\(\int \frac {7198-28800 x+e^x (3150-10800 x-7200 x^2)}{91125000-2186392500 x+21860281350 x^2-116581690799 x^3+349764501600 x^4-559716480000 x^5+373248000000 x^6+e^{3 x} (11390625-273375000 x+2733750000 x^2-14580000000 x^3+43740000000 x^4-69984000000 x^5+46656000000 x^6)+e^{2 x} (68343750-1640098125 x+16400070000 x^2-87465420000 x^3+262401120000 x^4-419865120000 x^5+279936000000 x^6)+e^x (136687500-3279892500 x+32795280675 x^2-174901685400 x^3+524724490800 x^4-839652480000 x^5+559872000000 x^6)} \, dx\) [99]

Optimal result

Integrand size = 158, antiderivative size = 25 \[ \int \frac {7198-28800 x+e^x \left (3150-10800 x-7200 x^2\right )}{91125000-2186392500 x+21860281350 x^2-116581690799 x^3+349764501600 x^4-559716480000 x^5+373248000000 x^6+e^{3 x} \left (11390625-273375000 x+2733750000 x^2-14580000000 x^3+43740000000 x^4-69984000000 x^5+46656000000 x^6\right )+e^{2 x} \left (68343750-1640098125 x+16400070000 x^2-87465420000 x^3+262401120000 x^4-419865120000 x^5+279936000000 x^6\right )+e^x \left (136687500-3279892500 x+32795280675 x^2-174901685400 x^3+524724490800 x^4-839652480000 x^5+559872000000 x^6\right )} \, dx=\frac {1}{\left (x+\frac {225 \left (2+e^x\right ) \left (-x+4 x^2\right )^2}{x^2}\right )^2} \] Output:

1/(x+225*(4*x^2-x)^2/x^2*(2+exp(x)))^2
                                                                                    
                                                                                    
 

Mathematica [A] (verified)

Time = 0.09 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.96 \[ \int \frac {7198-28800 x+e^x \left (3150-10800 x-7200 x^2\right )}{91125000-2186392500 x+21860281350 x^2-116581690799 x^3+349764501600 x^4-559716480000 x^5+373248000000 x^6+e^{3 x} \left (11390625-273375000 x+2733750000 x^2-14580000000 x^3+43740000000 x^4-69984000000 x^5+46656000000 x^6\right )+e^{2 x} \left (68343750-1640098125 x+16400070000 x^2-87465420000 x^3+262401120000 x^4-419865120000 x^5+279936000000 x^6\right )+e^x \left (136687500-3279892500 x+32795280675 x^2-174901685400 x^3+524724490800 x^4-839652480000 x^5+559872000000 x^6\right )} \, dx=\frac {1}{\left (450+225 e^x (1-4 x)^2-3599 x+7200 x^2\right )^2} \] Input:

Integrate[(7198 - 28800*x + E^x*(3150 - 10800*x - 7200*x^2))/(91125000 - 2 
186392500*x + 21860281350*x^2 - 116581690799*x^3 + 349764501600*x^4 - 5597 
16480000*x^5 + 373248000000*x^6 + E^(3*x)*(11390625 - 273375000*x + 273375 
0000*x^2 - 14580000000*x^3 + 43740000000*x^4 - 69984000000*x^5 + 466560000 
00*x^6) + E^(2*x)*(68343750 - 1640098125*x + 16400070000*x^2 - 87465420000 
*x^3 + 262401120000*x^4 - 419865120000*x^5 + 279936000000*x^6) + E^x*(1366 
87500 - 3279892500*x + 32795280675*x^2 - 174901685400*x^3 + 524724490800*x 
^4 - 839652480000*x^5 + 559872000000*x^6)),x]
 

Output:

(450 + 225*E^x*(1 - 4*x)^2 - 3599*x + 7200*x^2)^(-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.

\(\displaystyle \int \frac {e^x \left (-7200 x^2-10800 x+3150\right )-28800 x+7198}{373248000000 x^6-559716480000 x^5+349764501600 x^4-116581690799 x^3+21860281350 x^2+e^{3 x} \left (46656000000 x^6-69984000000 x^5+43740000000 x^4-14580000000 x^3+2733750000 x^2-273375000 x+11390625\right )+e^{2 x} \left (279936000000 x^6-419865120000 x^5+262401120000 x^4-87465420000 x^3+16400070000 x^2-1640098125 x+68343750\right )+e^x \left (559872000000 x^6-839652480000 x^5+524724490800 x^4-174901685400 x^3+32795280675 x^2-3279892500 x+136687500\right )-2186392500 x+91125000} \, dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {-450 e^x \left (16 x^2+24 x-7\right )-28800 x+7198}{\left (7200 x^2+225 e^x (1-4 x)^2-3599 x+450\right )^3}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {2 \left (28800 x^3-21596 x^2+5403 x-449\right )}{(4 x-1) \left (3600 e^x x^2+7200 x^2-1800 e^x x-3599 x+225 e^x+450\right )^3}-\frac {2 (4 x+7)}{(4 x-1) \left (3600 e^x x^2+7200 x^2-1800 e^x x-3599 x+225 e^x+450\right )^2}\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle 902 \int \frac {1}{\left (3600 e^x x^2+7200 x^2-1800 e^x x-3599 x+225 e^x+450\right )^3}dx-7198 \int \frac {x}{\left (3600 e^x x^2+7200 x^2-1800 e^x x-3599 x+225 e^x+450\right )^3}dx+14400 \int \frac {x^2}{\left (3600 e^x x^2+7200 x^2-1800 e^x x-3599 x+225 e^x+450\right )^3}dx+4 \int \frac {1}{(4 x-1) \left (3600 e^x x^2+7200 x^2-1800 e^x x-3599 x+225 e^x+450\right )^3}dx-2 \int \frac {1}{\left (3600 e^x x^2+7200 x^2-1800 e^x x-3599 x+225 e^x+450\right )^2}dx-16 \int \frac {1}{(4 x-1) \left (3600 e^x x^2+7200 x^2-1800 e^x x-3599 x+225 e^x+450\right )^2}dx\)

Input:

Int[(7198 - 28800*x + E^x*(3150 - 10800*x - 7200*x^2))/(91125000 - 2186392 
500*x + 21860281350*x^2 - 116581690799*x^3 + 349764501600*x^4 - 5597164800 
00*x^5 + 373248000000*x^6 + E^(3*x)*(11390625 - 273375000*x + 2733750000*x 
^2 - 14580000000*x^3 + 43740000000*x^4 - 69984000000*x^5 + 46656000000*x^6 
) + E^(2*x)*(68343750 - 1640098125*x + 16400070000*x^2 - 87465420000*x^3 + 
 262401120000*x^4 - 419865120000*x^5 + 279936000000*x^6) + E^x*(136687500 
- 3279892500*x + 32795280675*x^2 - 174901685400*x^3 + 524724490800*x^4 - 8 
39652480000*x^5 + 559872000000*x^6)),x]
 

Output:

$Aborted
 

Maple [A] (verified)

Time = 0.38 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.16

method	result	size
norman	\(\frac {1}{\left (3600 \,{\mathrm e}^{x} x^{2}-1800 \,{\mathrm e}^{x} x +7200 x^{2}+225 \,{\mathrm e}^{x}-3599 x +450\right )^{2}}\)	\(29\)
risch	\(\frac {1}{\left (3600 \,{\mathrm e}^{x} x^{2}-1800 \,{\mathrm e}^{x} x +7200 x^{2}+225 \,{\mathrm e}^{x}-3599 x +450\right )^{2}}\)	\(29\)
parallelrisch	\(\frac {1}{12960000 \,{\mathrm e}^{2 x} x^{4}[phone] \,{\mathrm e}^{x} x^{4}-12960000 \,{\mathrm e}^{2 x} x^{3}[phone] x^{4}-51832800 \,{\mathrm e}^{x} x^{3}+4860000 \,{\mathrm e}^{2 x} x^{2}-51825600 x^{3}[phone] \,{\mathrm e}^{x} x^{2}-810000 x \,{\mathrm e}^{2 x}[phone] x^{2}-3239550 \,{\mathrm e}^{x} x +50625 \,{\mathrm e}^{2 x}-3239100 x +202500 \,{\mathrm e}^{x}+202500}\)	\(93\)

Input:

int(((-7200*x^2-10800*x+3150)*exp(x)-28800*x+7198)/((46656000000*x^6-69984 
000000*x^5+43740000000*x^4-14580000000*x^3+2733750000*x^2-273375000*x+1139 
0625)*exp(x)^3+(279936000000*x^6-419865120000*x^5+262401120000*x^4-8746542 
0000*x^3+16400070000*x^2-1640098125*x[phone])*exp(x)^2+(559872000000*x^6 
-839652480000*x^5+524724490800*x^4-174901685400*x^3+32795280675*x^2-327989 
2500*x[phone])*exp(x)[phone]*x^6-559716480000*x^5+349764501600*x^ 
4-116581690799*x^3+21860281350*x^2-2186392500*x[phone]),x,method=_RETURN 
VERBOSE)
 

Output:

1/(3600*exp(x)*x^2-1800*exp(x)*x+7200*x^2+225*exp(x)-3599*x+450)^2
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 72 vs. \(2 (24) = 48\).

Time = 0.09 (sec) , antiderivative size = 72, normalized size of antiderivative = 2.88 \[ \int \frac {7198-28800 x+e^x \left (3150-10800 x-7200 x^2\right )}{91125000-2186392500 x+21860281350 x^2-116581690799 x^3+349764501600 x^4-559716480000 x^5+373248000000 x^6+e^{3 x} \left (11390625-273375000 x+2733750000 x^2-14580000000 x^3+43740000000 x^4-69984000000 x^5+46656000000 x^6\right )+e^{2 x} \left (68343750-1640098125 x+16400070000 x^2-87465420000 x^3+262401120000 x^4-419865120000 x^5+279936000000 x^6\right )+e^x \left (136687500-3279892500 x+32795280675 x^2-174901685400 x^3+524724490800 x^4-839652480000 x^5+559872000000 x^6\right )} \, dx=\frac {1}{51840000 \, x^{4} - 51825600 \, x^{3} + 19432801 \, x^{2} + 50625 \, {\left (256 \, x^{4} - 256 \, x^{3} + 96 \, x^{2} - 16 \, x + 1\right )} e^{\left (2 \, x\right )} + 450 \, {\left (115200 \, x^{4} - 115184 \, x^{3} + 43192 \, x^{2} - 7199 \, x + 450\right )} e^{x} - 3239100 \, x + 202500} \] Input:

integrate(((-7200*x^2-10800*x+3150)*exp(x)-28800*x+7198)/((46656000000*x^6 
-69984000000*x^5+43740000000*x^4-14580000000*x^3+2733750000*x^2-273375000* 
x[phone])*exp(x)^3+(279936000000*x^6-419865120000*x^5+262401120000*x^4-8 
7465420000*x^3+16400070000*x^2-1640098125*x[phone])*exp(x)^2+(5598720000 
00*x^6-839652480000*x^5+524724490800*x^4-174901685400*x^3+32795280675*x^2- 
3279892500*x[phone])*exp(x)[phone]*x^6-559716480000*x^5+349764501 
600*x^4-116581690799*x^3+21860281350*x^2-2186392500*x[phone]),x, algorit 
hm="fricas")
 

Output:

1/(51840000*x^4 - 51825600*x^3 + 19432801*x^2 + 50625*(256*x^4 - 256*x^3 + 
 96*x^2 - 16*x + 1)*e^(2*x) + 450*(115200*x^4 - 115184*x^3 + 43192*x^2 - 7 
199*x + 450)*e^x - 3239100*x + 202500)
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 70 vs. \(2 (22) = 44\).

Time = 0.35 (sec) , antiderivative size = 70, normalized size of antiderivative = 2.80 \[ \int \frac {7198-28800 x+e^x \left (3150-10800 x-7200 x^2\right )}{91125000-2186392500 x+21860281350 x^2-116581690799 x^3+349764501600 x^4-559716480000 x^5+373248000000 x^6+e^{3 x} \left (11390625-273375000 x+2733750000 x^2-14580000000 x^3+43740000000 x^4-69984000000 x^5+46656000000 x^6\right )+e^{2 x} \left (68343750-1640098125 x+16400070000 x^2-87465420000 x^3+262401120000 x^4-419865120000 x^5+279936000000 x^6\right )+e^x \left (136687500-3279892500 x+32795280675 x^2-174901685400 x^3+524724490800 x^4-839652480000 x^5+559872000000 x^6\right )} \, dx=\frac {1}{51840000 x^{4} - 51825600 x^{3} + 19432801 x^{2} - 3239100 x + \left (12960000 x^{4} - 12960000 x^{3} + 4860000 x^{2} - 810000 x + 50625\right ) e^{2 x} + \left (51840000 x^{4} - 51832800 x^{3} + 19436400 x^{2} - 3239550 x + 202500\right ) e^{x} + 202500} \] Input:

integrate(((-7200*x**2-10800*x+3150)*exp(x)-28800*x+7198)/((46656000000*x* 
*6-69984000000*x**5+43740000000*x**4-14580000000*x**3+2733750000*x**2-2733 
75000*x[phone])*exp(x)**3+(279936000000*x**6-419865120000*x**5+262401120 
000*x**4-87465420000*x**3+16400070000*x**2-1640098125*x[phone])*exp(x)** 
2+(559872000000*x**6-839652480000*x**5+524724490800*x**4-174901685400*x**3 
[phone]*x**2-3279892500*x[phone])*exp(x)[phone]*x**6-5597164 
80000*x**5+349764501600*x**4-116581690799*x**3+21860281350*x**2-2186392500 
*x[phone]),x)
 

Output:

1/(51840000*x**4 - 51825600*x**3 + 19432801*x**2 - 3239100*x + (12960000*x 
**4 - 12960000*x**3 + 4860000*x**2 - 810000*x + 50625)*exp(2*x) + (5184000 
0*x**4 - 51832800*x**3 + 19436400*x**2 - 3239550*x + 202500)*exp(x) + 2025 
00)
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 72 vs. \(2 (24) = 48\).

Time = 0.23 (sec) , antiderivative size = 72, normalized size of antiderivative = 2.88 \[ \int \frac {7198-28800 x+e^x \left (3150-10800 x-7200 x^2\right )}{91125000-2186392500 x+21860281350 x^2-116581690799 x^3+349764501600 x^4-559716480000 x^5+373248000000 x^6+e^{3 x} \left (11390625-273375000 x+2733750000 x^2-14580000000 x^3+43740000000 x^4-69984000000 x^5+46656000000 x^6\right )+e^{2 x} \left (68343750-1640098125 x+16400070000 x^2-87465420000 x^3+262401120000 x^4-419865120000 x^5+279936000000 x^6\right )+e^x \left (136687500-3279892500 x+32795280675 x^2-174901685400 x^3+524724490800 x^4-839652480000 x^5+559872000000 x^6\right )} \, dx=\frac {1}{51840000 \, x^{4} - 51825600 \, x^{3} + 19432801 \, x^{2} + 50625 \, {\left (256 \, x^{4} - 256 \, x^{3} + 96 \, x^{2} - 16 \, x + 1\right )} e^{\left (2 \, x\right )} + 450 \, {\left (115200 \, x^{4} - 115184 \, x^{3} + 43192 \, x^{2} - 7199 \, x + 450\right )} e^{x} - 3239100 \, x + 202500} \] Input:

integrate(((-7200*x^2-10800*x+3150)*exp(x)-28800*x+7198)/((46656000000*x^6 
-69984000000*x^5+43740000000*x^4-14580000000*x^3+2733750000*x^2-273375000* 
x[phone])*exp(x)^3+(279936000000*x^6-419865120000*x^5+262401120000*x^4-8 
7465420000*x^3+16400070000*x^2-1640098125*x[phone])*exp(x)^2+(5598720000 
00*x^6-839652480000*x^5+524724490800*x^4-174901685400*x^3+32795280675*x^2- 
3279892500*x[phone])*exp(x)[phone]*x^6-559716480000*x^5+349764501 
600*x^4-116581690799*x^3+21860281350*x^2-2186392500*x[phone]),x, algorit 
hm="maxima")
 

Output:

1/(51840000*x^4 - 51825600*x^3 + 19432801*x^2 + 50625*(256*x^4 - 256*x^3 + 
 96*x^2 - 16*x + 1)*e^(2*x) + 450*(115200*x^4 - 115184*x^3 + 43192*x^2 - 7 
199*x + 450)*e^x - 3239100*x + 202500)
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 92 vs. \(2 (24) = 48\).

Time = 0.14 (sec) , antiderivative size = 92, normalized size of antiderivative = 3.68 \[ \int \frac {7198-28800 x+e^x \left (3150-10800 x-7200 x^2\right )}{91125000-2186392500 x+21860281350 x^2-116581690799 x^3+349764501600 x^4-559716480000 x^5+373248000000 x^6+e^{3 x} \left (11390625-273375000 x+2733750000 x^2-14580000000 x^3+43740000000 x^4-69984000000 x^5+46656000000 x^6\right )+e^{2 x} \left (68343750-1640098125 x+16400070000 x^2-87465420000 x^3+262401120000 x^4-419865120000 x^5+279936000000 x^6\right )+e^x \left (136687500-3279892500 x+32795280675 x^2-174901685400 x^3+524724490800 x^4-839652480000 x^5+559872000000 x^6\right )} \, dx=\frac {1}{12960000 \, x^{4} e^{\left (2 \, x\right )} + 51840000 \, x^{4} e^{x} + 51840000 \, x^{4} - 12960000 \, x^{3} e^{\left (2 \, x\right )} - 51832800 \, x^{3} e^{x} - 51825600 \, x^{3} + 4860000 \, x^{2} e^{\left (2 \, x\right )} + 19436400 \, x^{2} e^{x} + 19432801 \, x^{2} - 810000 \, x e^{\left (2 \, x\right )} - 3239550 \, x e^{x} - 3239100 \, x + 50625 \, e^{\left (2 \, x\right )} + 202500 \, e^{x} + 202500} \] Input:

integrate(((-7200*x^2-10800*x+3150)*exp(x)-28800*x+7198)/((46656000000*x^6 
-69984000000*x^5+43740000000*x^4-14580000000*x^3+2733750000*x^2-273375000* 
x[phone])*exp(x)^3+(279936000000*x^6-419865120000*x^5+262401120000*x^4-8 
7465420000*x^3+16400070000*x^2-1640098125*x[phone])*exp(x)^2+(5598720000 
00*x^6-839652480000*x^5+524724490800*x^4-174901685400*x^3+32795280675*x^2- 
3279892500*x[phone])*exp(x)[phone]*x^6-559716480000*x^5+349764501 
600*x^4-116581690799*x^3+21860281350*x^2-2186392500*x[phone]),x, algorit 
hm="giac")
 

Output:

1/(12960000*x^4*e^(2*x) + 51840000*x^4*e^x + 51840000*x^4 - 12960000*x^3*e 
^(2*x) - 51832800*x^3*e^x - 51825600*x^3 + 4860000*x^2*e^(2*x) + 19436400* 
x^2*e^x + 19432801*x^2 - 810000*x*e^(2*x) - 3239550*x*e^x - 3239100*x + 50 
625*e^(2*x) + 202500*e^x + 202500)
 

Mupad [F(-1)]

Timed out. \[ \int \frac {7198-28800 x+e^x \left (3150-10800 x-7200 x^2\right )}{91125000-2186392500 x+21860281350 x^2-116581690799 x^3+349764501600 x^4-559716480000 x^5+373248000000 x^6+e^{3 x} \left (11390625-273375000 x+2733750000 x^2-14580000000 x^3+43740000000 x^4-69984000000 x^5+46656000000 x^6\right )+e^{2 x} \left (68343750-1640098125 x+16400070000 x^2-87465420000 x^3+262401120000 x^4-419865120000 x^5+279936000000 x^6\right )+e^x \left (136687500-3279892500 x+32795280675 x^2-174901685400 x^3+524724490800 x^4-839652480000 x^5+559872000000 x^6\right )} \, dx=\int -\frac {28800\,x+{\mathrm {e}}^x\,\left (7200\,x^2+10800\,x-3150\right )-7198}{{\mathrm {e}}^{3\,x}\,\left (46656000000\,x^6-69984000000\,x^5+43740000000\,x^4-14580000000\,x^3+2733750000\,x^2-273375000\,x+11390625\right )-2186392500\,x+{\mathrm {e}}^{2\,x}\,\left (279936000000\,x^6-419865120000\,x^5+262401120000\,x^4-87465420000\,x^3+16400070000\,x^2-1640098125\,x+68343750\right )+{\mathrm {e}}^x\,\left (559872000000\,x^6-839652480000\,x^5+524724490800\,x^4-174901685400\,x^3+32795280675\,x^2-3279892500\,x+136687500\right )[phone]\,x^2-116581690799\,x^3+349764501600\,x^4-559716480000\,x^5+373248000000\,x^6+91125000} \,d x \] Input:

int(-(28800*x + exp(x)*(10800*x + 7200*x^2 - 3150) - 7198)/(exp(3*x)*(2733 
750000*x^2 - 273375000*x - 14580000000*x^3 + 43740000000*x^4 - 69984000000 
*x^5 + 46656000000*x^6 + 11390625) - 2186392500*x + exp(2*x)*(16400070000* 
x^2 - 1640098125*x - 87465420000*x^3 + 262401120000*x^4 - 419865120000*x^5 
 + 279936000000*x^6 + 68343750) + exp(x)*(32795280675*x^2 - 3279892500*x - 
 174901685400*x^3 + 524724490800*x^4 - 839652480000*x^5 + 559872000000*x^6 
 + 136687500) + 21860281350*x^2 - 116581690799*x^3 + 349764501600*x^4 - 55 
9716480000*x^5 + 373248000000*x^6 + 91125000),x)
 

Output:

int(-(28800*x + exp(x)*(10800*x + 7200*x^2 - 3150) - 7198)/(exp(3*x)*(2733 
750000*x^2 - 273375000*x - 14580000000*x^3 + 43740000000*x^4 - 69984000000 
*x^5 + 46656000000*x^6 + 11390625) - 2186392500*x + exp(2*x)*(16400070000* 
x^2 - 1640098125*x - 87465420000*x^3 + 262401120000*x^4 - 419865120000*x^5 
 + 279936000000*x^6 + 68343750) + exp(x)*(32795280675*x^2 - 3279892500*x - 
 174901685400*x^3 + 524724490800*x^4 - 839652480000*x^5 + 559872000000*x^6 
 + 136687500) + 21860281350*x^2 - 116581690799*x^3 + 349764501600*x^4 - 55 
9716480000*x^5 + 373248000000*x^6 + 91125000), x)
 

Reduce [B] (verification not implemented)

Time = 0.15 (sec) , antiderivative size = 102, normalized size of antiderivative = 4.08 \[ \int \frac {7198-28800 x+e^x \left (3150-10800 x-7200 x^2\right )}{91125000-2186392500 x+21860281350 x^2-116581690799 x^3+349764501600 x^4-559716480000 x^5+373248000000 x^6+e^{3 x} \left (11390625-273375000 x+2733750000 x^2-14580000000 x^3+43740000000 x^4-69984000000 x^5+46656000000 x^6\right )+e^{2 x} \left (68343750-1640098125 x+16400070000 x^2-87465420000 x^3+262401120000 x^4-419865120000 x^5+279936000000 x^6\right )+e^x \left (136687500-3279892500 x+32795280675 x^2-174901685400 x^3+524724490800 x^4-839652480000 x^5+559872000000 x^6\right )} \, dx=\frac {1}{12960000 e^{2 x} x^{4}-12960000 e^{2 x} x^{3}+4860000 e^{2 x} x^{2}-810000 e^{2 x} x +50625 e^{2 x}[phone] e^{x} x^{4}-51832800 e^{x} x^{3}[phone] e^{x} x^{2}-3239550 e^{x} x +202500 e^{x}[phone] x^{4}-51825600 x^{3}[phone] x^{2}-3239100 x +202500} \] Input:

int(((-7200*x^2-10800*x+3150)*exp(x)-28800*x+7198)/((46656000000*x^6-69984 
000000*x^5+43740000000*x^4-14580000000*x^3+2733750000*x^2-273375000*x+1139 
0625)*exp(x)^3+(279936000000*x^6-419865120000*x^5+262401120000*x^4-8746542 
0000*x^3+16400070000*x^2-1640098125*x[phone])*exp(x)^2+(559872000000*x^6 
-839652480000*x^5+524724490800*x^4-174901685400*x^3+32795280675*x^2-327989 
2500*x[phone])*exp(x)[phone]*x^6-559716480000*x^5+349764501600*x^ 
4-116581690799*x^3+21860281350*x^2-2186392500*x[phone]),x)
 

Output:

1/(12960000*e**(2*x)*x**4 - 12960000*e**(2*x)*x**3 + 4860000*e**(2*x)*x**2 
 - 810000*e**(2*x)*x + 50625*e**(2*x) + 51840000*e**x*x**4 - 51832800*e**x 
*x**3 + 19436400*e**x*x**2 - 3239550*e**x*x + 202500*e**x + 51840000*x**4 
- 51825600*x**3 + 19432801*x**2 - 3239100*x + 202500)