\(\int \frac {e^{2 e^{6 x}-4 e^{3 x} x^2+2 x^4} ((24-8 x^2) \log (\frac {3+x^2-x \log (2)}{x})+(-96 x^4-32 x^6+32 x^5 \log (2)+e^{6 x} (-144 x-48 x^3+48 x^2 \log (2))+e^{3 x} (96 x^2+144 x^3+32 x^4+48 x^5+(-32 x^3-48 x^4) \log (2))) \log ^2(\frac {3+x^2-x \log (2)}{x}))}{-3 x-x^3+x^2 \log (2)} \, dx\) [1584]

Optimal result

Integrand size = 166, antiderivative size = 36 \[ \int \frac {e^{2 e^{6 x}-4 e^{3 x} x^2+2 x^4} \left (\left (24-8 x^2\right ) \log \left (\frac {3+x^2-x \log (2)}{x}\right )+\left (-96 x^4-32 x^6+32 x^5 \log (2)+e^{6 x} \left (-144 x-48 x^3+48 x^2 \log (2)\right )+e^{3 x} \left (96 x^2+144 x^3+32 x^4+48 x^5+\left (-32 x^3-48 x^4\right ) \log (2)\right )\right ) \log ^2\left (\frac {3+x^2-x \log (2)}{x}\right )\right )}{-3 x-x^3+x^2 \log (2)} \, dx=4 e^{2 \left (e^{3 x}-x^2\right )^2} \log ^2\left (\frac {3+x^2}{x}-\log (2)\right ) \] Output:

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

Mathematica [A] (verified)

Time = 0.10 (sec) , antiderivative size = 33, normalized size of antiderivative = 0.92 \[ \int \frac {e^{2 e^{6 x}-4 e^{3 x} x^2+2 x^4} \left (\left (24-8 x^2\right ) \log \left (\frac {3+x^2-x \log (2)}{x}\right )+\left (-96 x^4-32 x^6+32 x^5 \log (2)+e^{6 x} \left (-144 x-48 x^3+48 x^2 \log (2)\right )+e^{3 x} \left (96 x^2+144 x^3+32 x^4+48 x^5+\left (-32 x^3-48 x^4\right ) \log (2)\right )\right ) \log ^2\left (\frac {3+x^2-x \log (2)}{x}\right )\right )}{-3 x-x^3+x^2 \log (2)} \, dx=4 e^{2 \left (e^{3 x}-x^2\right )^2} \log ^2\left (\frac {3}{x}+x-\log (2)\right ) \] Input:

Integrate[(E^(2*E^(6*x) - 4*E^(3*x)*x^2 + 2*x^4)*((24 - 8*x^2)*Log[(3 + x^ 
2 - x*Log[2])/x] + (-96*x^4 - 32*x^6 + 32*x^5*Log[2] + E^(6*x)*(-144*x - 4 
8*x^3 + 48*x^2*Log[2]) + E^(3*x)*(96*x^2 + 144*x^3 + 32*x^4 + 48*x^5 + (-3 
2*x^3 - 48*x^4)*Log[2]))*Log[(3 + x^2 - x*Log[2])/x]^2))/(-3*x - x^3 + x^2 
*Log[2]),x]
 

Output:

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

Rubi [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(174\) vs. \(2(36)=72\).

Time = 1.09 (sec) , antiderivative size = 174, normalized size of antiderivative = 4.83, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.012, Rules used = {2026, 2726}

Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.

\(\displaystyle \int \frac {e^{2 x^4-4 e^{3 x} x^2+2 e^{6 x}} \left (\left (24-8 x^2\right ) \log \left (\frac {x^2-x \log (2)+3}{x}\right )+\left (-32 x^6+32 x^5 \log (2)-96 x^4+e^{6 x} \left (-48 x^3+48 x^2 \log (2)-144 x\right )+e^{3 x} \left (48 x^5+32 x^4+144 x^3+96 x^2+\left (-48 x^4-32 x^3\right ) \log (2)\right )\right ) \log ^2\left (\frac {x^2-x \log (2)+3}{x}\right )\right )}{-x^3+x^2 \log (2)-3 x} \, dx\)

\(\Big \downarrow \) 2026

\(\displaystyle \int \frac {e^{2 x^4-4 e^{3 x} x^2+2 e^{6 x}} \left (\left (24-8 x^2\right ) \log \left (\frac {x^2-x \log (2)+3}{x}\right )+\left (-32 x^6+32 x^5 \log (2)-96 x^4+e^{6 x} \left (-48 x^3+48 x^2 \log (2)-144 x\right )+e^{3 x} \left (48 x^5+32 x^4+144 x^3+96 x^2+\left (-48 x^4-32 x^3\right ) \log (2)\right )\right ) \log ^2\left (\frac {x^2-x \log (2)+3}{x}\right )\right )}{x \left (-x^2+x \log (2)-3\right )}dx\)

\(\Big \downarrow \) 2726

\(\displaystyle \frac {4 e^{2 x^4-4 e^{3 x} x^2+2 e^{6 x}} \left (2 x^6-2 x^5 \log (2)+6 x^4+3 e^{6 x} \left (x^3-x^2 \log (2)+3 x\right )-e^{3 x} \left (3 x^5+2 x^4+9 x^3+6 x^2-\left (3 x^4+2 x^3\right ) \log (2)\right )\right ) \log ^2\left (\frac {x^2-x \log (2)+3}{x}\right )}{x \left (2 x^3-3 e^{3 x} x^2-2 e^{3 x} x+3 e^{6 x}\right ) \left (x^2-x \log (2)+3\right )}\)

Input:

Int[(E^(2*E^(6*x) - 4*E^(3*x)*x^2 + 2*x^4)*((24 - 8*x^2)*Log[(3 + x^2 - x* 
Log[2])/x] + (-96*x^4 - 32*x^6 + 32*x^5*Log[2] + E^(6*x)*(-144*x - 48*x^3 
+ 48*x^2*Log[2]) + E^(3*x)*(96*x^2 + 144*x^3 + 32*x^4 + 48*x^5 + (-32*x^3 
- 48*x^4)*Log[2]))*Log[(3 + x^2 - x*Log[2])/x]^2))/(-3*x - x^3 + x^2*Log[2 
]),x]
 

Output:

(4*E^(2*E^(6*x) - 4*E^(3*x)*x^2 + 2*x^4)*(6*x^4 + 2*x^6 - 2*x^5*Log[2] + 3 
*E^(6*x)*(3*x + x^3 - x^2*Log[2]) - E^(3*x)*(6*x^2 + 9*x^3 + 2*x^4 + 3*x^5 
 - (2*x^3 + 3*x^4)*Log[2]))*Log[(3 + x^2 - x*Log[2])/x]^2)/(x*(3*E^(6*x) - 
 2*E^(3*x)*x - 3*E^(3*x)*x^2 + 2*x^3)*(3 + x^2 - x*Log[2]))
 

Defintions of rubi rules used

rule 2026

Int[(Fx_.)*(Px_)^(p_.), x_Symbol] :> With[{r = Expon[Px, x, Min]}, Int[x^(p 
*r)*ExpandToSum[Px/x^r, x]^p*Fx, x] /; IGtQ[r, 0]] /; PolyQ[Px, x] && Integ 
erQ[p] &&  !MonomialQ[Px, x] && (ILtQ[p, 0] ||  !PolyQ[u, x])
 

rule 2726

Int[(y_.)*(F_)^(u_)*((v_) + (w_)), x_Symbol] :> With[{z = v*(y/(Log[F]*D[u, 
 x]))}, Simp[F^u*z, x] /; EqQ[D[z, x], w*y]] /; FreeQ[F, x]
 

Maple [C] (warning: unable to verify)

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

Time = 0.07 (sec) , antiderivative size = 1142, normalized size of antiderivative = 31.72

\[\text {Expression too large to display}\]

Input:

int((((48*x^2*ln(2)-48*x^3-144*x)*exp(3*x)^2+((-48*x^4-32*x^3)*ln(2)+48*x^ 
5+32*x^4+144*x^3+96*x^2)*exp(3*x)+32*x^5*ln(2)-32*x^6-96*x^4)*ln((-x*ln(2) 
+x^2+3)/x)^2+(-8*x^2+24)*ln((-x*ln(2)+x^2+3)/x))*exp(exp(3*x)^2-2*x^2*exp( 
3*x)+x^4)^2/(x^2*ln(2)-x^3-3*x),x)
 

Output:

(-4*Pi^2+8*I*ln(x)*Pi*csgn(I/x*(x*ln(2)-x^2-3))^2-8*I*ln(x*ln(2)-x^2-3)*Pi 
*csgn(I/x*(x*ln(2)-x^2-3))^2+2*Pi^2*csgn(I*(x*ln(2)-x^2-3))^2*csgn(I/x*(x* 
ln(2)-x^2-3))^3*csgn(I/x)+8*Pi^2*csgn(I/x*(x*ln(2)-x^2-3))^2-4*I*ln(x)*Pi* 
csgn(I*(x*ln(2)-x^2-3))*csgn(I/x*(x*ln(2)-x^2-3))^2-4*I*ln(x)*Pi*csgn(I/x* 
(x*ln(2)-x^2-3))^2*csgn(I/x)+4*I*ln(x*ln(2)-x^2-3)*Pi*csgn(I*(x*ln(2)-x^2- 
3))*csgn(I/x*(x*ln(2)-x^2-3))^2+4*I*ln(x*ln(2)-x^2-3)*Pi*csgn(I/x*(x*ln(2) 
-x^2-3))^2*csgn(I/x)+4*ln(x)^2-8*ln(x)*ln(x*ln(2)-x^2-3)+4*Pi^2*csgn(I/x*( 
x*ln(2)-x^2-3))^4*csgn(I/x)-2*Pi^2*csgn(I*(x*ln(2)-x^2-3))*csgn(I/x*(x*ln( 
2)-x^2-3))^5-2*Pi^2*csgn(I/x*(x*ln(2)-x^2-3))^5*csgn(I/x)-4*Pi^2*csgn(I*(x 
*ln(2)-x^2-3))*csgn(I/x*(x*ln(2)-x^2-3))^2-4*Pi^2*csgn(I/x*(x*ln(2)-x^2-3) 
)^2*csgn(I/x)-Pi^2*csgn(I*(x*ln(2)-x^2-3))^2*csgn(I/x*(x*ln(2)-x^2-3))^4-P 
i^2*csgn(I/x*(x*ln(2)-x^2-3))^4*csgn(I/x)^2-4*I*ln(x)*Pi*csgn(I/x*(x*ln(2) 
-x^2-3))^3+4*I*ln(x*ln(2)-x^2-3)*Pi*csgn(I/x*(x*ln(2)-x^2-3))^3-4*Pi^2*csg 
n(I/x*(x*ln(2)-x^2-3))^3-Pi^2*csgn(I/x*(x*ln(2)-x^2-3))^6+4*Pi^2*csgn(I/x* 
(x*ln(2)-x^2-3))^5-4*Pi^2*csgn(I/x*(x*ln(2)-x^2-3))^4+8*I*Pi*ln(x*ln(2)-x^ 
2-3)-8*I*Pi*ln(x)-Pi^2*csgn(I*(x*ln(2)-x^2-3))^2*csgn(I/x*(x*ln(2)-x^2-3)) 
^2*csgn(I/x)^2+2*Pi^2*csgn(I*(x*ln(2)-x^2-3))*csgn(I/x*(x*ln(2)-x^2-3))^3* 
csgn(I/x)^2+4*Pi^2*csgn(I*(x*ln(2)-x^2-3))*csgn(I/x*(x*ln(2)-x^2-3))*csgn( 
I/x)-4*Pi^2*csgn(I*(x*ln(2)-x^2-3))*csgn(I/x*(x*ln(2)-x^2-3))^3*csgn(I/x)+ 
4*Pi^2*csgn(I*(x*ln(2)-x^2-3))*csgn(I/x*(x*ln(2)-x^2-3))^4+4*ln(x*ln(2)...
 

Fricas [A] (verification not implemented)

Time = 0.10 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.14 \[ \int \frac {e^{2 e^{6 x}-4 e^{3 x} x^2+2 x^4} \left (\left (24-8 x^2\right ) \log \left (\frac {3+x^2-x \log (2)}{x}\right )+\left (-96 x^4-32 x^6+32 x^5 \log (2)+e^{6 x} \left (-144 x-48 x^3+48 x^2 \log (2)\right )+e^{3 x} \left (96 x^2+144 x^3+32 x^4+48 x^5+\left (-32 x^3-48 x^4\right ) \log (2)\right )\right ) \log ^2\left (\frac {3+x^2-x \log (2)}{x}\right )\right )}{-3 x-x^3+x^2 \log (2)} \, dx=4 \, e^{\left (2 \, x^{4} - 4 \, x^{2} e^{\left (3 \, x\right )} + 2 \, e^{\left (6 \, x\right )}\right )} \log \left (\frac {x^{2} - x \log \left (2\right ) + 3}{x}\right )^{2} \] Input:

integrate((((48*x^2*log(2)-48*x^3-144*x)*exp(3*x)^2+((-48*x^4-32*x^3)*log( 
2)+48*x^5+32*x^4+144*x^3+96*x^2)*exp(3*x)+32*x^5*log(2)-32*x^6-96*x^4)*log 
((-x*log(2)+x^2+3)/x)^2+(-8*x^2+24)*log((-x*log(2)+x^2+3)/x))*exp(exp(3*x) 
^2-2*x^2*exp(3*x)+x^4)^2/(x^2*log(2)-x^3-3*x),x, algorithm="fricas")
 

Output:

4*e^(2*x^4 - 4*x^2*e^(3*x) + 2*e^(6*x))*log((x^2 - x*log(2) + 3)/x)^2
 

Sympy [F(-1)]

Timed out. \[ \int \frac {e^{2 e^{6 x}-4 e^{3 x} x^2+2 x^4} \left (\left (24-8 x^2\right ) \log \left (\frac {3+x^2-x \log (2)}{x}\right )+\left (-96 x^4-32 x^6+32 x^5 \log (2)+e^{6 x} \left (-144 x-48 x^3+48 x^2 \log (2)\right )+e^{3 x} \left (96 x^2+144 x^3+32 x^4+48 x^5+\left (-32 x^3-48 x^4\right ) \log (2)\right )\right ) \log ^2\left (\frac {3+x^2-x \log (2)}{x}\right )\right )}{-3 x-x^3+x^2 \log (2)} \, dx=\text {Timed out} \] Input:

integrate((((48*x**2*ln(2)-48*x**3-144*x)*exp(3*x)**2+((-48*x**4-32*x**3)* 
ln(2)+48*x**5+32*x**4+144*x**3+96*x**2)*exp(3*x)+32*x**5*ln(2)-32*x**6-96* 
x**4)*ln((-x*ln(2)+x**2+3)/x)**2+(-8*x**2+24)*ln((-x*ln(2)+x**2+3)/x))*exp 
(exp(3*x)**2-2*x**2*exp(3*x)+x**4)**2/(x**2*ln(2)-x**3-3*x),x)
 

Output:

Timed out
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 103 vs. \(2 (34) = 68\).

Time = 0.29 (sec) , antiderivative size = 103, normalized size of antiderivative = 2.86 \[ \int \frac {e^{2 e^{6 x}-4 e^{3 x} x^2+2 x^4} \left (\left (24-8 x^2\right ) \log \left (\frac {3+x^2-x \log (2)}{x}\right )+\left (-96 x^4-32 x^6+32 x^5 \log (2)+e^{6 x} \left (-144 x-48 x^3+48 x^2 \log (2)\right )+e^{3 x} \left (96 x^2+144 x^3+32 x^4+48 x^5+\left (-32 x^3-48 x^4\right ) \log (2)\right )\right ) \log ^2\left (\frac {3+x^2-x \log (2)}{x}\right )\right )}{-3 x-x^3+x^2 \log (2)} \, dx=4 \, e^{\left (2 \, x^{4} - 4 \, x^{2} e^{\left (3 \, x\right )} + 2 \, e^{\left (6 \, x\right )}\right )} \log \left (x^{2} - x \log \left (2\right ) + 3\right )^{2} - 8 \, e^{\left (2 \, x^{4} - 4 \, x^{2} e^{\left (3 \, x\right )} + 2 \, e^{\left (6 \, x\right )}\right )} \log \left (x^{2} - x \log \left (2\right ) + 3\right ) \log \left (x\right ) + 4 \, e^{\left (2 \, x^{4} - 4 \, x^{2} e^{\left (3 \, x\right )} + 2 \, e^{\left (6 \, x\right )}\right )} \log \left (x\right )^{2} \] Input:

integrate((((48*x^2*log(2)-48*x^3-144*x)*exp(3*x)^2+((-48*x^4-32*x^3)*log( 
2)+48*x^5+32*x^4+144*x^3+96*x^2)*exp(3*x)+32*x^5*log(2)-32*x^6-96*x^4)*log 
((-x*log(2)+x^2+3)/x)^2+(-8*x^2+24)*log((-x*log(2)+x^2+3)/x))*exp(exp(3*x) 
^2-2*x^2*exp(3*x)+x^4)^2/(x^2*log(2)-x^3-3*x),x, algorithm="maxima")
 

Output:

4*e^(2*x^4 - 4*x^2*e^(3*x) + 2*e^(6*x))*log(x^2 - x*log(2) + 3)^2 - 8*e^(2 
*x^4 - 4*x^2*e^(3*x) + 2*e^(6*x))*log(x^2 - x*log(2) + 3)*log(x) + 4*e^(2* 
x^4 - 4*x^2*e^(3*x) + 2*e^(6*x))*log(x)^2
 

Giac [F]

\[ \int \frac {e^{2 e^{6 x}-4 e^{3 x} x^2+2 x^4} \left (\left (24-8 x^2\right ) \log \left (\frac {3+x^2-x \log (2)}{x}\right )+\left (-96 x^4-32 x^6+32 x^5 \log (2)+e^{6 x} \left (-144 x-48 x^3+48 x^2 \log (2)\right )+e^{3 x} \left (96 x^2+144 x^3+32 x^4+48 x^5+\left (-32 x^3-48 x^4\right ) \log (2)\right )\right ) \log ^2\left (\frac {3+x^2-x \log (2)}{x}\right )\right )}{-3 x-x^3+x^2 \log (2)} \, dx=\int { \frac {8 \, {\left (2 \, {\left (2 \, x^{6} - 2 \, x^{5} \log \left (2\right ) + 6 \, x^{4} + 3 \, {\left (x^{3} - x^{2} \log \left (2\right ) + 3 \, x\right )} e^{\left (6 \, x\right )} - {\left (3 \, x^{5} + 2 \, x^{4} + 9 \, x^{3} + 6 \, x^{2} - {\left (3 \, x^{4} + 2 \, x^{3}\right )} \log \left (2\right )\right )} e^{\left (3 \, x\right )}\right )} \log \left (\frac {x^{2} - x \log \left (2\right ) + 3}{x}\right )^{2} + {\left (x^{2} - 3\right )} \log \left (\frac {x^{2} - x \log \left (2\right ) + 3}{x}\right )\right )} e^{\left (2 \, x^{4} - 4 \, x^{2} e^{\left (3 \, x\right )} + 2 \, e^{\left (6 \, x\right )}\right )}}{x^{3} - x^{2} \log \left (2\right ) + 3 \, x} \,d x } \] Input:

integrate((((48*x^2*log(2)-48*x^3-144*x)*exp(3*x)^2+((-48*x^4-32*x^3)*log( 
2)+48*x^5+32*x^4+144*x^3+96*x^2)*exp(3*x)+32*x^5*log(2)-32*x^6-96*x^4)*log 
((-x*log(2)+x^2+3)/x)^2+(-8*x^2+24)*log((-x*log(2)+x^2+3)/x))*exp(exp(3*x) 
^2-2*x^2*exp(3*x)+x^4)^2/(x^2*log(2)-x^3-3*x),x, algorithm="giac")
 

Output:

integrate(8*(2*(2*x^6 - 2*x^5*log(2) + 6*x^4 + 3*(x^3 - x^2*log(2) + 3*x)* 
e^(6*x) - (3*x^5 + 2*x^4 + 9*x^3 + 6*x^2 - (3*x^4 + 2*x^3)*log(2))*e^(3*x) 
)*log((x^2 - x*log(2) + 3)/x)^2 + (x^2 - 3)*log((x^2 - x*log(2) + 3)/x))*e 
^(2*x^4 - 4*x^2*e^(3*x) + 2*e^(6*x))/(x^3 - x^2*log(2) + 3*x), x)
 

Mupad [F(-1)]

Timed out. \[ \int \frac {e^{2 e^{6 x}-4 e^{3 x} x^2+2 x^4} \left (\left (24-8 x^2\right ) \log \left (\frac {3+x^2-x \log (2)}{x}\right )+\left (-96 x^4-32 x^6+32 x^5 \log (2)+e^{6 x} \left (-144 x-48 x^3+48 x^2 \log (2)\right )+e^{3 x} \left (96 x^2+144 x^3+32 x^4+48 x^5+\left (-32 x^3-48 x^4\right ) \log (2)\right )\right ) \log ^2\left (\frac {3+x^2-x \log (2)}{x}\right )\right )}{-3 x-x^3+x^2 \log (2)} \, dx=\int \frac {{\mathrm {e}}^{2\,{\mathrm {e}}^{6\,x}-4\,x^2\,{\mathrm {e}}^{3\,x}+2\,x^4}\,\left (\left ({\mathrm {e}}^{6\,x}\,\left (48\,x^3-48\,\ln \left (2\right )\,x^2+144\,x\right )-32\,x^5\,\ln \left (2\right )-{\mathrm {e}}^{3\,x}\,\left (96\,x^2-\ln \left (2\right )\,\left (48\,x^4+32\,x^3\right )+144\,x^3+32\,x^4+48\,x^5\right )+96\,x^4+32\,x^6\right )\,{\ln \left (\frac {x^2-\ln \left (2\right )\,x+3}{x}\right )}^2+\left (8\,x^2-24\right )\,\ln \left (\frac {x^2-\ln \left (2\right )\,x+3}{x}\right )\right )}{x^3-\ln \left (2\right )\,x^2+3\,x} \,d x \] Input:

int((exp(2*exp(6*x) - 4*x^2*exp(3*x) + 2*x^4)*(log((x^2 - x*log(2) + 3)/x) 
*(8*x^2 - 24) + log((x^2 - x*log(2) + 3)/x)^2*(exp(6*x)*(144*x - 48*x^2*lo 
g(2) + 48*x^3) - 32*x^5*log(2) - exp(3*x)*(96*x^2 - log(2)*(32*x^3 + 48*x^ 
4) + 144*x^3 + 32*x^4 + 48*x^5) + 96*x^4 + 32*x^6)))/(3*x - x^2*log(2) + x 
^3),x)
 

Output:

int((exp(2*exp(6*x) - 4*x^2*exp(3*x) + 2*x^4)*(log((x^2 - x*log(2) + 3)/x) 
*(8*x^2 - 24) + log((x^2 - x*log(2) + 3)/x)^2*(exp(6*x)*(144*x - 48*x^2*lo 
g(2) + 48*x^3) - 32*x^5*log(2) - exp(3*x)*(96*x^2 - log(2)*(32*x^3 + 48*x^ 
4) + 144*x^3 + 32*x^4 + 48*x^5) + 96*x^4 + 32*x^6)))/(3*x - x^2*log(2) + x 
^3), x)
 

Reduce [B] (verification not implemented)

Time = 0.22 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.33 \[ \int \frac {e^{2 e^{6 x}-4 e^{3 x} x^2+2 x^4} \left (\left (24-8 x^2\right ) \log \left (\frac {3+x^2-x \log (2)}{x}\right )+\left (-96 x^4-32 x^6+32 x^5 \log (2)+e^{6 x} \left (-144 x-48 x^3+48 x^2 \log (2)\right )+e^{3 x} \left (96 x^2+144 x^3+32 x^4+48 x^5+\left (-32 x^3-48 x^4\right ) \log (2)\right )\right ) \log ^2\left (\frac {3+x^2-x \log (2)}{x}\right )\right )}{-3 x-x^3+x^2 \log (2)} \, dx=\frac {4 e^{2 e^{6 x}+2 x^{4}} \mathrm {log}\left (\frac {-\mathrm {log}\left (2\right ) x +x^{2}+3}{x}\right )^{2}}{e^{4 e^{3 x} x^{2}}} \] Input:

int((((48*x^2*log(2)-48*x^3-144*x)*exp(3*x)^2+((-48*x^4-32*x^3)*log(2)+48* 
x^5+32*x^4+144*x^3+96*x^2)*exp(3*x)+32*x^5*log(2)-32*x^6-96*x^4)*log((-x*l 
og(2)+x^2+3)/x)^2+(-8*x^2+24)*log((-x*log(2)+x^2+3)/x))*exp(exp(3*x)^2-2*x 
^2*exp(3*x)+x^4)^2/(x^2*log(2)-x^3-3*x),x)
 

Output:

(4*e**(2*e**(6*x) + 2*x**4)*log(( - log(2)*x + x**2 + 3)/x)**2)/e**(4*e**( 
3*x)*x**2)