3.33.80 $\int \frac{e^{5x}(-396+4e^3+80x-4x^2)+e^{4x}(-1584x+1904x^2-336x^3+16x^4+e^3(16x-16x^2))+e^{3x}(-48-2376x^2+5232x^3-3360x^4+528x^5-24x^6+e^3(24x^2-48x^3+24x^4))+e^{2x}(-32+64x^2-1584x^3+5072x^4-5728x^5+2592x^6-368x^7+16x^8+e^3(16x^3-48x^4+48x^5-16x^6))+e^x(-32x+80x^2-32x^3-412x^4+1664x^5-2700x^6+2080x^7-740x^8+96x^9-4x^{10}+e^3(4x^4-16x^5+24x^6-16x^7+4x^8))}{16+648x^2-1440x^3+7505x^4-29320x^5+51524x^6-45720x^7+21286x^8-5080x^9+636x^{10}-40x^{11}+x^{12}+e^6(x^4-4x^5+6x^6-4x^7+x^8)+e^3(-8x^2+16x^3-170x^4+684x^5-1118x^6+872x^7-318x^8+44x^9-2x^{10})+e^{4x}(6561+e^6-2916x+486x^2-36x^3+x^4+e^3(-162+36x-2x^2))+e^{3x}(26244x-37908x^2+13608x^3-2088x^4+148x^5-4x^6+e^6(4x-4x^2)+e^3(-648x+792x^2-152x^3+8x^4))+e^{2x}(648-144x+39374x^2-96228x^3+77274x^4-23544x^5+3354x^6-228x^7+6x^8+e^6(6x^2-12x^3+6x^4)+e^3(-8-972x^2+2160x^3-1416x^4+240x^5-12x^6))+e^x(1296x-1584x^2+26548x^3-90412x^4+115668x^5-67212x^6+17932x^7-2388x^8+156x^9-4x^{10}+e^6(4x^3-12x^4+12x^5-4x^6)+e^3(-16x+16x^2-648x^3+2088x^4-2384x^5+1104x^6-168x^7+8x^8))}dx$

Optimal. Leaf size=34 $$\frac{4e^x}{e^3-(9-x{)}^2-\frac{4}{{(e^x+x-x^2)}^2}}$$

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Rubi [F]  time = 180.00, 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 = {} $$\begin{array}{c}\text{\$Aborted}\end{array}$$

Verification is not applicable to the result.

[In]

Int[(E^(5*x)*(-396 + 4*E^3 + 80*x - 4*x^2) + E^(4*x)*(-1584*x + 1904*x^2 - 336*x^3 + 16*x^4 + E^3*(16*x - 16*x
^2)) + E^(3*x)*(-48 - 2376*x^2 + 5232*x^3 - 3360*x^4 + 528*x^5 - 24*x^6 + E^3*(24*x^2 - 48*x^3 + 24*x^4)) + E^
(2*x)*(-32 + 64*x^2 - 1584*x^3 + 5072*x^4 - 5728*x^5 + 2592*x^6 - 368*x^7 + 16*x^8 + E^3*(16*x^3 - 48*x^4 + 48
*x^5 - 16*x^6)) + E^x*(-32*x + 80*x^2 - 32*x^3 - 412*x^4 + 1664*x^5 - 2700*x^6 + 2080*x^7 - 740*x^8 + 96*x^9 -
4*x^10 + E^3*(4*x^4 - 16*x^5 + 24*x^6 - 16*x^7 + 4*x^8)))/(16 + 648*x^2 - 1440*x^3 + 7505*x^4 - 29320*x^5 + 5
1524*x^6 - 45720*x^7 + 21286*x^8 - 5080*x^9 + 636*x^10 - 40*x^11 + x^12 + E^6*(x^4 - 4*x^5 + 6*x^6 - 4*x^7 + x
^8) + E^3*(-8*x^2 + 16*x^3 - 170*x^4 + 684*x^5 - 1118*x^6 + 872*x^7 - 318*x^8 + 44*x^9 - 2*x^10) + E^(4*x)*(65
61 + E^6 - 2916*x + 486*x^2 - 36*x^3 + x^4 + E^3*(-162 + 36*x - 2*x^2)) + E^(3*x)*(26244*x - 37908*x^2 + 13608
*x^3 - 2088*x^4 + 148*x^5 - 4*x^6 + E^6*(4*x - 4*x^2) + E^3*(-648*x + 792*x^2 - 152*x^3 + 8*x^4)) + E^(2*x)*(6
48 - 144*x + 39374*x^2 - 96228*x^3 + 77274*x^4 - 23544*x^5 + 3354*x^6 - 228*x^7 + 6*x^8 + E^6*(6*x^2 - 12*x^3
+ 6*x^4) + E^3*(-8 - 972*x^2 + 2160*x^3 - 1416*x^4 + 240*x^5 - 12*x^6)) + E^x*(1296*x - 1584*x^2 + 26548*x^3 -
90412*x^4 + 115668*x^5 - 67212*x^6 + 17932*x^7 - 2388*x^8 + 156*x^9 - 4*x^10 + E^6*(4*x^3 - 12*x^4 + 12*x^5 -
4*x^6) + E^3*(-16*x + 16*x^2 - 648*x^3 + 2088*x^4 - 2384*x^5 + 1104*x^6 - 168*x^7 + 8*x^8))),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [B]  time = 0.40, size = 102, normalized size = 3.00 $$\begin{array}{c}-\frac{4e^x{(e^x+x-x^2)}^2}{4-e^{3+2x}+e^{2x}(-9+x{)}^2+2e^{3+x}(-1+x)x-2e^x(-9+x{)}^2(-1+x)x+81x^2-e^3(-1+x{)}^2{x}^2-180x^3+118x^4-20x^5+x^6}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(E^(5*x)*(-396 + 4*E^3 + 80*x - 4*x^2) + E^(4*x)*(-1584*x + 1904*x^2 - 336*x^3 + 16*x^4 + E^3*(16*x
- 16*x^2)) + E^(3*x)*(-48 - 2376*x^2 + 5232*x^3 - 3360*x^4 + 528*x^5 - 24*x^6 + E^3*(24*x^2 - 48*x^3 + 24*x^4)
) + E^(2*x)*(-32 + 64*x^2 - 1584*x^3 + 5072*x^4 - 5728*x^5 + 2592*x^6 - 368*x^7 + 16*x^8 + E^3*(16*x^3 - 48*x^
4 + 48*x^5 - 16*x^6)) + E^x*(-32*x + 80*x^2 - 32*x^3 - 412*x^4 + 1664*x^5 - 2700*x^6 + 2080*x^7 - 740*x^8 + 96
*x^9 - 4*x^10 + E^3*(4*x^4 - 16*x^5 + 24*x^6 - 16*x^7 + 4*x^8)))/(16 + 648*x^2 - 1440*x^3 + 7505*x^4 - 29320*x
^5 + 51524*x^6 - 45720*x^7 + 21286*x^8 - 5080*x^9 + 636*x^10 - 40*x^11 + x^12 + E^6*(x^4 - 4*x^5 + 6*x^6 - 4*x
^7 + x^8) + E^3*(-8*x^2 + 16*x^3 - 170*x^4 + 684*x^5 - 1118*x^6 + 872*x^7 - 318*x^8 + 44*x^9 - 2*x^10) + E^(4*
x)*(6561 + E^6 - 2916*x + 486*x^2 - 36*x^3 + x^4 + E^3*(-162 + 36*x - 2*x^2)) + E^(3*x)*(26244*x - 37908*x^2 +
13608*x^3 - 2088*x^4 + 148*x^5 - 4*x^6 + E^6*(4*x - 4*x^2) + E^3*(-648*x + 792*x^2 - 152*x^3 + 8*x^4)) + E^(2
*x)*(648 - 144*x + 39374*x^2 - 96228*x^3 + 77274*x^4 - 23544*x^5 + 3354*x^6 - 228*x^7 + 6*x^8 + E^6*(6*x^2 - 1
2*x^3 + 6*x^4) + E^3*(-8 - 972*x^2 + 2160*x^3 - 1416*x^4 + 240*x^5 - 12*x^6)) + E^x*(1296*x - 1584*x^2 + 26548
*x^3 - 90412*x^4 + 115668*x^5 - 67212*x^6 + 17932*x^7 - 2388*x^8 + 156*x^9 - 4*x^10 + E^6*(4*x^3 - 12*x^4 + 12
*x^5 - 4*x^6) + E^3*(-16*x + 16*x^2 - 648*x^3 + 2088*x^4 - 2384*x^5 + 1104*x^6 - 168*x^7 + 8*x^8))),x]

[Out]

(-4*E^x*(E^x + x - x^2)^2)/(4 - E^(3 + 2*x) + E^(2*x)*(-9 + x)^2 + 2*E^(3 + x)*(-1 + x)*x - 2*E^x*(-9 + x)^2*(
-1 + x)*x + 81*x^2 - E^3*(-1 + x)^2*x^2 - 180*x^3 + 118*x^4 - 20*x^5 + x^6)

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fricas [B]  time = 0.66, size = 130, normalized size = 3.82 $$\begin{array}{c}\frac{4(2(x^2-x)e^{\left(2x\right)}-(x^4-2x^3+x^2)e^x-e^{\left(3x\right)})}{x^6-20x^5+118x^4-180x^3+81x^2-(x^4-2x^3+x^2)e^3+(x^2-18x-e^3+81)e^{\left(2x\right)}-2(x^4-19x^3+99x^2-(x^2-x)e^3-81x)e^x+4}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*exp(3)-4*x^2+80*x-396)*exp(x)^5+((-16*x^2+16*x)*exp(3)+16*x^4-336*x^3+1904*x^2-1584*x)*exp(x)^4+
((24*x^4-48*x^3+24*x^2)*exp(3)-24*x^6+528*x^5-3360*x^4+5232*x^3-2376*x^2-48)*exp(x)^3+((-16*x^6+48*x^5-48*x^4+
16*x^3)*exp(3)+16*x^8-368*x^7+2592*x^6-5728*x^5+5072*x^4-1584*x^3+64*x^2-32)*exp(x)^2+((4*x^8-16*x^7+24*x^6-16
*x^5+4*x^4)*exp(3)-4*x^10+96*x^9-740*x^8+2080*x^7-2700*x^6+1664*x^5-412*x^4-32*x^3+80*x^2-32*x)*exp(x))/((exp(
3)^2+(-2*x^2+36*x-162)*exp(3)+x^4-36*x^3+486*x^2-2916*x+6561)*exp(x)^4+((-4*x^2+4*x)*exp(3)^2+(8*x^4-152*x^3+7
92*x^2-648*x)*exp(3)-4*x^6+148*x^5-2088*x^4+13608*x^3-37908*x^2+26244*x)*exp(x)^3+((6*x^4-12*x^3+6*x^2)*exp(3)
^2+(-12*x^6+240*x^5-1416*x^4+2160*x^3-972*x^2-8)*exp(3)+6*x^8-228*x^7+3354*x^6-23544*x^5+77274*x^4-96228*x^3+3
9374*x^2-144*x+648)*exp(x)^2+((-4*x^6+12*x^5-12*x^4+4*x^3)*exp(3)^2+(8*x^8-168*x^7+1104*x^6-2384*x^5+2088*x^4-
648*x^3+16*x^2-16*x)*exp(3)-4*x^10+156*x^9-2388*x^8+17932*x^7-67212*x^6+115668*x^5-90412*x^4+26548*x^3-1584*x^
2+1296*x)*exp(x)+(x^8-4*x^7+6*x^6-4*x^5+x^4)*exp(3)^2+(-2*x^10+44*x^9-318*x^8+872*x^7-1118*x^6+684*x^5-170*x^4
+16*x^3-8*x^2)*exp(3)+x^12-40*x^11+636*x^10-5080*x^9+21286*x^8-45720*x^7+51524*x^6-29320*x^5+7505*x^4-1440*x^3
+648*x^2+16),x, algorithm="fricas")

[Out]

4*(2*(x^2 - x)*e^(2*x) - (x^4 - 2*x^3 + x^2)*e^x - e^(3*x))/(x^6 - 20*x^5 + 118*x^4 - 180*x^3 + 81*x^2 - (x^4
- 2*x^3 + x^2)*e^3 + (x^2 - 18*x - e^3 + 81)*e^(2*x) - 2*(x^4 - 19*x^3 + 99*x^2 - (x^2 - x)*e^3 - 81*x)*e^x +
4)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*exp(3)-4*x^2+80*x-396)*exp(x)^5+((-16*x^2+16*x)*exp(3)+16*x^4-336*x^3+1904*x^2-1584*x)*exp(x)^4+
((24*x^4-48*x^3+24*x^2)*exp(3)-24*x^6+528*x^5-3360*x^4+5232*x^3-2376*x^2-48)*exp(x)^3+((-16*x^6+48*x^5-48*x^4+
16*x^3)*exp(3)+16*x^8-368*x^7+2592*x^6-5728*x^5+5072*x^4-1584*x^3+64*x^2-32)*exp(x)^2+((4*x^8-16*x^7+24*x^6-16
*x^5+4*x^4)*exp(3)-4*x^10+96*x^9-740*x^8+2080*x^7-2700*x^6+1664*x^5-412*x^4-32*x^3+80*x^2-32*x)*exp(x))/((exp(
3)^2+(-2*x^2+36*x-162)*exp(3)+x^4-36*x^3+486*x^2-2916*x+6561)*exp(x)^4+((-4*x^2+4*x)*exp(3)^2+(8*x^4-152*x^3+7
92*x^2-648*x)*exp(3)-4*x^6+148*x^5-2088*x^4+13608*x^3-37908*x^2+26244*x)*exp(x)^3+((6*x^4-12*x^3+6*x^2)*exp(3)
^2+(-12*x^6+240*x^5-1416*x^4+2160*x^3-972*x^2-8)*exp(3)+6*x^8-228*x^7+3354*x^6-23544*x^5+77274*x^4-96228*x^3+3
9374*x^2-144*x+648)*exp(x)^2+((-4*x^6+12*x^5-12*x^4+4*x^3)*exp(3)^2+(8*x^8-168*x^7+1104*x^6-2384*x^5+2088*x^4-
648*x^3+16*x^2-16*x)*exp(3)-4*x^10+156*x^9-2388*x^8+17932*x^7-67212*x^6+115668*x^5-90412*x^4+26548*x^3-1584*x^
2+1296*x)*exp(x)+(x^8-4*x^7+6*x^6-4*x^5+x^4)*exp(3)^2+(-2*x^10+44*x^9-318*x^8+872*x^7-1118*x^6+684*x^5-170*x^4
+16*x^3-8*x^2)*exp(3)+x^12-40*x^11+636*x^10-5080*x^9+21286*x^8-45720*x^7+51524*x^6-29320*x^5+7505*x^4-1440*x^3
+648*x^2+16),x, algorithm="giac")

[Out]

Timed out

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maple [F]  time = 0.31, size = 0, normalized size = 0.00 $$\int \frac{(4{\mathrm{e}}^3-4x^2+80x-396){\mathrm{e}}^{5x}+((-16x^2+16x){\mathrm{e}}^3+16x^4-336x^3+1904x^2-1584x){\mathrm{e}}^{4x}+((24x^4-48x^3+24x^2){\mathrm{e}}^3-24x^6+528x^5-3360x^4+5232x^3-2376x^2-48){\mathrm{e}}^{3x}+((-16x^6+48x^5-48x^4+16x^3){\mathrm{e}}^3+16x^8-368x^7+2592x^6-5728x^5+5072x^4-1584x^3+64x^2-32){\mathrm{e}}^{2x}+((4x^8-16x^7+24x^6-16x^5+4x^4){\mathrm{e}}^3-4x^{10}+96x^9-740x^8+2080x^7-2700x^6+1664x^5-412x^4-32x^3+80x^2-32x){\mathrm{e}}^x}{({\mathrm{e}}^6+(-2x^2+36x-162){\mathrm{e}}^3+x^4-36x^3+486x^2-2916x+6561){\mathrm{e}}^{4x}+((-4x^2+4x){\mathrm{e}}^6+(8x^4-152x^3+792x^2-648x){\mathrm{e}}^3-4x^6+148x^5-2088x^4+13608x^3-37908x^2+26244x){\mathrm{e}}^{3x}+((6x^4-12x^3+6x^2){\mathrm{e}}^6+(-12x^6+240x^5-1416x^4+2160x^3-972x^2-8){\mathrm{e}}^3+6x^8-228x^7+3354x^6-23544x^5+77274x^4-96228x^3+39374x^2-144x+648){\mathrm{e}}^{2x}+((-4x^6+12x^5-12x^4+4x^3){\mathrm{e}}^6+(8x^8-168x^7+1104x^6-2384x^5+2088x^4-648x^3+16x^2-16x){\mathrm{e}}^3-4x^{10}+156x^9-2388x^8+17932x^7-67212x^6+115668x^5-90412x^4+26548x^3-1584x^2+1296x){\mathrm{e}}^x+(x^8-4x^7+6x^6-4x^5+x^4){\mathrm{e}}^6+(-2x^{10}+44x^9-318x^8+872x^7-1118x^6+684x^5-170x^4+16x^3-8x^2){\mathrm{e}}^3+x^{12}-40x^{11}+636x^{10}-5080x^9+21286x^8-45720x^7+51524x^6-29320x^5+7505x^4-1440x^3+648x^2+16}dx$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((4*exp(3)-4*x^2+80*x-396)*exp(x)^5+((-16*x^2+16*x)*exp(3)+16*x^4-336*x^3+1904*x^2-1584*x)*exp(x)^4+((24*x
^4-48*x^3+24*x^2)*exp(3)-24*x^6+528*x^5-3360*x^4+5232*x^3-2376*x^2-48)*exp(x)^3+((-16*x^6+48*x^5-48*x^4+16*x^3
)*exp(3)+16*x^8-368*x^7+2592*x^6-5728*x^5+5072*x^4-1584*x^3+64*x^2-32)*exp(x)^2+((4*x^8-16*x^7+24*x^6-16*x^5+4
*x^4)*exp(3)-4*x^10+96*x^9-740*x^8+2080*x^7-2700*x^6+1664*x^5-412*x^4-32*x^3+80*x^2-32*x)*exp(x))/((exp(3)^2+(
-2*x^2+36*x-162)*exp(3)+x^4-36*x^3+486*x^2-2916*x+6561)*exp(x)^4+((-4*x^2+4*x)*exp(3)^2+(8*x^4-152*x^3+792*x^2
-648*x)*exp(3)-4*x^6+148*x^5-2088*x^4+13608*x^3-37908*x^2+26244*x)*exp(x)^3+((6*x^4-12*x^3+6*x^2)*exp(3)^2+(-1
2*x^6+240*x^5-1416*x^4+2160*x^3-972*x^2-8)*exp(3)+6*x^8-228*x^7+3354*x^6-23544*x^5+77274*x^4-96228*x^3+39374*x
^2-144*x+648)*exp(x)^2+((-4*x^6+12*x^5-12*x^4+4*x^3)*exp(3)^2+(8*x^8-168*x^7+1104*x^6-2384*x^5+2088*x^4-648*x^
3+16*x^2-16*x)*exp(3)-4*x^10+156*x^9-2388*x^8+17932*x^7-67212*x^6+115668*x^5-90412*x^4+26548*x^3-1584*x^2+1296
*x)*exp(x)+(x^8-4*x^7+6*x^6-4*x^5+x^4)*exp(3)^2+(-2*x^10+44*x^9-318*x^8+872*x^7-1118*x^6+684*x^5-170*x^4+16*x^
3-8*x^2)*exp(3)+x^12-40*x^11+636*x^10-5080*x^9+21286*x^8-45720*x^7+51524*x^6-29320*x^5+7505*x^4-1440*x^3+648*x
^2+16),x)

[Out]

int(((4*exp(3)-4*x^2+80*x-396)*exp(x)^5+((-16*x^2+16*x)*exp(3)+16*x^4-336*x^3+1904*x^2-1584*x)*exp(x)^4+((24*x
^4-48*x^3+24*x^2)*exp(3)-24*x^6+528*x^5-3360*x^4+5232*x^3-2376*x^2-48)*exp(x)^3+((-16*x^6+48*x^5-48*x^4+16*x^3
)*exp(3)+16*x^8-368*x^7+2592*x^6-5728*x^5+5072*x^4-1584*x^3+64*x^2-32)*exp(x)^2+((4*x^8-16*x^7+24*x^6-16*x^5+4
*x^4)*exp(3)-4*x^10+96*x^9-740*x^8+2080*x^7-2700*x^6+1664*x^5-412*x^4-32*x^3+80*x^2-32*x)*exp(x))/((exp(3)^2+(
-2*x^2+36*x-162)*exp(3)+x^4-36*x^3+486*x^2-2916*x+6561)*exp(x)^4+((-4*x^2+4*x)*exp(3)^2+(8*x^4-152*x^3+792*x^2
-648*x)*exp(3)-4*x^6+148*x^5-2088*x^4+13608*x^3-37908*x^2+26244*x)*exp(x)^3+((6*x^4-12*x^3+6*x^2)*exp(3)^2+(-1
2*x^6+240*x^5-1416*x^4+2160*x^3-972*x^2-8)*exp(3)+6*x^8-228*x^7+3354*x^6-23544*x^5+77274*x^4-96228*x^3+39374*x
^2-144*x+648)*exp(x)^2+((-4*x^6+12*x^5-12*x^4+4*x^3)*exp(3)^2+(8*x^8-168*x^7+1104*x^6-2384*x^5+2088*x^4-648*x^
3+16*x^2-16*x)*exp(3)-4*x^10+156*x^9-2388*x^8+17932*x^7-67212*x^6+115668*x^5-90412*x^4+26548*x^3-1584*x^2+1296
*x)*exp(x)+(x^8-4*x^7+6*x^6-4*x^5+x^4)*exp(3)^2+(-2*x^10+44*x^9-318*x^8+872*x^7-1118*x^6+684*x^5-170*x^4+16*x^
3-8*x^2)*exp(3)+x^12-40*x^11+636*x^10-5080*x^9+21286*x^8-45720*x^7+51524*x^6-29320*x^5+7505*x^4-1440*x^3+648*x
^2+16),x)

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maxima [B]  time = 1.05, size = 122, normalized size = 3.59 $$\begin{array}{c}\frac{4(2(x^2-x)e^{\left(2x\right)}-(x^4-2x^3+x^2)e^x-e^{\left(3x\right)})}{x^6-20x^5-x^4(e^3-118)+2x^3(e^3-90)-x^2(e^3-81)+(x^2-18x-e^3+81)e^{\left(2x\right)}-2(x^4-19x^3-x^2(e^3-99)+x(e^3-81))e^x+4}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*exp(3)-4*x^2+80*x-396)*exp(x)^5+((-16*x^2+16*x)*exp(3)+16*x^4-336*x^3+1904*x^2-1584*x)*exp(x)^4+
((24*x^4-48*x^3+24*x^2)*exp(3)-24*x^6+528*x^5-3360*x^4+5232*x^3-2376*x^2-48)*exp(x)^3+((-16*x^6+48*x^5-48*x^4+
16*x^3)*exp(3)+16*x^8-368*x^7+2592*x^6-5728*x^5+5072*x^4-1584*x^3+64*x^2-32)*exp(x)^2+((4*x^8-16*x^7+24*x^6-16
*x^5+4*x^4)*exp(3)-4*x^10+96*x^9-740*x^8+2080*x^7-2700*x^6+1664*x^5-412*x^4-32*x^3+80*x^2-32*x)*exp(x))/((exp(
3)^2+(-2*x^2+36*x-162)*exp(3)+x^4-36*x^3+486*x^2-2916*x+6561)*exp(x)^4+((-4*x^2+4*x)*exp(3)^2+(8*x^4-152*x^3+7
92*x^2-648*x)*exp(3)-4*x^6+148*x^5-2088*x^4+13608*x^3-37908*x^2+26244*x)*exp(x)^3+((6*x^4-12*x^3+6*x^2)*exp(3)
^2+(-12*x^6+240*x^5-1416*x^4+2160*x^3-972*x^2-8)*exp(3)+6*x^8-228*x^7+3354*x^6-23544*x^5+77274*x^4-96228*x^3+3
9374*x^2-144*x+648)*exp(x)^2+((-4*x^6+12*x^5-12*x^4+4*x^3)*exp(3)^2+(8*x^8-168*x^7+1104*x^6-2384*x^5+2088*x^4-
648*x^3+16*x^2-16*x)*exp(3)-4*x^10+156*x^9-2388*x^8+17932*x^7-67212*x^6+115668*x^5-90412*x^4+26548*x^3-1584*x^
2+1296*x)*exp(x)+(x^8-4*x^7+6*x^6-4*x^5+x^4)*exp(3)^2+(-2*x^10+44*x^9-318*x^8+872*x^7-1118*x^6+684*x^5-170*x^4
+16*x^3-8*x^2)*exp(3)+x^12-40*x^11+636*x^10-5080*x^9+21286*x^8-45720*x^7+51524*x^6-29320*x^5+7505*x^4-1440*x^3
+648*x^2+16),x, algorithm="maxima")

[Out]

4*(2*(x^2 - x)*e^(2*x) - (x^4 - 2*x^3 + x^2)*e^x - e^(3*x))/(x^6 - 20*x^5 - x^4*(e^3 - 118) + 2*x^3*(e^3 - 90)
- x^2*(e^3 - 81) + (x^2 - 18*x - e^3 + 81)*e^(2*x) - 2*(x^4 - 19*x^3 - x^2*(e^3 - 99) + x*(e^3 - 81))*e^x + 4
)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 $$\begin{array}{c}\int \frac{{\mathrm{e}}^{2x}(64x^2-1584x^3+5072x^4-5728x^5+2592x^6-368x^7+16x^8+{\mathrm{e}}^3(-16x^6+48x^5-48x^4+16x^3)-32)-{\mathrm{e}}^x(32x-{\mathrm{e}}^3(4x^8-16x^7+24x^6-16x^5+4x^4)-80x^2+32x^3+412x^4-1664x^5+2700x^6-2080x^7+740x^8-96x^9+4x^{10})+{\mathrm{e}}^{4x}({\mathrm{e}}^3(16x-16x^2)-1584x+1904x^2-336x^3+16x^4)+{\mathrm{e}}^{5x}(-4x^2+80x+4{\mathrm{e}}^3-396)-{\mathrm{e}}^{3x}(2376x^2-{\mathrm{e}}^3(24x^4-48x^3+24x^2)-5232x^3+3360x^4-528x^5+24x^6+48)}{{\mathrm{e}}^{2x}({\mathrm{e}}^6(6x^4-12x^3+6x^2)-{\mathrm{e}}^3(12x^6-240x^5+1416x^4-2160x^3+972x^2+8)-144x+39374x^2-96228x^3+77274x^4-23544x^5+3354x^6-228x^7+6x^8+648)-{\mathrm{e}}^3(2x^{10}-44x^9+318x^8-872x^7+1118x^6-684x^5+170x^4-16x^3+8x^2)+{\mathrm{e}}^6(x^8-4x^7+6x^6-4x^5+x^4)+{\mathrm{e}}^{4x}({\mathrm{e}}^6-2916x-{\mathrm{e}}^3(2x^2-36x+162)+486x^2-36x^3+x^4+6561)+{\mathrm{e}}^{3x}(26244x+{\mathrm{e}}^6(4x-4x^2)-{\mathrm{e}}^3(-8x^4+152x^3-792x^2+648x)-37908x^2+13608x^3-2088x^4+148x^5-4x^6)+648x^2-1440x^3+7505x^4-29320x^5+51524x^6-45720x^7+21286x^8-5080x^9+636x^{10}-40x^{11}+x^{12}+{\mathrm{e}}^x(1296x-{\mathrm{e}}^3(-8x^8+168x^7-1104x^6+2384x^5-2088x^4+648x^3-16x^2+16x)-1584x^2+26548x^3-90412x^4+115668x^5-67212x^6+17932x^7-2388x^8+156x^9-4x^{10}+{\mathrm{e}}^6(-4x^6+12x^5-12x^4+4x^3))+16}dx\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(2*x)*(64*x^2 - 1584*x^3 + 5072*x^4 - 5728*x^5 + 2592*x^6 - 368*x^7 + 16*x^8 + exp(3)*(16*x^3 - 48*x^4
+ 48*x^5 - 16*x^6) - 32) - exp(x)*(32*x - exp(3)*(4*x^4 - 16*x^5 + 24*x^6 - 16*x^7 + 4*x^8) - 80*x^2 + 32*x^3
+ 412*x^4 - 1664*x^5 + 2700*x^6 - 2080*x^7 + 740*x^8 - 96*x^9 + 4*x^10) + exp(4*x)*(exp(3)*(16*x - 16*x^2) -
1584*x + 1904*x^2 - 336*x^3 + 16*x^4) + exp(5*x)*(80*x + 4*exp(3) - 4*x^2 - 396) - exp(3*x)*(2376*x^2 - exp(3)
*(24*x^2 - 48*x^3 + 24*x^4) - 5232*x^3 + 3360*x^4 - 528*x^5 + 24*x^6 + 48))/(exp(2*x)*(exp(6)*(6*x^2 - 12*x^3
+ 6*x^4) - exp(3)*(972*x^2 - 2160*x^3 + 1416*x^4 - 240*x^5 + 12*x^6 + 8) - 144*x + 39374*x^2 - 96228*x^3 + 772
74*x^4 - 23544*x^5 + 3354*x^6 - 228*x^7 + 6*x^8 + 648) - exp(3)*(8*x^2 - 16*x^3 + 170*x^4 - 684*x^5 + 1118*x^6
- 872*x^7 + 318*x^8 - 44*x^9 + 2*x^10) + exp(6)*(x^4 - 4*x^5 + 6*x^6 - 4*x^7 + x^8) + exp(4*x)*(exp(6) - 2916
*x - exp(3)*(2*x^2 - 36*x + 162) + 486*x^2 - 36*x^3 + x^4 + 6561) + exp(3*x)*(26244*x + exp(6)*(4*x - 4*x^2) -
exp(3)*(648*x - 792*x^2 + 152*x^3 - 8*x^4) - 37908*x^2 + 13608*x^3 - 2088*x^4 + 148*x^5 - 4*x^6) + 648*x^2 -
1440*x^3 + 7505*x^4 - 29320*x^5 + 51524*x^6 - 45720*x^7 + 21286*x^8 - 5080*x^9 + 636*x^10 - 40*x^11 + x^12 + e
xp(x)*(1296*x - exp(3)*(16*x - 16*x^2 + 648*x^3 - 2088*x^4 + 2384*x^5 - 1104*x^6 + 168*x^7 - 8*x^8) - 1584*x^2
+ 26548*x^3 - 90412*x^4 + 115668*x^5 - 67212*x^6 + 17932*x^7 - 2388*x^8 + 156*x^9 - 4*x^10 + exp(6)*(4*x^3 -
12*x^4 + 12*x^5 - 4*x^6)) + 16),x)

[Out]

int((exp(2*x)*(64*x^2 - 1584*x^3 + 5072*x^4 - 5728*x^5 + 2592*x^6 - 368*x^7 + 16*x^8 + exp(3)*(16*x^3 - 48*x^4
+ 48*x^5 - 16*x^6) - 32) - exp(x)*(32*x - exp(3)*(4*x^4 - 16*x^5 + 24*x^6 - 16*x^7 + 4*x^8) - 80*x^2 + 32*x^3
+ 412*x^4 - 1664*x^5 + 2700*x^6 - 2080*x^7 + 740*x^8 - 96*x^9 + 4*x^10) + exp(4*x)*(exp(3)*(16*x - 16*x^2) -
1584*x + 1904*x^2 - 336*x^3 + 16*x^4) + exp(5*x)*(80*x + 4*exp(3) - 4*x^2 - 396) - exp(3*x)*(2376*x^2 - exp(3)
*(24*x^2 - 48*x^3 + 24*x^4) - 5232*x^3 + 3360*x^4 - 528*x^5 + 24*x^6 + 48))/(exp(2*x)*(exp(6)*(6*x^2 - 12*x^3
+ 6*x^4) - exp(3)*(972*x^2 - 2160*x^3 + 1416*x^4 - 240*x^5 + 12*x^6 + 8) - 144*x + 39374*x^2 - 96228*x^3 + 772
74*x^4 - 23544*x^5 + 3354*x^6 - 228*x^7 + 6*x^8 + 648) - exp(3)*(8*x^2 - 16*x^3 + 170*x^4 - 684*x^5 + 1118*x^6
- 872*x^7 + 318*x^8 - 44*x^9 + 2*x^10) + exp(6)*(x^4 - 4*x^5 + 6*x^6 - 4*x^7 + x^8) + exp(4*x)*(exp(6) - 2916
*x - exp(3)*(2*x^2 - 36*x + 162) + 486*x^2 - 36*x^3 + x^4 + 6561) + exp(3*x)*(26244*x + exp(6)*(4*x - 4*x^2) -
exp(3)*(648*x - 792*x^2 + 152*x^3 - 8*x^4) - 37908*x^2 + 13608*x^3 - 2088*x^4 + 148*x^5 - 4*x^6) + 648*x^2 -
1440*x^3 + 7505*x^4 - 29320*x^5 + 51524*x^6 - 45720*x^7 + 21286*x^8 - 5080*x^9 + 636*x^10 - 40*x^11 + x^12 + e
xp(x)*(1296*x - exp(3)*(16*x - 16*x^2 + 648*x^3 - 2088*x^4 + 2384*x^5 - 1104*x^6 + 168*x^7 - 8*x^8) - 1584*x^2
+ 26548*x^3 - 90412*x^4 + 115668*x^5 - 67212*x^6 + 17932*x^7 - 2388*x^8 + 156*x^9 - 4*x^10 + exp(6)*(4*x^3 -
12*x^4 + 12*x^5 - 4*x^6)) + 16), x)

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sympy [B]  time = 3.33, size = 257, normalized size = 7.56 $$\begin{array}{c}\frac{16e^x}{x^8-38x^7-2x^6{e}^3+559x^6-3924x^5+40x^5{e}^3-236x^4{e}^3+x^4{e}^6+12879x^4-16038x^3-2x^3{e}^6+360x^3{e}^3-162x^2{e}^3+x^2{e}^6+6565x^2-72x+(x^4-36x^3-2x^2{e}^3+486x^2-2916x+36x{e}^3-162e^3+e^6+6561)e^{2x}+(-2x^6+74x^5-1044x^4+4x^4{e}^3-76x^3{e}^3+6804x^3-18954x^2-2x^2{e}^6+396x^2{e}^3-324x{e}^3+2x{e}^6+13122x)e^x-4e^3+324}-\frac{4e^x}{x^2-18x-e^3+81}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*exp(3)-4*x**2+80*x-396)*exp(x)**5+((-16*x**2+16*x)*exp(3)+16*x**4-336*x**3+1904*x**2-1584*x)*exp
(x)**4+((24*x**4-48*x**3+24*x**2)*exp(3)-24*x**6+528*x**5-3360*x**4+5232*x**3-2376*x**2-48)*exp(x)**3+((-16*x*
*6+48*x**5-48*x**4+16*x**3)*exp(3)+16*x**8-368*x**7+2592*x**6-5728*x**5+5072*x**4-1584*x**3+64*x**2-32)*exp(x)
**2+((4*x**8-16*x**7+24*x**6-16*x**5+4*x**4)*exp(3)-4*x**10+96*x**9-740*x**8+2080*x**7-2700*x**6+1664*x**5-412
*x**4-32*x**3+80*x**2-32*x)*exp(x))/((exp(3)**2+(-2*x**2+36*x-162)*exp(3)+x**4-36*x**3+486*x**2-2916*x+6561)*e
xp(x)**4+((-4*x**2+4*x)*exp(3)**2+(8*x**4-152*x**3+792*x**2-648*x)*exp(3)-4*x**6+148*x**5-2088*x**4+13608*x**3
-37908*x**2+26244*x)*exp(x)**3+((6*x**4-12*x**3+6*x**2)*exp(3)**2+(-12*x**6+240*x**5-1416*x**4+2160*x**3-972*x
**2-8)*exp(3)+6*x**8-228*x**7+3354*x**6-23544*x**5+77274*x**4-96228*x**3+39374*x**2-144*x+648)*exp(x)**2+((-4*
x**6+12*x**5-12*x**4+4*x**3)*exp(3)**2+(8*x**8-168*x**7+1104*x**6-2384*x**5+2088*x**4-648*x**3+16*x**2-16*x)*e
xp(3)-4*x**10+156*x**9-2388*x**8+17932*x**7-67212*x**6+115668*x**5-90412*x**4+26548*x**3-1584*x**2+1296*x)*exp
(x)+(x**8-4*x**7+6*x**6-4*x**5+x**4)*exp(3)**2+(-2*x**10+44*x**9-318*x**8+872*x**7-1118*x**6+684*x**5-170*x**4
+16*x**3-8*x**2)*exp(3)+x**12-40*x**11+636*x**10-5080*x**9+21286*x**8-45720*x**7+51524*x**6-29320*x**5+7505*x*
*4-1440*x**3+648*x**2+16),x)

[Out]

16*exp(x)/(x**8 - 38*x**7 - 2*x**6*exp(3) + 559*x**6 - 3924*x**5 + 40*x**5*exp(3) - 236*x**4*exp(3) + x**4*exp
(6) + 12879*x**4 - 16038*x**3 - 2*x**3*exp(6) + 360*x**3*exp(3) - 162*x**2*exp(3) + x**2*exp(6) + 6565*x**2 -
72*x + (x**4 - 36*x**3 - 2*x**2*exp(3) + 486*x**2 - 2916*x + 36*x*exp(3) - 162*exp(3) + exp(6) + 6561)*exp(2*x
) + (-2*x**6 + 74*x**5 - 1044*x**4 + 4*x**4*exp(3) - 76*x**3*exp(3) + 6804*x**3 - 18954*x**2 - 2*x**2*exp(6) +
396*x**2*exp(3) - 324*x*exp(3) + 2*x*exp(6) + 13122*x)*exp(x) - 4*exp(3) + 324) - 4*exp(x)/(x**2 - 18*x - exp
(3) + 81)

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