\(\int \frac {e^{-\frac {1}{4} e^x (16-8 x+x^2)} (128-192 x-160 x^3-200 x^4+100 x^5+e^{3 x} (200 x^3-350 x^4+175 x^5-25 x^6)+e^{2 x} (-320 x^2+260 x^3-480 x^4+740 x^5-350 x^6+50 x^7)+e^x (-32 x+256 x^2+472 x^3-376 x^4+280 x^5-390 x^6+175 x^7-25 x^8))}{100 x^3-200 x^4+100 x^5} \, dx\) [2319]

Optimal result

Integrand size = 163, antiderivative size = 36 \[ \int \frac {e^{-\frac {1}{4} e^x \left (16-8 x+x^2\right )} \left (128-192 x-160 x^3-200 x^4+100 x^5+e^{3 x} \left (200 x^3-350 x^4+175 x^5-25 x^6\right )+e^{2 x} \left (-320 x^2+260 x^3-480 x^4+740 x^5-350 x^6+50 x^7\right )+e^x \left (-32 x+256 x^2+472 x^3-376 x^4+280 x^5-390 x^6+175 x^7-25 x^8\right )\right )}{100 x^3-200 x^4+100 x^5} \, dx=\frac {e^{-\frac {1}{4} e^x (-4+x)^2} \left (-e^x+\frac {4}{5 x}+x\right )^2}{-1+x} \] Output:

(4/5/x+x-exp(x))^2/(-1+x)/exp(1/4*(-4+x)^2*exp(x))
                                                                                    
                                                                                    
 

Mathematica [A] (verified)

Time = 0.08 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.14 \[ \int \frac {e^{-\frac {1}{4} e^x \left (16-8 x+x^2\right )} \left (128-192 x-160 x^3-200 x^4+100 x^5+e^{3 x} \left (200 x^3-350 x^4+175 x^5-25 x^6\right )+e^{2 x} \left (-320 x^2+260 x^3-480 x^4+740 x^5-350 x^6+50 x^7\right )+e^x \left (-32 x+256 x^2+472 x^3-376 x^4+280 x^5-390 x^6+175 x^7-25 x^8\right )\right )}{100 x^3-200 x^4+100 x^5} \, dx=\frac {e^{-\frac {1}{4} e^x (-4+x)^2} \left (4-5 e^x x+5 x^2\right )^2}{25 (-1+x) x^2} \] Input:

Integrate[(128 - 192*x - 160*x^3 - 200*x^4 + 100*x^5 + E^(3*x)*(200*x^3 - 
350*x^4 + 175*x^5 - 25*x^6) + E^(2*x)*(-320*x^2 + 260*x^3 - 480*x^4 + 740* 
x^5 - 350*x^6 + 50*x^7) + E^x*(-32*x + 256*x^2 + 472*x^3 - 376*x^4 + 280*x 
^5 - 390*x^6 + 175*x^7 - 25*x^8))/(E^((E^x*(16 - 8*x + x^2))/4)*(100*x^3 - 
 200*x^4 + 100*x^5)),x]
 

Output:

(4 - 5*E^x*x + 5*x^2)^2/(25*E^((E^x*(-4 + x)^2)/4)*(-1 + x)*x^2)
 

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.

\(\displaystyle \int \frac {e^{-\frac {1}{4} e^x \left (x^2-8 x+16\right )} \left (100 x^5-200 x^4-160 x^3+e^{3 x} \left (-25 x^6+175 x^5-350 x^4+200 x^3\right )+e^{2 x} \left (50 x^7-350 x^6+740 x^5-480 x^4+260 x^3-320 x^2\right )+e^x \left (-25 x^8+175 x^7-390 x^6+280 x^5-376 x^4+472 x^3+256 x^2-32 x\right )-192 x+128\right )}{100 x^5-200 x^4+100 x^3} \, dx\)

\(\Big \downarrow \) 2026

\(\displaystyle \int \frac {e^{-\frac {1}{4} e^x \left (x^2-8 x+16\right )} \left (100 x^5-200 x^4-160 x^3+e^{3 x} \left (-25 x^6+175 x^5-350 x^4+200 x^3\right )+e^{2 x} \left (50 x^7-350 x^6+740 x^5-480 x^4+260 x^3-320 x^2\right )+e^x \left (-25 x^8+175 x^7-390 x^6+280 x^5-376 x^4+472 x^3+256 x^2-32 x\right )-192 x+128\right )}{x^3 \left (100 x^2-200 x+100\right )}dx\)

\(\Big \downarrow \) 7277

\(\displaystyle 400 \int \frac {e^{-\frac {1}{4} e^x \left (x^2-8 x+16\right )} \left (100 x^5-200 x^4-160 x^3-192 x+25 e^{3 x} \left (-x^6+7 x^5-14 x^4+8 x^3\right )-10 e^{2 x} \left (-5 x^7+35 x^6-74 x^5+48 x^4-26 x^3+32 x^2\right )-e^x \left (25 x^8-175 x^7+390 x^6-280 x^5+376 x^4-472 x^3-256 x^2+32 x\right )+128\right )}{40000 (1-x)^2 x^3}dx\)

\(\Big \downarrow \) 27

\(\displaystyle \frac {1}{100} \int \frac {e^{-\frac {1}{4} e^x \left (x^2-8 x+16\right )} \left (100 x^5-200 x^4-160 x^3-192 x+25 e^{3 x} \left (-x^6+7 x^5-14 x^4+8 x^3\right )-10 e^{2 x} \left (-5 x^7+35 x^6-74 x^5+48 x^4-26 x^3+32 x^2\right )-e^x \left (25 x^8-175 x^7+390 x^6-280 x^5+376 x^4-472 x^3-256 x^2+32 x\right )+128\right )}{(1-x)^2 x^3}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \frac {1}{100} \int \left (\frac {100 e^{-\frac {1}{4} e^x \left (x^2-8 x+16\right )} x^2}{(x-1)^2}-\frac {200 e^{-\frac {1}{4} e^x \left (x^2-8 x+16\right )} x}{(x-1)^2}-\frac {25 e^{3 x-\frac {1}{4} e^x \left (x^2-8 x+16\right )} (x-4) (x-2)}{x-1}-\frac {160 e^{-\frac {1}{4} e^x \left (x^2-8 x+16\right )}}{(x-1)^2}+\frac {10 e^{2 x-\frac {1}{4} e^x \left (x^2-8 x+16\right )} \left (5 x^5-35 x^4+74 x^3-48 x^2+26 x-32\right )}{(x-1)^2 x}-\frac {e^{x-\frac {1}{4} e^x \left (x^2-8 x+16\right )} \left (25 x^7-175 x^6+390 x^5-280 x^4+376 x^3-472 x^2-256 x+32\right )}{(x-1)^2 x^2}-\frac {192 e^{-\frac {1}{4} e^x \left (x^2-8 x+16\right )}}{(x-1)^2 x^2}+\frac {128 e^{-\frac {1}{4} e^x \left (x^2-8 x+16\right )}}{(x-1)^2 x^3}\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle \frac {1}{100} \left (100 \int e^{-\frac {1}{4} e^x \left (x^2-8 x+16\right )}dx-75 \int e^{x-\frac {1}{4} e^x \left (x^2-8 x+16\right )}dx+190 \int e^{2 x-\frac {1}{4} e^x \left (x^2-8 x+16\right )}dx+125 \int e^{3 x-\frac {1}{4} e^x \left (x^2-8 x+16\right )}dx-324 \int \frac {e^{-\frac {1}{4} e^x \left (x^2-8 x+16\right )}}{(x-1)^2}dx+360 \int \frac {e^{x-\frac {1}{4} e^x \left (x^2-8 x+16\right )}}{(x-1)^2}dx-100 \int \frac {e^{2 x-\frac {1}{4} e^x \left (x^2-8 x+16\right )}}{(x-1)^2}dx-603 \int \frac {e^{x-\frac {1}{4} e^x \left (x^2-8 x+16\right )}}{x-1}dx+470 \int \frac {e^{2 x-\frac {1}{4} e^x \left (x^2-8 x+16\right )}}{x-1}dx-75 \int \frac {e^{3 x-\frac {1}{4} e^x \left (x^2-8 x+16\right )}}{x-1}dx+64 \int \frac {e^{-\frac {1}{4} e^x \left (x^2-8 x+16\right )}}{x^2}dx-32 \int \frac {e^{x-\frac {1}{4} e^x \left (x^2-8 x+16\right )}}{x^2}dx+192 \int \frac {e^{x-\frac {1}{4} e^x \left (x^2-8 x+16\right )}}{x}dx-320 \int \frac {e^{2 x-\frac {1}{4} e^x \left (x^2-8 x+16\right )}}{x}dx-115 \int e^{x-\frac {1}{4} e^x \left (x^2-8 x+16\right )} xdx-250 \int e^{2 x-\frac {1}{4} e^x \left (x^2-8 x+16\right )} xdx-25 \int e^{3 x-\frac {1}{4} e^x \left (x^2-8 x+16\right )} xdx+125 \int e^{x-\frac {1}{4} e^x \left (x^2-8 x+16\right )} x^2dx+50 \int e^{2 x-\frac {1}{4} e^x \left (x^2-8 x+16\right )} x^2dx+128 \int \frac {e^{-\frac {1}{4} e^x \left (x^2-8 x+16\right )}}{x^3}dx-25 \int e^{x-\frac {1}{4} e^x \left (x^2-8 x+16\right )} x^3dx\right )\)

Input:

Int[(128 - 192*x - 160*x^3 - 200*x^4 + 100*x^5 + E^(3*x)*(200*x^3 - 350*x^ 
4 + 175*x^5 - 25*x^6) + E^(2*x)*(-320*x^2 + 260*x^3 - 480*x^4 + 740*x^5 - 
350*x^6 + 50*x^7) + E^x*(-32*x + 256*x^2 + 472*x^3 - 376*x^4 + 280*x^5 - 3 
90*x^6 + 175*x^7 - 25*x^8))/(E^((E^x*(16 - 8*x + x^2))/4)*(100*x^3 - 200*x 
^4 + 100*x^5)),x]
 

Output:

$Aborted
 

Maple [A] (verified)

Time = 0.89 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.50

method	result	size
risch	\(\frac {\left (25 x^{4}-50 \,{\mathrm e}^{x} x^{3}+25 \,{\mathrm e}^{2 x} x^{2}+40 x^{2}-40 \,{\mathrm e}^{x} x +16\right ) {\mathrm e}^{-\frac {\left (x -4\right )^{2} {\mathrm e}^{x}}{4}}}{25 x^{2} \left (-1+x \right )}\)	\(54\)
parallelrisch	\(\frac {\left (64+100 x^{4}-200 \,{\mathrm e}^{x} x^{3}+100 \,{\mathrm e}^{2 x} x^{2}+160 x^{2}-160 \,{\mathrm e}^{x} x \right ) {\mathrm e}^{-\frac {\left (x^{2}-8 x +16\right ) {\mathrm e}^{x}}{4}}}{100 x^{2} \left (-1+x \right )}\)	\(59\)

Input:

int(((-25*x^6+175*x^5-350*x^4+200*x^3)*exp(x)^3+(50*x^7-350*x^6+740*x^5-48 
0*x^4+260*x^3-320*x^2)*exp(x)^2+(-25*x^8+175*x^7-390*x^6+280*x^5-376*x^4+4 
72*x^3+256*x^2-32*x)*exp(x)+100*x^5-200*x^4-160*x^3-192*x+128)/(100*x^5-20 
0*x^4+100*x^3)/exp(1/4*(x^2-8*x+16)*exp(x)),x,method=_RETURNVERBOSE)
 

Output:

1/25/x^2*(25*x^4-50*exp(x)*x^3+25*exp(2*x)*x^2+40*x^2-40*exp(x)*x+16)/(-1+ 
x)*exp(-1/4*(x-4)^2*exp(x))
 

Fricas [A] (verification not implemented)

Time = 0.07 (sec) , antiderivative size = 60, normalized size of antiderivative = 1.67 \[ \int \frac {e^{-\frac {1}{4} e^x \left (16-8 x+x^2\right )} \left (128-192 x-160 x^3-200 x^4+100 x^5+e^{3 x} \left (200 x^3-350 x^4+175 x^5-25 x^6\right )+e^{2 x} \left (-320 x^2+260 x^3-480 x^4+740 x^5-350 x^6+50 x^7\right )+e^x \left (-32 x+256 x^2+472 x^3-376 x^4+280 x^5-390 x^6+175 x^7-25 x^8\right )\right )}{100 x^3-200 x^4+100 x^5} \, dx=\frac {{\left (25 \, x^{4} + 25 \, x^{2} e^{\left (2 \, x\right )} + 40 \, x^{2} - 10 \, {\left (5 \, x^{3} + 4 \, x\right )} e^{x} + 16\right )} e^{\left (-\frac {1}{4} \, {\left (x^{2} - 8 \, x + 16\right )} e^{x}\right )}}{25 \, {\left (x^{3} - x^{2}\right )}} \] Input:

integrate(((-25*x^6+175*x^5-350*x^4+200*x^3)*exp(x)^3+(50*x^7-350*x^6+740* 
x^5-480*x^4+260*x^3-320*x^2)*exp(x)^2+(-25*x^8+175*x^7-390*x^6+280*x^5-376 
*x^4+472*x^3+256*x^2-32*x)*exp(x)+100*x^5-200*x^4-160*x^3-192*x+128)/(100* 
x^5-200*x^4+100*x^3)/exp(1/4*(x^2-8*x+16)*exp(x)),x, algorithm="fricas")
 

Output:

1/25*(25*x^4 + 25*x^2*e^(2*x) + 40*x^2 - 10*(5*x^3 + 4*x)*e^x + 16)*e^(-1/ 
4*(x^2 - 8*x + 16)*e^x)/(x^3 - x^2)
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 61 vs. \(2 (26) = 52\).

Time = 0.27 (sec) , antiderivative size = 61, normalized size of antiderivative = 1.69 \[ \int \frac {e^{-\frac {1}{4} e^x \left (16-8 x+x^2\right )} \left (128-192 x-160 x^3-200 x^4+100 x^5+e^{3 x} \left (200 x^3-350 x^4+175 x^5-25 x^6\right )+e^{2 x} \left (-320 x^2+260 x^3-480 x^4+740 x^5-350 x^6+50 x^7\right )+e^x \left (-32 x+256 x^2+472 x^3-376 x^4+280 x^5-390 x^6+175 x^7-25 x^8\right )\right )}{100 x^3-200 x^4+100 x^5} \, dx=\frac {\left (25 x^{4} - 50 x^{3} e^{x} + 25 x^{2} e^{2 x} + 40 x^{2} - 40 x e^{x} + 16\right ) e^{- \left (\frac {x^{2}}{4} - 2 x + 4\right ) e^{x}}}{25 x^{3} - 25 x^{2}} \] Input:

integrate(((-25*x**6+175*x**5-350*x**4+200*x**3)*exp(x)**3+(50*x**7-350*x* 
*6+740*x**5-480*x**4+260*x**3-320*x**2)*exp(x)**2+(-25*x**8+175*x**7-390*x 
**6+280*x**5-376*x**4+472*x**3+256*x**2-32*x)*exp(x)+100*x**5-200*x**4-160 
*x**3-192*x+128)/(100*x**5-200*x**4+100*x**3)/exp(1/4*(x**2-8*x+16)*exp(x) 
),x)
 

Output:

(25*x**4 - 50*x**3*exp(x) + 25*x**2*exp(2*x) + 40*x**2 - 40*x*exp(x) + 16) 
*exp(-(x**2/4 - 2*x + 4)*exp(x))/(25*x**3 - 25*x**2)
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 65 vs. \(2 (32) = 64\).

Time = 0.15 (sec) , antiderivative size = 65, normalized size of antiderivative = 1.81 \[ \int \frac {e^{-\frac {1}{4} e^x \left (16-8 x+x^2\right )} \left (128-192 x-160 x^3-200 x^4+100 x^5+e^{3 x} \left (200 x^3-350 x^4+175 x^5-25 x^6\right )+e^{2 x} \left (-320 x^2+260 x^3-480 x^4+740 x^5-350 x^6+50 x^7\right )+e^x \left (-32 x+256 x^2+472 x^3-376 x^4+280 x^5-390 x^6+175 x^7-25 x^8\right )\right )}{100 x^3-200 x^4+100 x^5} \, dx=\frac {{\left (25 \, x^{4} + 25 \, x^{2} e^{\left (2 \, x\right )} + 40 \, x^{2} - 10 \, {\left (5 \, x^{3} + 4 \, x\right )} e^{x} + 16\right )} e^{\left (-\frac {1}{4} \, x^{2} e^{x} + 2 \, x e^{x} - 4 \, e^{x}\right )}}{25 \, {\left (x^{3} - x^{2}\right )}} \] Input:

integrate(((-25*x^6+175*x^5-350*x^4+200*x^3)*exp(x)^3+(50*x^7-350*x^6+740* 
x^5-480*x^4+260*x^3-320*x^2)*exp(x)^2+(-25*x^8+175*x^7-390*x^6+280*x^5-376 
*x^4+472*x^3+256*x^2-32*x)*exp(x)+100*x^5-200*x^4-160*x^3-192*x+128)/(100* 
x^5-200*x^4+100*x^3)/exp(1/4*(x^2-8*x+16)*exp(x)),x, algorithm="maxima")
 

Output:

1/25*(25*x^4 + 25*x^2*e^(2*x) + 40*x^2 - 10*(5*x^3 + 4*x)*e^x + 16)*e^(-1/ 
4*x^2*e^x + 2*x*e^x - 4*e^x)/(x^3 - x^2)
 

Giac [F]

\[ \int \frac {e^{-\frac {1}{4} e^x \left (16-8 x+x^2\right )} \left (128-192 x-160 x^3-200 x^4+100 x^5+e^{3 x} \left (200 x^3-350 x^4+175 x^5-25 x^6\right )+e^{2 x} \left (-320 x^2+260 x^3-480 x^4+740 x^5-350 x^6+50 x^7\right )+e^x \left (-32 x+256 x^2+472 x^3-376 x^4+280 x^5-390 x^6+175 x^7-25 x^8\right )\right )}{100 x^3-200 x^4+100 x^5} \, dx=\int { \frac {{\left (100 \, x^{5} - 200 \, x^{4} - 160 \, x^{3} - 25 \, {\left (x^{6} - 7 \, x^{5} + 14 \, x^{4} - 8 \, x^{3}\right )} e^{\left (3 \, x\right )} + 10 \, {\left (5 \, x^{7} - 35 \, x^{6} + 74 \, x^{5} - 48 \, x^{4} + 26 \, x^{3} - 32 \, x^{2}\right )} e^{\left (2 \, x\right )} - {\left (25 \, x^{8} - 175 \, x^{7} + 390 \, x^{6} - 280 \, x^{5} + 376 \, x^{4} - 472 \, x^{3} - 256 \, x^{2} + 32 \, x\right )} e^{x} - 192 \, x + 128\right )} e^{\left (-\frac {1}{4} \, {\left (x^{2} - 8 \, x + 16\right )} e^{x}\right )}}{100 \, {\left (x^{5} - 2 \, x^{4} + x^{3}\right )}} \,d x } \] Input:

integrate(((-25*x^6+175*x^5-350*x^4+200*x^3)*exp(x)^3+(50*x^7-350*x^6+740* 
x^5-480*x^4+260*x^3-320*x^2)*exp(x)^2+(-25*x^8+175*x^7-390*x^6+280*x^5-376 
*x^4+472*x^3+256*x^2-32*x)*exp(x)+100*x^5-200*x^4-160*x^3-192*x+128)/(100* 
x^5-200*x^4+100*x^3)/exp(1/4*(x^2-8*x+16)*exp(x)),x, algorithm="giac")
 

Output:

integrate(1/100*(100*x^5 - 200*x^4 - 160*x^3 - 25*(x^6 - 7*x^5 + 14*x^4 - 
8*x^3)*e^(3*x) + 10*(5*x^7 - 35*x^6 + 74*x^5 - 48*x^4 + 26*x^3 - 32*x^2)*e 
^(2*x) - (25*x^8 - 175*x^7 + 390*x^6 - 280*x^5 + 376*x^4 - 472*x^3 - 256*x 
^2 + 32*x)*e^x - 192*x + 128)*e^(-1/4*(x^2 - 8*x + 16)*e^x)/(x^5 - 2*x^4 + 
 x^3), x)
 

Mupad [B] (verification not implemented)

Time = 2.12 (sec) , antiderivative size = 61, normalized size of antiderivative = 1.69 \[ \int \frac {e^{-\frac {1}{4} e^x \left (16-8 x+x^2\right )} \left (128-192 x-160 x^3-200 x^4+100 x^5+e^{3 x} \left (200 x^3-350 x^4+175 x^5-25 x^6\right )+e^{2 x} \left (-320 x^2+260 x^3-480 x^4+740 x^5-350 x^6+50 x^7\right )+e^x \left (-32 x+256 x^2+472 x^3-376 x^4+280 x^5-390 x^6+175 x^7-25 x^8\right )\right )}{100 x^3-200 x^4+100 x^5} \, dx=-\frac {{\mathrm {e}}^{2\,x\,{\mathrm {e}}^x-\frac {x^2\,{\mathrm {e}}^x}{4}-4\,{\mathrm {e}}^x}\,\left (x^2\,{\mathrm {e}}^{2\,x}-2\,x^3\,{\mathrm {e}}^x-\frac {8\,x\,{\mathrm {e}}^x}{5}+\frac {8\,x^2}{5}+x^4+\frac {16}{25}\right )}{x^2-x^3} \] Input:

int(-(exp(-(exp(x)*(x^2 - 8*x + 16))/4)*(192*x + exp(2*x)*(320*x^2 - 260*x 
^3 + 480*x^4 - 740*x^5 + 350*x^6 - 50*x^7) - exp(3*x)*(200*x^3 - 350*x^4 + 
 175*x^5 - 25*x^6) + 160*x^3 + 200*x^4 - 100*x^5 + exp(x)*(32*x - 256*x^2 
- 472*x^3 + 376*x^4 - 280*x^5 + 390*x^6 - 175*x^7 + 25*x^8) - 128))/(100*x 
^3 - 200*x^4 + 100*x^5),x)
 

Output:

-(exp(2*x*exp(x) - (x^2*exp(x))/4 - 4*exp(x))*(x^2*exp(2*x) - 2*x^3*exp(x) 
 - (8*x*exp(x))/5 + (8*x^2)/5 + x^4 + 16/25))/(x^2 - x^3)
 

Reduce [B] (verification not implemented)

Time = 0.19 (sec) , antiderivative size = 72, normalized size of antiderivative = 2.00 \[ \int \frac {e^{-\frac {1}{4} e^x \left (16-8 x+x^2\right )} \left (128-192 x-160 x^3-200 x^4+100 x^5+e^{3 x} \left (200 x^3-350 x^4+175 x^5-25 x^6\right )+e^{2 x} \left (-320 x^2+260 x^3-480 x^4+740 x^5-350 x^6+50 x^7\right )+e^x \left (-32 x+256 x^2+472 x^3-376 x^4+280 x^5-390 x^6+175 x^7-25 x^8\right )\right )}{100 x^3-200 x^4+100 x^5} \, dx=\frac {e^{2 e^{x} x} \left (25 e^{2 x} x^{2}-50 e^{x} x^{3}-40 e^{x} x +25 x^{4}+40 x^{2}+16\right )}{25 e^{\frac {e^{x} x^{2}}{4}+4 e^{x}} x^{2} \left (x -1\right )} \] Input:

int(((-25*x^6+175*x^5-350*x^4+200*x^3)*exp(x)^3+(50*x^7-350*x^6+740*x^5-48 
0*x^4+260*x^3-320*x^2)*exp(x)^2+(-25*x^8+175*x^7-390*x^6+280*x^5-376*x^4+4 
72*x^3+256*x^2-32*x)*exp(x)+100*x^5-200*x^4-160*x^3-192*x+128)/(100*x^5-20 
0*x^4+100*x^3)/exp(1/4*(x^2-8*x+16)*exp(x)),x)
 

Output:

(e**(2*e**x*x)*(25*e**(2*x)*x**2 - 50*e**x*x**3 - 40*e**x*x + 25*x**4 + 40 
*x**2 + 16))/(25*e**((e**x*x**2 + 16*e**x)/4)*x**2*(x - 1))