\(\int \frac {e^{\frac {4 x+x^3-x^4+x^2 \log (4 e^x+e^x \log (x^2))}{-4+x^3}} (-128-16 x-128 x^2+64 x^3+4 x^4+8 x^5-8 x^6+(-32-32 x^2+16 x^3+2 x^5-2 x^6) \log (x^2)+(-64 x-8 x^4+(-16 x-2 x^4) \log (x^2)) \log (4 e^x+e^x \log (x^2)))}{64-32 x^3+4 x^6+(16-8 x^3+x^6) \log (x^2)} \, dx\) [8577]

Optimal result

Integrand size = 167, antiderivative size = 31 \[ \int \frac {e^{\frac {4 x+x^3-x^4+x^2 \log \left (4 e^x+e^x \log \left (x^2\right )\right )}{-4+x^3}} \left (-128-16 x-128 x^2+64 x^3+4 x^4+8 x^5-8 x^6+\left (-32-32 x^2+16 x^3+2 x^5-2 x^6\right ) \log \left (x^2\right )+\left (-64 x-8 x^4+\left (-16 x-2 x^4\right ) \log \left (x^2\right )\right ) \log \left (4 e^x+e^x \log \left (x^2\right )\right )\right )}{64-32 x^3+4 x^6+\left (16-8 x^3+x^6\right ) \log \left (x^2\right )} \, dx=2 e^{-x+\frac {x+\log \left (e^x \left (4+\log \left (x^2\right )\right )\right )}{-\frac {4}{x^2}+x}} \]

[Out]

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

Rubi [F]

\[ \int \frac {e^{\frac {4 x+x^3-x^4+x^2 \log \left (4 e^x+e^x \log \left (x^2\right )\right )}{-4+x^3}} \left (-128-16 x-128 x^2+64 x^3+4 x^4+8 x^5-8 x^6+\left (-32-32 x^2+16 x^3+2 x^5-2 x^6\right ) \log \left (x^2\right )+\left (-64 x-8 x^4+\left (-16 x-2 x^4\right ) \log \left (x^2\right )\right ) \log \left (4 e^x+e^x \log \left (x^2\right )\right )\right )}{64-32 x^3+4 x^6+\left (16-8 x^3+x^6\right ) \log \left (x^2\right )} \, dx=\int \frac {\exp \left (\frac {4 x+x^3-x^4+x^2 \log \left (4 e^x+e^x \log \left (x^2\right )\right )}{-4+x^3}\right ) \left (-128-16 x-128 x^2+64 x^3+4 x^4+8 x^5-8 x^6+\left (-32-32 x^2+16 x^3+2 x^5-2 x^6\right ) \log \left (x^2\right )+\left (-64 x-8 x^4+\left (-16 x-2 x^4\right ) \log \left (x^2\right )\right ) \log \left (4 e^x+e^x \log \left (x^2\right )\right )\right )}{64-32 x^3+4 x^6+\left (16-8 x^3+x^6\right ) \log \left (x^2\right )} \, dx \]

[In]

Int[(E^((4*x + x^3 - x^4 + x^2*Log[4*E^x + E^x*Log[x^2]])/(-4 + x^3))*(-128 - 16*x - 128*x^2 + 64*x^3 + 4*x^4
+ 8*x^5 - 8*x^6 + (-32 - 32*x^2 + 16*x^3 + 2*x^5 - 2*x^6)*Log[x^2] + (-64*x - 8*x^4 + (-16*x - 2*x^4)*Log[x^2]
)*Log[4*E^x + E^x*Log[x^2]]))/(64 - 32*x^3 + 4*x^6 + (16 - 8*x^3 + x^6)*Log[x^2]),x]

[Out]

-2*Defer[Int][E^((4*x + x^3 - x^4 + x^2*Log[4*E^x + E^x*Log[x^2]])/(-4 + x^3)), x] - (2*Defer[Int][E^((4*x + x
^3 - x^4 + x^2*Log[4*E^x + E^x*Log[x^2]])/(-4 + x^3))/((-2)^(2/3) - x), x])/3 - (2*Defer[Int][E^((4*x + x^3 -
x^4 + x^2*Log[4*E^x + E^x*Log[x^2]])/(-4 + x^3))/(2^(2/3) - x), x])/3 - (2*Defer[Int][E^((4*x + x^3 - x^4 + x^
2*Log[4*E^x + E^x*Log[x^2]])/(-4 + x^3))/(-((-1)^(1/3)*2^(2/3)) - x), x])/3 - 24*Defer[Int][(E^((4*x + x^3 - x
^4 + x^2*Log[4*E^x + E^x*Log[x^2]])/(-4 + x^3))*x^2)/(-4 + x^3)^2, x] - (2*2^(1/3)*Defer[Int][E^((4*x + x^3 -
x^4 + x^2*Log[4*E^x + E^x*Log[x^2]])/(-4 + x^3))/((2^(2/3) - x)*(4 + Log[x^2])), x])/3 - (2*(-1)^(2/3)*2^(1/3)
*Defer[Int][E^((4*x + x^3 - x^4 + x^2*Log[4*E^x + E^x*Log[x^2]])/(-4 + x^3))/((2^(2/3) + (-1)^(1/3)*x)*(4 + Lo
g[x^2])), x])/3 + (2*(-2)^(1/3)*Defer[Int][E^((4*x + x^3 - x^4 + x^2*Log[4*E^x + E^x*Log[x^2]])/(-4 + x^3))/((
2^(2/3) - (-1)^(2/3)*x)*(4 + Log[x^2])), x])/3 + (2^(1/3)*Defer[Int][(E^((4*x + x^3 - x^4 + x^2*Log[4*E^x + E^
x*Log[x^2]])/(-4 + x^3))*Log[E^x*(4 + Log[x^2])])/(2^(2/3) - x), x])/3 + ((-1)^(2/3)*2^(1/3)*Defer[Int][(E^((4
*x + x^3 - x^4 + x^2*Log[4*E^x + E^x*Log[x^2]])/(-4 + x^3))*Log[E^x*(4 + Log[x^2])])/(2^(2/3) + (-1)^(1/3)*x),
x])/3 - ((-2)^(1/3)*Defer[Int][(E^((4*x + x^3 - x^4 + x^2*Log[4*E^x + E^x*Log[x^2]])/(-4 + x^3))*Log[E^x*(4 +
Log[x^2])])/(2^(2/3) - (-1)^(2/3)*x), x])/3 - 24*Defer[Int][(E^((4*x + x^3 - x^4 + x^2*Log[4*E^x + E^x*Log[x^
2]])/(-4 + x^3))*x*Log[E^x*(4 + Log[x^2])])/(-4 + x^3)^2, x]

Rubi steps Aborted

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(64\) vs. \(2(31)=62\).

Time = 0.35 (sec) , antiderivative size = 64, normalized size of antiderivative = 2.06 \[ \int \frac {e^{\frac {4 x+x^3-x^4+x^2 \log \left (4 e^x+e^x \log \left (x^2\right )\right )}{-4+x^3}} \left (-128-16 x-128 x^2+64 x^3+4 x^4+8 x^5-8 x^6+\left (-32-32 x^2+16 x^3+2 x^5-2 x^6\right ) \log \left (x^2\right )+\left (-64 x-8 x^4+\left (-16 x-2 x^4\right ) \log \left (x^2\right )\right ) \log \left (4 e^x+e^x \log \left (x^2\right )\right )\right )}{64-32 x^3+4 x^6+\left (16-8 x^3+x^6\right ) \log \left (x^2\right )} \, dx=2 e^{\frac {x \left (4+x^2-x^3-x \log \left (4+\log \left (x^2\right )\right )+x \log \left (e^x \left (4+\log \left (x^2\right )\right )\right )\right )}{-4+x^3}} \left (4+\log \left (x^2\right )\right )^{\frac {x^2}{-4+x^3}} \]

[In]

Integrate[(E^((4*x + x^3 - x^4 + x^2*Log[4*E^x + E^x*Log[x^2]])/(-4 + x^3))*(-128 - 16*x - 128*x^2 + 64*x^3 +
4*x^4 + 8*x^5 - 8*x^6 + (-32 - 32*x^2 + 16*x^3 + 2*x^5 - 2*x^6)*Log[x^2] + (-64*x - 8*x^4 + (-16*x - 2*x^4)*Lo
g[x^2])*Log[4*E^x + E^x*Log[x^2]]))/(64 - 32*x^3 + 4*x^6 + (16 - 8*x^3 + x^6)*Log[x^2]),x]

[Out]

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

Maple [C] (warning: unable to verify)

Result contains higher order function than in optimal. Order 9 vs. order 3.

Time = 0.20 (sec) , antiderivative size = 569, normalized size of antiderivative = 18.35

\[2 \left (\frac {1}{2}\right )^{\frac {x^{2}}{x^{3}-4}} \left ({\mathrm e}^{x}\right )^{\frac {x^{2}}{x^{3}-4}} \left (8 i+4 i \ln \left (x \right )+\pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )-2 \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}+\pi \operatorname {csgn}\left (i x^{2}\right )^{3}\right )^{\frac {x^{2}}{x^{3}-4}} {\mathrm e}^{-\frac {x \left (i x \pi \,\operatorname {csgn}\left (-i \pi \,\operatorname {csgn}\left (i x^{2}\right ) \operatorname {csgn}\left (i x \right )^{2}+2 i \pi \operatorname {csgn}\left (i x^{2}\right )^{2} \operatorname {csgn}\left (i x \right )-i \pi \operatorname {csgn}\left (i x^{2}\right )^{3}+4 \ln \left (x \right )+8\right ) \operatorname {csgn}\left (i {\mathrm e}^{x} \left (8 i+4 i \ln \left (x \right )+\pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )-2 \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}+\pi \operatorname {csgn}\left (i x^{2}\right )^{3}\right )\right )^{2}-i x \pi \,\operatorname {csgn}\left (-i \pi \,\operatorname {csgn}\left (i x^{2}\right ) \operatorname {csgn}\left (i x \right )^{2}+2 i \pi \operatorname {csgn}\left (i x^{2}\right )^{2} \operatorname {csgn}\left (i x \right )-i \pi \operatorname {csgn}\left (i x^{2}\right )^{3}+4 \ln \left (x \right )+8\right ) \operatorname {csgn}\left (i {\mathrm e}^{x} \left (8 i+4 i \ln \left (x \right )+\pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )-2 \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}+\pi \operatorname {csgn}\left (i x^{2}\right )^{3}\right )\right ) \operatorname {csgn}\left (i {\mathrm e}^{x}\right )-i x \pi \operatorname {csgn}\left (i {\mathrm e}^{x} \left (8 i+4 i \ln \left (x \right )+\pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )-2 \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}+\pi \operatorname {csgn}\left (i x^{2}\right )^{3}\right )\right )^{3}-i x \pi \operatorname {csgn}\left (i {\mathrm e}^{x} \left (8 i+4 i \ln \left (x \right )+\pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )-2 \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}+\pi \operatorname {csgn}\left (i x^{2}\right )^{3}\right )\right )^{2} \operatorname {csgn}\left (i {\mathrm e}^{x}\right )+2 i x \pi \operatorname {csgn}\left (i {\mathrm e}^{x} \left (8 i+4 i \ln \left (x \right )+\pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )-2 \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}+\pi \operatorname {csgn}\left (i x^{2}\right )^{3}\right )\right )^{2}-2 i \pi x +2 x^{3}-2 x^{2}-8\right )}{2 \left (x^{3}-4\right )}}\]

[In]

int((((-2*x^4-16*x)*ln(x^2)-8*x^4-64*x)*ln(exp(x)*ln(x^2)+4*exp(x))+(-2*x^6+2*x^5+16*x^3-32*x^2-32)*ln(x^2)-8*
x^6+8*x^5+4*x^4+64*x^3-128*x^2-16*x-128)*exp((x^2*ln(exp(x)*ln(x^2)+4*exp(x))-x^4+x^3+4*x)/(x^3-4))/((x^6-8*x^
3+16)*ln(x^2)+4*x^6-32*x^3+64),x)

[Out]

2*(1/2)^(1/(x^3-4)*x^2)*exp(x)^(1/(x^3-4)*x^2)*(8*I+4*I*ln(x)+Pi*csgn(I*x)^2*csgn(I*x^2)-2*Pi*csgn(I*x)*csgn(I
*x^2)^2+Pi*csgn(I*x^2)^3)^(1/(x^3-4)*x^2)*exp(-1/2*x*(I*x*Pi*csgn(-I*Pi*csgn(I*x^2)*csgn(I*x)^2+2*I*Pi*csgn(I*
x^2)^2*csgn(I*x)-I*Pi*csgn(I*x^2)^3+4*ln(x)+8)*csgn(I*exp(x)*(8*I+4*I*ln(x)+Pi*csgn(I*x)^2*csgn(I*x^2)-2*Pi*cs
gn(I*x)*csgn(I*x^2)^2+Pi*csgn(I*x^2)^3))^2-I*x*Pi*csgn(-I*Pi*csgn(I*x^2)*csgn(I*x)^2+2*I*Pi*csgn(I*x^2)^2*csgn
(I*x)-I*Pi*csgn(I*x^2)^3+4*ln(x)+8)*csgn(I*exp(x)*(8*I+4*I*ln(x)+Pi*csgn(I*x)^2*csgn(I*x^2)-2*Pi*csgn(I*x)*csg
n(I*x^2)^2+Pi*csgn(I*x^2)^3))*csgn(I*exp(x))-I*x*Pi*csgn(I*exp(x)*(8*I+4*I*ln(x)+Pi*csgn(I*x)^2*csgn(I*x^2)-2*
Pi*csgn(I*x)*csgn(I*x^2)^2+Pi*csgn(I*x^2)^3))^3-I*x*Pi*csgn(I*exp(x)*(8*I+4*I*ln(x)+Pi*csgn(I*x)^2*csgn(I*x^2)
-2*Pi*csgn(I*x)*csgn(I*x^2)^2+Pi*csgn(I*x^2)^3))^2*csgn(I*exp(x))+2*I*x*Pi*csgn(I*exp(x)*(8*I+4*I*ln(x)+Pi*csg
n(I*x)^2*csgn(I*x^2)-2*Pi*csgn(I*x)*csgn(I*x^2)^2+Pi*csgn(I*x^2)^3))^2-2*I*Pi*x+2*x^3-2*x^2-8)/(x^3-4))

Fricas [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.35 \[ \int \frac {e^{\frac {4 x+x^3-x^4+x^2 \log \left (4 e^x+e^x \log \left (x^2\right )\right )}{-4+x^3}} \left (-128-16 x-128 x^2+64 x^3+4 x^4+8 x^5-8 x^6+\left (-32-32 x^2+16 x^3+2 x^5-2 x^6\right ) \log \left (x^2\right )+\left (-64 x-8 x^4+\left (-16 x-2 x^4\right ) \log \left (x^2\right )\right ) \log \left (4 e^x+e^x \log \left (x^2\right )\right )\right )}{64-32 x^3+4 x^6+\left (16-8 x^3+x^6\right ) \log \left (x^2\right )} \, dx=2 \, e^{\left (-\frac {x^{4} - x^{3} - x^{2} \log \left (e^{x} \log \left (x^{2}\right ) + 4 \, e^{x}\right ) - 4 \, x}{x^{3} - 4}\right )} \]

[In]

integrate((((-2*x^4-16*x)*log(x^2)-8*x^4-64*x)*log(exp(x)*log(x^2)+4*exp(x))+(-2*x^6+2*x^5+16*x^3-32*x^2-32)*l
og(x^2)-8*x^6+8*x^5+4*x^4+64*x^3-128*x^2-16*x-128)*exp((x^2*log(exp(x)*log(x^2)+4*exp(x))-x^4+x^3+4*x)/(x^3-4)
)/((x^6-8*x^3+16)*log(x^2)+4*x^6-32*x^3+64),x, algorithm="fricas")

[Out]

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

Sympy [F(-1)]

Timed out. \[ \int \frac {e^{\frac {4 x+x^3-x^4+x^2 \log \left (4 e^x+e^x \log \left (x^2\right )\right )}{-4+x^3}} \left (-128-16 x-128 x^2+64 x^3+4 x^4+8 x^5-8 x^6+\left (-32-32 x^2+16 x^3+2 x^5-2 x^6\right ) \log \left (x^2\right )+\left (-64 x-8 x^4+\left (-16 x-2 x^4\right ) \log \left (x^2\right )\right ) \log \left (4 e^x+e^x \log \left (x^2\right )\right )\right )}{64-32 x^3+4 x^6+\left (16-8 x^3+x^6\right ) \log \left (x^2\right )} \, dx=\text {Timed out} \]

[In]

integrate((((-2*x**4-16*x)*ln(x**2)-8*x**4-64*x)*ln(exp(x)*ln(x**2)+4*exp(x))+(-2*x**6+2*x**5+16*x**3-32*x**2-
32)*ln(x**2)-8*x**6+8*x**5+4*x**4+64*x**3-128*x**2-16*x-128)*exp((x**2*ln(exp(x)*ln(x**2)+4*exp(x))-x**4+x**3+
4*x)/(x**3-4))/((x**6-8*x**3+16)*ln(x**2)+4*x**6-32*x**3+64),x)

[Out]

Timed out

Maxima [A] (verification not implemented)

none

Time = 0.46 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.48 \[ \int \frac {e^{\frac {4 x+x^3-x^4+x^2 \log \left (4 e^x+e^x \log \left (x^2\right )\right )}{-4+x^3}} \left (-128-16 x-128 x^2+64 x^3+4 x^4+8 x^5-8 x^6+\left (-32-32 x^2+16 x^3+2 x^5-2 x^6\right ) \log \left (x^2\right )+\left (-64 x-8 x^4+\left (-16 x-2 x^4\right ) \log \left (x^2\right )\right ) \log \left (4 e^x+e^x \log \left (x^2\right )\right )\right )}{64-32 x^3+4 x^6+\left (16-8 x^3+x^6\right ) \log \left (x^2\right )} \, dx=2 \, e^{\left (\frac {x^{2} \log \left (2\right )}{x^{3} - 4} + \frac {x^{2} \log \left (\log \left (x\right ) + 2\right )}{x^{3} - 4} - x + \frac {8}{x^{3} - 4} + 2\right )} \]

[In]

integrate((((-2*x^4-16*x)*log(x^2)-8*x^4-64*x)*log(exp(x)*log(x^2)+4*exp(x))+(-2*x^6+2*x^5+16*x^3-32*x^2-32)*l
og(x^2)-8*x^6+8*x^5+4*x^4+64*x^3-128*x^2-16*x-128)*exp((x^2*log(exp(x)*log(x^2)+4*exp(x))-x^4+x^3+4*x)/(x^3-4)
)/((x^6-8*x^3+16)*log(x^2)+4*x^6-32*x^3+64),x, algorithm="maxima")

[Out]

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

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 61 vs. \(2 (29) = 58\).

Time = 0.66 (sec) , antiderivative size = 61, normalized size of antiderivative = 1.97 \[ \int \frac {e^{\frac {4 x+x^3-x^4+x^2 \log \left (4 e^x+e^x \log \left (x^2\right )\right )}{-4+x^3}} \left (-128-16 x-128 x^2+64 x^3+4 x^4+8 x^5-8 x^6+\left (-32-32 x^2+16 x^3+2 x^5-2 x^6\right ) \log \left (x^2\right )+\left (-64 x-8 x^4+\left (-16 x-2 x^4\right ) \log \left (x^2\right )\right ) \log \left (4 e^x+e^x \log \left (x^2\right )\right )\right )}{64-32 x^3+4 x^6+\left (16-8 x^3+x^6\right ) \log \left (x^2\right )} \, dx=2 \, e^{\left (-\frac {x^{4}}{x^{3} - 4} + \frac {x^{3}}{x^{3} - 4} + \frac {x^{2} \log \left (e^{x} \log \left (x^{2}\right ) + 4 \, e^{x}\right )}{x^{3} - 4} + \frac {4 \, x}{x^{3} - 4}\right )} \]

[In]

integrate((((-2*x^4-16*x)*log(x^2)-8*x^4-64*x)*log(exp(x)*log(x^2)+4*exp(x))+(-2*x^6+2*x^5+16*x^3-32*x^2-32)*l
og(x^2)-8*x^6+8*x^5+4*x^4+64*x^3-128*x^2-16*x-128)*exp((x^2*log(exp(x)*log(x^2)+4*exp(x))-x^4+x^3+4*x)/(x^3-4)
)/((x^6-8*x^3+16)*log(x^2)+4*x^6-32*x^3+64),x, algorithm="giac")

[Out]

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

Mupad [B] (verification not implemented)

Time = 14.02 (sec) , antiderivative size = 62, normalized size of antiderivative = 2.00 \[ \int \frac {e^{\frac {4 x+x^3-x^4+x^2 \log \left (4 e^x+e^x \log \left (x^2\right )\right )}{-4+x^3}} \left (-128-16 x-128 x^2+64 x^3+4 x^4+8 x^5-8 x^6+\left (-32-32 x^2+16 x^3+2 x^5-2 x^6\right ) \log \left (x^2\right )+\left (-64 x-8 x^4+\left (-16 x-2 x^4\right ) \log \left (x^2\right )\right ) \log \left (4 e^x+e^x \log \left (x^2\right )\right )\right )}{64-32 x^3+4 x^6+\left (16-8 x^3+x^6\right ) \log \left (x^2\right )} \, dx=2\,{\mathrm {e}}^{\frac {x^3}{x^3-4}}\,{\mathrm {e}}^{-\frac {x^4}{x^3-4}}\,{\mathrm {e}}^{\frac {4\,x}{x^3-4}}\,{\left (4\,{\mathrm {e}}^x+\ln \left (x^2\right )\,{\mathrm {e}}^x\right )}^{\frac {x^2}{x^3-4}} \]

[In]

int(-(exp((4*x + x^2*log(4*exp(x) + log(x^2)*exp(x)) + x^3 - x^4)/(x^3 - 4))*(16*x + log(4*exp(x) + log(x^2)*e
xp(x))*(64*x + log(x^2)*(16*x + 2*x^4) + 8*x^4) + 128*x^2 - 64*x^3 - 4*x^4 - 8*x^5 + 8*x^6 + log(x^2)*(32*x^2
- 16*x^3 - 2*x^5 + 2*x^6 + 32) + 128))/(log(x^2)*(x^6 - 8*x^3 + 16) - 32*x^3 + 4*x^6 + 64),x)

[Out]

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