\(\int \frac {-507 x^2+481 x^3-152 x^4+16 x^5+(-234 x^2+150 x^3-24 x^4) \log (81-108 x+54 x^2-12 x^3+x^4)+(-27 x^2+9 x^3) \log ^2(81-108 x+54 x^2-12 x^3+x^4)+e^{\frac {1}{13 x-4 x^2+3 x \log (81-108 x+54 x^2-12 x^3+x^4)}} (39-49 x+8 x^2+(9-3 x) \log (81-108 x+54 x^2-12 x^3+x^4))}{-507 x^2+481 x^3-152 x^4+16 x^5+(-234 x^2+150 x^3-24 x^4) \log (81-108 x+54 x^2-12 x^3+x^4)+(-27 x^2+9 x^3) \log ^2(81-108 x+54 x^2-12 x^3+x^4)} \, dx\) [1263]

Optimal result

Integrand size = 254, antiderivative size = 25 \[ \int \frac {-507 x^2+481 x^3-152 x^4+16 x^5+\left (-234 x^2+150 x^3-24 x^4\right ) \log \left (81-108 x+54 x^2-12 x^3+x^4\right )+\left (-27 x^2+9 x^3\right ) \log ^2\left (81-108 x+54 x^2-12 x^3+x^4\right )+e^{\frac {1}{13 x-4 x^2+3 x \log \left (81-108 x+54 x^2-12 x^3+x^4\right )}} \left (39-49 x+8 x^2+(9-3 x) \log \left (81-108 x+54 x^2-12 x^3+x^4\right )\right )}{-507 x^2+481 x^3-152 x^4+16 x^5+\left (-234 x^2+150 x^3-24 x^4\right ) \log \left (81-108 x+54 x^2-12 x^3+x^4\right )+\left (-27 x^2+9 x^3\right ) \log ^2\left (81-108 x+54 x^2-12 x^3+x^4\right )} \, dx=e^{\frac {1}{x \left (4-4 x+3 \left (3+\log \left ((-3+x)^4\right )\right )\right )}}+x \] Output:

x+exp(1/x/(-4*x+13+3*ln((-3+x)^4)))
 

Mathematica [A] (verified)

Time = 0.12 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.92 \[ \int \frac {-507 x^2+481 x^3-152 x^4+16 x^5+\left (-234 x^2+150 x^3-24 x^4\right ) \log \left (81-108 x+54 x^2-12 x^3+x^4\right )+\left (-27 x^2+9 x^3\right ) \log ^2\left (81-108 x+54 x^2-12 x^3+x^4\right )+e^{\frac {1}{13 x-4 x^2+3 x \log \left (81-108 x+54 x^2-12 x^3+x^4\right )}} \left (39-49 x+8 x^2+(9-3 x) \log \left (81-108 x+54 x^2-12 x^3+x^4\right )\right )}{-507 x^2+481 x^3-152 x^4+16 x^5+\left (-234 x^2+150 x^3-24 x^4\right ) \log \left (81-108 x+54 x^2-12 x^3+x^4\right )+\left (-27 x^2+9 x^3\right ) \log ^2\left (81-108 x+54 x^2-12 x^3+x^4\right )} \, dx=e^{\frac {1}{x \left (13-4 x+3 \log \left ((-3+x)^4\right )\right )}}+x \] Input:

Integrate[(-507*x^2 + 481*x^3 - 152*x^4 + 16*x^5 + (-234*x^2 + 150*x^3 - 2 
4*x^4)*Log[81 - 108*x + 54*x^2 - 12*x^3 + x^4] + (-27*x^2 + 9*x^3)*Log[81 
- 108*x + 54*x^2 - 12*x^3 + x^4]^2 + E^(13*x - 4*x^2 + 3*x*Log[81 - 108*x 
+ 54*x^2 - 12*x^3 + x^4])^(-1)*(39 - 49*x + 8*x^2 + (9 - 3*x)*Log[81 - 108 
*x + 54*x^2 - 12*x^3 + x^4]))/(-507*x^2 + 481*x^3 - 152*x^4 + 16*x^5 + (-2 
34*x^2 + 150*x^3 - 24*x^4)*Log[81 - 108*x + 54*x^2 - 12*x^3 + x^4] + (-27* 
x^2 + 9*x^3)*Log[81 - 108*x + 54*x^2 - 12*x^3 + x^4]^2),x]
 

Output:

E^(1/(x*(13 - 4*x + 3*Log[(-3 + x)^4]))) + x
 

Rubi [A] (verified)

Time = 4.39 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.92, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.012, Rules used = {7292, 7293, 2009}

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.

\(\displaystyle \int \frac {\left (8 x^2+(9-3 x) \log \left (x^4-12 x^3+54 x^2-108 x+81\right )-49 x+39\right ) \exp \left (\frac {1}{-4 x^2+3 x \log \left (x^4-12 x^3+54 x^2-108 x+81\right )+13 x}\right )+16 x^5-152 x^4+481 x^3-507 x^2+\left (9 x^3-27 x^2\right ) \log ^2\left (x^4-12 x^3+54 x^2-108 x+81\right )+\left (-24 x^4+150 x^3-234 x^2\right ) \log \left (x^4-12 x^3+54 x^2-108 x+81\right )}{16 x^5-152 x^4+481 x^3-507 x^2+\left (9 x^3-27 x^2\right ) \log ^2\left (x^4-12 x^3+54 x^2-108 x+81\right )+\left (-24 x^4+150 x^3-234 x^2\right ) \log \left (x^4-12 x^3+54 x^2-108 x+81\right )} \, dx\)

\(\Big \downarrow \) 7292

\(\displaystyle \int \frac {-\left (8 x^2+(9-3 x) \log \left (x^4-12 x^3+54 x^2-108 x+81\right )-49 x+39\right ) \exp \left (\frac {1}{-4 x^2+3 x \log \left (x^4-12 x^3+54 x^2-108 x+81\right )+13 x}\right )-16 x^5+152 x^4-481 x^3+507 x^2-\left (9 x^3-27 x^2\right ) \log ^2\left (x^4-12 x^3+54 x^2-108 x+81\right )-\left (-24 x^4+150 x^3-234 x^2\right ) \log \left (x^4-12 x^3+54 x^2-108 x+81\right )}{(3-x) x^2 \left (-4 x+3 \log \left ((x-3)^4\right )+13\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {16 x^3}{(x-3) \left (4 x-3 \log \left ((x-3)^4\right )-13\right )^2}-\frac {152 x^2}{(x-3) \left (4 x-3 \log \left ((x-3)^4\right )-13\right )^2}+\frac {e^{-\frac {1}{x \left (4 x-3 \log \left ((x-3)^4\right )-13\right )}} \left (8 x^2-49 x-3 x \log \left ((x-3)^4\right )+9 \log \left ((x-3)^4\right )+39\right )}{(x-3) x^2 \left (4 x-3 \log \left ((x-3)^4\right )-13\right )^2}+\frac {9 \log ^2\left ((x-3)^4\right )}{\left (-4 x+3 \log \left ((x-3)^4\right )+13\right )^2}+\frac {481 x}{(x-3) \left (4 x-3 \log \left ((x-3)^4\right )-13\right )^2}-\frac {6 (4 x-13) \log \left ((x-3)^4\right )}{\left (4 x-3 \log \left ((x-3)^4\right )-13\right )^2}-\frac {507}{(x-3) \left (4 x-3 \log \left ((x-3)^4\right )-13\right )^2}\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle x+e^{\frac {1}{x \left (-4 x+3 \log \left ((x-3)^4\right )+13\right )}}\)

Input:

Int[(-507*x^2 + 481*x^3 - 152*x^4 + 16*x^5 + (-234*x^2 + 150*x^3 - 24*x^4) 
*Log[81 - 108*x + 54*x^2 - 12*x^3 + x^4] + (-27*x^2 + 9*x^3)*Log[81 - 108* 
x + 54*x^2 - 12*x^3 + x^4]^2 + E^(13*x - 4*x^2 + 3*x*Log[81 - 108*x + 54*x 
^2 - 12*x^3 + x^4])^(-1)*(39 - 49*x + 8*x^2 + (9 - 3*x)*Log[81 - 108*x + 5 
4*x^2 - 12*x^3 + x^4]))/(-507*x^2 + 481*x^3 - 152*x^4 + 16*x^5 + (-234*x^2 
 + 150*x^3 - 24*x^4)*Log[81 - 108*x + 54*x^2 - 12*x^3 + x^4] + (-27*x^2 + 
9*x^3)*Log[81 - 108*x + 54*x^2 - 12*x^3 + x^4]^2),x]
 

Output:

E^(1/(x*(13 - 4*x + 3*Log[(-3 + x)^4]))) + x
 

Defintions of rubi rules used

rule 2009

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

rule 7292

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

rule 7293

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

Maple [A] (verified)

Time = 7.02 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.48

method	result	size
risch	\(x +{\mathrm e}^{-\frac {1}{x \left (-3 \ln \left (x^{4}-12 x^{3}+54 x^{2}-108 x +81\right )+4 x -13\right )}}\)	\(37\)
parallelrisch	\(\frac {37}{4}+x +{\mathrm e}^{\frac {1}{x \left (3 \ln \left (x^{4}-12 x^{3}+54 x^{2}-108 x +81\right )-4 x +13\right )}}\)	\(37\)

Input:

int((((-3*x+9)*ln(x^4-12*x^3+54*x^2-108*x+81)+8*x^2-49*x+39)*exp(1/(3*x*ln 
(x^4-12*x^3+54*x^2-108*x+81)-4*x^2+13*x))+(9*x^3-27*x^2)*ln(x^4-12*x^3+54* 
x^2-108*x+81)^2+(-24*x^4+150*x^3-234*x^2)*ln(x^4-12*x^3+54*x^2-108*x+81)+1 
6*x^5-152*x^4+481*x^3-507*x^2)/((9*x^3-27*x^2)*ln(x^4-12*x^3+54*x^2-108*x+ 
81)^2+(-24*x^4+150*x^3-234*x^2)*ln(x^4-12*x^3+54*x^2-108*x+81)+16*x^5-152* 
x^4+481*x^3-507*x^2),x,method=_RETURNVERBOSE)
 

Output:

x+exp(-1/x/(-3*ln(x^4-12*x^3+54*x^2-108*x+81)+4*x-13))
 

Fricas [A] (verification not implemented)

Time = 0.10 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.52 \[ \int \frac {-507 x^2+481 x^3-152 x^4+16 x^5+\left (-234 x^2+150 x^3-24 x^4\right ) \log \left (81-108 x+54 x^2-12 x^3+x^4\right )+\left (-27 x^2+9 x^3\right ) \log ^2\left (81-108 x+54 x^2-12 x^3+x^4\right )+e^{\frac {1}{13 x-4 x^2+3 x \log \left (81-108 x+54 x^2-12 x^3+x^4\right )}} \left (39-49 x+8 x^2+(9-3 x) \log \left (81-108 x+54 x^2-12 x^3+x^4\right )\right )}{-507 x^2+481 x^3-152 x^4+16 x^5+\left (-234 x^2+150 x^3-24 x^4\right ) \log \left (81-108 x+54 x^2-12 x^3+x^4\right )+\left (-27 x^2+9 x^3\right ) \log ^2\left (81-108 x+54 x^2-12 x^3+x^4\right )} \, dx=x + e^{\left (-\frac {1}{4 \, x^{2} - 3 \, x \log \left (x^{4} - 12 \, x^{3} + 54 \, x^{2} - 108 \, x + 81\right ) - 13 \, x}\right )} \] Input:

integrate((((-3*x+9)*log(x^4-12*x^3+54*x^2-108*x+81)+8*x^2-49*x+39)*exp(1/ 
(3*x*log(x^4-12*x^3+54*x^2-108*x+81)-4*x^2+13*x))+(9*x^3-27*x^2)*log(x^4-1 
2*x^3+54*x^2-108*x+81)^2+(-24*x^4+150*x^3-234*x^2)*log(x^4-12*x^3+54*x^2-1 
08*x+81)+16*x^5-152*x^4+481*x^3-507*x^2)/((9*x^3-27*x^2)*log(x^4-12*x^3+54 
*x^2-108*x+81)^2+(-24*x^4+150*x^3-234*x^2)*log(x^4-12*x^3+54*x^2-108*x+81) 
+16*x^5-152*x^4+481*x^3-507*x^2),x, algorithm="fricas")
 

Output:

x + e^(-1/(4*x^2 - 3*x*log(x^4 - 12*x^3 + 54*x^2 - 108*x + 81) - 13*x))
 

Sympy [F(-2)]

Exception generated. \[ \int \frac {-507 x^2+481 x^3-152 x^4+16 x^5+\left (-234 x^2+150 x^3-24 x^4\right ) \log \left (81-108 x+54 x^2-12 x^3+x^4\right )+\left (-27 x^2+9 x^3\right ) \log ^2\left (81-108 x+54 x^2-12 x^3+x^4\right )+e^{\frac {1}{13 x-4 x^2+3 x \log \left (81-108 x+54 x^2-12 x^3+x^4\right )}} \left (39-49 x+8 x^2+(9-3 x) \log \left (81-108 x+54 x^2-12 x^3+x^4\right )\right )}{-507 x^2+481 x^3-152 x^4+16 x^5+\left (-234 x^2+150 x^3-24 x^4\right ) \log \left (81-108 x+54 x^2-12 x^3+x^4\right )+\left (-27 x^2+9 x^3\right ) \log ^2\left (81-108 x+54 x^2-12 x^3+x^4\right )} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((((-3*x+9)*ln(x**4-12*x**3+54*x**2-108*x+81)+8*x**2-49*x+39)*exp 
(1/(3*x*ln(x**4-12*x**3+54*x**2-108*x+81)-4*x**2+13*x))+(9*x**3-27*x**2)*l 
n(x**4-12*x**3+54*x**2-108*x+81)**2+(-24*x**4+150*x**3-234*x**2)*ln(x**4-1 
2*x**3+54*x**2-108*x+81)+16*x**5-152*x**4+481*x**3-507*x**2)/((9*x**3-27*x 
**2)*ln(x**4-12*x**3+54*x**2-108*x+81)**2+(-24*x**4+150*x**3-234*x**2)*ln( 
x**4-12*x**3+54*x**2-108*x+81)+16*x**5-152*x**4+481*x**3-507*x**2),x)
 

Output:

Exception raised: TypeError >> '>' not supported between instances of 'Pol 
y' and 'int'
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 49 vs. \(2 (23) = 46\).

Time = 0.09 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.96 \[ \int \frac {-507 x^2+481 x^3-152 x^4+16 x^5+\left (-234 x^2+150 x^3-24 x^4\right ) \log \left (81-108 x+54 x^2-12 x^3+x^4\right )+\left (-27 x^2+9 x^3\right ) \log ^2\left (81-108 x+54 x^2-12 x^3+x^4\right )+e^{\frac {1}{13 x-4 x^2+3 x \log \left (81-108 x+54 x^2-12 x^3+x^4\right )}} \left (39-49 x+8 x^2+(9-3 x) \log \left (81-108 x+54 x^2-12 x^3+x^4\right )\right )}{-507 x^2+481 x^3-152 x^4+16 x^5+\left (-234 x^2+150 x^3-24 x^4\right ) \log \left (81-108 x+54 x^2-12 x^3+x^4\right )+\left (-27 x^2+9 x^3\right ) \log ^2\left (81-108 x+54 x^2-12 x^3+x^4\right )} \, dx=x + e^{\left (-\frac {4}{4 \, x {\left (12 \, \log \left (x - 3\right ) + 13\right )} - 144 \, \log \left (x - 3\right )^{2} - 312 \, \log \left (x - 3\right ) - 169} + \frac {1}{x {\left (12 \, \log \left (x - 3\right ) + 13\right )}}\right )} \] Input:

integrate((((-3*x+9)*log(x^4-12*x^3+54*x^2-108*x+81)+8*x^2-49*x+39)*exp(1/ 
(3*x*log(x^4-12*x^3+54*x^2-108*x+81)-4*x^2+13*x))+(9*x^3-27*x^2)*log(x^4-1 
2*x^3+54*x^2-108*x+81)^2+(-24*x^4+150*x^3-234*x^2)*log(x^4-12*x^3+54*x^2-1 
08*x+81)+16*x^5-152*x^4+481*x^3-507*x^2)/((9*x^3-27*x^2)*log(x^4-12*x^3+54 
*x^2-108*x+81)^2+(-24*x^4+150*x^3-234*x^2)*log(x^4-12*x^3+54*x^2-108*x+81) 
+16*x^5-152*x^4+481*x^3-507*x^2),x, algorithm="maxima")
 

Output:

x + e^(-4/(4*x*(12*log(x - 3) + 13) - 144*log(x - 3)^2 - 312*log(x - 3) - 
169) + 1/(x*(12*log(x - 3) + 13)))
 

Giac [A] (verification not implemented)

Time = 1.25 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.52 \[ \int \frac {-507 x^2+481 x^3-152 x^4+16 x^5+\left (-234 x^2+150 x^3-24 x^4\right ) \log \left (81-108 x+54 x^2-12 x^3+x^4\right )+\left (-27 x^2+9 x^3\right ) \log ^2\left (81-108 x+54 x^2-12 x^3+x^4\right )+e^{\frac {1}{13 x-4 x^2+3 x \log \left (81-108 x+54 x^2-12 x^3+x^4\right )}} \left (39-49 x+8 x^2+(9-3 x) \log \left (81-108 x+54 x^2-12 x^3+x^4\right )\right )}{-507 x^2+481 x^3-152 x^4+16 x^5+\left (-234 x^2+150 x^3-24 x^4\right ) \log \left (81-108 x+54 x^2-12 x^3+x^4\right )+\left (-27 x^2+9 x^3\right ) \log ^2\left (81-108 x+54 x^2-12 x^3+x^4\right )} \, dx=x + e^{\left (-\frac {1}{4 \, x^{2} - 3 \, x \log \left (x^{4} - 12 \, x^{3} + 54 \, x^{2} - 108 \, x + 81\right ) - 13 \, x}\right )} \] Input:

integrate((((-3*x+9)*log(x^4-12*x^3+54*x^2-108*x+81)+8*x^2-49*x+39)*exp(1/ 
(3*x*log(x^4-12*x^3+54*x^2-108*x+81)-4*x^2+13*x))+(9*x^3-27*x^2)*log(x^4-1 
2*x^3+54*x^2-108*x+81)^2+(-24*x^4+150*x^3-234*x^2)*log(x^4-12*x^3+54*x^2-1 
08*x+81)+16*x^5-152*x^4+481*x^3-507*x^2)/((9*x^3-27*x^2)*log(x^4-12*x^3+54 
*x^2-108*x+81)^2+(-24*x^4+150*x^3-234*x^2)*log(x^4-12*x^3+54*x^2-108*x+81) 
+16*x^5-152*x^4+481*x^3-507*x^2),x, algorithm="giac")
 

Output:

x + e^(-1/(4*x^2 - 3*x*log(x^4 - 12*x^3 + 54*x^2 - 108*x + 81) - 13*x))
 

Mupad [B] (verification not implemented)

Time = 7.72 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.44 \[ \int \frac {-507 x^2+481 x^3-152 x^4+16 x^5+\left (-234 x^2+150 x^3-24 x^4\right ) \log \left (81-108 x+54 x^2-12 x^3+x^4\right )+\left (-27 x^2+9 x^3\right ) \log ^2\left (81-108 x+54 x^2-12 x^3+x^4\right )+e^{\frac {1}{13 x-4 x^2+3 x \log \left (81-108 x+54 x^2-12 x^3+x^4\right )}} \left (39-49 x+8 x^2+(9-3 x) \log \left (81-108 x+54 x^2-12 x^3+x^4\right )\right )}{-507 x^2+481 x^3-152 x^4+16 x^5+\left (-234 x^2+150 x^3-24 x^4\right ) \log \left (81-108 x+54 x^2-12 x^3+x^4\right )+\left (-27 x^2+9 x^3\right ) \log ^2\left (81-108 x+54 x^2-12 x^3+x^4\right )} \, dx=x+{\mathrm {e}}^{\frac {1}{13\,x+3\,x\,\ln \left (x^4-12\,x^3+54\,x^2-108\,x+81\right )-4\,x^2}} \] Input:

int((exp(1/(13*x + 3*x*log(54*x^2 - 108*x - 12*x^3 + x^4 + 81) - 4*x^2))*( 
49*x + log(54*x^2 - 108*x - 12*x^3 + x^4 + 81)*(3*x - 9) - 8*x^2 - 39) + l 
og(54*x^2 - 108*x - 12*x^3 + x^4 + 81)*(234*x^2 - 150*x^3 + 24*x^4) + log( 
54*x^2 - 108*x - 12*x^3 + x^4 + 81)^2*(27*x^2 - 9*x^3) + 507*x^2 - 481*x^3 
 + 152*x^4 - 16*x^5)/(log(54*x^2 - 108*x - 12*x^3 + x^4 + 81)*(234*x^2 - 1 
50*x^3 + 24*x^4) + log(54*x^2 - 108*x - 12*x^3 + x^4 + 81)^2*(27*x^2 - 9*x 
^3) + 507*x^2 - 481*x^3 + 152*x^4 - 16*x^5),x)
 

Output:

x + exp(1/(13*x + 3*x*log(54*x^2 - 108*x - 12*x^3 + x^4 + 81) - 4*x^2))
 

Reduce [B] (verification not implemented)

Time = 0.18 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.48 \[ \int \frac {-507 x^2+481 x^3-152 x^4+16 x^5+\left (-234 x^2+150 x^3-24 x^4\right ) \log \left (81-108 x+54 x^2-12 x^3+x^4\right )+\left (-27 x^2+9 x^3\right ) \log ^2\left (81-108 x+54 x^2-12 x^3+x^4\right )+e^{\frac {1}{13 x-4 x^2+3 x \log \left (81-108 x+54 x^2-12 x^3+x^4\right )}} \left (39-49 x+8 x^2+(9-3 x) \log \left (81-108 x+54 x^2-12 x^3+x^4\right )\right )}{-507 x^2+481 x^3-152 x^4+16 x^5+\left (-234 x^2+150 x^3-24 x^4\right ) \log \left (81-108 x+54 x^2-12 x^3+x^4\right )+\left (-27 x^2+9 x^3\right ) \log ^2\left (81-108 x+54 x^2-12 x^3+x^4\right )} \, dx=e^{\frac {1}{3 \,\mathrm {log}\left (x^{4}-12 x^{3}+54 x^{2}-108 x +81\right ) x -4 x^{2}+13 x}}+x \] Input:

int((((-3*x+9)*log(x^4-12*x^3+54*x^2-108*x+81)+8*x^2-49*x+39)*exp(1/(3*x*l 
og(x^4-12*x^3+54*x^2-108*x+81)-4*x^2+13*x))+(9*x^3-27*x^2)*log(x^4-12*x^3+ 
54*x^2-108*x+81)^2+(-24*x^4+150*x^3-234*x^2)*log(x^4-12*x^3+54*x^2-108*x+8 
1)+16*x^5-152*x^4+481*x^3-507*x^2)/((9*x^3-27*x^2)*log(x^4-12*x^3+54*x^2-1 
08*x+81)^2+(-24*x^4+150*x^3-234*x^2)*log(x^4-12*x^3+54*x^2-108*x+81)+16*x^ 
5-152*x^4+481*x^3-507*x^2),x)
 

Output:

e**(1/(3*log(x**4 - 12*x**3 + 54*x**2 - 108*x + 81)*x - 4*x**2 + 13*x)) + 
x