\(\int \frac {e^{-4+\frac {25+40 \log (-3+x^2)+e^{4+e^x} x \log ^2(-3+x^2)+(16+e^4 x^2) \log ^2(-3+x^2)}{e^4 x \log ^2(-3+x^2)}} (-100 x^2+(75-105 x^2) \log (-3+x^2)+(120-40 x^2) \log ^2(-3+x^2)+e^{4+e^x+x} (-3 x^2+x^4) \log ^3(-3+x^2)+(48-16 x^2+e^4 (-3 x^2+x^4)) \log ^3(-3+x^2))}{(-3 x^2+x^4) \log ^3(-3+x^2)} \, dx\) [2935]

Optimal result

Integrand size = 175, antiderivative size = 30 \[ \int \frac {e^{-4+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}} \left (-100 x^2+\left (75-105 x^2\right ) \log \left (-3+x^2\right )+\left (120-40 x^2\right ) \log ^2\left (-3+x^2\right )+e^{4+e^x+x} \left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )+\left (48-16 x^2+e^4 \left (-3 x^2+x^4\right )\right ) \log ^3\left (-3+x^2\right )\right )}{\left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )} \, dx=e^{e^{e^x}+x+\frac {\left (4+\frac {5}{\log \left (-3+x^2\right )}\right )^2}{e^4 x}} \] Output:

exp(exp(exp(x))+(4+5/ln(x^2-3))^2/x/exp(4)+x)
 

Mathematica [A] (verified)

Time = 0.19 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.63 \[ \int \frac {e^{-4+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}} \left (-100 x^2+\left (75-105 x^2\right ) \log \left (-3+x^2\right )+\left (120-40 x^2\right ) \log ^2\left (-3+x^2\right )+e^{4+e^x+x} \left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )+\left (48-16 x^2+e^4 \left (-3 x^2+x^4\right )\right ) \log ^3\left (-3+x^2\right )\right )}{\left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )} \, dx=e^{e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}} \] Input:

Integrate[(E^(-4 + (25 + 40*Log[-3 + x^2] + E^(4 + E^x)*x*Log[-3 + x^2]^2 
+ (16 + E^4*x^2)*Log[-3 + x^2]^2)/(E^4*x*Log[-3 + x^2]^2))*(-100*x^2 + (75 
 - 105*x^2)*Log[-3 + x^2] + (120 - 40*x^2)*Log[-3 + x^2]^2 + E^(4 + E^x + 
x)*(-3*x^2 + x^4)*Log[-3 + x^2]^3 + (48 - 16*x^2 + E^4*(-3*x^2 + x^4))*Log 
[-3 + x^2]^3))/((-3*x^2 + x^4)*Log[-3 + x^2]^3),x]
 

Output:

E^(E^E^x + 16/(E^4*x) + x + 25/(E^4*x*Log[-3 + x^2]^2) + 40/(E^4*x*Log[-3 
+ x^2]))
 

Rubi [A] (verified)

Time = 19.97 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.63, number of steps used = 4, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.023, Rules used = {2026, 7276, 7239, 7257}

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.

\(\displaystyle \int \frac {\left (-100 x^2+\left (120-40 x^2\right ) \log ^2\left (x^2-3\right )+\left (75-105 x^2\right ) \log \left (x^2-3\right )+e^{x+e^x+4} \left (x^4-3 x^2\right ) \log ^3\left (x^2-3\right )+\left (-16 x^2+e^4 \left (x^4-3 x^2\right )+48\right ) \log ^3\left (x^2-3\right )\right ) \exp \left (\frac {e^{e^x+4} x \log ^2\left (x^2-3\right )+\left (e^4 x^2+16\right ) \log ^2\left (x^2-3\right )+40 \log \left (x^2-3\right )+25}{e^4 x \log ^2\left (x^2-3\right )}-4\right )}{\left (x^4-3 x^2\right ) \log ^3\left (x^2-3\right )} \, dx\)

\(\Big \downarrow \) 2026

\(\displaystyle \int \frac {\left (-100 x^2+\left (120-40 x^2\right ) \log ^2\left (x^2-3\right )+\left (75-105 x^2\right ) \log \left (x^2-3\right )+e^{x+e^x+4} \left (x^4-3 x^2\right ) \log ^3\left (x^2-3\right )+\left (-16 x^2+e^4 \left (x^4-3 x^2\right )+48\right ) \log ^3\left (x^2-3\right )\right ) \exp \left (\frac {e^{e^x+4} x \log ^2\left (x^2-3\right )+\left (e^4 x^2+16\right ) \log ^2\left (x^2-3\right )+40 \log \left (x^2-3\right )+25}{e^4 x \log ^2\left (x^2-3\right )}-4\right )}{x^2 \left (x^2-3\right ) \log ^3\left (x^2-3\right )}dx\)

\(\Big \downarrow \) 7276

\(\displaystyle \int \left (\exp \left (\frac {e^{e^x+4} x \log ^2\left (x^2-3\right )+\left (e^4 x^2+16\right ) \log ^2\left (x^2-3\right )+40 \log \left (x^2-3\right )+25}{e^4 x \log ^2\left (x^2-3\right )}+x+e^x\right )+\frac {\left (100 x^2+16 \left (1+\frac {3 e^4}{16}\right ) x^2 \log ^3\left (x^2-3\right )-48 \log ^3\left (x^2-3\right )+40 x^2 \log ^2\left (x^2-3\right )-120 \log ^2\left (x^2-3\right )+105 x^2 \log \left (x^2-3\right )-75 \log \left (x^2-3\right )-e^4 x^4 \log ^3\left (x^2-3\right )\right ) \exp \left (\frac {e^{e^x+4} x \log ^2\left (x^2-3\right )+\left (e^4 x^2+16\right ) \log ^2\left (x^2-3\right )+40 \log \left (x^2-3\right )+25}{e^4 x \log ^2\left (x^2-3\right )}-4\right )}{x^2 \left (3-x^2\right ) \log ^3\left (x^2-3\right )}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {\left (100 x^2-\left (\left (x^2-3\right ) \left (e^{x+e^x+4} x^2+e^4 x^2-16\right ) \log ^3\left (x^2-3\right )\right )+40 \left (x^2-3\right ) \log ^2\left (x^2-3\right )+15 \left (7 x^2-5\right ) \log \left (x^2-3\right )\right ) \exp \left (\frac {25}{e^4 x \log ^2\left (x^2-3\right )}+\frac {40}{e^4 x \log \left (x^2-3\right )}+x+e^{e^x}+\frac {16}{e^4 x}-4\right )}{x^2 \left (3-x^2\right ) \log ^3\left (x^2-3\right )}dx\)

\(\Big \downarrow \) 7257

\(\displaystyle \exp \left (\frac {25}{e^4 x \log ^2\left (x^2-3\right )}+\frac {40}{e^4 x \log \left (x^2-3\right )}+x+e^{e^x}+\frac {16}{e^4 x}\right )\)

Input:

Int[(E^(-4 + (25 + 40*Log[-3 + x^2] + E^(4 + E^x)*x*Log[-3 + x^2]^2 + (16 
+ E^4*x^2)*Log[-3 + x^2]^2)/(E^4*x*Log[-3 + x^2]^2))*(-100*x^2 + (75 - 105 
*x^2)*Log[-3 + x^2] + (120 - 40*x^2)*Log[-3 + x^2]^2 + E^(4 + E^x + x)*(-3 
*x^2 + x^4)*Log[-3 + x^2]^3 + (48 - 16*x^2 + E^4*(-3*x^2 + x^4))*Log[-3 + 
x^2]^3))/((-3*x^2 + x^4)*Log[-3 + x^2]^3),x]
 

Output:

E^(E^E^x + 16/(E^4*x) + x + 25/(E^4*x*Log[-3 + x^2]^2) + 40/(E^4*x*Log[-3 
+ x^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 7239

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

rule 7257

Int[(F_)^(v_)*(u_), x_Symbol] :> With[{q = DerivativeDivides[v, u, x]}, Sim 
p[q*(F^v/Log[F]), x] /;  !FalseQ[q]] /; FreeQ[F, x]
 

rule 7276

Int[(u_)/((a_) + (b_.)*(x_)^(n_)), x_Symbol] :> With[{v = RationalFunctionE 
xpand[u/(a + b*x^n), x]}, Int[v, x] /; SumQ[v]] /; FreeQ[{a, b}, x] && IGtQ 
[n, 0]
 

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(64\) vs. \(2(28)=56\).

Time = 0.08 (sec) , antiderivative size = 65, normalized size of antiderivative = 2.17

\[{\mathrm e}^{\frac {\left ({\mathrm e}^{4} \ln \left (x^{2}-3\right )^{2} x^{2}+x \ln \left (x^{2}-3\right )^{2} {\mathrm e}^{{\mathrm e}^{x}+4}+16 \ln \left (x^{2}-3\right )^{2}+40 \ln \left (x^{2}-3\right )+25\right ) {\mathrm e}^{-4}}{x \ln \left (x^{2}-3\right )^{2}}}\]

Input:

int(((x^4-3*x^2)*exp(4)*exp(x)*ln(x^2-3)^3*exp(exp(x))+((x^4-3*x^2)*exp(4) 
-16*x^2+48)*ln(x^2-3)^3+(-40*x^2+120)*ln(x^2-3)^2+(-105*x^2+75)*ln(x^2-3)- 
100*x^2)*exp((x*exp(4)*ln(x^2-3)^2*exp(exp(x))+(x^2*exp(4)+16)*ln(x^2-3)^2 
+40*ln(x^2-3)+25)/x/exp(4)/ln(x^2-3)^2)/(x^4-3*x^2)/exp(4)/ln(x^2-3)^3,x)
 

Output:

exp((exp(4)*ln(x^2-3)^2*x^2+x*ln(x^2-3)^2*exp(exp(x)+4)+16*ln(x^2-3)^2+40* 
ln(x^2-3)+25)*exp(-4)/x/ln(x^2-3)^2)
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 75 vs. \(2 (26) = 52\).

Time = 0.11 (sec) , antiderivative size = 75, normalized size of antiderivative = 2.50 \[ \int \frac {e^{-4+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}} \left (-100 x^2+\left (75-105 x^2\right ) \log \left (-3+x^2\right )+\left (120-40 x^2\right ) \log ^2\left (-3+x^2\right )+e^{4+e^x+x} \left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )+\left (48-16 x^2+e^4 \left (-3 x^2+x^4\right )\right ) \log ^3\left (-3+x^2\right )\right )}{\left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )} \, dx=e^{\left (\frac {{\left (x e^{\left (x + e^{x} + 4\right )} \log \left (x^{2} - 3\right )^{2} + {\left ({\left (x^{2} - 4 \, x\right )} e^{4} + 16\right )} e^{x} \log \left (x^{2} - 3\right )^{2} + 40 \, e^{x} \log \left (x^{2} - 3\right ) + 25 \, e^{x}\right )} e^{\left (-x - 4\right )}}{x \log \left (x^{2} - 3\right )^{2}} + 4\right )} \] Input:

integrate(((x^4-3*x^2)*exp(4)*exp(x)*log(x^2-3)^3*exp(exp(x))+((x^4-3*x^2) 
*exp(4)-16*x^2+48)*log(x^2-3)^3+(-40*x^2+120)*log(x^2-3)^2+(-105*x^2+75)*l 
og(x^2-3)-100*x^2)*exp((x*exp(4)*log(x^2-3)^2*exp(exp(x))+(x^2*exp(4)+16)* 
log(x^2-3)^2+40*log(x^2-3)+25)/x/exp(4)/log(x^2-3)^2)/(x^4-3*x^2)/exp(4)/l 
og(x^2-3)^3,x, algorithm="fricas")
 

Output:

e^((x*e^(x + e^x + 4)*log(x^2 - 3)^2 + ((x^2 - 4*x)*e^4 + 16)*e^x*log(x^2 
- 3)^2 + 40*e^x*log(x^2 - 3) + 25*e^x)*e^(-x - 4)/(x*log(x^2 - 3)^2) + 4)
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 60 vs. \(2 (24) = 48\).

Time = 1.86 (sec) , antiderivative size = 60, normalized size of antiderivative = 2.00 \[ \int \frac {e^{-4+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}} \left (-100 x^2+\left (75-105 x^2\right ) \log \left (-3+x^2\right )+\left (120-40 x^2\right ) \log ^2\left (-3+x^2\right )+e^{4+e^x+x} \left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )+\left (48-16 x^2+e^4 \left (-3 x^2+x^4\right )\right ) \log ^3\left (-3+x^2\right )\right )}{\left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )} \, dx=e^{\frac {x e^{4} e^{e^{x}} \log {\left (x^{2} - 3 \right )}^{2} + \left (x^{2} e^{4} + 16\right ) \log {\left (x^{2} - 3 \right )}^{2} + 40 \log {\left (x^{2} - 3 \right )} + 25}{x e^{4} \log {\left (x^{2} - 3 \right )}^{2}}} \] Input:

integrate(((x**4-3*x**2)*exp(4)*exp(x)*ln(x**2-3)**3*exp(exp(x))+((x**4-3* 
x**2)*exp(4)-16*x**2+48)*ln(x**2-3)**3+(-40*x**2+120)*ln(x**2-3)**2+(-105* 
x**2+75)*ln(x**2-3)-100*x**2)*exp((x*exp(4)*ln(x**2-3)**2*exp(exp(x))+(x** 
2*exp(4)+16)*ln(x**2-3)**2+40*ln(x**2-3)+25)/x/exp(4)/ln(x**2-3)**2)/(x**4 
-3*x**2)/exp(4)/ln(x**2-3)**3,x)
 

Output:

exp((x*exp(4)*exp(exp(x))*log(x**2 - 3)**2 + (x**2*exp(4) + 16)*log(x**2 - 
 3)**2 + 40*log(x**2 - 3) + 25)*exp(-4)/(x*log(x**2 - 3)**2))
 

Maxima [A] (verification not implemented)

Time = 0.30 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.43 \[ \int \frac {e^{-4+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}} \left (-100 x^2+\left (75-105 x^2\right ) \log \left (-3+x^2\right )+\left (120-40 x^2\right ) \log ^2\left (-3+x^2\right )+e^{4+e^x+x} \left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )+\left (48-16 x^2+e^4 \left (-3 x^2+x^4\right )\right ) \log ^3\left (-3+x^2\right )\right )}{\left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )} \, dx=e^{\left (x + \frac {16 \, e^{\left (-4\right )}}{x} + \frac {40 \, e^{\left (-4\right )}}{x \log \left (x^{2} - 3\right )} + \frac {25 \, e^{\left (-4\right )}}{x \log \left (x^{2} - 3\right )^{2}} + e^{\left (e^{x}\right )}\right )} \] Input:

integrate(((x^4-3*x^2)*exp(4)*exp(x)*log(x^2-3)^3*exp(exp(x))+((x^4-3*x^2) 
*exp(4)-16*x^2+48)*log(x^2-3)^3+(-40*x^2+120)*log(x^2-3)^2+(-105*x^2+75)*l 
og(x^2-3)-100*x^2)*exp((x*exp(4)*log(x^2-3)^2*exp(exp(x))+(x^2*exp(4)+16)* 
log(x^2-3)^2+40*log(x^2-3)+25)/x/exp(4)/log(x^2-3)^2)/(x^4-3*x^2)/exp(4)/l 
og(x^2-3)^3,x, algorithm="maxima")
 

Output:

e^(x + 16*e^(-4)/x + 40*e^(-4)/(x*log(x^2 - 3)) + 25*e^(-4)/(x*log(x^2 - 3 
)^2) + e^(e^x))
 

Giac [F]

\[ \int \frac {e^{-4+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}} \left (-100 x^2+\left (75-105 x^2\right ) \log \left (-3+x^2\right )+\left (120-40 x^2\right ) \log ^2\left (-3+x^2\right )+e^{4+e^x+x} \left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )+\left (48-16 x^2+e^4 \left (-3 x^2+x^4\right )\right ) \log ^3\left (-3+x^2\right )\right )}{\left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )} \, dx=\int { \frac {{\left ({\left (x^{4} - 3 \, x^{2}\right )} e^{\left (x + e^{x} + 4\right )} \log \left (x^{2} - 3\right )^{3} - {\left (16 \, x^{2} - {\left (x^{4} - 3 \, x^{2}\right )} e^{4} - 48\right )} \log \left (x^{2} - 3\right )^{3} - 40 \, {\left (x^{2} - 3\right )} \log \left (x^{2} - 3\right )^{2} - 100 \, x^{2} - 15 \, {\left (7 \, x^{2} - 5\right )} \log \left (x^{2} - 3\right )\right )} e^{\left (\frac {{\left (x e^{\left (e^{x} + 4\right )} \log \left (x^{2} - 3\right )^{2} + {\left (x^{2} e^{4} + 16\right )} \log \left (x^{2} - 3\right )^{2} + 40 \, \log \left (x^{2} - 3\right ) + 25\right )} e^{\left (-4\right )}}{x \log \left (x^{2} - 3\right )^{2}} - 4\right )}}{{\left (x^{4} - 3 \, x^{2}\right )} \log \left (x^{2} - 3\right )^{3}} \,d x } \] Input:

integrate(((x^4-3*x^2)*exp(4)*exp(x)*log(x^2-3)^3*exp(exp(x))+((x^4-3*x^2) 
*exp(4)-16*x^2+48)*log(x^2-3)^3+(-40*x^2+120)*log(x^2-3)^2+(-105*x^2+75)*l 
og(x^2-3)-100*x^2)*exp((x*exp(4)*log(x^2-3)^2*exp(exp(x))+(x^2*exp(4)+16)* 
log(x^2-3)^2+40*log(x^2-3)+25)/x/exp(4)/log(x^2-3)^2)/(x^4-3*x^2)/exp(4)/l 
og(x^2-3)^3,x, algorithm="giac")
 

Output:

undef
 

Mupad [B] (verification not implemented)

Time = 4.14 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.57 \[ \int \frac {e^{-4+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}} \left (-100 x^2+\left (75-105 x^2\right ) \log \left (-3+x^2\right )+\left (120-40 x^2\right ) \log ^2\left (-3+x^2\right )+e^{4+e^x+x} \left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )+\left (48-16 x^2+e^4 \left (-3 x^2+x^4\right )\right ) \log ^3\left (-3+x^2\right )\right )}{\left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )} \, dx={\mathrm {e}}^{\frac {16\,{\mathrm {e}}^{-4}}{x}}\,{\mathrm {e}}^{\frac {25\,{\mathrm {e}}^{-4}}{x\,{\ln \left (x^2-3\right )}^2}}\,{\mathrm {e}}^{\frac {40\,{\mathrm {e}}^{-4}}{x\,\ln \left (x^2-3\right )}}\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}\,{\mathrm {e}}^x \] Input:

int((exp((exp(-4)*(40*log(x^2 - 3) + log(x^2 - 3)^2*(x^2*exp(4) + 16) + x* 
exp(exp(x))*exp(4)*log(x^2 - 3)^2 + 25))/(x*log(x^2 - 3)^2))*exp(-4)*(log( 
x^2 - 3)^3*(exp(4)*(3*x^2 - x^4) + 16*x^2 - 48) + log(x^2 - 3)*(105*x^2 - 
75) + 100*x^2 + log(x^2 - 3)^2*(40*x^2 - 120) + exp(exp(x))*exp(4)*exp(x)* 
log(x^2 - 3)^3*(3*x^2 - x^4)))/(log(x^2 - 3)^3*(3*x^2 - x^4)),x)
 

Output:

exp((16*exp(-4))/x)*exp((25*exp(-4))/(x*log(x^2 - 3)^2))*exp((40*exp(-4))/ 
(x*log(x^2 - 3)))*exp(exp(exp(x)))*exp(x)
 

Reduce [F]

\[ \int \frac {e^{-4+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}} \left (-100 x^2+\left (75-105 x^2\right ) \log \left (-3+x^2\right )+\left (120-40 x^2\right ) \log ^2\left (-3+x^2\right )+e^{4+e^x+x} \left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )+\left (48-16 x^2+e^4 \left (-3 x^2+x^4\right )\right ) \log ^3\left (-3+x^2\right )\right )}{\left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )} \, dx=\int \frac {\left (\left (x^{4}-3 x^{2}\right ) {\mathrm e}^{4} {\mathrm e}^{x} \mathrm {log}\left (x^{2}-3\right )^{3} {\mathrm e}^{{\mathrm e}^{x}}+\left (\left (x^{4}-3 x^{2}\right ) {\mathrm e}^{4}-16 x^{2}+48\right ) \mathrm {log}\left (x^{2}-3\right )^{3}+\left (-40 x^{2}+120\right ) \mathrm {log}\left (x^{2}-3\right )^{2}+\left (-105 x^{2}+75\right ) \mathrm {log}\left (x^{2}-3\right )-100 x^{2}\right ) {\mathrm e}^{\frac {x \,{\mathrm e}^{4} \mathrm {log}\left (x^{2}-3\right )^{2} {\mathrm e}^{{\mathrm e}^{x}}+\left (x^{2} {\mathrm e}^{4}+16\right ) \mathrm {log}\left (x^{2}-3\right )^{2}+40 \,\mathrm {log}\left (x^{2}-3\right )+25}{x \,{\mathrm e}^{4} \mathrm {log}\left (x^{2}-3\right )^{2}}}}{\left (x^{4}-3 x^{2}\right ) {\mathrm e}^{4} \mathrm {log}\left (x^{2}-3\right )^{3}}d x \] Input:

int(((x^4-3*x^2)*exp(4)*exp(x)*log(x^2-3)^3*exp(exp(x))+((x^4-3*x^2)*exp(4 
)-16*x^2+48)*log(x^2-3)^3+(-40*x^2+120)*log(x^2-3)^2+(-105*x^2+75)*log(x^2 
-3)-100*x^2)*exp((x*exp(4)*log(x^2-3)^2*exp(exp(x))+(x^2*exp(4)+16)*log(x^ 
2-3)^2+40*log(x^2-3)+25)/x/exp(4)/log(x^2-3)^2)/(x^4-3*x^2)/exp(4)/log(x^2 
-3)^3,x)
 

Output:

int(((x^4-3*x^2)*exp(4)*exp(x)*log(x^2-3)^3*exp(exp(x))+((x^4-3*x^2)*exp(4 
)-16*x^2+48)*log(x^2-3)^3+(-40*x^2+120)*log(x^2-3)^2+(-105*x^2+75)*log(x^2 
-3)-100*x^2)*exp((x*exp(4)*log(x^2-3)^2*exp(exp(x))+(x^2*exp(4)+16)*log(x^ 
2-3)^2+40*log(x^2-3)+25)/x/exp(4)/log(x^2-3)^2)/(x^4-3*x^2)/exp(4)/log(x^2 
-3)^3,x)