\(\int \frac {10 x}{125-75 x+15 x^2-x^3+(600 x-240 x^2+24 x^3) (i \pi +\log (\frac {e}{4}))^2+(960 x^2-192 x^3) (i \pi +\log (\frac {e}{4}))^4+512 x^3 (i \pi +\log (\frac {e}{4}))^6} \, dx\) [8795]

Optimal result

Integrand size = 94, antiderivative size = 28 \[ \int \frac {10 x}{125-75 x+15 x^2-x^3+\left (600 x-240 x^2+24 x^3\right ) \left (i \pi +\log \left (\frac {e}{4}\right )\right )^2+\left (960 x^2-192 x^3\right ) \left (i \pi +\log \left (\frac {e}{4}\right )\right )^4+512 x^3 \left (i \pi +\log \left (\frac {e}{4}\right )\right )^6} \, dx=\frac {x^2}{\left (5-x+8 x \left (i \pi +\log \left (\frac {e}{4}\right )\right )^2\right )^2} \]

[Out]

x^2/(8*x*ln(-1/4*exp(1))^2+5-x)^2

Rubi [B] (verified)

Both result and optimal contain complex but leaf count is larger than twice the leaf count of optimal. \(133\) vs. \(2(28)=56\).

Time = 0.35 (sec) , antiderivative size = 133, normalized size of antiderivative = 4.75, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.032, Rules used = {6, 12, 2099} \[ \int \frac {10 x}{125-75 x+15 x^2-x^3+\left (600 x-240 x^2+24 x^3\right ) \left (i \pi +\log \left (\frac {e}{4}\right )\right )^2+\left (960 x^2-192 x^3\right ) \left (i \pi +\log \left (\frac {e}{4}\right )\right )^4+512 x^3 \left (i \pi +\log \left (\frac {e}{4}\right )\right )^6} \, dx=\frac {25}{\left (7-8 \pi ^2+8 \log ^2(4)+16 i \pi (1-\log (4))-16 \log (4)\right )^2 \left (5+x \left (7-8 \pi ^2+8 \log ^2(4)+16 i \pi (1-\log (4))-16 \log (4)\right )\right )^2}-\frac {10}{\left (7-8 \pi ^2+8 \log ^2(4)+16 i \pi (1-\log (4))-16 \log (4)\right )^2 \left (5+x \left (7-8 \pi ^2+8 \log ^2(4)+16 i \pi (1-\log (4))-16 \log (4)\right )\right )} \]

[In]

Int[(10*x)/(125 - 75*x + 15*x^2 - x^3 + (600*x - 240*x^2 + 24*x^3)*(I*Pi + Log[E/4])^2 + (960*x^2 - 192*x^3)*(
I*Pi + Log[E/4])^4 + 512*x^3*(I*Pi + Log[E/4])^6),x]

[Out]

25/((7 - 8*Pi^2 + (16*I)*Pi*(1 - Log[4]) - 16*Log[4] + 8*Log[4]^2)^2*(5 + x*(7 - 8*Pi^2 + (16*I)*Pi*(1 - Log[4
]) - 16*Log[4] + 8*Log[4]^2))^2) - 10/((7 - 8*Pi^2 + (16*I)*Pi*(1 - Log[4]) - 16*Log[4] + 8*Log[4]^2)^2*(5 + x
*(7 - 8*Pi^2 + (16*I)*Pi*(1 - Log[4]) - 16*Log[4] + 8*Log[4]^2)))

Rule 6

Int[(u_.)*((w_.) + (a_.)*(v_) + (b_.)*(v_))^(p_.), x_Symbol] :> Int[u*((a + b)*v + w)^p, x] /; FreeQ[{a, b}, x
] &&  !FreeQ[v, x]

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 2099

Int[(P_)^(p_)*(Q_)^(q_.), x_Symbol] :> With[{PP = Factor[P]}, Int[ExpandIntegrand[PP^p*Q^q, x], x] /;  !SumQ[N
onfreeFactors[PP, x]]] /; FreeQ[q, x] && PolyQ[P, x] && PolyQ[Q, x] && IntegerQ[p] && NeQ[P, x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {10 x}{125-75 x+15 x^2+\left (600 x-240 x^2+24 x^3\right ) \left (i \pi +\log \left (\frac {e}{4}\right )\right )^2+\left (960 x^2-192 x^3\right ) \left (i \pi +\log \left (\frac {e}{4}\right )\right )^4+x^3 \left (-1+512 \left (i \pi +\log \left (\frac {e}{4}\right )\right )^6\right )} \, dx \\ & = 10 \int \frac {x}{125-75 x+15 x^2+\left (600 x-240 x^2+24 x^3\right ) \left (i \pi +\log \left (\frac {e}{4}\right )\right )^2+\left (960 x^2-192 x^3\right ) \left (i \pi +\log \left (\frac {e}{4}\right )\right )^4+x^3 \left (-1+512 \left (i \pi +\log \left (\frac {e}{4}\right )\right )^6\right )} \, dx \\ & = 10 \int \left (\frac {5}{\left (-7+8 \pi ^2-16 i \pi (1-\log (4))+16 \log (4)-8 \log ^2(4)\right ) \left (5+x \left (7-8 \pi ^2+16 i \pi (1-\log (4))-16 \log (4)+8 \log ^2(4)\right )\right )^3}+\frac {1}{\left (7-8 \pi ^2+16 i \pi (1-\log (4))-16 \log (4)+8 \log ^2(4)\right ) \left (5+x \left (7-8 \pi ^2+16 i \pi (1-\log (4))-16 \log (4)+8 \log ^2(4)\right )\right )^2}\right ) \, dx \\ & = \frac {25}{\left (7-8 \pi ^2+16 i \pi (1-\log (4))-16 \log (4)+8 \log ^2(4)\right )^2 \left (5+x \left (7-8 \pi ^2+16 i \pi (1-\log (4))-16 \log (4)+8 \log ^2(4)\right )\right )^2}-\frac {10}{\left (7-8 \pi ^2+16 i \pi (1-\log (4))-16 \log (4)+8 \log ^2(4)\right )^2 \left (5+x \left (7-8 \pi ^2+16 i \pi (1-\log (4))-16 \log (4)+8 \log ^2(4)\right )\right )} \\ \end{align*}

Mathematica [B] (verified)

Both result and optimal contain complex but leaf count is larger than twice the leaf count of optimal. \(93\) vs. \(2(28)=56\).

Time = 0.07 (sec) , antiderivative size = 93, normalized size of antiderivative = 3.32 \[ \int \frac {10 x}{125-75 x+15 x^2-x^3+\left (600 x-240 x^2+24 x^3\right ) \left (i \pi +\log \left (\frac {e}{4}\right )\right )^2+\left (960 x^2-192 x^3\right ) \left (i \pi +\log \left (\frac {e}{4}\right )\right )^4+512 x^3 \left (i \pi +\log \left (\frac {e}{4}\right )\right )^6} \, dx=-\frac {5 \left (5-2 x \left (-7+8 \pi ^2+16 i \pi (-1+\log (4))+16 \log (4)-8 \log ^2(4)\right )\right )}{\left (-7+8 \pi ^2+16 i \pi (-1+\log (4))+16 \log (4)-8 \log ^2(4)\right )^2 \left (-5+x \left (-7+8 \pi ^2+16 i \pi (-1+\log (4))+16 \log (4)-8 \log ^2(4)\right )\right )^2} \]

[In]

Integrate[(10*x)/(125 - 75*x + 15*x^2 - x^3 + (600*x - 240*x^2 + 24*x^3)*(I*Pi + Log[E/4])^2 + (960*x^2 - 192*
x^3)*(I*Pi + Log[E/4])^4 + 512*x^3*(I*Pi + Log[E/4])^6),x]

[Out]

(-5*(5 - 2*x*(-7 + 8*Pi^2 + (16*I)*Pi*(-1 + Log[4]) + 16*Log[4] - 8*Log[4]^2)))/((-7 + 8*Pi^2 + (16*I)*Pi*(-1
+ Log[4]) + 16*Log[4] - 8*Log[4]^2)^2*(-5 + x*(-7 + 8*Pi^2 + (16*I)*Pi*(-1 + Log[4]) + 16*Log[4] - 8*Log[4]^2)
)^2)

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(48\) vs. \(2(21)=42\).

Time = 2.84 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.75

method	result	size
parallelrisch	\(\frac {x^{2}}{64 \ln \left (-\frac {{\mathrm e}}{4}\right )^{4} x^{2}-16 \ln \left (-\frac {{\mathrm e}}{4}\right )^{2} x^{2}+80 x \ln \left (-\frac {{\mathrm e}}{4}\right )^{2}+x^{2}-10 x +25}\)	\(49\)
default	\(-\frac {10}{\left (8 \ln \left (-\frac {{\mathrm e}}{4}\right )^{2}-1\right )^{2} \left (8 x \ln \left (-\frac {{\mathrm e}}{4}\right )^{2}+5-x \right )}+\frac {25}{\left (8 \ln \left (-\frac {{\mathrm e}}{4}\right )^{2}-1\right )^{2} \left (8 x \ln \left (-\frac {{\mathrm e}}{4}\right )^{2}+5-x \right )^{2}}\)	\(66\)
gosper	\(-\frac {5 \left (16 x \ln \left (-\frac {{\mathrm e}}{4}\right )^{2}-2 x +5\right )}{\left (64 \ln \left (-\frac {{\mathrm e}}{4}\right )^{4} x^{2}-16 \ln \left (-\frac {{\mathrm e}}{4}\right )^{2} x^{2}+80 x \ln \left (-\frac {{\mathrm e}}{4}\right )^{2}+x^{2}-10 x +25\right ) \left (8 \ln \left (-\frac {{\mathrm e}}{4}\right )^{2}-1\right )^{2}}\)	\(75\)
risch	\(\frac {\frac {10 x}{-448+2048 \ln \left (2\right )-1024 i \pi -2048 \ln \left (2\right )^{2}+2048 i \ln \left (2\right ) \pi +512 \pi ^{2}}-\frac {25}{64 \left (-7+32 \ln \left (2\right )-16 i \pi -32 \ln \left (2\right )^{2}+32 i \ln \left (2\right ) \pi +8 \pi ^{2}\right )^{2}}}{-23 i \pi \ln \left (2\right ) x^{2}+\frac {7 i \pi \,x^{2}}{2}+\pi ^{4} x^{2}+\frac {5 i \pi x}{2}-24 \pi ^{2} \ln \left (2\right )^{2} x^{2}+8 i \pi ^{3} \ln \left (2\right ) x^{2}+16 x^{2} \ln \left (2\right )^{4}+24 \pi ^{2} \ln \left (2\right ) x^{2}-5 i \pi \ln \left (2\right ) x -32 x^{2} \ln \left (2\right )^{3}-\frac {23 \pi ^{2} x^{2}}{4}-32 i \pi \ln \left (2\right )^{3} x^{2}-4 i \pi ^{3} x^{2}+23 x^{2} \ln \left (2\right )^{2}-\frac {5 x \,\pi ^{2}}{4}+48 i \pi \ln \left (2\right )^{2} x^{2}+5 x \ln \left (2\right )^{2}-7 x^{2} \ln \left (2\right )-5 x \ln \left (2\right )+\frac {49 x^{2}}{64}+\frac {35 x}{32}+\frac {25}{64}}\)	\(238\)

[In]

int(10*x/(512*x^3*ln(-1/4*exp(1))^6+(-192*x^3+960*x^2)*ln(-1/4*exp(1))^4+(24*x^3-240*x^2+600*x)*ln(-1/4*exp(1)
)^2-x^3+15*x^2-75*x+125),x,method=_RETURNVERBOSE)

[Out]

x^2/(64*ln(-1/4*exp(1))^4*x^2-16*ln(-1/4*exp(1))^2*x^2+80*x*ln(-1/4*exp(1))^2+x^2-10*x+25)

Fricas [C] (verification not implemented)

Result contains complex when optimal does not.

Time = 0.28 (sec) , antiderivative size = 199, normalized size of antiderivative = 7.11 \[ \int \frac {10 x}{125-75 x+15 x^2-x^3+\left (600 x-240 x^2+24 x^3\right ) \left (i \pi +\log \left (\frac {e}{4}\right )\right )^2+\left (960 x^2-192 x^3\right ) \left (i \pi +\log \left (\frac {e}{4}\right )\right )^4+512 x^3 \left (i \pi +\log \left (\frac {e}{4}\right )\right )^6} \, dx=-\frac {5 \, {\left (16 \, {\left (i \, \pi + 2 \, \log \left (2\right )\right )}^{2} x - 32 \, {\left (i \, \pi + 2 \, \log \left (2\right )\right )} x + 14 \, x + 5\right )}}{4096 \, {\left (i \, \pi + 2 \, \log \left (2\right )\right )}^{8} x^{2} - 32768 \, {\left (i \, \pi + 2 \, \log \left (2\right )\right )}^{7} x^{2} + 5120 \, {\left (i \, \pi + 2 \, \log \left (2\right )\right )}^{6} {\left (22 \, x^{2} + x\right )} - 2048 \, {\left (i \, \pi + 2 \, \log \left (2\right )\right )}^{5} {\left (106 \, x^{2} + 15 \, x\right )} + 64 \, {\left (i \, \pi + 2 \, \log \left (2\right )\right )}^{4} {\left (4006 \, x^{2} + 1170 \, x + 25\right )} - 256 \, {\left (i \, \pi + 2 \, \log \left (2\right )\right )}^{3} {\left (742 \, x^{2} + 370 \, x + 25\right )} + 80 \, {\left (i \, \pi + 2 \, \log \left (2\right )\right )}^{2} {\left (1078 \, x^{2} + 819 \, x + 115\right )} - 224 \, {\left (i \, \pi + 2 \, \log \left (2\right )\right )} {\left (98 \, x^{2} + 105 \, x + 25\right )} + 2401 \, x^{2} + 3430 \, x + 1225} \]

[In]

integrate(10*x/(512*x^3*log(-1/4*exp(1))^6+(-192*x^3+960*x^2)*log(-1/4*exp(1))^4+(24*x^3-240*x^2+600*x)*log(-1
/4*exp(1))^2-x^3+15*x^2-75*x+125),x, algorithm="fricas")

[Out]

-5*(16*(I*pi + 2*log(2))^2*x - 32*(I*pi + 2*log(2))*x + 14*x + 5)/(4096*(I*pi + 2*log(2))^8*x^2 - 32768*(I*pi
+ 2*log(2))^7*x^2 + 5120*(I*pi + 2*log(2))^6*(22*x^2 + x) - 2048*(I*pi + 2*log(2))^5*(106*x^2 + 15*x) + 64*(I*
pi + 2*log(2))^4*(4006*x^2 + 1170*x + 25) - 256*(I*pi + 2*log(2))^3*(742*x^2 + 370*x + 25) + 80*(I*pi + 2*log(
2))^2*(1078*x^2 + 819*x + 115) - 224*(I*pi + 2*log(2))*(98*x^2 + 105*x + 25) + 2401*x^2 + 3430*x + 1225)

Sympy [B] (verification not implemented)

Both result and optimal contain complex but leaf count of result is larger than twice the leaf count of optimal. 765 vs. \(2 (22) = 44\).

Time = 4.15 (sec) , antiderivative size = 765, normalized size of antiderivative = 27.32 \[ \int \frac {10 x}{125-75 x+15 x^2-x^3+\left (600 x-240 x^2+24 x^3\right ) \left (i \pi +\log \left (\frac {e}{4}\right )\right )^2+\left (960 x^2-192 x^3\right ) \left (i \pi +\log \left (\frac {e}{4}\right )\right )^4+512 x^3 \left (i \pi +\log \left (\frac {e}{4}\right )\right )^6} \, dx=\text {Too large to display} \]

[In]

integrate(10*x/(512*x**3*ln(-1/4*exp(1))**6+(-192*x**3+960*x**2)*ln(-1/4*exp(1))**4+(24*x**3-240*x**2+600*x)*l
n(-1/4*exp(1))**2-x**3+15*x**2-75*x+125),x)

[Out]

-10*(x*(-16*pi**2 - 64*log(2) + 14 + 64*log(2)**2 - 64*I*pi*log(2) + 32*I*pi) + 5)/(x**2*(-18350080*pi**4*log(
2)**3 - 917504*pi**6*log(2)**2 - 4341760*pi**4*log(2) - 225280*pi**6 - 54067200*pi**2*log(2)**4 - 12306432*pi*
*2*log(2)**2 - 14680064*pi**2*log(2)**6 - 13893632*log(2)**5 - 172480*pi**2 - 3039232*log(2)**3 - 8388608*log(
2)**7 - 87808*log(2) + 4802 + 2097152*log(2)**8 + 689920*log(2)**2 + 14417920*log(2)**6 + 8204288*log(2)**4 +
2279424*pi**2*log(2) + 512768*pi**4 + 44040192*pi**2*log(2)**5 + 8192*pi**8 + 34734080*pi**2*log(2)**3 + 91750
40*pi**4*log(2)**4 + 917504*pi**6*log(2) + 13516800*pi**4*log(2)**2 - 2703360*I*pi**5*log(2) - 3670016*I*pi**5
*log(2)**3 - 36700160*I*pi**3*log(2)**4 - 17367040*I*pi**3*log(2)**2 - 65536*I*pi**7 - 43253760*I*pi*log(2)**5
- 16408576*I*pi*log(2)**3 - 379904*I*pi**3 - 8388608*I*pi*log(2)**7 - 689920*I*pi*log(2) + 43904*I*pi + 45588
48*I*pi*log(2)**2 + 29360128*I*pi*log(2)**6 + 34734080*I*pi*log(2)**4 + 14680064*I*pi**3*log(2)**5 + 4102144*I
*pi**3*log(2) + 434176*I*pi**5 + 131072*I*pi**7*log(2) + 36044800*I*pi**3*log(2)**3 + 5505024*I*pi**5*log(2)**
2) + x*(-614400*pi**4*log(2) - 3594240*pi**2*log(2)**2 - 10240*pi**6 - 2457600*pi**2*log(2)**4 - 131040*pi**2
- 1515520*log(2)**3 - 1966080*log(2)**5 - 94080*log(2) + 6860 + 655360*log(2)**6 + 524160*log(2)**2 + 2396160*
log(2)**4 + 1136640*pi**2*log(2) + 149760*pi**4 + 4915200*pi**2*log(2)**3 + 614400*pi**4*log(2)**2 - 2457600*I
*pi**3*log(2)**2 - 122880*I*pi**5*log(2) - 189440*I*pi**3 - 4792320*I*pi*log(2)**3 - 524160*I*pi*log(2) - 1966
080*I*pi*log(2)**5 + 47040*I*pi + 2273280*I*pi*log(2)**2 + 4915200*I*pi*log(2)**4 + 1638400*I*pi**3*log(2)**3
+ 61440*I*pi**5 + 1198080*I*pi**3*log(2)) - 76800*pi**2*log(2)**2 - 18400*pi**2 - 102400*log(2)**3 - 22400*log
(2) + 2450 + 51200*log(2)**4 + 73600*log(2)**2 + 3200*pi**4 + 76800*pi**2*log(2) - 12800*I*pi**3 - 73600*I*pi*
log(2) - 102400*I*pi*log(2)**3 + 11200*I*pi + 153600*I*pi*log(2)**2 + 25600*I*pi**3*log(2))

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 114 vs. \(2 (21) = 42\).

Time = 0.20 (sec) , antiderivative size = 114, normalized size of antiderivative = 4.07 \[ \int \frac {10 x}{125-75 x+15 x^2-x^3+\left (600 x-240 x^2+24 x^3\right ) \left (i \pi +\log \left (\frac {e}{4}\right )\right )^2+\left (960 x^2-192 x^3\right ) \left (i \pi +\log \left (\frac {e}{4}\right )\right )^4+512 x^3 \left (i \pi +\log \left (\frac {e}{4}\right )\right )^6} \, dx=-\frac {5 \, {\left (2 \, {\left (8 \, \log \left (-\frac {1}{4} \, e\right )^{2} - 1\right )} x + 5\right )}}{1600 \, \log \left (-\frac {1}{4} \, e\right )^{4} + {\left (4096 \, \log \left (-\frac {1}{4} \, e\right )^{8} - 2048 \, \log \left (-\frac {1}{4} \, e\right )^{6} + 384 \, \log \left (-\frac {1}{4} \, e\right )^{4} - 32 \, \log \left (-\frac {1}{4} \, e\right )^{2} + 1\right )} x^{2} + 10 \, {\left (512 \, \log \left (-\frac {1}{4} \, e\right )^{6} - 192 \, \log \left (-\frac {1}{4} \, e\right )^{4} + 24 \, \log \left (-\frac {1}{4} \, e\right )^{2} - 1\right )} x - 400 \, \log \left (-\frac {1}{4} \, e\right )^{2} + 25} \]

[In]

integrate(10*x/(512*x^3*log(-1/4*exp(1))^6+(-192*x^3+960*x^2)*log(-1/4*exp(1))^4+(24*x^3-240*x^2+600*x)*log(-1
/4*exp(1))^2-x^3+15*x^2-75*x+125),x, algorithm="maxima")

[Out]

-5*(2*(8*log(-1/4*e)^2 - 1)*x + 5)/(1600*log(-1/4*e)^4 + (4096*log(-1/4*e)^8 - 2048*log(-1/4*e)^6 + 384*log(-1
/4*e)^4 - 32*log(-1/4*e)^2 + 1)*x^2 + 10*(512*log(-1/4*e)^6 - 192*log(-1/4*e)^4 + 24*log(-1/4*e)^2 - 1)*x - 40
0*log(-1/4*e)^2 + 25)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 56 vs. \(2 (21) = 42\).

Time = 0.27 (sec) , antiderivative size = 56, normalized size of antiderivative = 2.00 \[ \int \frac {10 x}{125-75 x+15 x^2-x^3+\left (600 x-240 x^2+24 x^3\right ) \left (i \pi +\log \left (\frac {e}{4}\right )\right )^2+\left (960 x^2-192 x^3\right ) \left (i \pi +\log \left (\frac {e}{4}\right )\right )^4+512 x^3 \left (i \pi +\log \left (\frac {e}{4}\right )\right )^6} \, dx=-\frac {5 \, {\left (16 \, x \log \left (-\frac {1}{4} \, e\right )^{2} - 2 \, x + 5\right )}}{{\left (64 \, \log \left (-\frac {1}{4} \, e\right )^{4} - 16 \, \log \left (-\frac {1}{4} \, e\right )^{2} + 1\right )} {\left (8 \, x \log \left (-\frac {1}{4} \, e\right )^{2} - x + 5\right )}^{2}} \]

[In]

integrate(10*x/(512*x^3*log(-1/4*exp(1))^6+(-192*x^3+960*x^2)*log(-1/4*exp(1))^4+(24*x^3-240*x^2+600*x)*log(-1
/4*exp(1))^2-x^3+15*x^2-75*x+125),x, algorithm="giac")

[Out]

-5*(16*x*log(-1/4*e)^2 - 2*x + 5)/((64*log(-1/4*e)^4 - 16*log(-1/4*e)^2 + 1)*(8*x*log(-1/4*e)^2 - x + 5)^2)

Mupad [B] (verification not implemented)

Time = 0.22 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.68 \[ \int \frac {10 x}{125-75 x+15 x^2-x^3+\left (600 x-240 x^2+24 x^3\right ) \left (i \pi +\log \left (\frac {e}{4}\right )\right )^2+\left (960 x^2-192 x^3\right ) \left (i \pi +\log \left (\frac {e}{4}\right )\right )^4+512 x^3 \left (i \pi +\log \left (\frac {e}{4}\right )\right )^6} \, dx=-\frac {5\,\left (16\,x\,{\ln \left (-\frac {\mathrm {e}}{4}\right )}^2-2\,x+5\right )}{{\left (8\,{\ln \left (-\frac {\mathrm {e}}{4}\right )}^2-1\right )}^2\,{\left (8\,x\,{\ln \left (-\frac {\mathrm {e}}{4}\right )}^2-x+5\right )}^2} \]

[In]

int((10*x)/(log(-exp(1)/4)^2*(600*x - 240*x^2 + 24*x^3) - 75*x + log(-exp(1)/4)^4*(960*x^2 - 192*x^3) + 512*x^
3*log(-exp(1)/4)^6 + 15*x^2 - x^3 + 125),x)

[Out]

-(5*(16*x*log(-exp(1)/4)^2 - 2*x + 5))/((8*log(-exp(1)/4)^2 - 1)^2*(8*x*log(-exp(1)/4)^2 - x + 5)^2)