\(\int \frac {(-12+3 e^{\frac {x}{3+x^2+x^3}}+2 x) (36+24 x^2+24 x^3+4 x^4+8 x^5+4 x^6+e^{\frac {x}{3+x^2+x^3}} (-9+3 x-6 x^2-7 x^3-3 x^4-2 x^5-x^6))}{(-4+e^{\frac {x}{3+x^2+x^3}}+x) (432-180 x+306 x^2+168 x^3-60 x^4+88 x^5+10 x^6-16 x^7+2 x^8+e^{\frac {2 x}{3+x^2+x^3}} (27+18 x^2+18 x^3+3 x^4+6 x^5+3 x^6)+e^{\frac {x}{3+x^2+x^3}} (-216+45 x-144 x^2-114 x^3+6 x^4-43 x^5-14 x^6+5 x^7))} \, dx\) [1088]

Optimal result

Integrand size = 248, antiderivative size = 25 \[ \int \frac {\left (-12+3 e^{\frac {x}{3+x^2+x^3}}+2 x\right ) \left (36+24 x^2+24 x^3+4 x^4+8 x^5+4 x^6+e^{\frac {x}{3+x^2+x^3}} \left (-9+3 x-6 x^2-7 x^3-3 x^4-2 x^5-x^6\right )\right )}{\left (-4+e^{\frac {x}{3+x^2+x^3}}+x\right ) \left (432-180 x+306 x^2+168 x^3-60 x^4+88 x^5+10 x^6-16 x^7+2 x^8+e^{\frac {2 x}{3+x^2+x^3}} \left (27+18 x^2+18 x^3+3 x^4+6 x^5+3 x^6\right )+e^{\frac {x}{3+x^2+x^3}} \left (-216+45 x-144 x^2-114 x^3+6 x^4-43 x^5-14 x^6+5 x^7\right )\right )} \, dx=3-\frac {x}{-4+e^{\frac {x}{3+x^2 (1+x)}}+x} \] Output:

exp(x)/exp(x-ln(3-x/(exp(x/(x^2*(1+x)+3))+x-4)))
 

Mathematica [A] (verified)

Time = 0.05 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.88 \[ \int \frac {\left (-12+3 e^{\frac {x}{3+x^2+x^3}}+2 x\right ) \left (36+24 x^2+24 x^3+4 x^4+8 x^5+4 x^6+e^{\frac {x}{3+x^2+x^3}} \left (-9+3 x-6 x^2-7 x^3-3 x^4-2 x^5-x^6\right )\right )}{\left (-4+e^{\frac {x}{3+x^2+x^3}}+x\right ) \left (432-180 x+306 x^2+168 x^3-60 x^4+88 x^5+10 x^6-16 x^7+2 x^8+e^{\frac {2 x}{3+x^2+x^3}} \left (27+18 x^2+18 x^3+3 x^4+6 x^5+3 x^6\right )+e^{\frac {x}{3+x^2+x^3}} \left (-216+45 x-144 x^2-114 x^3+6 x^4-43 x^5-14 x^6+5 x^7\right )\right )} \, dx=-\frac {x}{-4+e^{\frac {x}{3+x^2+x^3}}+x} \] Input:

Integrate[((-12 + 3*E^(x/(3 + x^2 + x^3)) + 2*x)*(36 + 24*x^2 + 24*x^3 + 4 
*x^4 + 8*x^5 + 4*x^6 + E^(x/(3 + x^2 + x^3))*(-9 + 3*x - 6*x^2 - 7*x^3 - 3 
*x^4 - 2*x^5 - x^6)))/((-4 + E^(x/(3 + x^2 + x^3)) + x)*(432 - 180*x + 306 
*x^2 + 168*x^3 - 60*x^4 + 88*x^5 + 10*x^6 - 16*x^7 + 2*x^8 + E^((2*x)/(3 + 
 x^2 + x^3))*(27 + 18*x^2 + 18*x^3 + 3*x^4 + 6*x^5 + 3*x^6) + E^(x/(3 + x^ 
2 + x^3))*(-216 + 45*x - 144*x^2 - 114*x^3 + 6*x^4 - 43*x^5 - 14*x^6 + 5*x 
^7))),x]
 

Output:

-(x/(-4 + E^(x/(3 + x^2 + x^3)) + x))
 

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.

\(\displaystyle \int \frac {\left (3 e^{\frac {x}{x^3+x^2+3}}+2 x-12\right ) \left (4 x^6+8 x^5+4 x^4+24 x^3+24 x^2+e^{\frac {x}{x^3+x^2+3}} \left (-x^6-2 x^5-3 x^4-7 x^3-6 x^2+3 x-9\right )+36\right )}{\left (e^{\frac {x}{x^3+x^2+3}}+x-4\right ) \left (2 x^8-16 x^7+10 x^6+88 x^5-60 x^4+168 x^3+306 x^2+e^{\frac {2 x}{x^3+x^2+3}} \left (3 x^6+6 x^5+3 x^4+18 x^3+18 x^2+27\right )+e^{\frac {x}{x^3+x^2+3}} \left (5 x^7-14 x^6-43 x^5+6 x^4-114 x^3-144 x^2+45 x-216\right )-180 x+432\right )} \, dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {4 \left (x^3+x^2+3\right )^2-e^{\frac {x}{x^3+x^2+3}} \left (x^6+2 x^5+3 x^4+7 x^3+6 x^2-3 x+9\right )}{\left (-e^{\frac {x}{x^3+x^2+3}}-x+4\right )^2 \left (x^3+x^2+3\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {x \left (x^6+2 x^5+3 x^4-x^3+2 x^2-3 x+21\right )}{\left (e^{\frac {x}{x^3+x^2+3}}+x-4\right )^2 \left (x^3+x^2+3\right )^2}-\frac {x^6+2 x^5+3 x^4+7 x^3+6 x^2-3 x+9}{\left (e^{\frac {x}{x^3+x^2+3}}+x-4\right ) \left (x^3+x^2+3\right )^2}\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle \int \frac {x}{\left (x+e^{\frac {x}{x^3+x^2+3}}-4\right )^2}dx-\int \frac {1}{x+e^{\frac {x}{x^3+x^2+3}}-4}dx-15 \int \frac {1}{\left (x+e^{\frac {x}{x^3+x^2+3}}-4\right )^2 \left (x^3+x^2+3\right )^2}dx+39 \int \frac {x}{\left (x+e^{\frac {x}{x^3+x^2+3}}-4\right )^2 \left (x^3+x^2+3\right )^2}dx-14 \int \frac {x^2}{\left (x+e^{\frac {x}{x^3+x^2+3}}-4\right )^2 \left (x^3+x^2+3\right )^2}dx-3 \int \frac {1}{\left (x+e^{\frac {x}{x^3+x^2+3}}-4\right ) \left (x^3+x^2+3\right )^2}dx+9 \int \frac {x}{\left (x+e^{\frac {x}{x^3+x^2+3}}-4\right ) \left (x^3+x^2+3\right )^2}dx-\int \frac {x^2}{\left (x+e^{\frac {x}{x^3+x^2+3}}-4\right ) \left (x^3+x^2+3\right )^2}dx+5 \int \frac {1}{\left (x+e^{\frac {x}{x^3+x^2+3}}-4\right )^2 \left (x^3+x^2+3\right )}dx-9 \int \frac {x}{\left (x+e^{\frac {x}{x^3+x^2+3}}-4\right )^2 \left (x^3+x^2+3\right )}dx+2 \int \frac {x^2}{\left (x+e^{\frac {x}{x^3+x^2+3}}-4\right )^2 \left (x^3+x^2+3\right )}dx+\int \frac {1}{\left (x+e^{\frac {x}{x^3+x^2+3}}-4\right ) \left (x^3+x^2+3\right )}dx-2 \int \frac {x}{\left (x+e^{\frac {x}{x^3+x^2+3}}-4\right ) \left (x^3+x^2+3\right )}dx\)

Input:

Int[((-12 + 3*E^(x/(3 + x^2 + x^3)) + 2*x)*(36 + 24*x^2 + 24*x^3 + 4*x^4 + 
 8*x^5 + 4*x^6 + E^(x/(3 + x^2 + x^3))*(-9 + 3*x - 6*x^2 - 7*x^3 - 3*x^4 - 
 2*x^5 - x^6)))/((-4 + E^(x/(3 + x^2 + x^3)) + x)*(432 - 180*x + 306*x^2 + 
 168*x^3 - 60*x^4 + 88*x^5 + 10*x^6 - 16*x^7 + 2*x^8 + E^((2*x)/(3 + x^2 + 
 x^3))*(27 + 18*x^2 + 18*x^3 + 3*x^4 + 6*x^5 + 3*x^6) + E^(x/(3 + x^2 + x^ 
3))*(-216 + 45*x - 144*x^2 - 114*x^3 + 6*x^4 - 43*x^5 - 14*x^6 + 5*x^7))), 
x]
 

Output:

$Aborted
 

Maple [C] (warning: unable to verify)

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

Time = 0.06 (sec) , antiderivative size = 197, normalized size of antiderivative = 7.88

\[-\frac {x \,{\mathrm e}^{-\frac {i \pi \,\operatorname {csgn}\left (\frac {i \left (\frac {3 \,{\mathrm e}^{\frac {x}{x^{3}+x^{2}+3}}}{2}+x -6\right )}{{\mathrm e}^{\frac {x}{x^{3}+x^{2}+3}}+x -4}\right ) \left (-\operatorname {csgn}\left (\frac {i \left (\frac {3 \,{\mathrm e}^{\frac {x}{x^{3}+x^{2}+3}}}{2}+x -6\right )}{{\mathrm e}^{\frac {x}{x^{3}+x^{2}+3}}+x -4}\right )+\operatorname {csgn}\left (\frac {i}{{\mathrm e}^{\frac {x}{x^{3}+x^{2}+3}}+x -4}\right )\right ) \left (-\operatorname {csgn}\left (\frac {i \left (\frac {3 \,{\mathrm e}^{\frac {x}{x^{3}+x^{2}+3}}}{2}+x -6\right )}{{\mathrm e}^{\frac {x}{x^{3}+x^{2}+3}}+x -4}\right )+\operatorname {csgn}\left (i \left (\frac {3 \,{\mathrm e}^{\frac {x}{x^{3}+x^{2}+3}}}{2}+x -6\right )\right )\right )}{2}}}{{\mathrm e}^{\frac {x}{x^{3}+x^{2}+3}}+x -4}\]

Input:

int(((-x^6-2*x^5-3*x^4-7*x^3-6*x^2+3*x-9)*exp(x/(x^3+x^2+3))+4*x^6+8*x^5+4 
*x^4+24*x^3+24*x^2+36)*exp(x)/((3*x^6+6*x^5+3*x^4+18*x^3+18*x^2+27)*exp(x/ 
(x^3+x^2+3))^2+(5*x^7-14*x^6-43*x^5+6*x^4-114*x^3-144*x^2+45*x-216)*exp(x/ 
(x^3+x^2+3))+2*x^8-16*x^7+10*x^6+88*x^5-60*x^4+168*x^3+306*x^2-180*x+432)/ 
exp(-ln((3*exp(x/(x^3+x^2+3))+2*x-12)/(exp(x/(x^3+x^2+3))+x-4))+x),x)
 

Output:

-1/(exp(x/(x^3+x^2+3))+x-4)*x*exp(-1/2*I*Pi*csgn(I/(exp(x/(x^3+x^2+3))+x-4 
)*(3/2*exp(x/(x^3+x^2+3))+x-6))*(-csgn(I/(exp(x/(x^3+x^2+3))+x-4)*(3/2*exp 
(x/(x^3+x^2+3))+x-6))+csgn(I/(exp(x/(x^3+x^2+3))+x-4)))*(-csgn(I/(exp(x/(x 
^3+x^2+3))+x-4)*(3/2*exp(x/(x^3+x^2+3))+x-6))+csgn(I*(3/2*exp(x/(x^3+x^2+3 
))+x-6))))
 

Fricas [A] (verification not implemented)

Time = 0.07 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.84 \[ \int \frac {\left (-12+3 e^{\frac {x}{3+x^2+x^3}}+2 x\right ) \left (36+24 x^2+24 x^3+4 x^4+8 x^5+4 x^6+e^{\frac {x}{3+x^2+x^3}} \left (-9+3 x-6 x^2-7 x^3-3 x^4-2 x^5-x^6\right )\right )}{\left (-4+e^{\frac {x}{3+x^2+x^3}}+x\right ) \left (432-180 x+306 x^2+168 x^3-60 x^4+88 x^5+10 x^6-16 x^7+2 x^8+e^{\frac {2 x}{3+x^2+x^3}} \left (27+18 x^2+18 x^3+3 x^4+6 x^5+3 x^6\right )+e^{\frac {x}{3+x^2+x^3}} \left (-216+45 x-144 x^2-114 x^3+6 x^4-43 x^5-14 x^6+5 x^7\right )\right )} \, dx=-\frac {x}{x + e^{\left (\frac {x}{x^{3} + x^{2} + 3}\right )} - 4} \] Input:

integrate(((-x^6-2*x^5-3*x^4-7*x^3-6*x^2+3*x-9)*exp(x/(x^3+x^2+3))+4*x^6+8 
*x^5+4*x^4+24*x^3+24*x^2+36)*exp(x)/((3*x^6+6*x^5+3*x^4+18*x^3+18*x^2+27)* 
exp(x/(x^3+x^2+3))^2+(5*x^7-14*x^6-43*x^5+6*x^4-114*x^3-144*x^2+45*x-216)* 
exp(x/(x^3+x^2+3))+2*x^8-16*x^7+10*x^6+88*x^5-60*x^4+168*x^3+306*x^2-180*x 
+432)/exp(-log((3*exp(x/(x^3+x^2+3))+2*x-12)/(exp(x/(x^3+x^2+3))+x-4))+x), 
x, algorithm="fricas")
 

Output:

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

Sympy [A] (verification not implemented)

Time = 0.19 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.68 \[ \int \frac {\left (-12+3 e^{\frac {x}{3+x^2+x^3}}+2 x\right ) \left (36+24 x^2+24 x^3+4 x^4+8 x^5+4 x^6+e^{\frac {x}{3+x^2+x^3}} \left (-9+3 x-6 x^2-7 x^3-3 x^4-2 x^5-x^6\right )\right )}{\left (-4+e^{\frac {x}{3+x^2+x^3}}+x\right ) \left (432-180 x+306 x^2+168 x^3-60 x^4+88 x^5+10 x^6-16 x^7+2 x^8+e^{\frac {2 x}{3+x^2+x^3}} \left (27+18 x^2+18 x^3+3 x^4+6 x^5+3 x^6\right )+e^{\frac {x}{3+x^2+x^3}} \left (-216+45 x-144 x^2-114 x^3+6 x^4-43 x^5-14 x^6+5 x^7\right )\right )} \, dx=- \frac {x}{x + e^{\frac {x}{x^{3} + x^{2} + 3}} - 4} \] Input:

integrate(((-x**6-2*x**5-3*x**4-7*x**3-6*x**2+3*x-9)*exp(x/(x**3+x**2+3))+ 
4*x**6+8*x**5+4*x**4+24*x**3+24*x**2+36)*exp(x)/((3*x**6+6*x**5+3*x**4+18* 
x**3+18*x**2+27)*exp(x/(x**3+x**2+3))**2+(5*x**7-14*x**6-43*x**5+6*x**4-11 
4*x**3-144*x**2+45*x-216)*exp(x/(x**3+x**2+3))+2*x**8-16*x**7+10*x**6+88*x 
**5-60*x**4+168*x**3+306*x**2-180*x+432)/exp(-ln((3*exp(x/(x**3+x**2+3))+2 
*x-12)/(exp(x/(x**3+x**2+3))+x-4))+x),x)
 

Output:

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

Maxima [A] (verification not implemented)

Time = 0.14 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.84 \[ \int \frac {\left (-12+3 e^{\frac {x}{3+x^2+x^3}}+2 x\right ) \left (36+24 x^2+24 x^3+4 x^4+8 x^5+4 x^6+e^{\frac {x}{3+x^2+x^3}} \left (-9+3 x-6 x^2-7 x^3-3 x^4-2 x^5-x^6\right )\right )}{\left (-4+e^{\frac {x}{3+x^2+x^3}}+x\right ) \left (432-180 x+306 x^2+168 x^3-60 x^4+88 x^5+10 x^6-16 x^7+2 x^8+e^{\frac {2 x}{3+x^2+x^3}} \left (27+18 x^2+18 x^3+3 x^4+6 x^5+3 x^6\right )+e^{\frac {x}{3+x^2+x^3}} \left (-216+45 x-144 x^2-114 x^3+6 x^4-43 x^5-14 x^6+5 x^7\right )\right )} \, dx=-\frac {x}{x + e^{\left (\frac {x}{x^{3} + x^{2} + 3}\right )} - 4} \] Input:

integrate(((-x^6-2*x^5-3*x^4-7*x^3-6*x^2+3*x-9)*exp(x/(x^3+x^2+3))+4*x^6+8 
*x^5+4*x^4+24*x^3+24*x^2+36)*exp(x)/((3*x^6+6*x^5+3*x^4+18*x^3+18*x^2+27)* 
exp(x/(x^3+x^2+3))^2+(5*x^7-14*x^6-43*x^5+6*x^4-114*x^3-144*x^2+45*x-216)* 
exp(x/(x^3+x^2+3))+2*x^8-16*x^7+10*x^6+88*x^5-60*x^4+168*x^3+306*x^2-180*x 
+432)/exp(-log((3*exp(x/(x^3+x^2+3))+2*x-12)/(exp(x/(x^3+x^2+3))+x-4))+x), 
x, algorithm="maxima")
 

Output:

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

Giac [A] (verification not implemented)

Time = 0.21 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.84 \[ \int \frac {\left (-12+3 e^{\frac {x}{3+x^2+x^3}}+2 x\right ) \left (36+24 x^2+24 x^3+4 x^4+8 x^5+4 x^6+e^{\frac {x}{3+x^2+x^3}} \left (-9+3 x-6 x^2-7 x^3-3 x^4-2 x^5-x^6\right )\right )}{\left (-4+e^{\frac {x}{3+x^2+x^3}}+x\right ) \left (432-180 x+306 x^2+168 x^3-60 x^4+88 x^5+10 x^6-16 x^7+2 x^8+e^{\frac {2 x}{3+x^2+x^3}} \left (27+18 x^2+18 x^3+3 x^4+6 x^5+3 x^6\right )+e^{\frac {x}{3+x^2+x^3}} \left (-216+45 x-144 x^2-114 x^3+6 x^4-43 x^5-14 x^6+5 x^7\right )\right )} \, dx=-\frac {x}{x + e^{\left (\frac {x}{x^{3} + x^{2} + 3}\right )} - 4} \] Input:

integrate(((-x^6-2*x^5-3*x^4-7*x^3-6*x^2+3*x-9)*exp(x/(x^3+x^2+3))+4*x^6+8 
*x^5+4*x^4+24*x^3+24*x^2+36)*exp(x)/((3*x^6+6*x^5+3*x^4+18*x^3+18*x^2+27)* 
exp(x/(x^3+x^2+3))^2+(5*x^7-14*x^6-43*x^5+6*x^4-114*x^3-144*x^2+45*x-216)* 
exp(x/(x^3+x^2+3))+2*x^8-16*x^7+10*x^6+88*x^5-60*x^4+168*x^3+306*x^2-180*x 
+432)/exp(-log((3*exp(x/(x^3+x^2+3))+2*x-12)/(exp(x/(x^3+x^2+3))+x-4))+x), 
x, algorithm="giac")
 

Output:

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

Mupad [B] (verification not implemented)

Time = 1.80 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.84 \[ \int \frac {\left (-12+3 e^{\frac {x}{3+x^2+x^3}}+2 x\right ) \left (36+24 x^2+24 x^3+4 x^4+8 x^5+4 x^6+e^{\frac {x}{3+x^2+x^3}} \left (-9+3 x-6 x^2-7 x^3-3 x^4-2 x^5-x^6\right )\right )}{\left (-4+e^{\frac {x}{3+x^2+x^3}}+x\right ) \left (432-180 x+306 x^2+168 x^3-60 x^4+88 x^5+10 x^6-16 x^7+2 x^8+e^{\frac {2 x}{3+x^2+x^3}} \left (27+18 x^2+18 x^3+3 x^4+6 x^5+3 x^6\right )+e^{\frac {x}{3+x^2+x^3}} \left (-216+45 x-144 x^2-114 x^3+6 x^4-43 x^5-14 x^6+5 x^7\right )\right )} \, dx=-\frac {x}{x+{\mathrm {e}}^{\frac {x}{x^3+x^2+3}}-4} \] Input:

int((exp(log((2*x + 3*exp(x/(x^2 + x^3 + 3)) - 12)/(x + exp(x/(x^2 + x^3 + 
 3)) - 4)) - x)*exp(x)*(24*x^2 + 24*x^3 + 4*x^4 + 8*x^5 + 4*x^6 - exp(x/(x 
^2 + x^3 + 3))*(6*x^2 - 3*x + 7*x^3 + 3*x^4 + 2*x^5 + x^6 + 9) + 36))/(exp 
((2*x)/(x^2 + x^3 + 3))*(18*x^2 + 18*x^3 + 3*x^4 + 6*x^5 + 3*x^6 + 27) - 1 
80*x - exp(x/(x^2 + x^3 + 3))*(144*x^2 - 45*x + 114*x^3 - 6*x^4 + 43*x^5 + 
 14*x^6 - 5*x^7 + 216) + 306*x^2 + 168*x^3 - 60*x^4 + 88*x^5 + 10*x^6 - 16 
*x^7 + 2*x^8 + 432),x)
 

Output:

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

Reduce [B] (verification not implemented)

Time = 0.26 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.88 \[ \int \frac {\left (-12+3 e^{\frac {x}{3+x^2+x^3}}+2 x\right ) \left (36+24 x^2+24 x^3+4 x^4+8 x^5+4 x^6+e^{\frac {x}{3+x^2+x^3}} \left (-9+3 x-6 x^2-7 x^3-3 x^4-2 x^5-x^6\right )\right )}{\left (-4+e^{\frac {x}{3+x^2+x^3}}+x\right ) \left (432-180 x+306 x^2+168 x^3-60 x^4+88 x^5+10 x^6-16 x^7+2 x^8+e^{\frac {2 x}{3+x^2+x^3}} \left (27+18 x^2+18 x^3+3 x^4+6 x^5+3 x^6\right )+e^{\frac {x}{3+x^2+x^3}} \left (-216+45 x-144 x^2-114 x^3+6 x^4-43 x^5-14 x^6+5 x^7\right )\right )} \, dx=-\frac {x}{e^{\frac {x}{x^{3}+x^{2}+3}}+x -4} \] Input:

int(((-x^6-2*x^5-3*x^4-7*x^3-6*x^2+3*x-9)*exp(x/(x^3+x^2+3))+4*x^6+8*x^5+4 
*x^4+24*x^3+24*x^2+36)*exp(x)/((3*x^6+6*x^5+3*x^4+18*x^3+18*x^2+27)*exp(x/ 
(x^3+x^2+3))^2+(5*x^7-14*x^6-43*x^5+6*x^4-114*x^3-144*x^2+45*x-216)*exp(x/ 
(x^3+x^2+3))+2*x^8-16*x^7+10*x^6+88*x^5-60*x^4+168*x^3+306*x^2-180*x+432)/ 
exp(-log((3*exp(x/(x^3+x^2+3))+2*x-12)/(exp(x/(x^3+x^2+3))+x-4))+x),x)
 

Output:

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