3.23.32 \(\int \frac {18 x+13 x^2+4 x^3-3 x^4+x^5+e^{25} (36 x^2+16 x^3-8 x^4+4 x^5)+(18 x+8 x^2-4 x^3+2 x^4+e^{25} (72 x+32 x^2-16 x^3+8 x^4)) \log (\frac {9+4 x-2 x^2+x^3}{x^2})+e^{25} (36+16 x-8 x^2+4 x^3) \log ^2(\frac {9+4 x-2 x^2+x^3}{x^2})}{e^{25} (9 x^2+4 x^3-2 x^4+x^5)+e^{25} (18 x+8 x^2-4 x^3+2 x^4) \log (\frac {9+4 x-2 x^2+x^3}{x^2})+e^{25} (9+4 x-2 x^2+x^3) \log ^2(\frac {9+4 x-2 x^2+x^3}{x^2})} \, dx\) [2232]

3.23.32.1 Optimal result

Integrand size = 252, antiderivative size = 26 \[ \int \frac {18 x+13 x^2+4 x^3-3 x^4+x^5+e^{25} \left (36 x^2+16 x^3-8 x^4+4 x^5\right )+\left (18 x+8 x^2-4 x^3+2 x^4+e^{25} \left (72 x+32 x^2-16 x^3+8 x^4\right )\right ) \log \left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )+e^{25} \left (36+16 x-8 x^2+4 x^3\right ) \log ^2\left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )}{e^{25} \left (9 x^2+4 x^3-2 x^4+x^5\right )+e^{25} \left (18 x+8 x^2-4 x^3+2 x^4\right ) \log \left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )+e^{25} \left (9+4 x-2 x^2+x^3\right ) \log ^2\left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )} \, dx=x \left (4+\frac {x}{e^{25} \left (x+\log \left (-2+x+\frac {9+4 x}{x^2}\right )\right )}\right ) \]

output

x*(4+x/exp(25)/(x+ln((4*x+9)/x^2-2+x)))
 

3.23.32.2 Mathematica [A] (verified)

Time = 0.09 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.27 \[ \int \frac {18 x+13 x^2+4 x^3-3 x^4+x^5+e^{25} \left (36 x^2+16 x^3-8 x^4+4 x^5\right )+\left (18 x+8 x^2-4 x^3+2 x^4+e^{25} \left (72 x+32 x^2-16 x^3+8 x^4\right )\right ) \log \left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )+e^{25} \left (36+16 x-8 x^2+4 x^3\right ) \log ^2\left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )}{e^{25} \left (9 x^2+4 x^3-2 x^4+x^5\right )+e^{25} \left (18 x+8 x^2-4 x^3+2 x^4\right ) \log \left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )+e^{25} \left (9+4 x-2 x^2+x^3\right ) \log ^2\left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )} \, dx=\frac {4 e^{25} x+\frac {x^2}{x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )}}{e^{25}} \]

input

Integrate[(18*x + 13*x^2 + 4*x^3 - 3*x^4 + x^5 + E^25*(36*x^2 + 16*x^3 - 8 
*x^4 + 4*x^5) + (18*x + 8*x^2 - 4*x^3 + 2*x^4 + E^25*(72*x + 32*x^2 - 16*x 
^3 + 8*x^4))*Log[(9 + 4*x - 2*x^2 + x^3)/x^2] + E^25*(36 + 16*x - 8*x^2 + 
4*x^3)*Log[(9 + 4*x - 2*x^2 + x^3)/x^2]^2)/(E^25*(9*x^2 + 4*x^3 - 2*x^4 + 
x^5) + E^25*(18*x + 8*x^2 - 4*x^3 + 2*x^4)*Log[(9 + 4*x - 2*x^2 + x^3)/x^2 
] + E^25*(9 + 4*x - 2*x^2 + x^3)*Log[(9 + 4*x - 2*x^2 + x^3)/x^2]^2),x]
 

output

(4*E^25*x + x^2/(x + Log[-2 + 9/x^2 + 4/x + x]))/E^25
 

3.23.32.3 Rubi [F]

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.

\(\displaystyle \int \frac {x^5-3 x^4+4 x^3+13 x^2+e^{25} \left (4 x^3-8 x^2+16 x+36\right ) \log ^2\left (\frac {x^3-2 x^2+4 x+9}{x^2}\right )+\left (2 x^4-4 x^3+8 x^2+e^{25} \left (8 x^4-16 x^3+32 x^2+72 x\right )+18 x\right ) \log \left (\frac {x^3-2 x^2+4 x+9}{x^2}\right )+e^{25} \left (4 x^5-8 x^4+16 x^3+36 x^2\right )+18 x}{e^{25} \left (x^3-2 x^2+4 x+9\right ) \log ^2\left (\frac {x^3-2 x^2+4 x+9}{x^2}\right )+e^{25} \left (2 x^4-4 x^3+8 x^2+18 x\right ) \log \left (\frac {x^3-2 x^2+4 x+9}{x^2}\right )+e^{25} \left (x^5-2 x^4+4 x^3+9 x^2\right )} \, dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {x^5-3 x^4+4 x^3+13 x^2+4 e^{25} \left (x^3-2 x^2+4 x+9\right ) x^2+4 e^{25} \left (x^3-2 x^2+4 x+9\right ) \log ^2\left (\frac {9}{x^2}+x+\frac {4}{x}-2\right )+2 \left (1+4 e^{25}\right ) \left (x^3-2 x^2+4 x+9\right ) x \log \left (\frac {9}{x^2}+x+\frac {4}{x}-2\right )+18 x}{e^{25} \left (x^3-2 x^2+4 x+9\right ) \left (\log \left (\frac {9}{x^2}+x+\frac {4}{x}-2\right )+x\right )^2}dx\)

\(\Big \downarrow \) 27

\(\displaystyle \frac {\int \frac {x^5-3 x^4+4 x^3+4 e^{25} \left (x^3-2 x^2+4 x+9\right ) x^2+13 x^2+2 \left (1+4 e^{25}\right ) \left (x^3-2 x^2+4 x+9\right ) \log \left (x-2+\frac {4}{x}+\frac {9}{x^2}\right ) x+18 x+4 e^{25} \left (x^3-2 x^2+4 x+9\right ) \log ^2\left (x-2+\frac {4}{x}+\frac {9}{x^2}\right )}{\left (x^3-2 x^2+4 x+9\right ) \left (x+\log \left (x-2+\frac {4}{x}+\frac {9}{x^2}\right )\right )^2}dx}{e^{25}}\)

\(\Big \downarrow \) 7293

\(\displaystyle \frac {\int \left (\frac {2 x}{x+\log \left (x-2+\frac {4}{x}+\frac {9}{x^2}\right )}-\frac {\left (x^4-x^3+4 x^2+5 x-18\right ) x}{\left (x^3-2 x^2+4 x+9\right ) \left (x+\log \left (x-2+\frac {4}{x}+\frac {9}{x^2}\right )\right )^2}+4 e^{25}\right )dx}{e^{25}}\)

\(\Big \downarrow \) 2009

\(\displaystyle \frac {-2 \int \frac {1}{\left (x+\log \left (x-2+\frac {4}{x}+\frac {9}{x^2}\right )\right )^2}dx-\int \frac {x}{\left (x+\log \left (x-2+\frac {4}{x}+\frac {9}{x^2}\right )\right )^2}dx-\int \frac {x^2}{\left (x+\log \left (x-2+\frac {4}{x}+\frac {9}{x^2}\right )\right )^2}dx+2 \int \frac {x}{x+\log \left (x-2+\frac {4}{x}+\frac {9}{x^2}\right )}dx+18 \int \frac {1}{\left (x^3-2 x^2+4 x+9\right ) \left (x+\log \left (x-2+\frac {4}{x}+\frac {9}{x^2}\right )\right )^2}dx+35 \int \frac {x}{\left (x^3-2 x^2+4 x+9\right ) \left (x+\log \left (x-2+\frac {4}{x}+\frac {9}{x^2}\right )\right )^2}dx+4 \int \frac {x^2}{\left (x^3-2 x^2+4 x+9\right ) \left (x+\log \left (x-2+\frac {4}{x}+\frac {9}{x^2}\right )\right )^2}dx+4 e^{25} x}{e^{25}}\)

input

Int[(18*x + 13*x^2 + 4*x^3 - 3*x^4 + x^5 + E^25*(36*x^2 + 16*x^3 - 8*x^4 + 
 4*x^5) + (18*x + 8*x^2 - 4*x^3 + 2*x^4 + E^25*(72*x + 32*x^2 - 16*x^3 + 8 
*x^4))*Log[(9 + 4*x - 2*x^2 + x^3)/x^2] + E^25*(36 + 16*x - 8*x^2 + 4*x^3) 
*Log[(9 + 4*x - 2*x^2 + x^3)/x^2]^2)/(E^25*(9*x^2 + 4*x^3 - 2*x^4 + x^5) + 
 E^25*(18*x + 8*x^2 - 4*x^3 + 2*x^4)*Log[(9 + 4*x - 2*x^2 + x^3)/x^2] + E^ 
25*(9 + 4*x - 2*x^2 + x^3)*Log[(9 + 4*x - 2*x^2 + x^3)/x^2]^2),x]
 

output

$Aborted
 

3.23.32.3.1 Defintions of rubi rules used

rule 27

Int[(a_)*(Fx_), x_Symbol] :> Simp[a   Int[Fx, x], x] /; FreeQ[a, x] &&  !Ma 
tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
 

rule 2009

Int[u_, x_Symbol] :> Simp[IntSum[u, x], x] /; SumQ[u]
 

rule 7239

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

rule 7293

Int[u_, x_Symbol] :> With[{v = ExpandIntegrand[u, x]}, Int[v, x] /; SumQ[v] 
]
 

3.23.32.4 Maple [A] (verified)

Time = 0.99 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.27

method	result	size
risch	\(4 x +\frac {x^{2} {\mathrm e}^{-25}}{\ln \left (\frac {x^{3}-2 x^{2}+4 x +9}{x^{2}}\right )+x}\)	\(33\)
norman	\(\frac {\left (4 \,{\mathrm e}^{25}+1\right ) {\mathrm e}^{-25} x^{2}+4 \ln \left (\frac {x^{3}-2 x^{2}+4 x +9}{x^{2}}\right ) x}{\ln \left (\frac {x^{3}-2 x^{2}+4 x +9}{x^{2}}\right )+x}\)	\(60\)
parallelrisch	\(\frac {\left (8 x^{2} {\mathrm e}^{25}+8 \,{\mathrm e}^{25} \ln \left (\frac {x^{3}-2 x^{2}+4 x +9}{x^{2}}\right ) x +32 x \,{\mathrm e}^{25}+32 \,{\mathrm e}^{25} \ln \left (\frac {x^{3}-2 x^{2}+4 x +9}{x^{2}}\right )+2 x^{2}\right ) {\mathrm e}^{-25}}{2 \ln \left (\frac {x^{3}-2 x^{2}+4 x +9}{x^{2}}\right )+2 x}\)	\(92\)

input

int(((4*x^3-8*x^2+16*x+36)*exp(25)*ln((x^3-2*x^2+4*x+9)/x^2)^2+((8*x^4-16* 
x^3+32*x^2+72*x)*exp(25)+2*x^4-4*x^3+8*x^2+18*x)*ln((x^3-2*x^2+4*x+9)/x^2) 
+(4*x^5-8*x^4+16*x^3+36*x^2)*exp(25)+x^5-3*x^4+4*x^3+13*x^2+18*x)/((x^3-2* 
x^2+4*x+9)*exp(25)*ln((x^3-2*x^2+4*x+9)/x^2)^2+(2*x^4-4*x^3+8*x^2+18*x)*ex 
p(25)*ln((x^3-2*x^2+4*x+9)/x^2)+(x^5-2*x^4+4*x^3+9*x^2)*exp(25)),x,method= 
_RETURNVERBOSE)
 

output

4*x+x^2*exp(-25)/(ln((x^3-2*x^2+4*x+9)/x^2)+x)
 

3.23.32.5 Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 63 vs. \(2 (25) = 50\).

Time = 0.25 (sec) , antiderivative size = 63, normalized size of antiderivative = 2.42 \[ \int \frac {18 x+13 x^2+4 x^3-3 x^4+x^5+e^{25} \left (36 x^2+16 x^3-8 x^4+4 x^5\right )+\left (18 x+8 x^2-4 x^3+2 x^4+e^{25} \left (72 x+32 x^2-16 x^3+8 x^4\right )\right ) \log \left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )+e^{25} \left (36+16 x-8 x^2+4 x^3\right ) \log ^2\left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )}{e^{25} \left (9 x^2+4 x^3-2 x^4+x^5\right )+e^{25} \left (18 x+8 x^2-4 x^3+2 x^4\right ) \log \left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )+e^{25} \left (9+4 x-2 x^2+x^3\right ) \log ^2\left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )} \, dx=\frac {4 \, x^{2} e^{25} + 4 \, x e^{25} \log \left (\frac {x^{3} - 2 \, x^{2} + 4 \, x + 9}{x^{2}}\right ) + x^{2}}{x e^{25} + e^{25} \log \left (\frac {x^{3} - 2 \, x^{2} + 4 \, x + 9}{x^{2}}\right )} \]

input

integrate(((4*x^3-8*x^2+16*x+36)*exp(25)*log((x^3-2*x^2+4*x+9)/x^2)^2+((8* 
x^4-16*x^3+32*x^2+72*x)*exp(25)+2*x^4-4*x^3+8*x^2+18*x)*log((x^3-2*x^2+4*x 
+9)/x^2)+(4*x^5-8*x^4+16*x^3+36*x^2)*exp(25)+x^5-3*x^4+4*x^3+13*x^2+18*x)/ 
((x^3-2*x^2+4*x+9)*exp(25)*log((x^3-2*x^2+4*x+9)/x^2)^2+(2*x^4-4*x^3+8*x^2 
+18*x)*exp(25)*log((x^3-2*x^2+4*x+9)/x^2)+(x^5-2*x^4+4*x^3+9*x^2)*exp(25)) 
,x, algorithm=\
 

output

(4*x^2*e^25 + 4*x*e^25*log((x^3 - 2*x^2 + 4*x + 9)/x^2) + x^2)/(x*e^25 + e 
^25*log((x^3 - 2*x^2 + 4*x + 9)/x^2))
 

3.23.32.6 Sympy [A] (verification not implemented)

Time = 0.12 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.23 \[ \int \frac {18 x+13 x^2+4 x^3-3 x^4+x^5+e^{25} \left (36 x^2+16 x^3-8 x^4+4 x^5\right )+\left (18 x+8 x^2-4 x^3+2 x^4+e^{25} \left (72 x+32 x^2-16 x^3+8 x^4\right )\right ) \log \left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )+e^{25} \left (36+16 x-8 x^2+4 x^3\right ) \log ^2\left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )}{e^{25} \left (9 x^2+4 x^3-2 x^4+x^5\right )+e^{25} \left (18 x+8 x^2-4 x^3+2 x^4\right ) \log \left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )+e^{25} \left (9+4 x-2 x^2+x^3\right ) \log ^2\left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )} \, dx=\frac {x^{2}}{x e^{25} + e^{25} \log {\left (\frac {x^{3} - 2 x^{2} + 4 x + 9}{x^{2}} \right )}} + 4 x \]

input

integrate(((4*x**3-8*x**2+16*x+36)*exp(25)*ln((x**3-2*x**2+4*x+9)/x**2)**2 
+((8*x**4-16*x**3+32*x**2+72*x)*exp(25)+2*x**4-4*x**3+8*x**2+18*x)*ln((x** 
3-2*x**2+4*x+9)/x**2)+(4*x**5-8*x**4+16*x**3+36*x**2)*exp(25)+x**5-3*x**4+ 
4*x**3+13*x**2+18*x)/((x**3-2*x**2+4*x+9)*exp(25)*ln((x**3-2*x**2+4*x+9)/x 
**2)**2+(2*x**4-4*x**3+8*x**2+18*x)*exp(25)*ln((x**3-2*x**2+4*x+9)/x**2)+( 
x**5-2*x**4+4*x**3+9*x**2)*exp(25)),x)
 

output

x**2/(x*exp(25) + exp(25)*log((x**3 - 2*x**2 + 4*x + 9)/x**2)) + 4*x
 

3.23.32.7 Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 68 vs. \(2 (25) = 50\).

Time = 0.25 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.62 \[ \int \frac {18 x+13 x^2+4 x^3-3 x^4+x^5+e^{25} \left (36 x^2+16 x^3-8 x^4+4 x^5\right )+\left (18 x+8 x^2-4 x^3+2 x^4+e^{25} \left (72 x+32 x^2-16 x^3+8 x^4\right )\right ) \log \left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )+e^{25} \left (36+16 x-8 x^2+4 x^3\right ) \log ^2\left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )}{e^{25} \left (9 x^2+4 x^3-2 x^4+x^5\right )+e^{25} \left (18 x+8 x^2-4 x^3+2 x^4\right ) \log \left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )+e^{25} \left (9+4 x-2 x^2+x^3\right ) \log ^2\left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )} \, dx=\frac {x^{2} {\left (4 \, e^{25} + 1\right )} + 4 \, x e^{25} \log \left (x^{3} - 2 \, x^{2} + 4 \, x + 9\right ) - 8 \, x e^{25} \log \left (x\right )}{x e^{25} + e^{25} \log \left (x^{3} - 2 \, x^{2} + 4 \, x + 9\right ) - 2 \, e^{25} \log \left (x\right )} \]

input

integrate(((4*x^3-8*x^2+16*x+36)*exp(25)*log((x^3-2*x^2+4*x+9)/x^2)^2+((8* 
x^4-16*x^3+32*x^2+72*x)*exp(25)+2*x^4-4*x^3+8*x^2+18*x)*log((x^3-2*x^2+4*x 
+9)/x^2)+(4*x^5-8*x^4+16*x^3+36*x^2)*exp(25)+x^5-3*x^4+4*x^3+13*x^2+18*x)/ 
((x^3-2*x^2+4*x+9)*exp(25)*log((x^3-2*x^2+4*x+9)/x^2)^2+(2*x^4-4*x^3+8*x^2 
+18*x)*exp(25)*log((x^3-2*x^2+4*x+9)/x^2)+(x^5-2*x^4+4*x^3+9*x^2)*exp(25)) 
,x, algorithm=\
 

output

(x^2*(4*e^25 + 1) + 4*x*e^25*log(x^3 - 2*x^2 + 4*x + 9) - 8*x*e^25*log(x)) 
/(x*e^25 + e^25*log(x^3 - 2*x^2 + 4*x + 9) - 2*e^25*log(x))
 

3.23.32.8 Giac [F(-2)]

Exception generated. \[ \int \frac {18 x+13 x^2+4 x^3-3 x^4+x^5+e^{25} \left (36 x^2+16 x^3-8 x^4+4 x^5\right )+\left (18 x+8 x^2-4 x^3+2 x^4+e^{25} \left (72 x+32 x^2-16 x^3+8 x^4\right )\right ) \log \left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )+e^{25} \left (36+16 x-8 x^2+4 x^3\right ) \log ^2\left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )}{e^{25} \left (9 x^2+4 x^3-2 x^4+x^5\right )+e^{25} \left (18 x+8 x^2-4 x^3+2 x^4\right ) \log \left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )+e^{25} \left (9+4 x-2 x^2+x^3\right ) \log ^2\left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )} \, dx=\text {Exception raised: TypeError} \]

input

integrate(((4*x^3-8*x^2+16*x+36)*exp(25)*log((x^3-2*x^2+4*x+9)/x^2)^2+((8* 
x^4-16*x^3+32*x^2+72*x)*exp(25)+2*x^4-4*x^3+8*x^2+18*x)*log((x^3-2*x^2+4*x 
+9)/x^2)+(4*x^5-8*x^4+16*x^3+36*x^2)*exp(25)+x^5-3*x^4+4*x^3+13*x^2+18*x)/ 
((x^3-2*x^2+4*x+9)*exp(25)*log((x^3-2*x^2+4*x+9)/x^2)^2+(2*x^4-4*x^3+8*x^2 
+18*x)*exp(25)*log((x^3-2*x^2+4*x+9)/x^2)+(x^5-2*x^4+4*x^3+9*x^2)*exp(25)) 
,x, algorithm=\
 

output

Exception raised: TypeError >> an error occurred running a Giac command:IN 
PUT:sage2:=int(sage0,sageVARx):;OUTPUT:sym2poly/r2sym(const gen & e,const 
index_m & i,const vecteur & l) Error: Bad Argument Value
 

3.23.32.9 Mupad [B] (verification not implemented)

Time = 13.51 (sec) , antiderivative size = 82, normalized size of antiderivative = 3.15 \[ \int \frac {18 x+13 x^2+4 x^3-3 x^4+x^5+e^{25} \left (36 x^2+16 x^3-8 x^4+4 x^5\right )+\left (18 x+8 x^2-4 x^3+2 x^4+e^{25} \left (72 x+32 x^2-16 x^3+8 x^4\right )\right ) \log \left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )+e^{25} \left (36+16 x-8 x^2+4 x^3\right ) \log ^2\left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )}{e^{25} \left (9 x^2+4 x^3-2 x^4+x^5\right )+e^{25} \left (18 x+8 x^2-4 x^3+2 x^4\right ) \log \left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )+e^{25} \left (9+4 x-2 x^2+x^3\right ) \log ^2\left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )} \, dx=\frac {{\mathrm {e}}^{-25}\,\left (2\,x+2\,\ln \left (\frac {x^3-2\,x^2+4\,x+9}{x^2}\right )+4\,x^2\,{\mathrm {e}}^{25}+x^2+4\,x\,{\mathrm {e}}^{25}\,\ln \left (\frac {x^3-2\,x^2+4\,x+9}{x^2}\right )\right )}{x+\ln \left (\frac {x^3-2\,x^2+4\,x+9}{x^2}\right )} \]

input

int((18*x + log((4*x - 2*x^2 + x^3 + 9)/x^2)*(18*x + exp(25)*(72*x + 32*x^ 
2 - 16*x^3 + 8*x^4) + 8*x^2 - 4*x^3 + 2*x^4) + 13*x^2 + 4*x^3 - 3*x^4 + x^ 
5 + exp(25)*(36*x^2 + 16*x^3 - 8*x^4 + 4*x^5) + exp(25)*log((4*x - 2*x^2 + 
 x^3 + 9)/x^2)^2*(16*x - 8*x^2 + 4*x^3 + 36))/(exp(25)*(9*x^2 + 4*x^3 - 2* 
x^4 + x^5) + exp(25)*log((4*x - 2*x^2 + x^3 + 9)/x^2)^2*(4*x - 2*x^2 + x^3 
 + 9) + exp(25)*log((4*x - 2*x^2 + x^3 + 9)/x^2)*(18*x + 8*x^2 - 4*x^3 + 2 
*x^4)),x)
 

output

(exp(-25)*(2*x + 2*log((4*x - 2*x^2 + x^3 + 9)/x^2) + 4*x^2*exp(25) + x^2 
+ 4*x*exp(25)*log((4*x - 2*x^2 + x^3 + 9)/x^2)))/(x + log((4*x - 2*x^2 + x 
^3 + 9)/x^2))