3.38.93 \(\int \frac {6 e^x+(-12 e^x-3 e^x \log (x^2)) \log (4+\log (x^2))+(e^x (-24 x+12 x^2)+e^x (-6 x+3 x^2) \log (x^2)+(e^x (-24+12 x)+e^x (-6+3 x) \log (x^2)) \log (4+\log (x^2))) \log (\frac {x}{x+\log (4+\log (x^2))})}{(4 x^4+x^4 \log (x^2)+(4 x^3+x^3 \log (x^2)) \log (4+\log (x^2))) \log ^2(\frac {x}{x+\log (4+\log (x^2))})} \, dx\)

Optimal. Leaf size=26 \[ 4+\frac {3 e^x}{x^2 \log \left (\frac {x}{x+\log \left (4+\log \left (x^2\right )\right )}\right )} \]

________________________________________________________________________________________

Rubi [F]  time = 7.52, 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 {6 e^x+\left (-12 e^x-3 e^x \log \left (x^2\right )\right ) \log \left (4+\log \left (x^2\right )\right )+\left (e^x \left (-24 x+12 x^2\right )+e^x \left (-6 x+3 x^2\right ) \log \left (x^2\right )+\left (e^x (-24+12 x)+e^x (-6+3 x) \log \left (x^2\right )\right ) \log \left (4+\log \left (x^2\right )\right )\right ) \log \left (\frac {x}{x+\log \left (4+\log \left (x^2\right )\right )}\right )}{\left (4 x^4+x^4 \log \left (x^2\right )+\left (4 x^3+x^3 \log \left (x^2\right )\right ) \log \left (4+\log \left (x^2\right )\right )\right ) \log ^2\left (\frac {x}{x+\log \left (4+\log \left (x^2\right )\right )}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(6*E^x + (-12*E^x - 3*E^x*Log[x^2])*Log[4 + Log[x^2]] + (E^x*(-24*x + 12*x^2) + E^x*(-6*x + 3*x^2)*Log[x^2
] + (E^x*(-24 + 12*x) + E^x*(-6 + 3*x)*Log[x^2])*Log[4 + Log[x^2]])*Log[x/(x + Log[4 + Log[x^2]])])/((4*x^4 +
x^4*Log[x^2] + (4*x^3 + x^3*Log[x^2])*Log[4 + Log[x^2]])*Log[x/(x + Log[4 + Log[x^2]])]^2),x]

[Out]

6*Defer[Int][E^x/(x^3*(4 + Log[x^2])*(x + Log[4 + Log[x^2]])*Log[x/(x + Log[4 + Log[x^2]])]^2), x] - 12*Defer[
Int][(E^x*Log[4 + Log[x^2]])/(x^3*(4 + Log[x^2])*(x + Log[4 + Log[x^2]])*Log[x/(x + Log[4 + Log[x^2]])]^2), x]
- 3*Defer[Int][(E^x*Log[x^2]*Log[4 + Log[x^2]])/(x^3*(4 + Log[x^2])*(x + Log[4 + Log[x^2]])*Log[x/(x + Log[4
+ Log[x^2]])]^2), x] - 6*Defer[Int][E^x/(x^3*Log[x/(x + Log[4 + Log[x^2]])]), x] + 3*Defer[Int][E^x/(x^2*Log[x
/(x + Log[4 + Log[x^2]])]), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3 e^x \left (2+(-2+x) x \left (4+\log \left (x^2\right )\right ) \log \left (\frac {x}{x+\log \left (4+\log \left (x^2\right )\right )}\right )+\left (4+\log \left (x^2\right )\right ) \log \left (4+\log \left (x^2\right )\right ) \left (-1+(-2+x) \log \left (\frac {x}{x+\log \left (4+\log \left (x^2\right )\right )}\right )\right )\right )}{x^3 \left (4+\log \left (x^2\right )\right ) \left (x+\log \left (4+\log \left (x^2\right )\right )\right ) \log ^2\left (\frac {x}{x+\log \left (4+\log \left (x^2\right )\right )}\right )} \, dx\\ &=3 \int \frac {e^x \left (2+(-2+x) x \left (4+\log \left (x^2\right )\right ) \log \left (\frac {x}{x+\log \left (4+\log \left (x^2\right )\right )}\right )+\left (4+\log \left (x^2\right )\right ) \log \left (4+\log \left (x^2\right )\right ) \left (-1+(-2+x) \log \left (\frac {x}{x+\log \left (4+\log \left (x^2\right )\right )}\right )\right )\right )}{x^3 \left (4+\log \left (x^2\right )\right ) \left (x+\log \left (4+\log \left (x^2\right )\right )\right ) \log ^2\left (\frac {x}{x+\log \left (4+\log \left (x^2\right )\right )}\right )} \, dx\\ &=3 \int \left (\frac {e^x \left (2-4 \log \left (4+\log \left (x^2\right )\right )-\log \left (x^2\right ) \log \left (4+\log \left (x^2\right )\right )\right )}{x^3 \left (4+\log \left (x^2\right )\right ) \left (x+\log \left (4+\log \left (x^2\right )\right )\right ) \log ^2\left (\frac {x}{x+\log \left (4+\log \left (x^2\right )\right )}\right )}+\frac {e^x (-2+x)}{x^3 \log \left (\frac {x}{x+\log \left (4+\log \left (x^2\right )\right )}\right )}\right ) \, dx\\ &=3 \int \frac {e^x \left (2-4 \log \left (4+\log \left (x^2\right )\right )-\log \left (x^2\right ) \log \left (4+\log \left (x^2\right )\right )\right )}{x^3 \left (4+\log \left (x^2\right )\right ) \left (x+\log \left (4+\log \left (x^2\right )\right )\right ) \log ^2\left (\frac {x}{x+\log \left (4+\log \left (x^2\right )\right )}\right )} \, dx+3 \int \frac {e^x (-2+x)}{x^3 \log \left (\frac {x}{x+\log \left (4+\log \left (x^2\right )\right )}\right )} \, dx\\ &=3 \int \left (-\frac {2 e^x}{x^3 \log \left (\frac {x}{x+\log \left (4+\log \left (x^2\right )\right )}\right )}+\frac {e^x}{x^2 \log \left (\frac {x}{x+\log \left (4+\log \left (x^2\right )\right )}\right )}\right ) \, dx+3 \int \frac {e^x \left (2-\left (4+\log \left (x^2\right )\right ) \log \left (4+\log \left (x^2\right )\right )\right )}{x^3 \left (4+\log \left (x^2\right )\right ) \left (x+\log \left (4+\log \left (x^2\right )\right )\right ) \log ^2\left (\frac {x}{x+\log \left (4+\log \left (x^2\right )\right )}\right )} \, dx\\ &=3 \int \left (\frac {2 e^x}{x^3 \left (4+\log \left (x^2\right )\right ) \left (x+\log \left (4+\log \left (x^2\right )\right )\right ) \log ^2\left (\frac {x}{x+\log \left (4+\log \left (x^2\right )\right )}\right )}-\frac {4 e^x \log \left (4+\log \left (x^2\right )\right )}{x^3 \left (4+\log \left (x^2\right )\right ) \left (x+\log \left (4+\log \left (x^2\right )\right )\right ) \log ^2\left (\frac {x}{x+\log \left (4+\log \left (x^2\right )\right )}\right )}-\frac {e^x \log \left (x^2\right ) \log \left (4+\log \left (x^2\right )\right )}{x^3 \left (4+\log \left (x^2\right )\right ) \left (x+\log \left (4+\log \left (x^2\right )\right )\right ) \log ^2\left (\frac {x}{x+\log \left (4+\log \left (x^2\right )\right )}\right )}\right ) \, dx+3 \int \frac {e^x}{x^2 \log \left (\frac {x}{x+\log \left (4+\log \left (x^2\right )\right )}\right )} \, dx-6 \int \frac {e^x}{x^3 \log \left (\frac {x}{x+\log \left (4+\log \left (x^2\right )\right )}\right )} \, dx\\ &=-\left (3 \int \frac {e^x \log \left (x^2\right ) \log \left (4+\log \left (x^2\right )\right )}{x^3 \left (4+\log \left (x^2\right )\right ) \left (x+\log \left (4+\log \left (x^2\right )\right )\right ) \log ^2\left (\frac {x}{x+\log \left (4+\log \left (x^2\right )\right )}\right )} \, dx\right )+3 \int \frac {e^x}{x^2 \log \left (\frac {x}{x+\log \left (4+\log \left (x^2\right )\right )}\right )} \, dx+6 \int \frac {e^x}{x^3 \left (4+\log \left (x^2\right )\right ) \left (x+\log \left (4+\log \left (x^2\right )\right )\right ) \log ^2\left (\frac {x}{x+\log \left (4+\log \left (x^2\right )\right )}\right )} \, dx-6 \int \frac {e^x}{x^3 \log \left (\frac {x}{x+\log \left (4+\log \left (x^2\right )\right )}\right )} \, dx-12 \int \frac {e^x \log \left (4+\log \left (x^2\right )\right )}{x^3 \left (4+\log \left (x^2\right )\right ) \left (x+\log \left (4+\log \left (x^2\right )\right )\right ) \log ^2\left (\frac {x}{x+\log \left (4+\log \left (x^2\right )\right )}\right )} \, dx\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.16, size = 24, normalized size = 0.92 \begin {gather*} \frac {3 e^x}{x^2 \log \left (\frac {x}{x+\log \left (4+\log \left (x^2\right )\right )}\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(6*E^x + (-12*E^x - 3*E^x*Log[x^2])*Log[4 + Log[x^2]] + (E^x*(-24*x + 12*x^2) + E^x*(-6*x + 3*x^2)*L
og[x^2] + (E^x*(-24 + 12*x) + E^x*(-6 + 3*x)*Log[x^2])*Log[4 + Log[x^2]])*Log[x/(x + Log[4 + Log[x^2]])])/((4*
x^4 + x^4*Log[x^2] + (4*x^3 + x^3*Log[x^2])*Log[4 + Log[x^2]])*Log[x/(x + Log[4 + Log[x^2]])]^2),x]

[Out]

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

________________________________________________________________________________________

fricas [A]  time = 1.14, size = 23, normalized size = 0.88 \begin {gather*} \frac {3 \, e^{x}}{x^{2} \log \left (\frac {x}{x + \log \left (\log \left (x^{2}\right ) + 4\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

giac [B]  time = 1.36, size = 288, normalized size = 11.08 \begin {gather*} -\frac {3 \, {\left (e^{x} \log \left (x^{2}\right ) \log \relax (x) \log \left (\log \left (x^{2}\right ) + 4\right ) + 2 \, e^{x} \log \left (x^{2}\right ) \log \left (\log \left (x^{2}\right ) + 4\right ) + 4 \, e^{x} \log \relax (x) \log \left (\log \left (x^{2}\right ) + 4\right ) - e^{x} \log \left (x^{2}\right ) + 8 \, e^{x} \log \left (\log \left (x^{2}\right ) + 4\right ) - 4 \, e^{x}\right )}}{x^{2} \log \left (x^{2}\right ) \log \left (x + \log \left (\log \left (x^{2}\right ) + 4\right )\right ) \log \relax (x) \log \left (\log \left (x^{2}\right ) + 4\right ) - x^{2} \log \left (x^{2}\right ) \log \relax (x)^{2} \log \left (\log \left (x^{2}\right ) + 4\right ) + 2 \, x^{2} \log \left (x^{2}\right ) \log \left (x + \log \left (\log \left (x^{2}\right ) + 4\right )\right ) \log \left (\log \left (x^{2}\right ) + 4\right ) - 2 \, x^{2} \log \left (x^{2}\right ) \log \relax (x) \log \left (\log \left (x^{2}\right ) + 4\right ) + 4 \, x^{2} \log \left (x + \log \left (\log \left (x^{2}\right ) + 4\right )\right ) \log \relax (x) \log \left (\log \left (x^{2}\right ) + 4\right ) - 4 \, x^{2} \log \relax (x)^{2} \log \left (\log \left (x^{2}\right ) + 4\right ) - 2 \, x^{2} \log \left (x + \log \left (\log \left (x^{2}\right ) + 4\right )\right ) \log \relax (x) + 2 \, x^{2} \log \relax (x)^{2} + 8 \, x^{2} \log \left (x + \log \left (\log \left (x^{2}\right ) + 4\right )\right ) \log \left (\log \left (x^{2}\right ) + 4\right ) - 8 \, x^{2} \log \relax (x) \log \left (\log \left (x^{2}\right ) + 4\right ) - 4 \, x^{2} \log \left (x + \log \left (\log \left (x^{2}\right ) + 4\right )\right ) + 4 \, x^{2} \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3*(e^x*log(x^2)*log(x)*log(log(x^2) + 4) + 2*e^x*log(x^2)*log(log(x^2) + 4) + 4*e^x*log(x)*log(log(x^2) + 4)
- e^x*log(x^2) + 8*e^x*log(log(x^2) + 4) - 4*e^x)/(x^2*log(x^2)*log(x + log(log(x^2) + 4))*log(x)*log(log(x^2)
+ 4) - x^2*log(x^2)*log(x)^2*log(log(x^2) + 4) + 2*x^2*log(x^2)*log(x + log(log(x^2) + 4))*log(log(x^2) + 4)
- 2*x^2*log(x^2)*log(x)*log(log(x^2) + 4) + 4*x^2*log(x + log(log(x^2) + 4))*log(x)*log(log(x^2) + 4) - 4*x^2*
log(x)^2*log(log(x^2) + 4) - 2*x^2*log(x + log(log(x^2) + 4))*log(x) + 2*x^2*log(x)^2 + 8*x^2*log(x + log(log(
x^2) + 4))*log(log(x^2) + 4) - 8*x^2*log(x)*log(log(x^2) + 4) - 4*x^2*log(x + log(log(x^2) + 4)) + 4*x^2*log(x
))

________________________________________________________________________________________

maple [C]  time = 0.37, size = 346, normalized size = 13.31

method	result	size
risch	\(\frac {6 i {\mathrm e}^{x}}{x^{2} \left (\pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (\frac {i}{\ln \left (4+2 \ln \relax (x )-\frac {i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \left (-\mathrm {csgn}\left (i x^{2}\right )+\mathrm {csgn}\left (i x \right )\right )^{2}}{2}\right )+x}\right ) \mathrm {csgn}\left (\frac {i x}{\ln \left (4+2 \ln \relax (x )-\frac {i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \left (-\mathrm {csgn}\left (i x^{2}\right )+\mathrm {csgn}\left (i x \right )\right )^{2}}{2}\right )+x}\right )-\pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (\frac {i x}{\ln \left (4+2 \ln \relax (x )-\frac {i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \left (-\mathrm {csgn}\left (i x^{2}\right )+\mathrm {csgn}\left (i x \right )\right )^{2}}{2}\right )+x}\right )^{2}-\pi \,\mathrm {csgn}\left (\frac {i}{\ln \left (4+2 \ln \relax (x )-\frac {i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \left (-\mathrm {csgn}\left (i x^{2}\right )+\mathrm {csgn}\left (i x \right )\right )^{2}}{2}\right )+x}\right ) \mathrm {csgn}\left (\frac {i x}{\ln \left (4+2 \ln \relax (x )-\frac {i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \left (-\mathrm {csgn}\left (i x^{2}\right )+\mathrm {csgn}\left (i x \right )\right )^{2}}{2}\right )+x}\right )^{2}+\pi \mathrm {csgn}\left (\frac {i x}{\ln \left (4+2 \ln \relax (x )-\frac {i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \left (-\mathrm {csgn}\left (i x^{2}\right )+\mathrm {csgn}\left (i x \right )\right )^{2}}{2}\right )+x}\right )^{3}+2 i \ln \relax (x )-2 i \ln \left (\ln \left (4+2 \ln \relax (x )-\frac {i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \left (-\mathrm {csgn}\left (i x^{2}\right )+\mathrm {csgn}\left (i x \right )\right )^{2}}{2}\right )+x \right )\right )}\)	\(346\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

6*I*exp(x)/x^2/(Pi*csgn(I*x)*csgn(I/(ln(4+2*ln(x)-1/2*I*Pi*csgn(I*x^2)*(-csgn(I*x^2)+csgn(I*x))^2)+x))*csgn(I*
x/(ln(4+2*ln(x)-1/2*I*Pi*csgn(I*x^2)*(-csgn(I*x^2)+csgn(I*x))^2)+x))-Pi*csgn(I*x)*csgn(I*x/(ln(4+2*ln(x)-1/2*I
*Pi*csgn(I*x^2)*(-csgn(I*x^2)+csgn(I*x))^2)+x))^2-Pi*csgn(I/(ln(4+2*ln(x)-1/2*I*Pi*csgn(I*x^2)*(-csgn(I*x^2)+c
sgn(I*x))^2)+x))*csgn(I*x/(ln(4+2*ln(x)-1/2*I*Pi*csgn(I*x^2)*(-csgn(I*x^2)+csgn(I*x))^2)+x))^2+Pi*csgn(I*x/(ln
(4+2*ln(x)-1/2*I*Pi*csgn(I*x^2)*(-csgn(I*x^2)+csgn(I*x))^2)+x))^3+2*I*ln(x)-2*I*ln(ln(4+2*ln(x)-1/2*I*Pi*csgn(
I*x^2)*(-csgn(I*x^2)+csgn(I*x))^2)+x))

________________________________________________________________________________________

maxima [A]  time = 0.51, size = 28, normalized size = 1.08 \begin {gather*} -\frac {3 \, e^{x}}{x^{2} \log \left (x + \log \relax (2) + \log \left (\log \relax (x) + 2\right )\right ) - x^{2} \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {\ln \left (\ln \left (x^2\right )+4\right )\,\left (12\,{\mathrm {e}}^x+3\,\ln \left (x^2\right )\,{\mathrm {e}}^x\right )-6\,{\mathrm {e}}^x+\ln \left (\frac {x}{x+\ln \left (\ln \left (x^2\right )+4\right )}\right )\,\left ({\mathrm {e}}^x\,\left (24\,x-12\,x^2\right )-\ln \left (\ln \left (x^2\right )+4\right )\,\left ({\mathrm {e}}^x\,\left (12\,x-24\right )+\ln \left (x^2\right )\,{\mathrm {e}}^x\,\left (3\,x-6\right )\right )+\ln \left (x^2\right )\,{\mathrm {e}}^x\,\left (6\,x-3\,x^2\right )\right )}{{\ln \left (\frac {x}{x+\ln \left (\ln \left (x^2\right )+4\right )}\right )}^2\,\left (x^4\,\ln \left (x^2\right )+\ln \left (\ln \left (x^2\right )+4\right )\,\left (x^3\,\ln \left (x^2\right )+4\,x^3\right )+4\,x^4\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

sympy [A]  time = 3.67, size = 20, normalized size = 0.77 \begin {gather*} \frac {3 e^{x}}{x^{2} \log {\left (\frac {x}{x + \log {\left (\log {\left (x^{2} \right )} + 4 \right )}} \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________