst[Int[(b + a*x^p)^m, x], x, v*w^(m*q + 1)], x] /; FreeQ[c, x]] /; FreeQ[{a, b, m, p, q}
, x] && EqQ[p + q*(m*p + 1), 0] && IntegerQ[p] && IntegerQ[m]

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

Mathematica [A] (verified)

Time = 0.51 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.84 \[ \int \frac {-32+(32-2 x) \log (x)+\left (2 x \log (x)-32 \log (x) \log \left (\frac {x}{\log (x)}\right )\right ) \log \left (-x+16 \log \left (\frac {x}{\log (x)}\right )\right )}{-x^3 \log (x)+16 x^2 \log (x) \log \left (\frac {x}{\log (x)}\right )+\left (-2 x^2 \log (x)+32 x \log (x) \log \left (\frac {x}{\log (x)}\right )\right ) \log \left (-x+16 \log \left (\frac {x}{\log (x)}\right )\right )+\left (-x \log (x)+16 \log (x) \log \left (\frac {x}{\log (x)}\right )\right ) \log ^2\left (-x+16 \log \left (\frac {x}{\log (x)}\right )\right )} \, dx=-\frac {2 x}{x+\log \left (-x+16 \log \left (\frac {x}{\log (x)}\right )\right )} \]

[In]

Integrate[(-32 + (32 - 2*x)*Log[x] + (2*x*Log[x] - 32*Log[x]*Log[x/Log[x]])*Log[-x + 16*Log[x/Log[x]]])/(-(x^3
*Log[x]) + 16*x^2*Log[x]*Log[x/Log[x]] + (-2*x^2*Log[x] + 32*x*Log[x]*Log[x/Log[x]])*Log[-x + 16*Log[x/Log[x]]
] + (-(x*Log[x]) + 16*Log[x]*Log[x/Log[x]])*Log[-x + 16*Log[x/Log[x]]]^2),x]

[Out]

(-2*x)/(x + Log[-x + 16*Log[x/Log[x]]])

Maple [A] (verified)

Time = 90.28 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.88

method	result	size
parallelrisch	\(-\frac {2 x}{x +\ln \left (16 \ln \left (\frac {x}{\ln \left (x \right )}\right )-x \right )}\)	\(22\)
risch	\(-\frac {2 x}{x +\ln \left (-16 \ln \left (\ln \left (x \right )\right )+16 \ln \left (x \right )-8 i \pi \,\operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right ) \left (-\operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right )+\operatorname {csgn}\left (\frac {i}{\ln \left (x \right )}\right )\right ) \left (-\operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right )+\operatorname {csgn}\left (i x \right )\right )-x \right )}\)	\(72\)
default	\(-\frac {32 x}{\left (8 i \pi \ln \left (x \right ) \operatorname {csgn}\left (\frac {i}{\ln \left (x \right )}\right ) \operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right ) x -8 i \pi \ln \left (x \right ) \operatorname {csgn}\left (\frac {i}{\ln \left (x \right )}\right ) \operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right )^{2} x -8 i \pi \ln \left (x \right ) \operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right )^{2} x +8 i \pi \ln \left (x \right ) \operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right )^{3} x +x^{2} \ln \left (x \right )+16 x \ln \left (x \right ) \ln \left (\ln \left (x \right )\right )-16 x \ln \left (x \right )^{2}+x \ln \left (x \right )-16 \ln \left (x \right )+16\right ) \left (x +\ln \left (-16 \ln \left (\ln \left (x \right )\right )+16 \ln \left (x \right )-8 i \pi \,\operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right ) \left (-\operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right )+\operatorname {csgn}\left (\frac {i}{\ln \left (x \right )}\right )\right ) \left (-\operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right )+\operatorname {csgn}\left (i x \right )\right )-x \right )\right )}-\frac {2 \ln \left (x \right ) x \left (8 i \pi \,\operatorname {csgn}\left (\frac {i}{\ln \left (x \right )}\right ) \operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right ) x -8 i \pi \,\operatorname {csgn}\left (\frac {i}{\ln \left (x \right )}\right ) \operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right )^{2} x -8 i \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right )^{2} x +8 i \pi \operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right )^{3} x +x^{2}+16 x \ln \left (\ln \left (x \right )\right )-16 x \ln \left (x \right )+x -16\right )}{\left (8 i \pi \ln \left (x \right ) \operatorname {csgn}\left (\frac {i}{\ln \left (x \right )}\right ) \operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right ) x -8 i \pi \ln \left (x \right ) \operatorname {csgn}\left (\frac {i}{\ln \left (x \right )}\right ) \operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right )^{2} x -8 i \pi \ln \left (x \right ) \operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right )^{2} x +8 i \pi \ln \left (x \right ) \operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right )^{3} x +x^{2} \ln \left (x \right )+16 x \ln \left (x \right ) \ln \left (\ln \left (x \right )\right )-16 x \ln \left (x \right )^{2}+x \ln \left (x \right )-16 \ln \left (x \right )+16\right ) \left (x +\ln \left (-16 \ln \left (\ln \left (x \right )\right )+16 \ln \left (x \right )-8 i \pi \,\operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right ) \left (-\operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right )+\operatorname {csgn}\left (\frac {i}{\ln \left (x \right )}\right )\right ) \left (-\operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right )+\operatorname {csgn}\left (i x \right )\right )-x \right )\right )}\)	\(509\)
parts	\(-\frac {32 x}{\left (8 i \pi \ln \left (x \right ) \operatorname {csgn}\left (\frac {i}{\ln \left (x \right )}\right ) \operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right ) x -8 i \pi \ln \left (x \right ) \operatorname {csgn}\left (\frac {i}{\ln \left (x \right )}\right ) \operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right )^{2} x -8 i \pi \ln \left (x \right ) \operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right )^{2} x +8 i \pi \ln \left (x \right ) \operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right )^{3} x +x^{2} \ln \left (x \right )+16 x \ln \left (x \right ) \ln \left (\ln \left (x \right )\right )-16 x \ln \left (x \right )^{2}+x \ln \left (x \right )-16 \ln \left (x \right )+16\right ) \left (x +\ln \left (-16 \ln \left (\ln \left (x \right )\right )+16 \ln \left (x \right )-8 i \pi \,\operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right ) \left (-\operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right )+\operatorname {csgn}\left (\frac {i}{\ln \left (x \right )}\right )\right ) \left (-\operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right )+\operatorname {csgn}\left (i x \right )\right )-x \right )\right )}-\frac {2 \ln \left (x \right ) x \left (8 i \pi \,\operatorname {csgn}\left (\frac {i}{\ln \left (x \right )}\right ) \operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right ) x -8 i \pi \,\operatorname {csgn}\left (\frac {i}{\ln \left (x \right )}\right ) \operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right )^{2} x -8 i \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right )^{2} x +8 i \pi \operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right )^{3} x +x^{2}+16 x \ln \left (\ln \left (x \right )\right )-16 x \ln \left (x \right )+x -16\right )}{\left (8 i \pi \ln \left (x \right ) \operatorname {csgn}\left (\frac {i}{\ln \left (x \right )}\right ) \operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right ) x -8 i \pi \ln \left (x \right ) \operatorname {csgn}\left (\frac {i}{\ln \left (x \right )}\right ) \operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right )^{2} x -8 i \pi \ln \left (x \right ) \operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right )^{2} x +8 i \pi \ln \left (x \right ) \operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right )^{3} x +x^{2} \ln \left (x \right )+16 x \ln \left (x \right ) \ln \left (\ln \left (x \right )\right )-16 x \ln \left (x \right )^{2}+x \ln \left (x \right )-16 \ln \left (x \right )+16\right ) \left (x +\ln \left (-16 \ln \left (\ln \left (x \right )\right )+16 \ln \left (x \right )-8 i \pi \,\operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right ) \left (-\operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right )+\operatorname {csgn}\left (\frac {i}{\ln \left (x \right )}\right )\right ) \left (-\operatorname {csgn}\left (\frac {i x}{\ln \left (x \right )}\right )+\operatorname {csgn}\left (i x \right )\right )-x \right )\right )}\)	\(509\)

[In]

int(((-32*ln(x)*ln(x/ln(x))+2*x*ln(x))*ln(16*ln(x/ln(x))-x)+(-2*x+32)*ln(x)-32)/((16*ln(x)*ln(x/ln(x))-x*ln(x)
)*ln(16*ln(x/ln(x))-x)^2+(32*x*ln(x)*ln(x/ln(x))-2*x^2*ln(x))*ln(16*ln(x/ln(x))-x)+16*x^2*ln(x)*ln(x/ln(x))-x^
3*ln(x)),x,method=_RETURNVERBOSE)

[Out]

-2*x/(x+ln(16*ln(x/ln(x))-x))

Fricas [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.84 \[ \int \frac {-32+(32-2 x) \log (x)+\left (2 x \log (x)-32 \log (x) \log \left (\frac {x}{\log (x)}\right )\right ) \log \left (-x+16 \log \left (\frac {x}{\log (x)}\right )\right )}{-x^3 \log (x)+16 x^2 \log (x) \log \left (\frac {x}{\log (x)}\right )+\left (-2 x^2 \log (x)+32 x \log (x) \log \left (\frac {x}{\log (x)}\right )\right ) \log \left (-x+16 \log \left (\frac {x}{\log (x)}\right )\right )+\left (-x \log (x)+16 \log (x) \log \left (\frac {x}{\log (x)}\right )\right ) \log ^2\left (-x+16 \log \left (\frac {x}{\log (x)}\right )\right )} \, dx=-\frac {2 \, x}{x + \log \left (-x + 16 \, \log \left (\frac {x}{\log \left (x\right )}\right )\right )} \]

[In]

integrate(((-32*log(x)*log(x/log(x))+2*x*log(x))*log(16*log(x/log(x))-x)+(-2*x+32)*log(x)-32)/((16*log(x)*log(
x/log(x))-x*log(x))*log(16*log(x/log(x))-x)^2+(32*x*log(x)*log(x/log(x))-2*x^2*log(x))*log(16*log(x/log(x))-x)
+16*x^2*log(x)*log(x/log(x))-x^3*log(x)),x, algorithm="fricas")

[Out]

-2*x/(x + log(-x + 16*log(x/log(x))))

Sympy [A] (verification not implemented)

Time = 0.28 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.68 \[ \int \frac {-32+(32-2 x) \log (x)+\left (2 x \log (x)-32 \log (x) \log \left (\frac {x}{\log (x)}\right )\right ) \log \left (-x+16 \log \left (\frac {x}{\log (x)}\right )\right )}{-x^3 \log (x)+16 x^2 \log (x) \log \left (\frac {x}{\log (x)}\right )+\left (-2 x^2 \log (x)+32 x \log (x) \log \left (\frac {x}{\log (x)}\right )\right ) \log \left (-x+16 \log \left (\frac {x}{\log (x)}\right )\right )+\left (-x \log (x)+16 \log (x) \log \left (\frac {x}{\log (x)}\right )\right ) \log ^2\left (-x+16 \log \left (\frac {x}{\log (x)}\right )\right )} \, dx=- \frac {2 x}{x + \log {\left (- x + 16 \log {\left (\frac {x}{\log {\left (x \right )}} \right )} \right )}} \]

[In]

integrate(((-32*ln(x)*ln(x/ln(x))+2*x*ln(x))*ln(16*ln(x/ln(x))-x)+(-2*x+32)*ln(x)-32)/((16*ln(x)*ln(x/ln(x))-x
*ln(x))*ln(16*ln(x/ln(x))-x)**2+(32*x*ln(x)*ln(x/ln(x))-2*x**2*ln(x))*ln(16*ln(x/ln(x))-x)+16*x**2*ln(x)*ln(x/
ln(x))-x**3*ln(x)),x)

[Out]

-2*x/(x + log(-x + 16*log(x/log(x))))

Maxima [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.84 \[ \int \frac {-32+(32-2 x) \log (x)+\left (2 x \log (x)-32 \log (x) \log \left (\frac {x}{\log (x)}\right )\right ) \log \left (-x+16 \log \left (\frac {x}{\log (x)}\right )\right )}{-x^3 \log (x)+16 x^2 \log (x) \log \left (\frac {x}{\log (x)}\right )+\left (-2 x^2 \log (x)+32 x \log (x) \log \left (\frac {x}{\log (x)}\right )\right ) \log \left (-x+16 \log \left (\frac {x}{\log (x)}\right )\right )+\left (-x \log (x)+16 \log (x) \log \left (\frac {x}{\log (x)}\right )\right ) \log ^2\left (-x+16 \log \left (\frac {x}{\log (x)}\right )\right )} \, dx=-\frac {2 \, x}{x + \log \left (-x + 16 \, \log \left (x\right ) - 16 \, \log \left (\log \left (x\right )\right )\right )} \]

[In]

integrate(((-32*log(x)*log(x/log(x))+2*x*log(x))*log(16*log(x/log(x))-x)+(-2*x+32)*log(x)-32)/((16*log(x)*log(
x/log(x))-x*log(x))*log(16*log(x/log(x))-x)^2+(32*x*log(x)*log(x/log(x))-2*x^2*log(x))*log(16*log(x/log(x))-x)
+16*x^2*log(x)*log(x/log(x))-x^3*log(x)),x, algorithm="maxima")

[Out]

-2*x/(x + log(-x + 16*log(x) - 16*log(log(x))))

Giac [A] (verification not implemented)

none

Time = 0.49 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.84 \[ \int \frac {-32+(32-2 x) \log (x)+\left (2 x \log (x)-32 \log (x) \log \left (\frac {x}{\log (x)}\right )\right ) \log \left (-x+16 \log \left (\frac {x}{\log (x)}\right )\right )}{-x^3 \log (x)+16 x^2 \log (x) \log \left (\frac {x}{\log (x)}\right )+\left (-2 x^2 \log (x)+32 x \log (x) \log \left (\frac {x}{\log (x)}\right )\right ) \log \left (-x+16 \log \left (\frac {x}{\log (x)}\right )\right )+\left (-x \log (x)+16 \log (x) \log \left (\frac {x}{\log (x)}\right )\right ) \log ^2\left (-x+16 \log \left (\frac {x}{\log (x)}\right )\right )} \, dx=-\frac {2 \, x}{x + \log \left (-x + 16 \, \log \left (x\right ) - 16 \, \log \left (\log \left (x\right )\right )\right )} \]

[In]

integrate(((-32*log(x)*log(x/log(x))+2*x*log(x))*log(16*log(x/log(x))-x)+(-2*x+32)*log(x)-32)/((16*log(x)*log(
x/log(x))-x*log(x))*log(16*log(x/log(x))-x)^2+(32*x*log(x)*log(x/log(x))-2*x^2*log(x))*log(16*log(x/log(x))-x)
+16*x^2*log(x)*log(x/log(x))-x^3*log(x)),x, algorithm="giac")

[Out]

-2*x/(x + log(-x + 16*log(x) - 16*log(log(x))))

Mupad [B] (verification not implemented)

Time = 13.66 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.84 \[ \int \frac {-32+(32-2 x) \log (x)+\left (2 x \log (x)-32 \log (x) \log \left (\frac {x}{\log (x)}\right )\right ) \log \left (-x+16 \log \left (\frac {x}{\log (x)}\right )\right )}{-x^3 \log (x)+16 x^2 \log (x) \log \left (\frac {x}{\log (x)}\right )+\left (-2 x^2 \log (x)+32 x \log (x) \log \left (\frac {x}{\log (x)}\right )\right ) \log \left (-x+16 \log \left (\frac {x}{\log (x)}\right )\right )+\left (-x \log (x)+16 \log (x) \log \left (\frac {x}{\log (x)}\right )\right ) \log ^2\left (-x+16 \log \left (\frac {x}{\log (x)}\right )\right )} \, dx=-\frac {2\,x}{x+\ln \left (16\,\ln \left (\frac {x}{\ln \left (x\right )}\right )-x\right )} \]

[In]

int((log(x)*(2*x - 32) - log(16*log(x/log(x)) - x)*(2*x*log(x) - 32*log(x/log(x))*log(x)) + 32)/(x^3*log(x) +
log(16*log(x/log(x)) - x)^2*(x*log(x) - 16*log(x/log(x))*log(x)) + log(16*log(x/log(x)) - x)*(2*x^2*log(x) - 3
2*x*log(x/log(x))*log(x)) - 16*x^2*log(x/log(x))*log(x)),x)

[Out]

-(2*x)/(x + log(16*log(x/log(x)) - x))