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3.102.24 \(\int \frac {e^x (18-18 x+27 x^2-3 x^3+e^5 (-75 x+15 x^2))}{-7776 x^2-6480 x^4-2160 x^6+3125 e^{25} x^7-360 x^8-30 x^{10}-x^{12}+e^{20} (-18750 x^6-3125 x^8)+e^{15} (45000 x^5+15000 x^7+1250 x^9)+e^{10} (-54000 x^4-27000 x^6-4500 x^8-250 x^{10})+e^5 (32400 x^3+21600 x^5+5400 x^7+600 x^9+25 x^{11})} \, dx\)

Optimal. Leaf size=21 \[ \frac {3 e^x}{x \left (6-5 e^5 x+x^2\right )^4} \]

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Rubi [C]  time = 14.70, antiderivative size = 8979, normalized size of antiderivative = 427.57, number of steps used = 171, number of rules used = 6, integrand size = 163, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.037, Rules used = {6688, 12, 6742, 2177, 2178, 2270}

result too large to display

Antiderivative was successfully verified.

[In]

Int[(E^x*(18 - 18*x + 27*x^2 - 3*x^3 + E^5*(-75*x + 15*x^2)))/(-7776*x^2 - 6480*x^4 - 2160*x^6 + 3125*E^25*x^7
 - 360*x^8 - 30*x^10 - x^12 + E^20*(-18750*x^6 - 3125*x^8) + E^15*(45000*x^5 + 15000*x^7 + 1250*x^9) + E^10*(-
54000*x^4 - 27000*x^6 - 4500*x^8 - 250*x^10) + E^5*(32400*x^3 + 21600*x^5 + 5400*x^7 + 600*x^9 + 25*x^11)),x]

[Out]

(-8*E^x*(12 - 25*E^10))/((-24 + 25*E^10)^(5/2)*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)^4) - (20*E^(5 + x)*(5*E^5 -
 Sqrt[-24 + 25*E^10]))/((-24 + 25*E^10)^(5/2)*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)^4) - (80*E^x*(12 - 25*E^10))
/(3*(24 - 25*E^10)^3*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)^3) + (4*E^x*(12 - 25*E^10))/(3*(-24 + 25*E^10)^(5/2)*
(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)^3) + (2*E^x*(2 + 10*E^5 + 25*E^10))/(3*(24 - 25*E^10)^2*(5*E^5 - Sqrt[-24
+ 25*E^10] - 2*x)^3) - (40*E^(5 + x)*(25*E^5 - 3*Sqrt[-24 + 25*E^10]))/(3*(24 - 25*E^10)^3*(5*E^5 - Sqrt[-24 +
 25*E^10] - 2*x)^3) - (E^x*(2 + 5*E^5)*(5*E^5 - Sqrt[-24 + 25*E^10]))/(3*(24 - 25*E^10)^2*(5*E^5 - Sqrt[-24 +
25*E^10] - 2*x)^3) + (10*E^(5 + x)*(5*E^5 - Sqrt[-24 + 25*E^10]))/(3*(-24 + 25*E^10)^(5/2)*(5*E^5 - Sqrt[-24 +
 25*E^10] - 2*x)^3) + (20*E^x*(12 - 25*E^10))/(3*(24 - 25*E^10)^3*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)^2) - (60
*E^x*(12 - 25*E^10))/((-24 + 25*E^10)^(7/2)*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)^2) - (E^x*(12 - 25*E^10))/(3*(
-24 + 25*E^10)^(5/2)*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)^2) - (E^x*(2 + 10*E^5 + 25*E^10))/(6*(24 - 25*E^10)^2
*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)^2) - (2*E^x*(2 + 10*E^5 + 25*E^10))/((-24 + 25*E^10)^(5/2)*(5*E^5 - Sqrt[
-24 + 25*E^10] - 2*x)^2) + (E^x*(3 + 15*E^5 + 25*E^10))/(18*(-24 + 25*E^10)^(3/2)*(5*E^5 - Sqrt[-24 + 25*E^10]
 - 2*x)^2) + (10*E^(5 + x)*(25*E^5 - 3*Sqrt[-24 + 25*E^10]))/(3*(24 - 25*E^10)^3*(5*E^5 - Sqrt[-24 + 25*E^10]
- 2*x)^2) + (E^x*(2 + 5*E^5)*(5*E^5 - Sqrt[-24 + 25*E^10]))/(12*(24 - 25*E^10)^2*(5*E^5 - Sqrt[-24 + 25*E^10]
- 2*x)^2) - (5*E^(5 + x)*(5*E^5 - Sqrt[-24 + 25*E^10]))/(6*(-24 + 25*E^10)^(5/2)*(5*E^5 - Sqrt[-24 + 25*E^10]
- 2*x)^2) - (E^x*(3 + 5*E^5)*(5*E^5 - Sqrt[-24 + 25*E^10]))/(36*(-24 + 25*E^10)^(3/2)*(5*E^5 - Sqrt[-24 + 25*E
^10] - 2*x)^2) + (E^x*(2 + 5*E^5)*(10*E^5 - Sqrt[-24 + 25*E^10]))/(2*(-24 + 25*E^10)^(5/2)*(5*E^5 - Sqrt[-24 +
 25*E^10] - 2*x)^2) - (50*E^(5 + x)*(15*E^5 - Sqrt[-24 + 25*E^10]))/((-24 + 25*E^10)^(7/2)*(5*E^5 - Sqrt[-24 +
 25*E^10] - 2*x)^2) + (140*E^x*(12 - 25*E^10))/((24 - 25*E^10)^4*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)) - (10*E^
x*(12 - 25*E^10))/(3*(24 - 25*E^10)^3*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)) + (30*E^x*(12 - 25*E^10))/((-24 + 2
5*E^10)^(7/2)*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)) + (E^x*(12 - 25*E^10))/(6*(-24 + 25*E^10)^(5/2)*(5*E^5 - Sq
rt[-24 + 25*E^10] - 2*x)) - (5*E^x*(2 + 10*E^5 + 25*E^10))/((24 - 25*E^10)^3*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*
x)) + (E^x*(2 + 10*E^5 + 25*E^10))/(12*(24 - 25*E^10)^2*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)) + (E^x*(2 + 10*E^
5 + 25*E^10))/((-24 + 25*E^10)^(5/2)*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)) - (E^x*(3 + 15*E^5 + 25*E^10))/(6*(2
4 - 25*E^10)^2*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)) - (E^x*(3 + 15*E^5 + 25*E^10))/(36*(-24 + 25*E^10)^(3/2)*(
5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)) - (E^x*(6 + 30*E^5 + 25*E^10))/(216*(24 - 25*E^10)*(5*E^5 - Sqrt[-24 + 25*
E^10] - 2*x)) - (5*E^(5 + x)*(25*E^5 - 3*Sqrt[-24 + 25*E^10]))/(3*(24 - 25*E^10)^3*(5*E^5 - Sqrt[-24 + 25*E^10
] - 2*x)) - (E^x*(2 + 5*E^5)*(5*E^5 - Sqrt[-24 + 25*E^10]))/(24*(24 - 25*E^10)^2*(5*E^5 - Sqrt[-24 + 25*E^10]
- 2*x)) + (E^x*(6 + 5*E^5)*(5*E^5 - Sqrt[-24 + 25*E^10]))/(432*(24 - 25*E^10)*(5*E^5 - Sqrt[-24 + 25*E^10] - 2
*x)) + (5*E^(5 + x)*(5*E^5 - Sqrt[-24 + 25*E^10]))/(12*(-24 + 25*E^10)^(5/2)*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*
x)) + (E^x*(3 + 5*E^5)*(5*E^5 - Sqrt[-24 + 25*E^10]))/(72*(-24 + 25*E^10)^(3/2)*(5*E^5 - Sqrt[-24 + 25*E^10] -
 2*x)) - (E^x*(2 + 5*E^5)*(10*E^5 - Sqrt[-24 + 25*E^10]))/(4*(-24 + 25*E^10)^(5/2)*(5*E^5 - Sqrt[-24 + 25*E^10
] - 2*x)) + (E^x*(3 + 5*E^5)*(15*E^5 - Sqrt[-24 + 25*E^10]))/(36*(24 - 25*E^10)^2*(5*E^5 - Sqrt[-24 + 25*E^10]
 - 2*x)) + (25*E^(5 + x)*(15*E^5 - Sqrt[-24 + 25*E^10]))/((-24 + 25*E^10)^(7/2)*(5*E^5 - Sqrt[-24 + 25*E^10] -
 2*x)) + (E^x*(2 + 5*E^5)*(25*E^5 - Sqrt[-24 + 25*E^10]))/(2*(24 - 25*E^10)^3*(5*E^5 - Sqrt[-24 + 25*E^10] - 2
*x)) + (50*E^(5 + x)*(35*E^5 - Sqrt[-24 + 25*E^10]))/((24 - 25*E^10)^4*(5*E^5 - Sqrt[-24 + 25*E^10] - 2*x)) +
(8*E^x*(12 - 25*E^10))/((-24 + 25*E^10)^(5/2)*(5*E^5 + Sqrt[-24 + 25*E^10] - 2*x)^4) + (20*E^(5 + x)*(5*E^5 +
Sqrt[-24 + 25*E^10]))/((-24 + 25*E^10)^(5/2)*(5*E^5 + Sqrt[-24 + 25*E^10] - 2*x)^4) - (80*E^x*(12 - 25*E^10))/
(3*(24 - 25*E^10)^3*(5*E^5 + Sqrt[-24 + 25*E^10] - 2*x)^3) - (4*E^x*(12 - 25*E^10))/(3*(-24 + 25*E^10)^(5/2)*(
5*E^5 + Sqrt[-24 + 25*E^10] - 2*x)^3) + (2*E^x*(2 + 10*E^5 + 25*E^10))/(3*(24 - 25*E^10)^2*(5*E^5 + Sqrt[-24 +
 25*E^10] - 2*x)^3) - (E^x*(2 + 5*E^5)*(5*E^5 + Sqrt[-24 + 25*E^10]))/(3*(24 - 25*E^10)^2*(5*E^5 + Sqrt[-24 +
25*E^10] - 2*x)^3) - (10*E^(5 + x)*(5*E^5 + Sqrt[-24 + 25*E^10]))/(3*(-24 + 25*E^10)^(5/2)*(5*E^5 + Sqrt[-24 +
 25*E^10] - 2*x)^3) - (40*E^(5 + x)*(25*E^5 + 3*Sqrt[-24 + 25*E^10]))/(3*(24 - 25*E^10)^3*(5*E^5 + Sqrt[-24 +
25*E^10] - 2*x)^3) + (20*E^x*(12 - 25*E^10))/(3*(24 - 25*E^10)^3*(5*E^5 + Sqrt[-24 + 25*E^10] - 2*x)^2) + (60*
E^x*(12 - 25*E^10))/((-24 + 25*E^10)^(7/2)*(5*E^5 + Sqrt[-24 + 25*E^10] - 2*x)^2) + (E^x*(12 - 25*E^10))/(3*(-
24 + 25*E^10)^(5/2)*(5*E^5 + Sqrt[-24 + 25*E^10] - 2*x)^2) - (E^x*(2 + 10*E^5 + 25*E^10))/(6*(24 - 25*E^10)^2*
(5*E^5 + Sqrt[-24 + 25*E^10] - 2*x)^2) + (2*E^x*(2 + 10*E^5 + 25*E^10))/((-24 + 25*E^10)^(5/2)*(5*E^5 + Sqrt[-
24 + 25*E^10] - 2*x)^2) - (E^x*(3 + 15*E^5 + 25*E^10))/(18*(-24 + 25*E^10)^(3/2)*(5*E^5 + Sqrt[-24 + 25*E^10]
- 2*x)^2) + (E^x*(2 + 5*E^5)*(5*E^5 + Sqrt[-24 + 25*E^10]))/(12*(24 - 25*E^10)^2*(5*E^5 + Sqrt[-24 + 25*E^10]
- 2*x)^2) + (5*E^(5 + x)*(5*E^5 + Sqrt[-24 + 25*E^10]))/(6*(-24 + 25*E^10)^(5/2)*(5*E^5 + Sqrt[-24 + 25*E^10]
- 2*x)^2) + (E^x*(3 + 5*E^5)*(5*E^5 + Sqrt[-24 + 25*E^10]))/(36*(-24 + 25*E^10)^(3/2)*(5*E^5 + Sqrt[-24 + 25*E
^10] - 2*x)^2) - (E^x*(2 + 5*E^5)*(10*E^5 + Sqrt[-24 + 25*E^10]))/(2*(-24 + 25*E^10)^(5/2)*(5*E^5 + Sqrt[-24 +
 25*E^10] - 2*x)^2) + (50*E^(5 + x)*(15*E^5 + Sqrt[-24 + 25*E^10]))/((-24 + 25*E^10)^(7/2)*(5*E^5 + Sqrt[-24 +
 25*E^10] - 2*x)^2) + (10*E^(5 + x)*(25*E^5 + 3*Sqrt[-24 + 25*E^10]))/(3*(24 - 25*E^10)^3*(5*E^5 + Sqrt[-24 +
25*E^10] - 2*x)^2) + (140*E^x*(12 - 25*E^10))/((24 - 25*E^10)^4*(5*E^5 + Sqrt[-24 + 25*E^10] - 2*x)) - (10*E^x
*(12 - 25*E^10))/(3*(24 - 25*E^10)^3*(5*E^5 + Sqrt[-24 + 25*E^10] - 2*x)) - (30*E^x*(12 - 25*E^10))/((-24 + 25
*E^10)^(7/2)*(5*E^5 + Sqrt[-24 + 25*E^10] - 2*x)) - (E^x*(12 - 25*E^10))/(6*(-24 + 25*E^10)^(5/2)*(5*E^5 + Sqr
t[-24 + 25*E^10] - 2*x)) - (5*E^x*(2 + 10*E^5 + 25*E^10))/((24 - 25*E^10)^3*(5*E^5 + Sqrt[-24 + 25*E^10] - 2*x
)) + (E^x*(2 + 10*E^5 + 25*E^10))/(12*(24 - 25*E^10)^2*(5*E^5 + Sqrt[-24 + 25*E^10] - 2*x)) - (E^x*(2 + 10*E^5
 + 25*E^10))/((-24 + 25*E^10)^(5/2)*(5*E^5 + Sqrt[-24 + 25*E^10] - 2*x)) - (E^x*(3 + 15*E^5 + 25*E^10))/(6*(24
 - 25*E^10)^2*(5*E^5 + Sqrt[-24 + 25*E^10] - 2*x)) + (E^x*(3 + 15*E^5 + 25*E^10))/(36*(-24 + 25*E^10)^(3/2)*(5
*E^5 + Sqrt[-24 + 25*E^10] - 2*x)) - (E^x*(6 + 30*E^5 + 25*E^10))/(216*(24 - 25*E^10)*(5*E^5 + Sqrt[-24 + 25*E
^10] - 2*x)) - (E^x*(2 + 5*E^5)*(5*E^5 + Sqrt[-24 + 25*E^10]))/(24*(24 - 25*E^10)^2*(5*E^5 + Sqrt[-24 + 25*E^1
0] - 2*x)) + (E^x*(6 + 5*E^5)*(5*E^5 + Sqrt[-24 + 25*E^10]))/(432*(24 - 25*E^10)*(5*E^5 + Sqrt[-24 + 25*E^10]
- 2*x)) - (5*E^(5 + x)*(5*E^5 + Sqrt[-24 + 25*E^10]))/(12*(-24 + 25*E^10)^(5/2)*(5*E^5 + Sqrt[-24 + 25*E^10] -
 2*x)) - (E^x*(3 + 5*E^5)*(5*E^5 + Sqrt[-24 + 25*E^10]))/(72*(-24 + 25*E^10)^(3/2)*(5*E^5 + Sqrt[-24 + 25*E^10
] - 2*x)) + (E^x*(2 + 5*E^5)*(10*E^5 + Sqrt[-24 + 25*E^10]))/(4*(-24 + 25*E^10)^(5/2)*(5*E^5 + Sqrt[-24 + 25*E
^10] - 2*x)) + (E^x*(3 + 5*E^5)*(15*E^5 + Sqrt[-24 + 25*E^10]))/(36*(24 - 25*E^10)^2*(5*E^5 + Sqrt[-24 + 25*E^
10] - 2*x)) - (25*E^(5 + x)*(15*E^5 + Sqrt[-24 + 25*E^10]))/((-24 + 25*E^10)^(7/2)*(5*E^5 + Sqrt[-24 + 25*E^10
] - 2*x)) + (E^x*(2 + 5*E^5)*(25*E^5 + Sqrt[-24 + 25*E^10]))/(2*(24 - 25*E^10)^3*(5*E^5 + Sqrt[-24 + 25*E^10]
- 2*x)) + (50*E^(5 + x)*(35*E^5 + Sqrt[-24 + 25*E^10]))/((24 - 25*E^10)^4*(5*E^5 + Sqrt[-24 + 25*E^10] - 2*x))
 - (5*E^(5 + x)*(25*E^5 + 3*Sqrt[-24 + 25*E^10]))/(3*(24 - 25*E^10)^3*(5*E^5 + Sqrt[-24 + 25*E^10] - 2*x)) + E
^x/(432*x) + (70*E^((5*E^5 + Sqrt[-24 + 25*E^10])/2)*(12 - 25*E^10)*ExpIntegralEi[(-5*E^5 - Sqrt[-24 + 25*E^10
] + 2*x)/2])/(24 - 25*E^10)^4 - (5*E^((5*E^5 + Sqrt[-24 + 25*E^10])/2)*(12 - 25*E^10)*ExpIntegralEi[(-5*E^5 -
Sqrt[-24 + 25*E^10] + 2*x)/2])/(3*(24 - 25*E^10)^3) - (1750*E^((20 + 5*E^5 + Sqrt[-24 + 25*E^10])/2)*ExpIntegr
alEi[(-5*E^5 - Sqrt[-24 + 25*E^10] + 2*x)/2])/(-24 + 25*E^10)^(9/2) - (140*E^((5*E^5 + Sqrt[-24 + 25*E^10])/2)
*(12 - 25*E^10)*ExpIntegralEi[(-5*E^5 - Sqrt[-24 + 25*E^10] + 2*x)/2])/(-24 + 25*E^10)^(9/2) + (25*E^((10 + 5*
E^5 + Sqrt[-24 + 25*E^10])/2)*(2 + 5*E^5)*ExpIntegralEi[(-5*E^5 - Sqrt[-24 + 25*E^10] + 2*x)/2])/(2*(-24 + 25*
E^10)^(7/2)) - (15*E^((5*E^5 + Sqrt[-24 + 25*E^10])/2)*(12 - 25*E^10)*ExpIntegralEi[(-5*E^5 - Sqrt[-24 + 25*E^
10] + 2*x)/2])/(-24 + 25*E^10)^(7/2) - (5*E^((10 + 5*E^5 + Sqrt[-24 + 25*E^10])/2)*(3 + 5*E^5)*ExpIntegralEi[(
-5*E^5 - Sqrt[-24 + 25*E^10] + 2*x)/2])/(12*(-24 + 25*E^10)^(5/2)) - (E^((5*E^5 + Sqrt[-24 + 25*E^10])/2)*(12
- 25*E^10)*ExpIntegralEi[(-5*E^5 - Sqrt[-24 + 25*E^10] + 2*x)/2])/(12*(-24 + 25*E^10)^(5/2)) + (5*E^((10 + 5*E
^5 + Sqrt[-24 + 25*E^10])/2)*(6 + 5*E^5)*ExpIntegralEi[(-5*E^5 - Sqrt[-24 + 25*E^10] + 2*x)/2])/(432*(-24 + 25
*E^10)^(3/2)) - (5*E^((5*E^5 + Sqrt[-24 + 25*E^10])/2)*(2 + 5*E^5*(2 + 5*E^5))*ExpIntegralEi[(-5*E^5 - Sqrt[-2
4 + 25*E^10] + 2*x)/2])/(2*(24 - 25*E^10)^3) + (E^((5*E^5 + Sqrt[-24 + 25*E^10])/2)*(2 + 5*E^5*(2 + 5*E^5))*Ex
pIntegralEi[(-5*E^5 - Sqrt[-24 + 25*E^10] + 2*x)/2])/(24*(24 - 25*E^10)^2) - (5*E^((5*E^5 + Sqrt[-24 + 25*E^10
])/2)*(2 + 5*E^5*(2 + 5*E^5))*ExpIntegralEi[(-5*E^5 - Sqrt[-24 + 25*E^10] + 2*x)/2])/(-24 + 25*E^10)^(7/2) - (
E^((5*E^5 + Sqrt[-24 + 25*E^10])/2)*(2 + 5*E^5*(2 + 5*E^5))*ExpIntegralEi[(-5*E^5 - Sqrt[-24 + 25*E^10] + 2*x)
/2])/(2*(-24 + 25*E^10)^(5/2)) - (E^((5*E^5 + Sqrt[-24 + 25*E^10])/2)*(3 + 5*E^5*(3 + 5*E^5))*ExpIntegralEi[(-
5*E^5 - Sqrt[-24 + 25*E^10] + 2*x)/2])/(12*(24 - 25*E^10)^2) + (E^((5*E^5 + Sqrt[-24 + 25*E^10])/2)*(3 + 5*E^5
*(3 + 5*E^5))*ExpIntegralEi[(-5*E^5 - Sqrt[-24 + 25*E^10] + 2*x)/2])/(6*(-24 + 25*E^10)^(5/2)) + (E^((5*E^5 +
Sqrt[-24 + 25*E^10])/2)*(3 + 5*E^5*(3 + 5*E^5))*ExpIntegralEi[(-5*E^5 - Sqrt[-24 + 25*E^10] + 2*x)/2])/(72*(-2
4 + 25*E^10)^(3/2)) - (E^((5*E^5 + Sqrt[-24 + 25*E^10])/2)*(6 + 5*E^5*(6 + 5*E^5))*ExpIntegralEi[(-5*E^5 - Sqr
t[-24 + 25*E^10] + 2*x)/2])/(432*(24 - 25*E^10)) - (E^((5*E^5 + Sqrt[-24 + 25*E^10])/2)*(6 + 5*E^5*(6 + 5*E^5)
)*ExpIntegralEi[(-5*E^5 - Sqrt[-24 + 25*E^10] + 2*x)/2])/(216*(-24 + 25*E^10)^(3/2)) - (E^((5*E^5 + Sqrt[-24 +
 25*E^10])/2)*(1 - (2 + 5*E^5)/Sqrt[-24 + 25*E^10])*ExpIntegralEi[(-5*E^5 - Sqrt[-24 + 25*E^10] + 2*x)/2])/864
 - (E^((5*E^5 + Sqrt[-24 + 25*E^10])/2)*(2 + 5*E^5)*(5*E^5 + Sqrt[-24 + 25*E^10])*ExpIntegralEi[(-5*E^5 - Sqrt
[-24 + 25*E^10] + 2*x)/2])/(48*(24 - 25*E^10)^2) + (E^((5*E^5 + Sqrt[-24 + 25*E^10])/2)*(6 + 5*E^5)*(5*E^5 + S
qrt[-24 + 25*E^10])*ExpIntegralEi[(-5*E^5 - Sqrt[-24 + 25*E^10] + 2*x)/2])/(864*(24 - 25*E^10)) - (5*E^((10 +
5*E^5 + Sqrt[-24 + 25*E^10])/2)*(5*E^5 + Sqrt[-24 + 25*E^10])*ExpIntegralEi[(-5*E^5 - Sqrt[-24 + 25*E^10] + 2*
x)/2])/(24*(-24 + 25*E^10)^(5/2)) - (E^((5*E^5 + Sqrt[-24 + 25*E^10])/2)*(3 + 5*E^5)*(5*E^5 + Sqrt[-24 + 25*E^
10])*ExpIntegralEi[(-5*E^5 - Sqrt[-24 + 25*E^10] + 2*x)/2])/(144*(-24 + 25*E^10)^(3/2)) + (E^((5*E^5 + Sqrt[-2
4 + 25*E^10])/2)*(2 + 5*E^5)*(10*E^5 + Sqrt[-24 + 25*E^10])*ExpIntegralEi[(-5*E^5 - Sqrt[-24 + 25*E^10] + 2*x)
/2])/(8*(-24 + 25*E^10)^(5/2)) + (E^((5*E^5 + Sqrt[-24 + 25*E^10])/2)*(3 + 5*E^5)*(15*E^5 + Sqrt[-24 + 25*E^10
])*ExpIntegralEi[(-5*E^5 - Sqrt[-24 + 25*E^10] + 2*x)/2])/(72*(24 - 25*E^10)^2) - (25*E^((10 + 5*E^5 + Sqrt[-2
4 + 25*E^10])/2)*(15*E^5 + Sqrt[-24 + 25*E^10])*ExpIntegralEi[(-5*E^5 - Sqrt[-24 + 25*E^10] + 2*x)/2])/(2*(-24
 + 25*E^10)^(7/2)) + (E^((5*E^5 + Sqrt[-24 + 25*E^10])/2)*(2 + 5*E^5)*(25*E^5 + Sqrt[-24 + 25*E^10])*ExpIntegr
alEi[(-5*E^5 - Sqrt[-24 + 25*E^10] + 2*x)/2])/(4*(24 - 25*E^10)^3) + (25*E^((10 + 5*E^5 + Sqrt[-24 + 25*E^10])
/2)*(35*E^5 + Sqrt[-24 + 25*E^10])*ExpIntegralEi[(-5*E^5 - Sqrt[-24 + 25*E^10] + 2*x)/2])/(24 - 25*E^10)^4 - (
5*E^((10 + 5*E^5 + Sqrt[-24 + 25*E^10])/2)*(25*E^5 + 3*Sqrt[-24 + 25*E^10])*ExpIntegralEi[(-5*E^5 - Sqrt[-24 +
 25*E^10] + 2*x)/2])/(6*(24 - 25*E^10)^3) + (70*E^((5*E^5)/2 - Sqrt[-24 + 25*E^10]/2)*(12 - 25*E^10)*ExpIntegr
alEi[(-5*E^5 + Sqrt[-24 + 25*E^10] + 2*x)/2])/(24 - 25*E^10)^4 - (5*E^((5*E^5)/2 - Sqrt[-24 + 25*E^10]/2)*(12
- 25*E^10)*ExpIntegralEi[(-5*E^5 + Sqrt[-24 + 25*E^10] + 2*x)/2])/(3*(24 - 25*E^10)^3) + (1750*E^(10 + (5*E^5)
/2 - Sqrt[-24 + 25*E^10]/2)*ExpIntegralEi[(-5*E^5 + Sqrt[-24 + 25*E^10] + 2*x)/2])/(-24 + 25*E^10)^(9/2) + (14
0*E^((5*E^5)/2 - Sqrt[-24 + 25*E^10]/2)*(12 - 25*E^10)*ExpIntegralEi[(-5*E^5 + Sqrt[-24 + 25*E^10] + 2*x)/2])/
(-24 + 25*E^10)^(9/2) - (25*E^(5 + (5*E^5)/2 - Sqrt[-24 + 25*E^10]/2)*(2 + 5*E^5)*ExpIntegralEi[(-5*E^5 + Sqrt
[-24 + 25*E^10] + 2*x)/2])/(2*(-24 + 25*E^10)^(7/2)) + (15*E^((5*E^5)/2 - Sqrt[-24 + 25*E^10]/2)*(12 - 25*E^10
)*ExpIntegralEi[(-5*E^5 + Sqrt[-24 + 25*E^10] + 2*x)/2])/(-24 + 25*E^10)^(7/2) + (5*E^(5 + (5*E^5)/2 - Sqrt[-2
4 + 25*E^10]/2)*(3 + 5*E^5)*ExpIntegralEi[(-5*E^5 + Sqrt[-24 + 25*E^10] + 2*x)/2])/(12*(-24 + 25*E^10)^(5/2))
+ (E^((5*E^5)/2 - Sqrt[-24 + 25*E^10]/2)*(12 - 25*E^10)*ExpIntegralEi[(-5*E^5 + Sqrt[-24 + 25*E^10] + 2*x)/2])
/(12*(-24 + 25*E^10)^(5/2)) - (5*E^(5 + (5*E^5)/2 - Sqrt[-24 + 25*E^10]/2)*(6 + 5*E^5)*ExpIntegralEi[(-5*E^5 +
 Sqrt[-24 + 25*E^10] + 2*x)/2])/(432*(-24 + 25*E^10)^(3/2)) - (5*E^((5*E^5)/2 - Sqrt[-24 + 25*E^10]/2)*(2 + 10
*E^5 + 25*E^10)*ExpIntegralEi[(-5*E^5 + Sqrt[-24 + 25*E^10] + 2*x)/2])/(2*(24 - 25*E^10)^3) + (E^((5*E^5)/2 -
Sqrt[-24 + 25*E^10]/2)*(2 + 10*E^5 + 25*E^10)*ExpIntegralEi[(-5*E^5 + Sqrt[-24 + 25*E^10] + 2*x)/2])/(24*(24 -
 25*E^10)^2) + (5*E^((5*E^5)/2 - Sqrt[-24 + 25*E^10]/2)*(2 + 10*E^5 + 25*E^10)*ExpIntegralEi[(-5*E^5 + Sqrt[-2
4 + 25*E^10] + 2*x)/2])/(-24 + 25*E^10)^(7/2) + (E^((5*E^5)/2 - Sqrt[-24 + 25*E^10]/2)*(2 + 10*E^5 + 25*E^10)*
ExpIntegralEi[(-5*E^5 + Sqrt[-24 + 25*E^10] + 2*x)/2])/(2*(-24 + 25*E^10)^(5/2)) - (E^((5*E^5)/2 - Sqrt[-24 +
25*E^10]/2)*(3 + 15*E^5 + 25*E^10)*ExpIntegralEi[(-5*E^5 + Sqrt[-24 + 25*E^10] + 2*x)/2])/(12*(24 - 25*E^10)^2
) - (E^((5*E^5)/2 - Sqrt[-24 + 25*E^10]/2)*(3 + 15*E^5 + 25*E^10)*ExpIntegralEi[(-5*E^5 + Sqrt[-24 + 25*E^10]
+ 2*x)/2])/(6*(-24 + 25*E^10)^(5/2)) - (E^((5*E^5)/2 - Sqrt[-24 + 25*E^10]/2)*(3 + 15*E^5 + 25*E^10)*ExpIntegr
alEi[(-5*E^5 + Sqrt[-24 + 25*E^10] + 2*x)/2])/(72*(-24 + 25*E^10)^(3/2)) - (E^((5*E^5)/2 - Sqrt[-24 + 25*E^10]
/2)*(6 + 30*E^5 + 25*E^10)*ExpIntegralEi[(-5*E^5 + Sqrt[-24 + 25*E^10] + 2*x)/2])/(432*(24 - 25*E^10)) + (E^((
5*E^5)/2 - Sqrt[-24 + 25*E^10]/2)*(6 + 30*E^5 + 25*E^10)*ExpIntegralEi[(-5*E^5 + Sqrt[-24 + 25*E^10] + 2*x)/2]
)/(216*(-24 + 25*E^10)^(3/2)) - (E^((5*E^5)/2 - Sqrt[-24 + 25*E^10]/2)*(1 + (2 + 5*E^5)/Sqrt[-24 + 25*E^10])*E
xpIntegralEi[(-5*E^5 + Sqrt[-24 + 25*E^10] + 2*x)/2])/864 - (5*E^(5 + (5*E^5)/2 - Sqrt[-24 + 25*E^10]/2)*(25*E
^5 - 3*Sqrt[-24 + 25*E^10])*ExpIntegralEi[(-5*E^5 + Sqrt[-24 + 25*E^10] + 2*x)/2])/(6*(24 - 25*E^10)^3) - (E^(
(5*E^5)/2 - Sqrt[-24 + 25*E^10]/2)*(2 + 5*E^5)*(5*E^5 - Sqrt[-24 + 25*E^10])*ExpIntegralEi[(-5*E^5 + Sqrt[-24
+ 25*E^10] + 2*x)/2])/(48*(24 - 25*E^10)^2) + (E^((5*E^5)/2 - Sqrt[-24 + 25*E^10]/2)*(6 + 5*E^5)*(5*E^5 - Sqrt
[-24 + 25*E^10])*ExpIntegralEi[(-5*E^5 + Sqrt[-24 + 25*E^10] + 2*x)/2])/(864*(24 - 25*E^10)) + (5*E^(5 + (5*E^
5)/2 - Sqrt[-24 + 25*E^10]/2)*(5*E^5 - Sqrt[-24 + 25*E^10])*ExpIntegralEi[(-5*E^5 + Sqrt[-24 + 25*E^10] + 2*x)
/2])/(24*(-24 + 25*E^10)^(5/2)) + (E^((5*E^5)/2 - Sqrt[-24 + 25*E^10]/2)*(3 + 5*E^5)*(5*E^5 - Sqrt[-24 + 25*E^
10])*ExpIntegralEi[(-5*E^5 + Sqrt[-24 + 25*E^10] + 2*x)/2])/(144*(-24 + 25*E^10)^(3/2)) - (E^((5*E^5)/2 - Sqrt
[-24 + 25*E^10]/2)*(2 + 5*E^5)*(10*E^5 - Sqrt[-24 + 25*E^10])*ExpIntegralEi[(-5*E^5 + Sqrt[-24 + 25*E^10] + 2*
x)/2])/(8*(-24 + 25*E^10)^(5/2)) + (E^((5*E^5)/2 - Sqrt[-24 + 25*E^10]/2)*(3 + 5*E^5)*(15*E^5 - Sqrt[-24 + 25*
E^10])*ExpIntegralEi[(-5*E^5 + Sqrt[-24 + 25*E^10] + 2*x)/2])/(72*(24 - 25*E^10)^2) + (25*E^(5 + (5*E^5)/2 - S
qrt[-24 + 25*E^10]/2)*(15*E^5 - Sqrt[-24 + 25*E^10])*ExpIntegralEi[(-5*E^5 + Sqrt[-24 + 25*E^10] + 2*x)/2])/(2
*(-24 + 25*E^10)^(7/2)) + (E^((5*E^5)/2 - Sqrt[-24 + 25*E^10]/2)*(2 + 5*E^5)*(25*E^5 - Sqrt[-24 + 25*E^10])*Ex
pIntegralEi[(-5*E^5 + Sqrt[-24 + 25*E^10] + 2*x)/2])/(4*(24 - 25*E^10)^3) + (25*E^(5 + (5*E^5)/2 - Sqrt[-24 +
25*E^10]/2)*(35*E^5 - Sqrt[-24 + 25*E^10])*ExpIntegralEi[(-5*E^5 + Sqrt[-24 + 25*E^10] + 2*x)/2])/(24 - 25*E^1
0)^4

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 2177

Int[((b_.)*(F_)^((g_.)*((e_.) + (f_.)*(x_))))^(n_.)*((c_.) + (d_.)*(x_))^(m_), x_Symbol] :> Simp[((c + d*x)^(m
 + 1)*(b*F^(g*(e + f*x)))^n)/(d*(m + 1)), x] - Dist[(f*g*n*Log[F])/(d*(m + 1)), Int[(c + d*x)^(m + 1)*(b*F^(g*
(e + f*x)))^n, x], x] /; FreeQ[{F, b, c, d, e, f, g, n}, x] && LtQ[m, -1] && IntegerQ[2*m] &&  !$UseGamma ===
True

Rule 2178

Int[(F_)^((g_.)*((e_.) + (f_.)*(x_)))/((c_.) + (d_.)*(x_)), x_Symbol] :> Simp[(F^(g*(e - (c*f)/d))*ExpIntegral
Ei[(f*g*(c + d*x)*Log[F])/d])/d, x] /; FreeQ[{F, c, d, e, f, g}, x] &&  !$UseGamma === True

Rule 2270

Int[((F_)^((g_.)*((d_.) + (e_.)*(x_))^(n_.))*(u_)^(m_.))/((a_.) + (b_.)*(x_) + (c_)*(x_)^2), x_Symbol] :> Int[
ExpandIntegrand[F^(g*(d + e*x)^n), u^m/(a + b*x + c*x^2), x], x] /; FreeQ[{F, a, b, c, d, e, g, n}, x] && Poly
nomialQ[u, x] && IntegerQ[m]

Rule 6688

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

Rule 6742

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3 e^x \left (-6+\left (6+25 e^5\right ) x-\left (9+5 e^5\right ) x^2+x^3\right )}{x^2 \left (6-5 e^5 x+x^2\right )^5} \, dx\\ &=3 \int \frac {e^x \left (-6+\left (6+25 e^5\right ) x-\left (9+5 e^5\right ) x^2+x^3\right )}{x^2 \left (6-5 e^5 x+x^2\right )^5} \, dx\\ &=3 \int \left (-\frac {e^x}{1296 x^2}+\frac {e^x}{1296 x}-\frac {2 e^x \left (-12+25 e^{10}-5 e^5 x\right )}{3 \left (-6+5 e^5 x-x^2\right )^5}+\frac {e^x \left (-1-5 e^5+x\right )}{1296 \left (-6+5 e^5 x-x^2\right )}+\frac {e^x \left (2+10 e^5+25 e^{10}-\left (2+5 e^5\right ) x\right )}{12 \left (6-5 e^5 x+x^2\right )^4}+\frac {e^x \left (3+15 e^5+25 e^{10}-\left (3+5 e^5\right ) x\right )}{108 \left (6-5 e^5 x+x^2\right )^3}+\frac {e^x \left (6+30 e^5+25 e^{10}-\left (6+5 e^5\right ) x\right )}{1296 \left (6-5 e^5 x+x^2\right )^2}\right ) \, dx\\ &=-\left (\frac {1}{432} \int \frac {e^x}{x^2} \, dx\right )+\frac {1}{432} \int \frac {e^x}{x} \, dx+\frac {1}{432} \int \frac {e^x \left (-1-5 e^5+x\right )}{-6+5 e^5 x-x^2} \, dx+\frac {1}{432} \int \frac {e^x \left (6+30 e^5+25 e^{10}-\left (6+5 e^5\right ) x\right )}{\left (6-5 e^5 x+x^2\right )^2} \, dx+\frac {1}{36} \int \frac {e^x \left (3+15 e^5+25 e^{10}-\left (3+5 e^5\right ) x\right )}{\left (6-5 e^5 x+x^2\right )^3} \, dx+\frac {1}{4} \int \frac {e^x \left (2+10 e^5+25 e^{10}-\left (2+5 e^5\right ) x\right )}{\left (6-5 e^5 x+x^2\right )^4} \, dx-2 \int \frac {e^x \left (-12+25 e^{10}-5 e^5 x\right )}{\left (-6+5 e^5 x-x^2\right )^5} \, dx\\ &=\frac {e^x}{432 x}+\frac {\text {Ei}(x)}{432}+\frac {1}{432} \int \left (\frac {e^x \left (1+\frac {2+5 e^5}{\sqrt {-24+25 e^{10}}}\right )}{5 e^5-\sqrt {-24+25 e^{10}}-2 x}+\frac {e^x \left (1-\frac {2+5 e^5}{\sqrt {-24+25 e^{10}}}\right )}{5 e^5+\sqrt {-24+25 e^{10}}-2 x}\right ) \, dx-\frac {1}{432} \int \frac {e^x}{x} \, dx+\frac {1}{432} \int \left (\frac {6 e^x \left (1+\frac {5}{6} e^5 \left (6+5 e^5\right )\right )}{\left (-6+5 e^5 x-x^2\right )^2}-\frac {e^x \left (6+5 e^5\right ) x}{\left (-6+5 e^5 x-x^2\right )^2}\right ) \, dx+\frac {1}{36} \int \left (-\frac {3 e^x \left (1+\frac {5}{3} e^5 \left (3+5 e^5\right )\right )}{\left (-6+5 e^5 x-x^2\right )^3}+\frac {e^x \left (3+5 e^5\right ) x}{\left (-6+5 e^5 x-x^2\right )^3}\right ) \, dx+\frac {1}{4} \int \left (\frac {2 e^x \left (1+\frac {5}{2} e^5 \left (2+5 e^5\right )\right )}{\left (-6+5 e^5 x-x^2\right )^4}-\frac {e^x \left (2+5 e^5\right ) x}{\left (-6+5 e^5 x-x^2\right )^4}\right ) \, dx-2 \int \left (-\frac {12 e^x \left (1-\frac {25 e^{10}}{12}\right )}{\left (-6+5 e^5 x-x^2\right )^5}-\frac {5 e^{5+x} x}{\left (-6+5 e^5 x-x^2\right )^5}\right ) \, dx\\ &=\frac {e^x}{432 x}+10 \int \frac {e^{5+x} x}{\left (-6+5 e^5 x-x^2\right )^5} \, dx+\frac {1}{432} \left (-6-5 e^5\right ) \int \frac {e^x x}{\left (-6+5 e^5 x-x^2\right )^2} \, dx+\frac {1}{4} \left (-2-5 e^5\right ) \int \frac {e^x x}{\left (-6+5 e^5 x-x^2\right )^4} \, dx+\frac {1}{36} \left (3+5 e^5\right ) \int \frac {e^x x}{\left (-6+5 e^5 x-x^2\right )^3} \, dx+\left (2 \left (12-25 e^{10}\right )\right ) \int \frac {e^x}{\left (-6+5 e^5 x-x^2\right )^5} \, dx+\frac {1}{36} \left (-3-15 e^5-25 e^{10}\right ) \int \frac {e^x}{\left (-6+5 e^5 x-x^2\right )^3} \, dx+\frac {1}{4} \left (2+10 e^5+25 e^{10}\right ) \int \frac {e^x}{\left (-6+5 e^5 x-x^2\right )^4} \, dx+\frac {1}{432} \left (6+30 e^5+25 e^{10}\right ) \int \frac {e^x}{\left (-6+5 e^5 x-x^2\right )^2} \, dx+\frac {1}{432} \left (1-\frac {2+5 e^5}{\sqrt {-24+25 e^{10}}}\right ) \int \frac {e^x}{5 e^5+\sqrt {-24+25 e^{10}}-2 x} \, dx+\frac {1}{432} \left (1+\frac {2+5 e^5}{\sqrt {-24+25 e^{10}}}\right ) \int \frac {e^x}{5 e^5-\sqrt {-24+25 e^{10}}-2 x} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 2.95, size = 21, normalized size = 1.00 \begin {gather*} \frac {3 e^x}{x \left (6-5 e^5 x+x^2\right )^4} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^x*(18 - 18*x + 27*x^2 - 3*x^3 + E^5*(-75*x + 15*x^2)))/(-7776*x^2 - 6480*x^4 - 2160*x^6 + 3125*E^
25*x^7 - 360*x^8 - 30*x^10 - x^12 + E^20*(-18750*x^6 - 3125*x^8) + E^15*(45000*x^5 + 15000*x^7 + 1250*x^9) + E
^10*(-54000*x^4 - 27000*x^6 - 4500*x^8 - 250*x^10) + E^5*(32400*x^3 + 21600*x^5 + 5400*x^7 + 600*x^9 + 25*x^11
)),x]

[Out]

(3*E^x)/(x*(6 - 5*E^5*x + x^2)^4)

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fricas [B]  time = 0.63, size = 89, normalized size = 4.24 \begin {gather*} \frac {3 \, e^{x}}{x^{9} + 24 \, x^{7} + 625 \, x^{5} e^{20} + 216 \, x^{5} + 864 \, x^{3} - 500 \, {\left (x^{6} + 6 \, x^{4}\right )} e^{15} + 150 \, {\left (x^{7} + 12 \, x^{5} + 36 \, x^{3}\right )} e^{10} - 20 \, {\left (x^{8} + 18 \, x^{6} + 108 \, x^{4} + 216 \, x^{2}\right )} e^{5} + 1296 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((15*x^2-75*x)*exp(5)-3*x^3+27*x^2-18*x+18)*exp(x)/(3125*x^7*exp(5)^5+(-3125*x^8-18750*x^6)*exp(5)^4
+(1250*x^9+15000*x^7+45000*x^5)*exp(5)^3+(-250*x^10-4500*x^8-27000*x^6-54000*x^4)*exp(5)^2+(25*x^11+600*x^9+54
00*x^7+21600*x^5+32400*x^3)*exp(5)-x^12-30*x^10-360*x^8-2160*x^6-6480*x^4-7776*x^2),x, algorithm="fricas")

[Out]

3*e^x/(x^9 + 24*x^7 + 625*x^5*e^20 + 216*x^5 + 864*x^3 - 500*(x^6 + 6*x^4)*e^15 + 150*(x^7 + 12*x^5 + 36*x^3)*
e^10 - 20*(x^8 + 18*x^6 + 108*x^4 + 216*x^2)*e^5 + 1296*x)

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giac [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((15*x^2-75*x)*exp(5)-3*x^3+27*x^2-18*x+18)*exp(x)/(3125*x^7*exp(5)^5+(-3125*x^8-18750*x^6)*exp(5)^4
+(1250*x^9+15000*x^7+45000*x^5)*exp(5)^3+(-250*x^10-4500*x^8-27000*x^6-54000*x^4)*exp(5)^2+(25*x^11+600*x^9+54
00*x^7+21600*x^5+32400*x^3)*exp(5)-x^12-30*x^10-360*x^8-2160*x^6-6480*x^4-7776*x^2),x, algorithm="giac")

[Out]

Timed out

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maple [A]  time = 0.68, size = 22, normalized size = 1.05

method result size
norman \(\frac {3 \,{\mathrm e}^{x}}{x \left (5 x \,{\mathrm e}^{5}-x^{2}-6\right )^{4}}\) \(22\)
gosper \(\frac {3 \,{\mathrm e}^{x}}{x \left (625 x^{4} {\mathrm e}^{20}-500 x^{5} {\mathrm e}^{15}+150 x^{6} {\mathrm e}^{10}-20 x^{7} {\mathrm e}^{5}+x^{8}-3000 x^{3} {\mathrm e}^{15}+1800 x^{4} {\mathrm e}^{10}-360 x^{5} {\mathrm e}^{5}+24 x^{6}+5400 x^{2} {\mathrm e}^{10}-2160 x^{3} {\mathrm e}^{5}+216 x^{4}-4320 x \,{\mathrm e}^{5}+864 x^{2}+1296\right )}\) \(110\)
default \(\text {Expression too large to display}\) \(14908\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((15*x^2-75*x)*exp(5)-3*x^3+27*x^2-18*x+18)*exp(x)/(3125*x^7*exp(5)^5+(-3125*x^8-18750*x^6)*exp(5)^4+(1250
*x^9+15000*x^7+45000*x^5)*exp(5)^3+(-250*x^10-4500*x^8-27000*x^6-54000*x^4)*exp(5)^2+(25*x^11+600*x^9+5400*x^7
+21600*x^5+32400*x^3)*exp(5)-x^12-30*x^10-360*x^8-2160*x^6-6480*x^4-7776*x^2),x,method=_RETURNVERBOSE)

[Out]

3*exp(x)/x/(5*x*exp(5)-x^2-6)^4

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maxima [B]  time = 0.40, size = 91, normalized size = 4.33 \begin {gather*} \frac {3 \, e^{x}}{x^{9} - 20 \, x^{8} e^{5} + 6 \, x^{7} {\left (25 \, e^{10} + 4\right )} - 20 \, x^{6} {\left (25 \, e^{15} + 18 \, e^{5}\right )} + x^{5} {\left (625 \, e^{20} + 1800 \, e^{10} + 216\right )} - 120 \, x^{4} {\left (25 \, e^{15} + 18 \, e^{5}\right )} + 216 \, x^{3} {\left (25 \, e^{10} + 4\right )} - 4320 \, x^{2} e^{5} + 1296 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((15*x^2-75*x)*exp(5)-3*x^3+27*x^2-18*x+18)*exp(x)/(3125*x^7*exp(5)^5+(-3125*x^8-18750*x^6)*exp(5)^4
+(1250*x^9+15000*x^7+45000*x^5)*exp(5)^3+(-250*x^10-4500*x^8-27000*x^6-54000*x^4)*exp(5)^2+(25*x^11+600*x^9+54
00*x^7+21600*x^5+32400*x^3)*exp(5)-x^12-30*x^10-360*x^8-2160*x^6-6480*x^4-7776*x^2),x, algorithm="maxima")

[Out]

3*e^x/(x^9 - 20*x^8*e^5 + 6*x^7*(25*e^10 + 4) - 20*x^6*(25*e^15 + 18*e^5) + x^5*(625*e^20 + 1800*e^10 + 216) -
 120*x^4*(25*e^15 + 18*e^5) + 216*x^3*(25*e^10 + 4) - 4320*x^2*e^5 + 1296*x)

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mupad [F(-1)]  time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \text {Hanged} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(x)*(18*x + exp(5)*(75*x - 15*x^2) - 27*x^2 + 3*x^3 - 18))/(exp(20)*(18750*x^6 + 3125*x^8) - exp(5)*(3
2400*x^3 + 21600*x^5 + 5400*x^7 + 600*x^9 + 25*x^11) - 3125*x^7*exp(25) - exp(15)*(45000*x^5 + 15000*x^7 + 125
0*x^9) + 7776*x^2 + 6480*x^4 + 2160*x^6 + 360*x^8 + 30*x^10 + x^12 + exp(10)*(54000*x^4 + 27000*x^6 + 4500*x^8
 + 250*x^10)),x)

[Out]

\text{Hanged}

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sympy [B]  time = 0.43, size = 110, normalized size = 5.24 \begin {gather*} \frac {3 e^{x}}{x^{9} - 20 x^{8} e^{5} + 24 x^{7} + 150 x^{7} e^{10} - 500 x^{6} e^{15} - 360 x^{6} e^{5} + 216 x^{5} + 1800 x^{5} e^{10} + 625 x^{5} e^{20} - 3000 x^{4} e^{15} - 2160 x^{4} e^{5} + 864 x^{3} + 5400 x^{3} e^{10} - 4320 x^{2} e^{5} + 1296 x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((15*x**2-75*x)*exp(5)-3*x**3+27*x**2-18*x+18)*exp(x)/(3125*x**7*exp(5)**5+(-3125*x**8-18750*x**6)*e
xp(5)**4+(1250*x**9+15000*x**7+45000*x**5)*exp(5)**3+(-250*x**10-4500*x**8-27000*x**6-54000*x**4)*exp(5)**2+(2
5*x**11+600*x**9+5400*x**7+21600*x**5+32400*x**3)*exp(5)-x**12-30*x**10-360*x**8-2160*x**6-6480*x**4-7776*x**2
),x)

[Out]

3*exp(x)/(x**9 - 20*x**8*exp(5) + 24*x**7 + 150*x**7*exp(10) - 500*x**6*exp(15) - 360*x**6*exp(5) + 216*x**5 +
 1800*x**5*exp(10) + 625*x**5*exp(20) - 3000*x**4*exp(15) - 2160*x**4*exp(5) + 864*x**3 + 5400*x**3*exp(10) -
4320*x**2*exp(5) + 1296*x)

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