\(\int \frac {-192-672 x-912 x^2-600 x^3-192 x^4-24 x^5+e^x (-12-30 x-18 x^2)+(96+144 x+72 x^2+12 x^3+e^x (6+3 x)) \log (\frac {e^{-2 x} (6400+25 e^{2 x}+12800 x+9600 x^2+3200 x^3+400 x^4+e^x (800+800 x+200 x^2))}{16 x^2+32 x^3+24 x^4+8 x^5+x^6})}{160+560 x+760 x^2+500 x^3+160 x^4+20 x^5+e^x (10+25 x+20 x^2+5 x^3)} \, dx\) [2282]

Optimal result

Integrand size = 185, antiderivative size = 36 \[ \int \frac {-192-672 x-912 x^2-600 x^3-192 x^4-24 x^5+e^x \left (-12-30 x-18 x^2\right )+\left (96+144 x+72 x^2+12 x^3+e^x (6+3 x)\right ) \log \left (\frac {e^{-2 x} \left (6400+25 e^{2 x}+12800 x+9600 x^2+3200 x^3+400 x^4+e^x \left (800+800 x+200 x^2\right )\right )}{16 x^2+32 x^3+24 x^4+8 x^5+x^6}\right )}{160+560 x+760 x^2+500 x^3+160 x^4+20 x^5+e^x \left (10+25 x+20 x^2+5 x^3\right )} \, dx=\frac {3 \log \left (\frac {25 \left (4 e^{-x}+\frac {4}{(4+2 x)^2}\right )^2}{x^2}\right )}{5+\frac {5}{x}} \] Output:

3*ln(25*(4/exp(x)+4/(4+2*x)^2)^2/x^2)/(5/x+5)
 

Mathematica [B] (warning: unable to verify)

Leaf count is larger than twice the leaf count of optimal. \(93\) vs. \(2(36)=72\).

Time = 0.12 (sec) , antiderivative size = 93, normalized size of antiderivative = 2.58 \[ \int \frac {-192-672 x-912 x^2-600 x^3-192 x^4-24 x^5+e^x \left (-12-30 x-18 x^2\right )+\left (96+144 x+72 x^2+12 x^3+e^x (6+3 x)\right ) \log \left (\frac {e^{-2 x} \left (6400+25 e^{2 x}+12800 x+9600 x^2+3200 x^3+400 x^4+e^x \left (800+800 x+200 x^2\right )\right )}{16 x^2+32 x^3+24 x^4+8 x^5+x^6}\right )}{160+560 x+760 x^2+500 x^3+160 x^4+20 x^5+e^x \left (10+25 x+20 x^2+5 x^3\right )} \, dx=-\frac {3 \left (2+4 x+2 x^2+2 (1+x) \log (x)+4 (1+x) \log (2+x)-2 \log \left (e^x+4 (2+x)^2\right )-2 x \log \left (e^x+4 (2+x)^2\right )+\log \left (\frac {25 e^{-2 x} \left (e^x+4 (2+x)^2\right )^2}{x^2 (2+x)^4}\right )\right )}{5 (1+x)} \] Input:

Integrate[(-192 - 672*x - 912*x^2 - 600*x^3 - 192*x^4 - 24*x^5 + E^x*(-12 
- 30*x - 18*x^2) + (96 + 144*x + 72*x^2 + 12*x^3 + E^x*(6 + 3*x))*Log[(640 
0 + 25*E^(2*x) + 12800*x + 9600*x^2 + 3200*x^3 + 400*x^4 + E^x*(800 + 800* 
x + 200*x^2))/(E^(2*x)*(16*x^2 + 32*x^3 + 24*x^4 + 8*x^5 + x^6))])/(160 + 
560*x + 760*x^2 + 500*x^3 + 160*x^4 + 20*x^5 + E^x*(10 + 25*x + 20*x^2 + 5 
*x^3)),x]
 

Output:

(-3*(2 + 4*x + 2*x^2 + 2*(1 + x)*Log[x] + 4*(1 + x)*Log[2 + x] - 2*Log[E^x 
 + 4*(2 + x)^2] - 2*x*Log[E^x + 4*(2 + x)^2] + Log[(25*(E^x + 4*(2 + x)^2) 
^2)/(E^(2*x)*x^2*(2 + x)^4)]))/(5*(1 + 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.

\(\displaystyle \int \frac {-24 x^5-192 x^4-600 x^3-912 x^2+e^x \left (-18 x^2-30 x-12\right )+\left (12 x^3+72 x^2+144 x+e^x (3 x+6)+96\right ) \log \left (\frac {e^{-2 x} \left (400 x^4+3200 x^3+9600 x^2+e^x \left (200 x^2+800 x+800\right )+12800 x+25 e^{2 x}+6400\right )}{x^6+8 x^5+24 x^4+32 x^3+16 x^2}\right )-672 x-192}{20 x^5+160 x^4+500 x^3+760 x^2+e^x \left (5 x^3+20 x^2+25 x+10\right )+560 x+160} \, dx\)

\(\Big \downarrow \) 7292

\(\displaystyle \int \frac {-24 x^5-192 x^4-600 x^3-912 x^2+e^x \left (-18 x^2-30 x-12\right )+\left (12 x^3+72 x^2+144 x+e^x (3 x+6)+96\right ) \log \left (\frac {e^{-2 x} \left (400 x^4+3200 x^3+9600 x^2+e^x \left (200 x^2+800 x+800\right )+12800 x+25 e^{2 x}+6400\right )}{x^6+8 x^5+24 x^4+32 x^3+16 x^2}\right )-672 x-192}{5 (x+1)^2 (x+2) \left (4 x^2+16 x+e^x+16\right )}dx\)

\(\Big \downarrow \) 27

\(\displaystyle \frac {1}{5} \int -\frac {3 \left (8 x^5+64 x^4+200 x^3+304 x^2+224 x+2 e^x \left (3 x^2+5 x+2\right )-\left (4 x^3+24 x^2+48 x+e^x (x+2)+32\right ) \log \left (\frac {25 e^{-2 x} \left (16 x^4+128 x^3+384 x^2+512 x+e^{2 x}+8 e^x \left (x^2+4 x+4\right )+256\right )}{x^6+8 x^5+24 x^4+32 x^3+16 x^2}\right )+64\right )}{(x+1)^2 (x+2) \left (4 x^2+16 x+e^x+16\right )}dx\)

\(\Big \downarrow \) 27

\(\displaystyle -\frac {3}{5} \int \frac {8 x^5+64 x^4+200 x^3+304 x^2+224 x+2 e^x \left (3 x^2+5 x+2\right )-\left (4 x^3+24 x^2+48 x+e^x (x+2)+32\right ) \log \left (\frac {25 e^{-2 x} \left (16 x^4+128 x^3+384 x^2+512 x+e^{2 x}+8 e^x \left (x^2+4 x+4\right )+256\right )}{x^6+8 x^5+24 x^4+32 x^3+16 x^2}\right )+64}{(x+1)^2 (x+2) \left (4 x^2+16 x+e^x+16\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -\frac {3}{5} \int \left (\frac {8 (x+2) x^2}{(x+1) \left (4 x^2+16 x+e^x+16\right )}+\frac {6 x^2-\log \left (\frac {25 e^{-2 x} \left (4 (x+2)^2+e^x\right )^2}{x^2 (x+2)^4}\right ) x+10 x-2 \log \left (\frac {25 e^{-2 x} \left (4 (x+2)^2+e^x\right )^2}{x^2 (x+2)^4}\right )+4}{(x+1)^2 (x+2)}\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle -\frac {3}{5} \left (16 \int \frac {x}{4 x^2+16 x+e^x+16}dx+8 \int \frac {x^2}{4 x^2+16 x+e^x+16}dx+\frac {\log \left (\frac {25 e^{-2 x} \left (4 (x+2)^2+e^x\right )^2}{x^2 (x+2)^4}\right )}{x+1}+2 \log (x)+4 \log (x+2)\right )\)

Input:

Int[(-192 - 672*x - 912*x^2 - 600*x^3 - 192*x^4 - 24*x^5 + E^x*(-12 - 30*x 
 - 18*x^2) + (96 + 144*x + 72*x^2 + 12*x^3 + E^x*(6 + 3*x))*Log[(6400 + 25 
*E^(2*x) + 12800*x + 9600*x^2 + 3200*x^3 + 400*x^4 + E^x*(800 + 800*x + 20 
0*x^2))/(E^(2*x)*(16*x^2 + 32*x^3 + 24*x^4 + 8*x^5 + x^6))])/(160 + 560*x 
+ 760*x^2 + 500*x^3 + 160*x^4 + 20*x^5 + E^x*(10 + 25*x + 20*x^2 + 5*x^3)) 
,x]
 

Output:

$Aborted
 

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(76\) vs. \(2(35)=70\).

Time = 3.38 (sec) , antiderivative size = 77, normalized size of antiderivative = 2.14

method	result	size
parallelrisch	\(\frac {3 \ln \left (\frac {\left (25 \,{\mathrm e}^{2 x}+\left (200 x^{2}+800 x +800\right ) {\mathrm e}^{x}+400 x^{4}+3200 x^{3}+9600 x^{2}+12800 x +6400\right ) {\mathrm e}^{-2 x}}{x^{2} \left (x^{4}+8 x^{3}+24 x^{2}+32 x +16\right )}\right ) x}{5 \left (1+x \right )}\)	\(77\)
risch	\(\text {Expression too large to display}\)	\(1110\)

Input:

int(((exp(x)*(6+3*x)+12*x^3+72*x^2+144*x+96)*ln((25*exp(x)^2+(200*x^2+800* 
x+800)*exp(x)+400*x^4+3200*x^3+9600*x^2+12800*x+6400)/(x^6+8*x^5+24*x^4+32 
*x^3+16*x^2)/exp(x)^2)+(-18*x^2-30*x-12)*exp(x)-24*x^5-192*x^4-600*x^3-912 
*x^2-672*x-192)/((5*x^3+20*x^2+25*x+10)*exp(x)+20*x^5+160*x^4+500*x^3+760* 
x^2+560*x+160),x,method=_RETURNVERBOSE)
 

Output:

3/5*ln((25*exp(x)^2+(200*x^2+800*x+800)*exp(x)+400*x^4+3200*x^3+9600*x^2+1 
2800*x+6400)/x^2/(x^4+8*x^3+24*x^2+32*x+16)/exp(x)^2)*x/(1+x)
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 77 vs. \(2 (29) = 58\).

Time = 0.10 (sec) , antiderivative size = 77, normalized size of antiderivative = 2.14 \[ \int \frac {-192-672 x-912 x^2-600 x^3-192 x^4-24 x^5+e^x \left (-12-30 x-18 x^2\right )+\left (96+144 x+72 x^2+12 x^3+e^x (6+3 x)\right ) \log \left (\frac {e^{-2 x} \left (6400+25 e^{2 x}+12800 x+9600 x^2+3200 x^3+400 x^4+e^x \left (800+800 x+200 x^2\right )\right )}{16 x^2+32 x^3+24 x^4+8 x^5+x^6}\right )}{160+560 x+760 x^2+500 x^3+160 x^4+20 x^5+e^x \left (10+25 x+20 x^2+5 x^3\right )} \, dx=\frac {3 \, x \log \left (\frac {25 \, {\left (16 \, x^{4} + 128 \, x^{3} + 384 \, x^{2} + 8 \, {\left (x^{2} + 4 \, x + 4\right )} e^{x} + 512 \, x + e^{\left (2 \, x\right )} + 256\right )} e^{\left (-2 \, x\right )}}{x^{6} + 8 \, x^{5} + 24 \, x^{4} + 32 \, x^{3} + 16 \, x^{2}}\right )}{5 \, {\left (x + 1\right )}} \] Input:

integrate(((exp(x)*(6+3*x)+12*x^3+72*x^2+144*x+96)*log((25*exp(x)^2+(200*x 
^2+800*x+800)*exp(x)+400*x^4+3200*x^3+9600*x^2+12800*x+6400)/(x^6+8*x^5+24 
*x^4+32*x^3+16*x^2)/exp(x)^2)+(-18*x^2-30*x-12)*exp(x)-24*x^5-192*x^4-600* 
x^3-912*x^2-672*x-192)/((5*x^3+20*x^2+25*x+10)*exp(x)+20*x^5+160*x^4+500*x 
^3+760*x^2+560*x+160),x, algorithm="fricas")
 

Output:

3/5*x*log(25*(16*x^4 + 128*x^3 + 384*x^2 + 8*(x^2 + 4*x + 4)*e^x + 512*x + 
 e^(2*x) + 256)*e^(-2*x)/(x^6 + 8*x^5 + 24*x^4 + 32*x^3 + 16*x^2))/(x + 1)
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 105 vs. \(2 (27) = 54\).

Time = 0.63 (sec) , antiderivative size = 105, normalized size of antiderivative = 2.92 \[ \int \frac {-192-672 x-912 x^2-600 x^3-192 x^4-24 x^5+e^x \left (-12-30 x-18 x^2\right )+\left (96+144 x+72 x^2+12 x^3+e^x (6+3 x)\right ) \log \left (\frac {e^{-2 x} \left (6400+25 e^{2 x}+12800 x+9600 x^2+3200 x^3+400 x^4+e^x \left (800+800 x+200 x^2\right )\right )}{16 x^2+32 x^3+24 x^4+8 x^5+x^6}\right )}{160+560 x+760 x^2+500 x^3+160 x^4+20 x^5+e^x \left (10+25 x+20 x^2+5 x^3\right )} \, dx=- \frac {6 \log {\left (x \right )}}{5} + \frac {6 \log {\left (e^{- x} + \frac {1}{4 x^{2} + 16 x + 16} \right )}}{5} - \frac {3 \log {\left (\frac {\left (400 x^{4} + 3200 x^{3} + 9600 x^{2} + 12800 x + \left (200 x^{2} + 800 x + 800\right ) e^{x} + 25 e^{2 x} + 6400\right ) e^{- 2 x}}{x^{6} + 8 x^{5} + 24 x^{4} + 32 x^{3} + 16 x^{2}} \right )}}{5 x + 5} \] Input:

integrate(((exp(x)*(6+3*x)+12*x**3+72*x**2+144*x+96)*ln((25*exp(x)**2+(200 
*x**2+800*x+800)*exp(x)+400*x**4+3200*x**3+9600*x**2+12800*x+6400)/(x**6+8 
*x**5+24*x**4+32*x**3+16*x**2)/exp(x)**2)+(-18*x**2-30*x-12)*exp(x)-24*x** 
5-192*x**4-600*x**3-912*x**2-672*x-192)/((5*x**3+20*x**2+25*x+10)*exp(x)+2 
0*x**5+160*x**4+500*x**3+760*x**2+560*x+160),x)
 

Output:

-6*log(x)/5 + 6*log(exp(-x) + 1/(4*x**2 + 16*x + 16))/5 - 3*log((400*x**4 
+ 3200*x**3 + 9600*x**2 + 12800*x + (200*x**2 + 800*x + 800)*exp(x) + 25*e 
xp(2*x) + 6400)*exp(-2*x)/(x**6 + 8*x**5 + 24*x**4 + 32*x**3 + 16*x**2))/( 
5*x + 5)
 

Maxima [A] (verification not implemented)

Time = 0.27 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.17 \[ \int \frac {-192-672 x-912 x^2-600 x^3-192 x^4-24 x^5+e^x \left (-12-30 x-18 x^2\right )+\left (96+144 x+72 x^2+12 x^3+e^x (6+3 x)\right ) \log \left (\frac {e^{-2 x} \left (6400+25 e^{2 x}+12800 x+9600 x^2+3200 x^3+400 x^4+e^x \left (800+800 x+200 x^2\right )\right )}{16 x^2+32 x^3+24 x^4+8 x^5+x^6}\right )}{160+560 x+760 x^2+500 x^3+160 x^4+20 x^5+e^x \left (10+25 x+20 x^2+5 x^3\right )} \, dx=-\frac {6 \, {\left (x^{2} - x \log \left (4 \, x^{2} + 16 \, x + e^{x} + 16\right ) + 2 \, x \log \left (x + 2\right ) + x \log \left (x\right ) + x + \log \left (5\right ) + 1\right )}}{5 \, {\left (x + 1\right )}} \] Input:

integrate(((exp(x)*(6+3*x)+12*x^3+72*x^2+144*x+96)*log((25*exp(x)^2+(200*x 
^2+800*x+800)*exp(x)+400*x^4+3200*x^3+9600*x^2+12800*x+6400)/(x^6+8*x^5+24 
*x^4+32*x^3+16*x^2)/exp(x)^2)+(-18*x^2-30*x-12)*exp(x)-24*x^5-192*x^4-600* 
x^3-912*x^2-672*x-192)/((5*x^3+20*x^2+25*x+10)*exp(x)+20*x^5+160*x^4+500*x 
^3+760*x^2+560*x+160),x, algorithm="maxima")
 

Output:

-6/5*(x^2 - x*log(4*x^2 + 16*x + e^x + 16) + 2*x*log(x + 2) + x*log(x) + x 
 + log(5) + 1)/(x + 1)
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 143 vs. \(2 (29) = 58\).

Time = 0.32 (sec) , antiderivative size = 143, normalized size of antiderivative = 3.97 \[ \int \frac {-192-672 x-912 x^2-600 x^3-192 x^4-24 x^5+e^x \left (-12-30 x-18 x^2\right )+\left (96+144 x+72 x^2+12 x^3+e^x (6+3 x)\right ) \log \left (\frac {e^{-2 x} \left (6400+25 e^{2 x}+12800 x+9600 x^2+3200 x^3+400 x^4+e^x \left (800+800 x+200 x^2\right )\right )}{16 x^2+32 x^3+24 x^4+8 x^5+x^6}\right )}{160+560 x+760 x^2+500 x^3+160 x^4+20 x^5+e^x \left (10+25 x+20 x^2+5 x^3\right )} \, dx=-\frac {3 \, {\left (2 \, x^{2} - 2 \, x \log \left (-4 \, x^{2} - 16 \, x - e^{x} - 16\right ) + 4 \, x \log \left (x + 2\right ) + 2 \, x \log \left (x\right ) + 2 \, x - 2 \, \log \left (-4 \, x^{2} - 16 \, x - e^{x} - 16\right ) + 4 \, \log \left (x + 2\right ) + 2 \, \log \left (x\right ) + \log \left (\frac {25 \, {\left (16 \, x^{4} + 128 \, x^{3} + 8 \, x^{2} e^{x} + 384 \, x^{2} + 32 \, x e^{x} + 512 \, x + e^{\left (2 \, x\right )} + 32 \, e^{x} + 256\right )}}{x^{6} + 8 \, x^{5} + 24 \, x^{4} + 32 \, x^{3} + 16 \, x^{2}}\right ) + 2\right )}}{5 \, {\left (x + 1\right )}} \] Input:

integrate(((exp(x)*(6+3*x)+12*x^3+72*x^2+144*x+96)*log((25*exp(x)^2+(200*x 
^2+800*x+800)*exp(x)+400*x^4+3200*x^3+9600*x^2+12800*x+6400)/(x^6+8*x^5+24 
*x^4+32*x^3+16*x^2)/exp(x)^2)+(-18*x^2-30*x-12)*exp(x)-24*x^5-192*x^4-600* 
x^3-912*x^2-672*x-192)/((5*x^3+20*x^2+25*x+10)*exp(x)+20*x^5+160*x^4+500*x 
^3+760*x^2+560*x+160),x, algorithm="giac")
 

Output:

-3/5*(2*x^2 - 2*x*log(-4*x^2 - 16*x - e^x - 16) + 4*x*log(x + 2) + 2*x*log 
(x) + 2*x - 2*log(-4*x^2 - 16*x - e^x - 16) + 4*log(x + 2) + 2*log(x) + lo 
g(25*(16*x^4 + 128*x^3 + 8*x^2*e^x + 384*x^2 + 32*x*e^x + 512*x + e^(2*x) 
+ 32*e^x + 256)/(x^6 + 8*x^5 + 24*x^4 + 32*x^3 + 16*x^2)) + 2)/(x + 1)
 

Mupad [F(-1)]

Timed out. \[ \int \frac {-192-672 x-912 x^2-600 x^3-192 x^4-24 x^5+e^x \left (-12-30 x-18 x^2\right )+\left (96+144 x+72 x^2+12 x^3+e^x (6+3 x)\right ) \log \left (\frac {e^{-2 x} \left (6400+25 e^{2 x}+12800 x+9600 x^2+3200 x^3+400 x^4+e^x \left (800+800 x+200 x^2\right )\right )}{16 x^2+32 x^3+24 x^4+8 x^5+x^6}\right )}{160+560 x+760 x^2+500 x^3+160 x^4+20 x^5+e^x \left (10+25 x+20 x^2+5 x^3\right )} \, dx=\int -\frac {672\,x-\ln \left (\frac {{\mathrm {e}}^{-2\,x}\,\left (12800\,x+25\,{\mathrm {e}}^{2\,x}+{\mathrm {e}}^x\,\left (200\,x^2+800\,x+800\right )+9600\,x^2+3200\,x^3+400\,x^4+6400\right )}{x^6+8\,x^5+24\,x^4+32\,x^3+16\,x^2}\right )\,\left (144\,x+{\mathrm {e}}^x\,\left (3\,x+6\right )+72\,x^2+12\,x^3+96\right )+{\mathrm {e}}^x\,\left (18\,x^2+30\,x+12\right )+912\,x^2+600\,x^3+192\,x^4+24\,x^5+192}{560\,x+760\,x^2+500\,x^3+160\,x^4+20\,x^5+{\mathrm {e}}^x\,\left (5\,x^3+20\,x^2+25\,x+10\right )+160} \,d x \] Input:

int(-(672*x - log((exp(-2*x)*(12800*x + 25*exp(2*x) + exp(x)*(800*x + 200* 
x^2 + 800) + 9600*x^2 + 3200*x^3 + 400*x^4 + 6400))/(16*x^2 + 32*x^3 + 24* 
x^4 + 8*x^5 + x^6))*(144*x + exp(x)*(3*x + 6) + 72*x^2 + 12*x^3 + 96) + ex 
p(x)*(30*x + 18*x^2 + 12) + 912*x^2 + 600*x^3 + 192*x^4 + 24*x^5 + 192)/(5 
60*x + 760*x^2 + 500*x^3 + 160*x^4 + 20*x^5 + exp(x)*(25*x + 20*x^2 + 5*x^ 
3 + 10) + 160),x)
 

Output:

int(-(672*x - log((exp(-2*x)*(12800*x + 25*exp(2*x) + exp(x)*(800*x + 200* 
x^2 + 800) + 9600*x^2 + 3200*x^3 + 400*x^4 + 6400))/(16*x^2 + 32*x^3 + 24* 
x^4 + 8*x^5 + x^6))*(144*x + exp(x)*(3*x + 6) + 72*x^2 + 12*x^3 + 96) + ex 
p(x)*(30*x + 18*x^2 + 12) + 912*x^2 + 600*x^3 + 192*x^4 + 24*x^5 + 192)/(5 
60*x + 760*x^2 + 500*x^3 + 160*x^4 + 20*x^5 + exp(x)*(25*x + 20*x^2 + 5*x^ 
3 + 10) + 160), x)
 

Reduce [F]

\[ \int \frac {-192-672 x-912 x^2-600 x^3-192 x^4-24 x^5+e^x \left (-12-30 x-18 x^2\right )+\left (96+144 x+72 x^2+12 x^3+e^x (6+3 x)\right ) \log \left (\frac {e^{-2 x} \left (6400+25 e^{2 x}+12800 x+9600 x^2+3200 x^3+400 x^4+e^x \left (800+800 x+200 x^2\right )\right )}{16 x^2+32 x^3+24 x^4+8 x^5+x^6}\right )}{160+560 x+760 x^2+500 x^3+160 x^4+20 x^5+e^x \left (10+25 x+20 x^2+5 x^3\right )} \, dx =\text {Too large to display} \] Input:

int(((exp(x)*(6+3*x)+12*x^3+72*x^2+144*x+96)*log((25*exp(x)^2+(200*x^2+800 
*x+800)*exp(x)+400*x^4+3200*x^3+9600*x^2+12800*x+6400)/(x^6+8*x^5+24*x^4+3 
2*x^3+16*x^2)/exp(x)^2)+(-18*x^2-30*x-12)*exp(x)-24*x^5-192*x^4-600*x^3-91 
2*x^2-672*x-192)/((5*x^3+20*x^2+25*x+10)*exp(x)+20*x^5+160*x^4+500*x^3+760 
*x^2+560*x+160),x)
 

Output:

(3*( - 24*int(x**4/(e**x*x**3 + 4*e**x*x**2 + 5*e**x*x + 2*e**x + 4*x**5 + 
 32*x**4 + 100*x**3 + 152*x**2 + 112*x + 32),x)*x - 24*int(x**4/(e**x*x**3 
 + 4*e**x*x**2 + 5*e**x*x + 2*e**x + 4*x**5 + 32*x**4 + 100*x**3 + 152*x** 
2 + 112*x + 32),x) - 136*int(x**3/(e**x*x**3 + 4*e**x*x**2 + 5*e**x*x + 2* 
e**x + 4*x**5 + 32*x**4 + 100*x**3 + 152*x**2 + 112*x + 32),x)*x - 136*int 
(x**3/(e**x*x**3 + 4*e**x*x**2 + 5*e**x*x + 2*e**x + 4*x**5 + 32*x**4 + 10 
0*x**3 + 152*x**2 + 112*x + 32),x) + 24*int(x**3/(e**x*x**2 + 2*e**x*x + e 
**x + 4*x**4 + 24*x**3 + 52*x**2 + 48*x + 16),x)*x + 24*int(x**3/(e**x*x** 
2 + 2*e**x*x + e**x + 4*x**4 + 24*x**3 + 52*x**2 + 48*x + 16),x) - 272*int 
(x**2/(e**x*x**3 + 4*e**x*x**2 + 5*e**x*x + 2*e**x + 4*x**5 + 32*x**4 + 10 
0*x**3 + 152*x**2 + 112*x + 32),x)*x - 272*int(x**2/(e**x*x**3 + 4*e**x*x* 
*2 + 5*e**x*x + 2*e**x + 4*x**5 + 32*x**4 + 100*x**3 + 152*x**2 + 112*x + 
32),x) + 88*int(x**2/(e**x*x**2 + 2*e**x*x + e**x + 4*x**4 + 24*x**3 + 52* 
x**2 + 48*x + 16),x)*x + 88*int(x**2/(e**x*x**2 + 2*e**x*x + e**x + 4*x**4 
 + 24*x**3 + 52*x**2 + 48*x + 16),x) - 224*int(x/(e**x*x**3 + 4*e**x*x**2 
+ 5*e**x*x + 2*e**x + 4*x**5 + 32*x**4 + 100*x**3 + 152*x**2 + 112*x + 32) 
,x)*x - 224*int(x/(e**x*x**3 + 4*e**x*x**2 + 5*e**x*x + 2*e**x + 4*x**5 + 
32*x**4 + 100*x**3 + 152*x**2 + 112*x + 32),x) + 96*int(x/(e**x*x**2 + 2*e 
**x*x + e**x + 4*x**4 + 24*x**3 + 52*x**2 + 48*x + 16),x)*x + 96*int(x/(e* 
*x*x**2 + 2*e**x*x + e**x + 4*x**4 + 24*x**3 + 52*x**2 + 48*x + 16),x) ...