3.85.80 $\int \frac{e^{1+2x}(-225-425x-10x^2+450x^3+287x^4-41x^5-99x^6-35x^7-4x^8)+e(1500-2700x^2-900x^3+1620x^4+1080x^5-144x^6-324x^7-108x^8-12x^9)}{-16000x^4+28800x^6+9600x^7-17280x^8-11520x^9+1536x^{10}+3456x^{11}+1152x^{12}+128x^{13}+e^{6x}(54x^4+54x^5+18x^6+2x^7)+e^{4x}(-1080x^4-720x^5+528x^6+648x^7+216x^8+24x^9)+e^{2x}(7200x^4+2400x^5-8640x^6-5760x^7+1632x^8+2592x^9+864x^{10}+96x^{11})}dx$

Optimal. Leaf size=35 $$\frac{e}{2x{(x+x(3+\frac{e^{2x}}{x^2-\frac{5}{3+x}}))}^2}$$

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Rubi [F]  time = 6.53, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.000, Rules used = {} $$\begin{array}{c}\int \frac{e^{1+2x}(-225-425x-10x^2+450x^3+287x^4-41x^5-99x^6-35x^7-4x^8)+e(1500-2700x^2-900x^3+1620x^4+1080x^5-144x^6-324x^7-108x^8-12x^9)}{-16000x^4+28800x^6+9600x^7-17280x^8-11520x^9+1536x^{10}+3456x^{11}+1152x^{12}+128x^{13}+e^{6x}(54x^4+54x^5+18x^6+2x^7)+e^{4x}(-1080x^4-720x^5+528x^6+648x^7+216x^8+24x^9)+e^{2x}(7200x^4+2400x^5-8640x^6-5760x^7+1632x^8+2592x^9+864x^{10}+96x^{11})}dx\end{array}$$

Verification is not applicable to the result.

[In]

Int[(E^(1 + 2*x)*(-225 - 425*x - 10*x^2 + 450*x^3 + 287*x^4 - 41*x^5 - 99*x^6 - 35*x^7 - 4*x^8) + E*(1500 - 27
00*x^2 - 900*x^3 + 1620*x^4 + 1080*x^5 - 144*x^6 - 324*x^7 - 108*x^8 - 12*x^9))/(-16000*x^4 + 28800*x^6 + 9600
*x^7 - 17280*x^8 - 11520*x^9 + 1536*x^10 + 3456*x^11 + 1152*x^12 + 128*x^13 + E^(6*x)*(54*x^4 + 54*x^5 + 18*x^
6 + 2*x^7) + E^(4*x)*(-1080*x^4 - 720*x^5 + 528*x^6 + 648*x^7 + 216*x^8 + 24*x^9) + E^(2*x)*(7200*x^4 + 2400*x
^5 - 8640*x^6 - 5760*x^7 + 1632*x^8 + 2592*x^9 + 864*x^10 + 96*x^11)),x]

[Out]

1320*E*Defer[Int][(-20 + 3*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x^3)^(-3), x] - (3500*E*Defer[Int][1/(x^3*(-20 + 3
*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x^3)^3), x])/3 - (4900*E*Defer[Int][1/(x^2*(-20 + 3*E^(2*x) + E^(2*x)*x + 12
*x^2 + 4*x^3)^3), x])/9 + (48100*E*Defer[Int][1/(x*(-20 + 3*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x^3)^3), x])/27 -
660*E*Defer[Int][x/(-20 + 3*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x^3)^3, x] - 876*E*Defer[Int][x^2/(-20 + 3*E^(2*
x) + E^(2*x)*x + 12*x^2 + 4*x^3)^3, x] - 120*E*Defer[Int][x^3/(-20 + 3*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x^3)^3
, x] + 144*E*Defer[Int][x^4/(-20 + 3*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x^3)^3, x] + 64*E*Defer[Int][x^5/(-20 +
3*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x^3)^3, x] + 8*E*Defer[Int][x^6/(-20 + 3*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x
^3)^3, x] + (500*E*Defer[Int][1/((3 + x)*(-20 + 3*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x^3)^3), x])/27 + (49*E*Def
er[Int][(-20 + 3*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x^3)^(-2), x])/2 - (75*E*Defer[Int][1/(x^4*(-20 + 3*E^(2*x)
+ E^(2*x)*x + 12*x^2 + 4*x^3)^2), x])/2 - (175*E*Defer[Int][1/(x^3*(-20 + 3*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x
^3)^2), x])/3 + (160*E*Defer[Int][1/(x^2*(-20 + 3*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x^3)^2), x])/9 + (1865*E*De
fer[Int][1/(x*(-20 + 3*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x^3)^2), x])/27 - 15*E*Defer[Int][x/(-20 + 3*E^(2*x) +
E^(2*x)*x + 12*x^2 + 4*x^3)^2, x] - (23*E*Defer[Int][x^2/(-20 + 3*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x^3)^2, x]
)/2 - 2*E*Defer[Int][x^3/(-20 + 3*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x^3)^2, x] + (25*E*Defer[Int][1/((3 + x)*(-
20 + 3*E^(2*x) + E^(2*x)*x + 12*x^2 + 4*x^3)^2), x])/27

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int \frac{e(5-3x^2-x^3)(12{(-5+3x^2+x^3)}^2+e^{2x}(-45-85x-29x^2+30x^3+23x^4+4x^5))}{2x^4{(e^{2x}(3+x)+4(-5+3x^2+x^3))}^3}dx\\ & =\frac{1}{2}e\int \frac{(5-3x^2-x^3)(12{(-5+3x^2+x^3)}^2+e^{2x}(-45-85x-29x^2+30x^3+23x^4+4x^5))}{x^4{(e^{2x}(3+x)+4(-5+3x^2+x^3))}^3}dx\\ & =\frac{1}{2}e\int (\frac{8{(-5+3x^2+x^3)}^2(-35-28x+6x^2+10x^3+2x^4)}{x^3(3+x){(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^3}-\frac{225+425x+10x^2-450x^3-287x^4+41x^5+99x^6+35x^7+4x^8}{x^4(3+x){(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^2})dx\\ & =-(\frac{1}{2}e\int \frac{225+425x+10x^2-450x^3-287x^4+41x^5+99x^6+35x^7+4x^8}{x^4(3+x){(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^2}dx)+(4e)\int \frac{{(-5+3x^2+x^3)}^2(-35-28x+6x^2+10x^3+2x^4)}{x^3(3+x){(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^3}dx\\ & =-(\frac{1}{2}e\int (-\frac{49}{{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^2}+\frac{75}{x^4{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^2}+\frac{350}{3x^3{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^2}-\frac{320}{9x^2{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^2}-\frac{3730}{27x{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^2}+\frac{30x}{{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^2}+\frac{23x^2}{{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^2}+\frac{4x^3}{{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^2}-\frac{50}{27(3+x){(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^2})dx)+(4e)\int (\frac{330}{{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^3}-\frac{875}{3x^3{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^3}-\frac{1225}{9x^2{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^3}+\frac{12025}{27x{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^3}-\frac{165x}{{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^3}-\frac{219x^2}{{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^3}-\frac{30x^3}{{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^3}+\frac{36x^4}{{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^3}+\frac{16x^5}{{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^3}+\frac{2x^6}{{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^3}+\frac{125}{27(3+x){(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^3})dx\\ & =\frac{1}{27}(25e)\int \frac{1}{(3+x){(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^2}dx-(2e)\int \frac{x^3}{{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^2}dx+(8e)\int \frac{x^6}{{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^3}dx-\frac{1}{2}(23e)\int \frac{x^2}{{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^2}dx-(15e)\int \frac{x}{{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^2}dx+\frac{1}{9}(160e)\int \frac{1}{x^2{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^2}dx+\frac{1}{27}(500e)\int \frac{1}{(3+x){(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^3}dx+\frac{1}{2}(49e)\int \frac{1}{{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^2}dx-\frac{1}{2}(75e)\int \frac{1}{x^4{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^2}dx-\frac{1}{3}(175e)\int \frac{1}{x^3{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^2}dx+(64e)\int \frac{x^5}{{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^3}dx+\frac{1}{27}(1865e)\int \frac{1}{x{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^2}dx-(120e)\int \frac{x^3}{{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^3}dx+(144e)\int \frac{x^4}{{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^3}dx-\frac{1}{9}(4900e)\int \frac{1}{x^2{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^3}dx-(660e)\int \frac{x}{{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^3}dx-(876e)\int \frac{x^2}{{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^3}dx-\frac{1}{3}(3500e)\int \frac{1}{x^3{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^3}dx+(1320e)\int \frac{1}{{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^3}dx+\frac{1}{27}(48100e)\int \frac{1}{x{(-20+3e^{2x}+e^{2x}x+12x^2+4x^3)}^3}dx\end{array}\end{array}$$

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Mathematica [A]  time = 0.07, size = 44, normalized size = 1.26 $$\begin{array}{c}\frac{e{(-5+3x^2+x^3)}^2}{2x^3{(e^{2x}(3+x)+4(-5+3x^2+x^3))}^2}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(E^(1 + 2*x)*(-225 - 425*x - 10*x^2 + 450*x^3 + 287*x^4 - 41*x^5 - 99*x^6 - 35*x^7 - 4*x^8) + E*(150
0 - 2700*x^2 - 900*x^3 + 1620*x^4 + 1080*x^5 - 144*x^6 - 324*x^7 - 108*x^8 - 12*x^9))/(-16000*x^4 + 28800*x^6
+ 9600*x^7 - 17280*x^8 - 11520*x^9 + 1536*x^10 + 3456*x^11 + 1152*x^12 + 128*x^13 + E^(6*x)*(54*x^4 + 54*x^5 +
18*x^6 + 2*x^7) + E^(4*x)*(-1080*x^4 - 720*x^5 + 528*x^6 + 648*x^7 + 216*x^8 + 24*x^9) + E^(2*x)*(7200*x^4 +
2400*x^5 - 8640*x^6 - 5760*x^7 + 1632*x^8 + 2592*x^9 + 864*x^10 + 96*x^11)),x]

[Out]

(E*(-5 + 3*x^2 + x^3)^2)/(2*x^3*(E^(2*x)*(3 + x) + 4*(-5 + 3*x^2 + x^3))^2)

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fricas [B]  time = 0.66, size = 118, normalized size = 3.37 $$\begin{array}{c}\frac{(x^6+6x^5+9x^4-10x^3-30x^2+25)e^3}{2(16(x^9+6x^8+9x^7-10x^6-30x^5+25x^3)e^2+(x^5+6x^4+9x^3)e^{(4x+2)}+8(x^7+6x^6+9x^5-5x^4-15x^3)e^{(2x+2)})}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x^8-35*x^7-99*x^6-41*x^5+287*x^4+450*x^3-10*x^2-425*x-225)*exp(1)*exp(x)^2+(-12*x^9-108*x^8-324
*x^7-144*x^6+1080*x^5+1620*x^4-900*x^3-2700*x^2+1500)*exp(1))/((2*x^7+18*x^6+54*x^5+54*x^4)*exp(x)^6+(24*x^9+2
16*x^8+648*x^7+528*x^6-720*x^5-1080*x^4)*exp(x)^4+(96*x^11+864*x^10+2592*x^9+1632*x^8-5760*x^7-8640*x^6+2400*x
^5+7200*x^4)*exp(x)^2+128*x^13+1152*x^12+3456*x^11+1536*x^10-11520*x^9-17280*x^8+9600*x^7+28800*x^6-16000*x^4)
,x, algorithm="fricas")

[Out]

1/2*(x^6 + 6*x^5 + 9*x^4 - 10*x^3 - 30*x^2 + 25)*e^3/(16*(x^9 + 6*x^8 + 9*x^7 - 10*x^6 - 30*x^5 + 25*x^3)*e^2
+ (x^5 + 6*x^4 + 9*x^3)*e^(4*x + 2) + 8*(x^7 + 6*x^6 + 9*x^5 - 5*x^4 - 15*x^3)*e^(2*x + 2))

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giac [B]  time = 0.22, size = 145, normalized size = 4.14 $$\begin{array}{c}\frac{x^{6}e+6x^{5}e+9x^{4}e-10x^{3}e-30x^{2}e+25e}{2(16x^9+96x^8+8x^7{e}^{\left(2x\right)}+144x^7+48x^6{e}^{\left(2x\right)}-160x^6+x^5{e}^{\left(4x\right)}+72x^5{e}^{\left(2x\right)}-480x^5+6x^4{e}^{\left(4x\right)}-40x^4{e}^{\left(2x\right)}+9x^3{e}^{\left(4x\right)}-120x^3{e}^{\left(2x\right)}+400x^3)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x^8-35*x^7-99*x^6-41*x^5+287*x^4+450*x^3-10*x^2-425*x-225)*exp(1)*exp(x)^2+(-12*x^9-108*x^8-324
*x^7-144*x^6+1080*x^5+1620*x^4-900*x^3-2700*x^2+1500)*exp(1))/((2*x^7+18*x^6+54*x^5+54*x^4)*exp(x)^6+(24*x^9+2
16*x^8+648*x^7+528*x^6-720*x^5-1080*x^4)*exp(x)^4+(96*x^11+864*x^10+2592*x^9+1632*x^8-5760*x^7-8640*x^6+2400*x
^5+7200*x^4)*exp(x)^2+128*x^13+1152*x^12+3456*x^11+1536*x^10-11520*x^9-17280*x^8+9600*x^7+28800*x^6-16000*x^4)
,x, algorithm="giac")

[Out]

1/2*(x^6*e + 6*x^5*e + 9*x^4*e - 10*x^3*e - 30*x^2*e + 25*e)/(16*x^9 + 96*x^8 + 8*x^7*e^(2*x) + 144*x^7 + 48*x
^6*e^(2*x) - 160*x^6 + x^5*e^(4*x) + 72*x^5*e^(2*x) - 480*x^5 + 6*x^4*e^(4*x) - 40*x^4*e^(2*x) + 9*x^3*e^(4*x)
- 120*x^3*e^(2*x) + 400*x^3)

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maple [A]  time = 0.08, size = 59, normalized size = 1.69

method	result	size
risch	$\frac{\mathrm{e}(x^6+6x^5+9x^4-10x^3-30x^2+25)}{2x^3{(x{\mathrm{e}}^{2x}+4x^3+3{\mathrm{e}}^{2x}+12x^2-20)}^2}$	$59$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-4*x^8-35*x^7-99*x^6-41*x^5+287*x^4+450*x^3-10*x^2-425*x-225)*exp(1)*exp(x)^2+(-12*x^9-108*x^8-324*x^7-1
44*x^6+1080*x^5+1620*x^4-900*x^3-2700*x^2+1500)*exp(1))/((2*x^7+18*x^6+54*x^5+54*x^4)*exp(x)^6+(24*x^9+216*x^8
+648*x^7+528*x^6-720*x^5-1080*x^4)*exp(x)^4+(96*x^11+864*x^10+2592*x^9+1632*x^8-5760*x^7-8640*x^6+2400*x^5+720
0*x^4)*exp(x)^2+128*x^13+1152*x^12+3456*x^11+1536*x^10-11520*x^9-17280*x^8+9600*x^7+28800*x^6-16000*x^4),x,met
hod=_RETURNVERBOSE)

[Out]

1/2*exp(1)*(x^6+6*x^5+9*x^4-10*x^3-30*x^2+25)/x^3/(x*exp(2*x)+4*x^3+3*exp(2*x)+12*x^2-20)^2

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maxima [B]  time = 0.71, size = 123, normalized size = 3.51 $$\begin{array}{c}\frac{x^{6}e+6x^{5}e+9x^{4}e-10x^{3}e-30x^{2}e+25e}{2(16x^9+96x^8+144x^7-160x^6-480x^5+400x^3+(x^5+6x^4+9x^3)e^{\left(4x\right)}+8(x^7+6x^6+9x^5-5x^4-15x^3)e^{\left(2x\right)})}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x^8-35*x^7-99*x^6-41*x^5+287*x^4+450*x^3-10*x^2-425*x-225)*exp(1)*exp(x)^2+(-12*x^9-108*x^8-324
*x^7-144*x^6+1080*x^5+1620*x^4-900*x^3-2700*x^2+1500)*exp(1))/((2*x^7+18*x^6+54*x^5+54*x^4)*exp(x)^6+(24*x^9+2
16*x^8+648*x^7+528*x^6-720*x^5-1080*x^4)*exp(x)^4+(96*x^11+864*x^10+2592*x^9+1632*x^8-5760*x^7-8640*x^6+2400*x
^5+7200*x^4)*exp(x)^2+128*x^13+1152*x^12+3456*x^11+1536*x^10-11520*x^9-17280*x^8+9600*x^7+28800*x^6-16000*x^4)
,x, algorithm="maxima")

[Out]

1/2*(x^6*e + 6*x^5*e + 9*x^4*e - 10*x^3*e - 30*x^2*e + 25*e)/(16*x^9 + 96*x^8 + 144*x^7 - 160*x^6 - 480*x^5 +
400*x^3 + (x^5 + 6*x^4 + 9*x^3)*e^(4*x) + 8*(x^7 + 6*x^6 + 9*x^5 - 5*x^4 - 15*x^3)*e^(2*x))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 $$\begin{array}{c}\int -\frac{\mathrm{e}(12x^9+108x^8+324x^7+144x^6-1080x^5-1620x^4+900x^3+2700x^2-1500)+{\mathrm{e}}^{2x}\mathrm{e}(4x^8+35x^7+99x^6+41x^5-287x^4-450x^3+10x^2+425x+225)}{{\mathrm{e}}^{4x}(24x^9+216x^8+648x^7+528x^6-720x^5-1080x^4)+{\mathrm{e}}^{2x}(96x^{11}+864x^{10}+2592x^9+1632x^8-5760x^7-8640x^6+2400x^5+7200x^4)+{\mathrm{e}}^{6x}(2x^7+18x^6+54x^5+54x^4)-16000x^4+28800x^6+9600x^7-17280x^8-11520x^9+1536x^{10}+3456x^{11}+1152x^{12}+128x^{13}}dx\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(1)*(2700*x^2 + 900*x^3 - 1620*x^4 - 1080*x^5 + 144*x^6 + 324*x^7 + 108*x^8 + 12*x^9 - 1500) + exp(2*
x)*exp(1)*(425*x + 10*x^2 - 450*x^3 - 287*x^4 + 41*x^5 + 99*x^6 + 35*x^7 + 4*x^8 + 225))/(exp(4*x)*(528*x^6 -
720*x^5 - 1080*x^4 + 648*x^7 + 216*x^8 + 24*x^9) + exp(2*x)*(7200*x^4 + 2400*x^5 - 8640*x^6 - 5760*x^7 + 1632*
x^8 + 2592*x^9 + 864*x^10 + 96*x^11) + exp(6*x)*(54*x^4 + 54*x^5 + 18*x^6 + 2*x^7) - 16000*x^4 + 28800*x^6 + 9
600*x^7 - 17280*x^8 - 11520*x^9 + 1536*x^10 + 3456*x^11 + 1152*x^12 + 128*x^13),x)

[Out]

int(-(exp(1)*(2700*x^2 + 900*x^3 - 1620*x^4 - 1080*x^5 + 144*x^6 + 324*x^7 + 108*x^8 + 12*x^9 - 1500) + exp(2*
x)*exp(1)*(425*x + 10*x^2 - 450*x^3 - 287*x^4 + 41*x^5 + 99*x^6 + 35*x^7 + 4*x^8 + 225))/(exp(4*x)*(528*x^6 -
720*x^5 - 1080*x^4 + 648*x^7 + 216*x^8 + 24*x^9) + exp(2*x)*(7200*x^4 + 2400*x^5 - 8640*x^6 - 5760*x^7 + 1632*
x^8 + 2592*x^9 + 864*x^10 + 96*x^11) + exp(6*x)*(54*x^4 + 54*x^5 + 18*x^6 + 2*x^7) - 16000*x^4 + 28800*x^6 + 9
600*x^7 - 17280*x^8 - 11520*x^9 + 1536*x^10 + 3456*x^11 + 1152*x^12 + 128*x^13), x)

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sympy [B]  time = 0.75, size = 126, normalized size = 3.60 $$\begin{array}{c}\frac{e{x}^6+6e{x}^5+9e{x}^4-10e{x}^3-30e{x}^2+25e}{32x^9+192x^8+288x^7-320x^6-960x^5+800x^3+(2x^5+12x^4+18x^3)e^{4x}+(16x^7+96x^6+144x^5-80x^4-240x^3)e^{2x}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x**8-35*x**7-99*x**6-41*x**5+287*x**4+450*x**3-10*x**2-425*x-225)*exp(1)*exp(x)**2+(-12*x**9-10
8*x**8-324*x**7-144*x**6+1080*x**5+1620*x**4-900*x**3-2700*x**2+1500)*exp(1))/((2*x**7+18*x**6+54*x**5+54*x**4
)*exp(x)**6+(24*x**9+216*x**8+648*x**7+528*x**6-720*x**5-1080*x**4)*exp(x)**4+(96*x**11+864*x**10+2592*x**9+16
32*x**8-5760*x**7-8640*x**6+2400*x**5+7200*x**4)*exp(x)**2+128*x**13+1152*x**12+3456*x**11+1536*x**10-11520*x*
*9-17280*x**8+9600*x**7+28800*x**6-16000*x**4),x)

[Out]

(E*x**6 + 6*E*x**5 + 9*E*x**4 - 10*E*x**3 - 30*E*x**2 + 25*E)/(32*x**9 + 192*x**8 + 288*x**7 - 320*x**6 - 960*
x**5 + 800*x**3 + (2*x**5 + 12*x**4 + 18*x**3)*exp(4*x) + (16*x**7 + 96*x**6 + 144*x**5 - 80*x**4 - 240*x**3)*
exp(2*x))

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