3.20.17 $\int \frac{1}{625}(38416+724416x+3677352x^2+6497568x^3+1502805x^4-3480840x^5+1094450x^6-132000x^7+5625x^8+(362208+2451568x+4873176x^2+1202244x^3-2900700x^4+938100x^5-115500x^6+5000x^7)\log (2)+e^{4e^{x}x}(16+320x+1800x^2+4000x^3+3125x^4+(160+1200x+3000x^2+2500x^3)\log (2)+e^x(64x+704x^2+3040x^3+6400x^4+6500x^5+2500x^6+(64+704x+3040x^2+6400x^3+6500x^4+2500x^5)\log (2)))+e^{3e^{x}x}(-448-8832x-48480x^2-102400x^3-67500x^4+15000x^5+(-4416-32320x-76800x^2-54000x^3+12500x^4)\log (2)+e^x(-1344x-14592x^2-61728x^3-125280x^4-117300x^5-33000x^6+7500x^7+(-1344-14592x-61728x^2-125280x^3-117300x^4-33000x^5+7500x^6)\log (2)))+e^{2e^{x}x}(4704+91392x+489168x^2+978240x^3+516750x^4-279000x^5+26250x^6+(45696+326112x+733680x^2+413400x^3-232500x^4+22500x^5)\log (2)+e^x(9408x+100800x^2+417504x^3+815232x^4+695820x^5+113700x^6-85500x^7+7500x^8+(9408+100800x+417504x^2+815232x^3+695820x^4+113700x^5-85500x^6+7500x^7)\log (2)))+e^{e^{x}x}(-21952-420224x-2191392x^2-4130304x^3-1596300x^4+1715400x^5-339500x^6+20000x^7+(-210112-1460928x-3097728x^2-1277040x^3+1429500x^4-291000x^5+17500x^6)\log (2)+e^x(-21952x-232064x^2-940576x^3-1763040x^4-1351836x^5-33360x^6+237400x^7-46000x^8+2500x^9+(-21952-232064x-940576x^2-1763040x^3-1351836x^4-33360x^5+237400x^6-46000x^7+2500x^8)\log (2))))dx$

Optimal. Leaf size=28 $${(7-e^{e^{x}x}-x)}^4{(\frac{2}{5}+x)}^4(x+\log (2))$$

________________________________________________________________________________________

Rubi [B]  time = 1.14, antiderivative size = 512, normalized size of antiderivative = 18.29, number of steps used = 7, number of rules used = 2, integrand size = 633, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.003, Rules used = {12, 2288} $$\begin{array}{c}{x}^9-\frac{132x^8}{5}+x^8\log (2)+\frac{6254x^7}{25}-\frac{132}{5}{x}^7\log (2)-\frac{116028x^6}{125}+\frac{6254}{25}{x}^6\log (2)+\frac{300561x^5}{625}-\frac{116028}{125}{x}^5\log (2)+\frac{1624392x^4}{625}+\frac{300561}{625}{x}^4\log (2)+\frac{1225784x^3}{625}+\frac{1624392}{625}{x}^3\log (2)+\frac{362208x^2}{625}+\frac{1225784}{625}{x}^2\log (2)+\frac{e^{4e^{x}x+x}(625x^6+1625x^5+1600x^4+760x^3+176x^2+(625x^5+1625x^4+1600x^3+760x^2+176x+16)\log (2)+16x)}{625(e^{x}x+e^x)}-\frac{4e^{3e^{x}x+x}(-625x^7+2750x^6+9775x^5+10440x^4+5144x^3+1216x^2+(-625x^6+2750x^5+9775x^4+10440x^3+5144x^2+1216x+112)\log (2)+112x)}{625(e^{x}x+e^x)}+\frac{6e^{2e^{x}x+x}(625x^8-7125x^7+9475x^6+57985x^5+67936x^4+34792x^3+8400x^2+(625x^7-7125x^6+9475x^5+57985x^4+67936x^3+34792x^2+8400x+784)\log (2)+784x)}{625(e^{x}x+e^x)}-\frac{4e^{e^{x}x+x}(-625x^9+11500x^8-59350x^7+8340x^6+337959x^5+440760x^4+235144x^3+58016x^2+(-625x^8+11500x^7-59350x^6+8340x^5+337959x^4+440760x^3+235144x^2+58016x+5488)\log (2)+5488x)}{625(e^{x}x+e^x)}+\frac{38416x}{625}+\frac{362208}{625}x\log (2)\end{array}$$

Antiderivative was successfully verified.

[In]

Int[(38416 + 724416*x + 3677352*x^2 + 6497568*x^3 + 1502805*x^4 - 3480840*x^5 + 1094450*x^6 - 132000*x^7 + 562
5*x^8 + (362208 + 2451568*x + 4873176*x^2 + 1202244*x^3 - 2900700*x^4 + 938100*x^5 - 115500*x^6 + 5000*x^7)*Lo
g[2] + E^(4*E^x*x)*(16 + 320*x + 1800*x^2 + 4000*x^3 + 3125*x^4 + (160 + 1200*x + 3000*x^2 + 2500*x^3)*Log[2]
+ E^x*(64*x + 704*x^2 + 3040*x^3 + 6400*x^4 + 6500*x^5 + 2500*x^6 + (64 + 704*x + 3040*x^2 + 6400*x^3 + 6500*x
^4 + 2500*x^5)*Log[2])) + E^(3*E^x*x)*(-448 - 8832*x - 48480*x^2 - 102400*x^3 - 67500*x^4 + 15000*x^5 + (-4416
- 32320*x - 76800*x^2 - 54000*x^3 + 12500*x^4)*Log[2] + E^x*(-1344*x - 14592*x^2 - 61728*x^3 - 125280*x^4 - 1
17300*x^5 - 33000*x^6 + 7500*x^7 + (-1344 - 14592*x - 61728*x^2 - 125280*x^3 - 117300*x^4 - 33000*x^5 + 7500*x
^6)*Log[2])) + E^(2*E^x*x)*(4704 + 91392*x + 489168*x^2 + 978240*x^3 + 516750*x^4 - 279000*x^5 + 26250*x^6 + (
45696 + 326112*x + 733680*x^2 + 413400*x^3 - 232500*x^4 + 22500*x^5)*Log[2] + E^x*(9408*x + 100800*x^2 + 41750
4*x^3 + 815232*x^4 + 695820*x^5 + 113700*x^6 - 85500*x^7 + 7500*x^8 + (9408 + 100800*x + 417504*x^2 + 815232*x
^3 + 695820*x^4 + 113700*x^5 - 85500*x^6 + 7500*x^7)*Log[2])) + E^(E^x*x)*(-21952 - 420224*x - 2191392*x^2 - 4
130304*x^3 - 1596300*x^4 + 1715400*x^5 - 339500*x^6 + 20000*x^7 + (-210112 - 1460928*x - 3097728*x^2 - 1277040
*x^3 + 1429500*x^4 - 291000*x^5 + 17500*x^6)*Log[2] + E^x*(-21952*x - 232064*x^2 - 940576*x^3 - 1763040*x^4 -
1351836*x^5 - 33360*x^6 + 237400*x^7 - 46000*x^8 + 2500*x^9 + (-21952 - 232064*x - 940576*x^2 - 1763040*x^3 -
1351836*x^4 - 33360*x^5 + 237400*x^6 - 46000*x^7 + 2500*x^8)*Log[2])))/625,x]

[Out]

(38416*x)/625 + (362208*x^2)/625 + (1225784*x^3)/625 + (1624392*x^4)/625 + (300561*x^5)/625 - (116028*x^6)/125
+ (6254*x^7)/25 - (132*x^8)/5 + x^9 + (362208*x*Log[2])/625 + (1225784*x^2*Log[2])/625 + (1624392*x^3*Log[2])
/625 + (300561*x^4*Log[2])/625 - (116028*x^5*Log[2])/125 + (6254*x^6*Log[2])/25 - (132*x^7*Log[2])/5 + x^8*Log
[2] + (E^(x + 4*E^x*x)*(16*x + 176*x^2 + 760*x^3 + 1600*x^4 + 1625*x^5 + 625*x^6 + (16 + 176*x + 760*x^2 + 160
0*x^3 + 1625*x^4 + 625*x^5)*Log[2]))/(625*(E^x + E^x*x)) - (4*E^(x + 3*E^x*x)*(112*x + 1216*x^2 + 5144*x^3 + 1
0440*x^4 + 9775*x^5 + 2750*x^6 - 625*x^7 + (112 + 1216*x + 5144*x^2 + 10440*x^3 + 9775*x^4 + 2750*x^5 - 625*x^
6)*Log[2]))/(625*(E^x + E^x*x)) + (6*E^(x + 2*E^x*x)*(784*x + 8400*x^2 + 34792*x^3 + 67936*x^4 + 57985*x^5 + 9
475*x^6 - 7125*x^7 + 625*x^8 + (784 + 8400*x + 34792*x^2 + 67936*x^3 + 57985*x^4 + 9475*x^5 - 7125*x^6 + 625*x
^7)*Log[2]))/(625*(E^x + E^x*x)) - (4*E^(x + E^x*x)*(5488*x + 58016*x^2 + 235144*x^3 + 440760*x^4 + 337959*x^5
+ 8340*x^6 - 59350*x^7 + 11500*x^8 - 625*x^9 + (5488 + 58016*x + 235144*x^2 + 440760*x^3 + 337959*x^4 + 8340*
x^5 - 59350*x^6 + 11500*x^7 - 625*x^8)*Log[2]))/(625*(E^x + E^x*x))

Rule 12

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

Rule 2288

Int[(y_.)*(F_)^(u_)*((v_) + (w_)), x_Symbol] :> With[{z = (v*y)/(Log[F]*D[u, x])}, Simp[F^u*z, x] /; EqQ[D[z,
x], w*y]] /; FreeQ[F, x]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\frac{1}{625}\int (38416+724416x+3677352x^2+6497568x^3+1502805x^4-3480840x^5+1094450x^6-132000x^7+5625x^8+(362208+2451568x+4873176x^2+1202244x^3-2900700x^4+938100x^5-115500x^6+5000x^7)\log (2)+e^{4e^{x}x}(16+320x+1800x^2+4000x^3+3125x^4+(160+1200x+3000x^2+2500x^3)\log (2)+e^x(64x+704x^2+3040x^3+6400x^4+6500x^5+2500x^6+(64+704x+3040x^2+6400x^3+6500x^4+2500x^5)\log (2)))+e^{3e^{x}x}(-448-8832x-48480x^2-102400x^3-67500x^4+15000x^5+(-4416-32320x-76800x^2-54000x^3+12500x^4)\log (2)+e^x(-1344x-14592x^2-61728x^3-125280x^4-117300x^5-33000x^6+7500x^7+(-1344-14592x-61728x^2-125280x^3-117300x^4-33000x^5+7500x^6)\log (2)))+e^{2e^{x}x}(4704+91392x+489168x^2+978240x^3+516750x^4-279000x^5+26250x^6+(45696+326112x+733680x^2+413400x^3-232500x^4+22500x^5)\log (2)+e^x(9408x+100800x^2+417504x^3+815232x^4+695820x^5+113700x^6-85500x^7+7500x^8+(9408+100800x+417504x^2+815232x^3+695820x^4+113700x^5-85500x^6+7500x^7)\log (2)))+e^{e^{x}x}(-21952-420224x-2191392x^2-4130304x^3-1596300x^4+1715400x^5-339500x^6+20000x^7+(-210112-1460928x-3097728x^2-1277040x^3+1429500x^4-291000x^5+17500x^6)\log (2)+e^x(-21952x-232064x^2-940576x^3-1763040x^4-1351836x^5-33360x^6+237400x^7-46000x^8+2500x^9+(-21952-232064x-940576x^2-1763040x^3-1351836x^4-33360x^5+237400x^6-46000x^7+2500x^8)\log (2))))dx\\ & =\frac{38416x}{625}+\frac{362208x^2}{625}+\frac{1225784x^3}{625}+\frac{1624392x^4}{625}+\frac{300561x^5}{625}-\frac{116028x^6}{125}+\frac{6254x^7}{25}-\frac{132x^8}{5}+x^9+\frac{1}{625}\int e^{4e^{x}x}(16+320x+1800x^2+4000x^3+3125x^4+(160+1200x+3000x^2+2500x^3)\log (2)+e^x(64x+704x^2+3040x^3+6400x^4+6500x^5+2500x^6+(64+704x+3040x^2+6400x^3+6500x^4+2500x^5)\log (2)))dx+\frac{1}{625}\int e^{3e^{x}x}(-448-8832x-48480x^2-102400x^3-67500x^4+15000x^5+(-4416-32320x-76800x^2-54000x^3+12500x^4)\log (2)+e^x(-1344x-14592x^2-61728x^3-125280x^4-117300x^5-33000x^6+7500x^7+(-1344-14592x-61728x^2-125280x^3-117300x^4-33000x^5+7500x^6)\log (2)))dx+\frac{1}{625}\int e^{2e^{x}x}(4704+91392x+489168x^2+978240x^3+516750x^4-279000x^5+26250x^6+(45696+326112x+733680x^2+413400x^3-232500x^4+22500x^5)\log (2)+e^x(9408x+100800x^2+417504x^3+815232x^4+695820x^5+113700x^6-85500x^7+7500x^8+(9408+100800x+417504x^2+815232x^3+695820x^4+113700x^5-85500x^6+7500x^7)\log (2)))dx+\frac{1}{625}\int e^{e^{x}x}(-21952-420224x-2191392x^2-4130304x^3-1596300x^4+1715400x^5-339500x^6+20000x^7+(-210112-1460928x-3097728x^2-1277040x^3+1429500x^4-291000x^5+17500x^6)\log (2)+e^x(-21952x-232064x^2-940576x^3-1763040x^4-1351836x^5-33360x^6+237400x^7-46000x^8+2500x^9+(-21952-232064x-940576x^2-1763040x^3-1351836x^4-33360x^5+237400x^6-46000x^7+2500x^8)\log (2)))dx+\frac{1}{625}\log (2)\int (362208+2451568x+4873176x^2+1202244x^3-2900700x^4+938100x^5-115500x^6+5000x^7)dx\\ & =\frac{38416x}{625}+\frac{362208x^2}{625}+\frac{1225784x^3}{625}+\frac{1624392x^4}{625}+\frac{300561x^5}{625}-\frac{116028x^6}{125}+\frac{6254x^7}{25}-\frac{132x^8}{5}+x^9+\frac{362208}{625}x\log (2)[phone]\frac{\mathrm{}}{\mathrm{}}{x}^2\log (2)[phone]\frac{\mathrm{}}{\mathrm{}}{x}^3\log (2)[phone]\frac{\mathrm{}}{\mathrm{}}{x}^4\log (2)-\frac{116028}{125}{x}^5\log (2)+\frac{6254}{25}{x}^6\log (2)-\frac{132}{5}{x}^7\log (2)+x^8\log (2)+\frac{e^{x+4e^{x}x}(16x+176x^2+760x^3+1600x^4+1625x^5+625x^6+(16+176x+760x^2+1600x^3+1625x^4+625x^5)\log (2))}{625(e^x+e^{x}x)}-\frac{4e^{x+3e^{x}x}(112x+1216x^2+5144x^3+10440x^4+9775x^5+2750x^6-625x^7+(112+1216x+5144x^2+10440x^3+9775x^4+2750x^5-625x^6)\log (2))}{625(e^x+e^{x}x)}+\frac{6e^{x+2e^{x}x}(784x+8400x^2+34792x^3+67936x^4+57985x^5+9475x^6-7125x^7+625x^8+(784+8400x+34792x^2+67936x^3+57985x^4+9475x^5-7125x^6+625x^7)\log (2))}{625(e^x+e^{x}x)}-\frac{4e^{x+e^{x}x}(5488x+58016x^2+235144x^3+440760x^4+337959x^5+8340x^6-59350x^7+11500x^8-625x^9+(5488+58016x+235144x^2+440760x^3+337959x^4+8340x^5-59350x^6+11500x^7-625x^8)\log (2))}{625(e^x+e^{x}x)}\end{array}\end{array}$$

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Mathematica [F]  time = 7.53, size = 635, normalized size = 22.68 $$\begin{array}{c}\frac{1}{625}\int (38416+724416x+3677352x^2+6497568x^3+1502805x^4-3480840x^5+1094450x^6-132000x^7+5625x^8+(362208+2451568x+4873176x^2+1202244x^3-2900700x^4+938100x^5-115500x^6+5000x^7)\log (2)+e^{4e^{x}x}(16+320x+1800x^2+4000x^3+3125x^4+(160+1200x+3000x^2+2500x^3)\log (2)+e^x(64x+704x^2+3040x^3+6400x^4+6500x^5+2500x^6+(64+704x+3040x^2+6400x^3+6500x^4+2500x^5)\log (2)))+e^{3e^{x}x}(-448-8832x-48480x^2-102400x^3-67500x^4+15000x^5+(-4416-32320x-76800x^2-54000x^3+12500x^4)\log (2)+e^x(-1344x-14592x^2-61728x^3-125280x^4-117300x^5-33000x^6+7500x^7+(-1344-14592x-61728x^2-125280x^3-117300x^4-33000x^5+7500x^6)\log (2)))+e^{2e^{x}x}(4704+91392x+489168x^2+978240x^3+516750x^4-279000x^5+26250x^6+(45696+326112x+733680x^2+413400x^3-232500x^4+22500x^5)\log (2)+e^x(9408x+100800x^2+417504x^3+815232x^4+695820x^5+113700x^6-85500x^7+7500x^8+(9408+100800x+417504x^2+815232x^3+695820x^4+113700x^5-85500x^6+7500x^7)\log (2)))+e^{e^{x}x}(-21952-420224x-2191392x^2-4130304x^3-1596300x^4+1715400x^5-339500x^6+20000x^7+(-210112-1460928x-3097728x^2-1277040x^3+1429500x^4-291000x^5+17500x^6)\log (2)+e^x(-21952x-232064x^2-940576x^3-1763040x^4-1351836x^5-33360x^6+237400x^7-46000x^8+2500x^9+(-21952-232064x-940576x^2-1763040x^3-1351836x^4-33360x^5+237400x^6-46000x^7+2500x^8)\log (2))))dx\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(38416 + 724416*x + 3677352*x^2 + 6497568*x^3 + 1502805*x^4 - 3480840*x^5 + 1094450*x^6 - 132000*x^7
+ 5625*x^8 + (362208 + 2451568*x + 4873176*x^2 + 1202244*x^3 - 2900700*x^4 + 938100*x^5 - 115500*x^6 + 5000*x
^7)*Log[2] + E^(4*E^x*x)*(16 + 320*x + 1800*x^2 + 4000*x^3 + 3125*x^4 + (160 + 1200*x + 3000*x^2 + 2500*x^3)*L
og[2] + E^x*(64*x + 704*x^2 + 3040*x^3 + 6400*x^4 + 6500*x^5 + 2500*x^6 + (64 + 704*x + 3040*x^2 + 6400*x^3 +
6500*x^4 + 2500*x^5)*Log[2])) + E^(3*E^x*x)*(-448 - 8832*x - 48480*x^2 - 102400*x^3 - 67500*x^4 + 15000*x^5 +
(-4416 - 32320*x - 76800*x^2 - 54000*x^3 + 12500*x^4)*Log[2] + E^x*(-1344*x - 14592*x^2 - 61728*x^3 - 125280*x
^4 - 117300*x^5 - 33000*x^6 + 7500*x^7 + (-1344 - 14592*x - 61728*x^2 - 125280*x^3 - 117300*x^4 - 33000*x^5 +
7500*x^6)*Log[2])) + E^(2*E^x*x)*(4704 + 91392*x + 489168*x^2 + 978240*x^3 + 516750*x^4 - 279000*x^5 + 26250*x
^6 + (45696 + 326112*x + 733680*x^2 + 413400*x^3 - 232500*x^4 + 22500*x^5)*Log[2] + E^x*(9408*x + 100800*x^2 +
417504*x^3 + 815232*x^4 + 695820*x^5 + 113700*x^6 - 85500*x^7 + 7500*x^8 + (9408 + 100800*x + 417504*x^2 + 81
5232*x^3 + 695820*x^4 + 113700*x^5 - 85500*x^6 + 7500*x^7)*Log[2])) + E^(E^x*x)*(-21952 - 420224*x - 2191392*x
^2 - 4130304*x^3 - 1596300*x^4 + 1715400*x^5 - 339500*x^6 + 20000*x^7 + (-210112 - 1460928*x - 3097728*x^2 - 1
277040*x^3 + 1429500*x^4 - 291000*x^5 + 17500*x^6)*Log[2] + E^x*(-21952*x - 232064*x^2 - 940576*x^3 - 1763040*
x^4 - 1351836*x^5 - 33360*x^6 + 237400*x^7 - 46000*x^8 + 2500*x^9 + (-21952 - 232064*x - 940576*x^2 - 1763040*
x^3 - 1351836*x^4 - 33360*x^5 + 237400*x^6 - 46000*x^7 + 2500*x^8)*Log[2])))/625,x]

[Out]

Integrate[38416 + 724416*x + 3677352*x^2 + 6497568*x^3 + 1502805*x^4 - 3480840*x^5 + 1094450*x^6 - 132000*x^7
+ 5625*x^8 + (362208 + 2451568*x + 4873176*x^2 + 1202244*x^3 - 2900700*x^4 + 938100*x^5 - 115500*x^6 + 5000*x^
7)*Log[2] + E^(4*E^x*x)*(16 + 320*x + 1800*x^2 + 4000*x^3 + 3125*x^4 + (160 + 1200*x + 3000*x^2 + 2500*x^3)*Lo
g[2] + E^x*(64*x + 704*x^2 + 3040*x^3 + 6400*x^4 + 6500*x^5 + 2500*x^6 + (64 + 704*x + 3040*x^2 + 6400*x^3 + 6
500*x^4 + 2500*x^5)*Log[2])) + E^(3*E^x*x)*(-448 - 8832*x - 48480*x^2 - 102400*x^3 - 67500*x^4 + 15000*x^5 + (
-4416 - 32320*x - 76800*x^2 - 54000*x^3 + 12500*x^4)*Log[2] + E^x*(-1344*x - 14592*x^2 - 61728*x^3 - 125280*x^
4 - 117300*x^5 - 33000*x^6 + 7500*x^7 + (-1344 - 14592*x - 61728*x^2 - 125280*x^3 - 117300*x^4 - 33000*x^5 + 7
500*x^6)*Log[2])) + E^(2*E^x*x)*(4704 + 91392*x + 489168*x^2 + 978240*x^3 + 516750*x^4 - 279000*x^5 + 26250*x^
6 + (45696 + 326112*x + 733680*x^2 + 413400*x^3 - 232500*x^4 + 22500*x^5)*Log[2] + E^x*(9408*x + 100800*x^2 +
417504*x^3 + 815232*x^4 + 695820*x^5 + 113700*x^6 - 85500*x^7 + 7500*x^8 + (9408 + 100800*x + 417504*x^2 + 815
232*x^3 + 695820*x^4 + 113700*x^5 - 85500*x^6 + 7500*x^7)*Log[2])) + E^(E^x*x)*(-21952 - 420224*x - 2191392*x^
2 - 4130304*x^3 - 1596300*x^4 + 1715400*x^5 - 339500*x^6 + 20000*x^7 + (-210112 - 1460928*x - 3097728*x^2 - 12
77040*x^3 + 1429500*x^4 - 291000*x^5 + 17500*x^6)*Log[2] + E^x*(-21952*x - 232064*x^2 - 940576*x^3 - 1763040*x
^4 - 1351836*x^5 - 33360*x^6 + 237400*x^7 - 46000*x^8 + 2500*x^9 + (-21952 - 232064*x - 940576*x^2 - 1763040*x
^3 - 1351836*x^4 - 33360*x^5 + 237400*x^6 - 46000*x^7 + 2500*x^8)*Log[2])), x]/625

________________________________________________________________________________________

fricas [B]  time = 0.91, size = 364, normalized size = 13.00 $$\begin{array}{c}{x}^9-\frac{132}{5}{x}^8+\frac{6254}{25}{x}^7-\frac{116028}{125}{x}^6+\frac{300561}{625}{x}^5+\frac{1624392}{625}{x}^4+\frac{1225784}{625}{x}^3+\frac{362208}{625}{x}^2+\frac{1}{625}(625x^5+1000x^4+600x^3+160x^2+(625x^4+1000x^3+600x^2+160x+16)\log (2)+16x)e^{\left(4x{e}^x\right)}+\frac{4}{625}(625x^6-3375x^5-6400x^4-4040x^3-1104x^2+(625x^5-3375x^4-6400x^3-4040x^2-1104x-112)\log (2)-112x)e^{\left(3x{e}^x\right)}+\frac{6}{625}(625x^7-7750x^6+17225x^5+40760x^4+27176x^3+7616x^2+(625x^6-7750x^5+17225x^4+40760x^3+27176x^2+7616x+784)\log (2)+784x)e^{\left(2x{e}^x\right)}+\frac{4}{625}(625x^8-12125x^7+71475x^6-79815x^5-258144x^4-182616x^3-52528x^2+(625x^7-12125x^6+71475x^5-79815x^4-258144x^3-182616x^2-52528x-5488)\log (2)-5488x)e^{\left(x{e}^x\right)}+\frac{1}{625}(625x^8-16500x^7+156350x^6-580140x^5+300561x^4+1624392x^3+1225784x^2+362208x)\log (2)[phone]\frac{\mathrm{}}{\mathrm{}}x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/625*(((2500*x^5+6500*x^4+6400*x^3+3040*x^2+704*x+64)*log(2)+2500*x^6+6500*x^5+6400*x^4+3040*x^3+70
4*x^2+64*x)*exp(x)+(2500*x^3+3000*x^2+1200*x+160)*log(2)+3125*x^4+4000*x^3+1800*x^2+320*x+16)*exp(exp(x)*x)^4+
1/625*(((7500*x^6-33000*x^5-117300*x^4-125280*x^3-61728*x^2-14592*x-1344)*log(2)+7500*x^7-33000*x^6-117300*x^5
-125280*x^4-61728*x^3-14592*x^2-1344*x)*exp(x)+(12500*x^4-54000*x^3-76800*x^2-32320*x-4416)*log(2)+15000*x^5-6
7500*x^4-102400*x^3-48480*x^2-8832*x-448)*exp(exp(x)*x)^3+1/625*(((7500*x^7-85500*x^6+113700*x^5+695820*x^4+81
5232*x^3+417504*x^2+100800*x+9408)*log(2)+7500*x^8-85500*x^7+113700*x^6+695820*x^5+815232*x^4+417504*x^3+10080
0*x^2+9408*x)*exp(x)+(22500*x^5-232500*x^4+413400*x^3+733680*x^2+326112*x+45696)*log(2)+26250*x^6-279000*x^5+5
16750*x^4+978240*x^3+489168*x^2+91392*x+4704)*exp(exp(x)*x)^2+1/625*(((2500*x^8-46000*x^7+237400*x^6-33360*x^5
-1351836*x^4-1763040*x^3-940576*x^2-232064*x-21952)*log(2)+2500*x^9-46000*x^8+237400*x^7-33360*x^6-1351836*x^5
-1763040*x^4-940576*x^3-232064*x^2-21952*x)*exp(x)+(17500*x^6-291000*x^5+1429500*x^4-1277040*x^3-3097728*x^2-1
460928*x-210112)*log(2)+20000*x^7-339500*x^6+1715400*x^5-1596300*x^4-4130304*x^3-2191392*x^2-420224*x-21952)*e
xp(exp(x)*x)+1/625*(5000*x^7-115500*x^6+938100*x^5-2900700*x^4+1202244*x^3+4873176*x^2+2451568*x+362208)*log(2
)+9*x^8-1056/5*x^7+43778/25*x^6-696168/125*x^5+300561/125*x^4+6497568/625*x^3+3677352/625*x^2+724416/625*x+384
16/625,x, algorithm="fricas")

[Out]

x^9 - 132/5*x^8 + 6254/25*x^7 - 116028/125*x^6 + 300561/625*x^5 + 1624392/625*x^4 + 1225784/625*x^3 + 362208/6
25*x^2 + 1/625*(625*x^5 + 1000*x^4 + 600*x^3 + 160*x^2 + (625*x^4 + 1000*x^3 + 600*x^2 + 160*x + 16)*log(2) +
16*x)*e^(4*x*e^x) + 4/625*(625*x^6 - 3375*x^5 - 6400*x^4 - 4040*x^3 - 1104*x^2 + (625*x^5 - 3375*x^4 - 6400*x^
3 - 4040*x^2 - 1104*x - 112)*log(2) - 112*x)*e^(3*x*e^x) + 6/625*(625*x^7 - 7750*x^6 + 17225*x^5 + 40760*x^4 +
27176*x^3 + 7616*x^2 + (625*x^6 - 7750*x^5 + 17225*x^4 + 40760*x^3 + 27176*x^2 + 7616*x + 784)*log(2) + 784*x
)*e^(2*x*e^x) + 4/625*(625*x^8 - 12125*x^7 + 71475*x^6 - 79815*x^5 - 258144*x^4 - 182616*x^3 - 52528*x^2 + (62
5*x^7 - 12125*x^6 + 71475*x^5 - 79815*x^4 - 258144*x^3 - 182616*x^2 - 52528*x - 5488)*log(2) - 5488*x)*e^(x*e^
x) + 1/625*(625*x^8 - 16500*x^7 + 156350*x^6 - 580140*x^5 + 300561*x^4 + 1624392*x^3 + 1225784*x^2 + 362208*x)
*log(2) + 38416/625*x

________________________________________________________________________________________

giac [B]  time = 1.99, size = 663, normalized size = 23.68 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/625*(((2500*x^5+6500*x^4+6400*x^3+3040*x^2+704*x+64)*log(2)+2500*x^6+6500*x^5+6400*x^4+3040*x^3+70
4*x^2+64*x)*exp(x)+(2500*x^3+3000*x^2+1200*x+160)*log(2)+3125*x^4+4000*x^3+1800*x^2+320*x+16)*exp(exp(x)*x)^4+
1/625*(((7500*x^6-33000*x^5-117300*x^4-125280*x^3-61728*x^2-14592*x-1344)*log(2)+7500*x^7-33000*x^6-117300*x^5
-125280*x^4-61728*x^3-14592*x^2-1344*x)*exp(x)+(12500*x^4-54000*x^3-76800*x^2-32320*x-4416)*log(2)+15000*x^5-6
7500*x^4-102400*x^3-48480*x^2-8832*x-448)*exp(exp(x)*x)^3+1/625*(((7500*x^7-85500*x^6+113700*x^5+695820*x^4+81
5232*x^3+417504*x^2+100800*x+9408)*log(2)+7500*x^8-85500*x^7+113700*x^6+695820*x^5+815232*x^4+417504*x^3+10080
0*x^2+9408*x)*exp(x)+(22500*x^5-232500*x^4+413400*x^3+733680*x^2+326112*x+45696)*log(2)+26250*x^6-279000*x^5+5
16750*x^4+978240*x^3+489168*x^2+91392*x+4704)*exp(exp(x)*x)^2+1/625*(((2500*x^8-46000*x^7+237400*x^6-33360*x^5
-1351836*x^4-1763040*x^3-940576*x^2-232064*x-21952)*log(2)+2500*x^9-46000*x^8+237400*x^7-33360*x^6-1351836*x^5
-1763040*x^4-940576*x^3-232064*x^2-21952*x)*exp(x)+(17500*x^6-291000*x^5+1429500*x^4-1277040*x^3-3097728*x^2-1
460928*x-210112)*log(2)+20000*x^7-339500*x^6+1715400*x^5-1596300*x^4-4130304*x^3-2191392*x^2-420224*x-21952)*e
xp(exp(x)*x)+1/625*(5000*x^7-115500*x^6+938100*x^5-2900700*x^4+1202244*x^3+4873176*x^2+2451568*x+362208)*log(2
)+9*x^8-1056/5*x^7+43778/25*x^6-696168/125*x^5+300561/125*x^4+6497568/625*x^3+3677352/625*x^2+724416/625*x+384
16/625,x, algorithm="giac")

[Out]

x^9 + 4*x^8*e^(x*e^x) + 4*x^7*e^(x*e^x)*log(2) - 132/5*x^8 + 6*x^7*e^(2*x*e^x) - 388/5*x^7*e^(x*e^x) + 6*x^6*e
^(2*x*e^x)*log(2) - 388/5*x^6*e^(x*e^x)*log(2) + 6254/25*x^7 + 4*x^6*e^(3*x*e^x) - 372/5*x^6*e^(2*x*e^x) + 114
36/25*x^6*e^(x*e^x) + 4*x^5*e^(3*x*e^x)*log(2) - 372/5*x^5*e^(2*x*e^x)*log(2) + 11436/25*x^5*e^(x*e^x)*log(2)
- 116028/125*x^6 + x^5*e^(4*x*e^x) - 108/5*x^5*e^(3*x*e^x) + 4134/25*x^5*e^(2*x*e^x) - 63852/125*x^5*e^(x*e^x)
+ x^4*e^(4*x*e^x)*log(2) - 108/5*x^4*e^(3*x*e^x)*log(2) + 4134/25*x^4*e^(2*x*e^x)*log(2) - 63852/125*x^4*e^(x
*e^x)*log(2) + 300561/625*x^5 + 8/5*x^4*e^(4*x*e^x) - 1024/25*x^4*e^(3*x*e^x) + 48912/125*x^4*e^(2*x*e^x) - 10
32576/625*x^4*e^(x*e^x) + 8/5*x^3*e^(4*x*e^x)*log(2) - 1024/25*x^3*e^(3*x*e^x)*log(2) + 48912/125*x^3*e^(2*x*e
^x)*log(2) - 1032576/625*x^3*e^(x*e^x)*log(2) + 1624392/625*x^4 + 24/25*x^3*e^(4*x*e^x) - 3232/125*x^3*e^(3*x*
e^x) + 163056/625*x^3*e^(2*x*e^x) - 730464/625*x^3*e^(x*e^x) + 24/25*x^2*e^(4*x*e^x)*log(2) - 3232/125*x^2*e^(
3*x*e^x)*log(2) + 163056/625*x^2*e^(2*x*e^x)*log(2) - 730464/625*x^2*e^(x*e^x)*log(2) + 1225784/625*x^3 + 32/1
25*x^2*e^(4*x*e^x) - 4416/625*x^2*e^(3*x*e^x) + 45696/625*x^2*e^(2*x*e^x) - 210112/625*x^2*e^(x*e^x) + 32/125*
x*e^(4*x*e^x)*log(2) - 4416/625*x*e^(3*x*e^x)*log(2) + 45696/625*x*e^(2*x*e^x)*log(2) - 210112/625*x*e^(x*e^x)
*log(2) + 362208/625*x^2 + 16/625*x*e^(4*x*e^x) - 448/625*x*e^(3*x*e^x) + 4704/625*x*e^(2*x*e^x) - 21952/625*x
*e^(x*e^x) + 1/625*(625*x^8 - 16500*x^7 + 156350*x^6 - 580140*x^5 + 300561*x^4 + 1624392*x^3 + 1225784*x^2 + 3
62208*x)*log(2) + 16/625*e^(4*x*e^x)*log(2) - 448/625*e^(3*x*e^x)*log(2) + 4704/625*e^(2*x*e^x)*log(2) - 21952
/625*e^(x*e^x)*log(2) + 38416/625*x

________________________________________________________________________________________

maple [B]  time = 0.14, size = 415, normalized size = 14.82

method	result	size
risch	$\frac{(625x^4\ln (2)+625x^5+1000x^3\ln (2)+1000x^4+600x^2\ln (2)+600x^3+160x\ln (2)+160x^2+16\ln (2)+16x){\mathrm{e}}^{4{\mathrm{e}}^{x}x}}{625}+\frac{(2500x^5\ln (2)+2500x^6-13500x^4\ln (2)-13500x^5-25600x^3\ln (2)-25600x^4-16160x^2\ln (2)-16160x^3-4416x\ln (2)-4416x^2-448\ln (2)-448x){\mathrm{e}}^{3{\mathrm{e}}^{x}x}}{625}+\frac{(3750x^6\ln (2)+3750x^7-46500x^5\ln (2)-46500x^6+103350x^4\ln (2)+103350x^5+244560x^3\ln (2)+244560x^4+163056x^2\ln (2)+163056x^3+45696x\ln (2)+45696x^2+4704\ln (2)+4704x){\mathrm{e}}^{2{\mathrm{e}}^{x}x}}{625}+\frac{(2500x^7\ln (2)+2500x^8-48500x^6\ln (2)-48500x^7+285900x^5\ln (2)+285900x^6-319260x^4\ln (2)-319260x^5-1032576x^3\ln (2)-1032576x^4-730464x^2\ln (2)-730464x^3-210112x\ln (2)-210112x^2-21952\ln (2)-21952x){\mathrm{e}}^{{\mathrm{e}}^{x}x}}{625}+x^8\ln (2)-\frac{132x^7\ln (2)}{5}+\frac{6254x^6\ln (2)}{25}-\frac{116028x^5\ln (2)}{125}+\frac{300561x^4\ln (2)}{625}+\frac{1624392x^3\ln (2)}{625}+\frac{1225784x^2\ln (2)}{625}+\frac{362208x\ln (2)}{625}+x^9-\frac{132x^8}{5}+\frac{6254x^7}{25}-\frac{116028x^6}{125}+\frac{300561x^5}{625}+\frac{1624392x^4}{625}+\frac{1225784x^3}{625}+\frac{362208x^2}{625}+\frac{38416x}{625}$	$415$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/625*(((2500*x^5+6500*x^4+6400*x^3+3040*x^2+704*x+64)*ln(2)+2500*x^6+6500*x^5+6400*x^4+3040*x^3+704*x^2+6
4*x)*exp(x)+(2500*x^3+3000*x^2+1200*x+160)*ln(2)+3125*x^4+4000*x^3+1800*x^2+320*x+16)*exp(exp(x)*x)^4+1/625*((
(7500*x^6-33000*x^5-117300*x^4-125280*x^3-61728*x^2-14592*x-1344)*ln(2)+7500*x^7-33000*x^6-117300*x^5-125280*x
^4-61728*x^3-14592*x^2-1344*x)*exp(x)+(12500*x^4-54000*x^3-76800*x^2-32320*x-4416)*ln(2)+15000*x^5-67500*x^4-1
02400*x^3-48480*x^2-8832*x-448)*exp(exp(x)*x)^3+1/625*(((7500*x^7-85500*x^6+113700*x^5+695820*x^4+815232*x^3+4
17504*x^2+100800*x+9408)*ln(2)+7500*x^8-85500*x^7+113700*x^6+695820*x^5+815232*x^4+417504*x^3+100800*x^2+9408*
x)*exp(x)+(22500*x^5-232500*x^4+413400*x^3+733680*x^2+326112*x+45696)*ln(2)+26250*x^6-279000*x^5+516750*x^4+97
8240*x^3+489168*x^2+91392*x+4704)*exp(exp(x)*x)^2+1/625*(((2500*x^8-46000*x^7+237400*x^6-33360*x^5-1351836*x^4
-1763040*x^3-940576*x^2-232064*x-21952)*ln(2)+2500*x^9-46000*x^8+237400*x^7-33360*x^6-1351836*x^5-1763040*x^4-
940576*x^3-232064*x^2-21952*x)*exp(x)+(17500*x^6-291000*x^5+1429500*x^4-1277040*x^3-3097728*x^2-1460928*x-2101
12)*ln(2)+20000*x^7-339500*x^6+1715400*x^5-1596300*x^4-4130304*x^3-2191392*x^2-420224*x-21952)*exp(exp(x)*x)+1
/625*(5000*x^7-115500*x^6+938100*x^5-2900700*x^4+1202244*x^3+4873176*x^2+2451568*x+362208)*ln(2)+9*x^8-1056/5*
x^7+43778/25*x^6-696168/125*x^5+300561/125*x^4+6497568/625*x^3+3677352/625*x^2+724416/625*x+38416/625,x,method
=_RETURNVERBOSE)

[Out]

1/625*(625*x^4*ln(2)+625*x^5+1000*x^3*ln(2)+1000*x^4+600*x^2*ln(2)+600*x^3+160*x*ln(2)+160*x^2+16*ln(2)+16*x)*
exp(4*exp(x)*x)+1/625*(2500*x^5*ln(2)+2500*x^6-13500*x^4*ln(2)-13500*x^5-25600*x^3*ln(2)-25600*x^4-16160*x^2*l
n(2)-16160*x^3-4416*x*ln(2)-4416*x^2-448*ln(2)-448*x)*exp(3*exp(x)*x)+1/625*(3750*x^6*ln(2)+3750*x^7-46500*x^5
*ln(2)-46500*x^6+103350*x^4*ln(2)+103350*x^5+244560*x^3*ln(2)+244560*x^4+163056*x^2*ln(2)+163056*x^3+45696*x*l
n(2)+45696*x^2+4704*ln(2)+4704*x)*exp(2*exp(x)*x)+1/625*(2500*x^7*ln(2)+2500*x^8-48500*x^6*ln(2)-48500*x^7+285
900*x^5*ln(2)+285900*x^6-319260*x^4*ln(2)-319260*x^5-1032576*x^3*ln(2)-1032576*x^4-730464*x^2*ln(2)-730464*x^3
-210112*x*ln(2)-210112*x^2-21952*ln(2)-21952*x)*exp(exp(x)*x)+x^8*ln(2)-132/5*x^7*ln(2)+6254/25*x^6*ln(2)-1160
28/125*x^5*ln(2)+300561/625*x^4*ln(2)+1624392/625*x^3*ln(2)+1225784/625*x^2*ln(2)+362208/625*x*ln(2)+x^9-132/5
*x^8+6254/25*x^7-116028/125*x^6+300561/625*x^5+1624392/625*x^4+1225784/625*x^3+362208/625*x^2+38416/625*x

________________________________________________________________________________________

maxima [B]  time = 0.82, size = 390, normalized size = 13.93 $$\begin{array}{c}{x}^9-\frac{132}{5}{x}^8+\frac{6254}{25}{x}^7-\frac{116028}{125}{x}^6+\frac{300561}{625}{x}^5+\frac{1624392}{625}{x}^4+\frac{1225784}{625}{x}^3+\frac{362208}{625}{x}^2+\frac{1}{625}(625x^5+125x^4(5\log (2)+8)+200x^3(5\log (2)+3)+40x^2(15\log (2)+4)+16x(10\log (2)+1)+16\log (2))e^{\left(4x{e}^x\right)}+\frac{4}{625}(625x^6+125x^5(5\log (2)-27)-25x^4(135\log (2)+256)-40x^3(160\log (2)+101)-8x^2(505\log (2)+138)-16x(69\log (2)+7)-112\log (2))e^{\left(3x{e}^x\right)}+\frac{6}{625}(625x^7+125x^6(5\log (2)-62)-25x^5(310\log (2)-689)+5x^4(3445\log (2)+8152)+8x^3(5095\log (2)+3397)+8x^2(3397\log (2)+952)+112x(68\log (2)+7)+784\log (2))e^{\left(2x{e}^x\right)}+\frac{4}{625}(625x^8+125x^7(5\log (2)-97)-25x^6(485\log (2)-2859)+15x^5(4765\log (2)-5321)-3x^4(26605\log (2)+86048)-24x^3(10756\log (2)+7609)-56x^2(3261\log (2)+938)-784x(67\log (2)+7)-5488\log (2))e^{\left(x{e}^x\right)}+\frac{1}{625}(625x^8-16500x^7+156350x^6-580140x^5+300561x^4+1624392x^3+1225784x^2+362208x)\log (2)[phone]\frac{\mathrm{}}{\mathrm{}}x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/625*(((2500*x^5+6500*x^4+6400*x^3+3040*x^2+704*x+64)*log(2)+2500*x^6+6500*x^5+6400*x^4+3040*x^3+70
4*x^2+64*x)*exp(x)+(2500*x^3+3000*x^2+1200*x+160)*log(2)+3125*x^4+4000*x^3+1800*x^2+320*x+16)*exp(exp(x)*x)^4+
1/625*(((7500*x^6-33000*x^5-117300*x^4-125280*x^3-61728*x^2-14592*x-1344)*log(2)+7500*x^7-33000*x^6-117300*x^5
-125280*x^4-61728*x^3-14592*x^2-1344*x)*exp(x)+(12500*x^4-54000*x^3-76800*x^2-32320*x-4416)*log(2)+15000*x^5-6
7500*x^4-102400*x^3-48480*x^2-8832*x-448)*exp(exp(x)*x)^3+1/625*(((7500*x^7-85500*x^6+113700*x^5+695820*x^4+81
5232*x^3+417504*x^2+100800*x+9408)*log(2)+7500*x^8-85500*x^7+113700*x^6+695820*x^5+815232*x^4+417504*x^3+10080
0*x^2+9408*x)*exp(x)+(22500*x^5-232500*x^4+413400*x^3+733680*x^2+326112*x+45696)*log(2)+26250*x^6-279000*x^5+5
16750*x^4+978240*x^3+489168*x^2+91392*x+4704)*exp(exp(x)*x)^2+1/625*(((2500*x^8-46000*x^7+237400*x^6-33360*x^5
-1351836*x^4-1763040*x^3-940576*x^2-232064*x-21952)*log(2)+2500*x^9-46000*x^8+237400*x^7-33360*x^6-1351836*x^5
-1763040*x^4-940576*x^3-232064*x^2-21952*x)*exp(x)+(17500*x^6-291000*x^5+1429500*x^4-1277040*x^3-3097728*x^2-1
460928*x-210112)*log(2)+20000*x^7-339500*x^6+1715400*x^5-1596300*x^4-4130304*x^3-2191392*x^2-420224*x-21952)*e
xp(exp(x)*x)+1/625*(5000*x^7-115500*x^6+938100*x^5-2900700*x^4+1202244*x^3+4873176*x^2+2451568*x+362208)*log(2
)+9*x^8-1056/5*x^7+43778/25*x^6-696168/125*x^5+300561/125*x^4+6497568/625*x^3+3677352/625*x^2+724416/625*x+384
16/625,x, algorithm="maxima")

[Out]

x^9 - 132/5*x^8 + 6254/25*x^7 - 116028/125*x^6 + 300561/625*x^5 + 1624392/625*x^4 + 1225784/625*x^3 + 362208/6
25*x^2 + 1/625*(625*x^5 + 125*x^4*(5*log(2) + 8) + 200*x^3*(5*log(2) + 3) + 40*x^2*(15*log(2) + 4) + 16*x*(10*
log(2) + 1) + 16*log(2))*e^(4*x*e^x) + 4/625*(625*x^6 + 125*x^5*(5*log(2) - 27) - 25*x^4*(135*log(2) + 256) -
40*x^3*(160*log(2) + 101) - 8*x^2*(505*log(2) + 138) - 16*x*(69*log(2) + 7) - 112*log(2))*e^(3*x*e^x) + 6/625*
(625*x^7 + 125*x^6*(5*log(2) - 62) - 25*x^5*(310*log(2) - 689) + 5*x^4*(3445*log(2) + 8152) + 8*x^3*(5095*log(
2) + 3397) + 8*x^2*(3397*log(2) + 952) + 112*x*(68*log(2) + 7) + 784*log(2))*e^(2*x*e^x) + 4/625*(625*x^8 + 12
5*x^7*(5*log(2) - 97) - 25*x^6*(485*log(2) - 2859) + 15*x^5*(4765*log(2) - 5321) - 3*x^4*(26605*log(2) + 86048
) - 24*x^3*(10756*log(2) + 7609) - 56*x^2*(3261*log(2) + 938) - 784*x*(67*log(2) + 7) - 5488*log(2))*e^(x*e^x)
+ 1/625*(625*x^8 - 16500*x^7 + 156350*x^6 - 580140*x^5 + 300561*x^4 + 1624392*x^3 + 1225784*x^2 + 362208*x)*l
og(2) + 38416/625*x

________________________________________________________________________________________

mupad [B]  time = 2.50, size = 365, normalized size = 13.04 $$\begin{array}{c}x(\frac{362208\ln (2)}{625}+\frac{38416}{625})-{\mathrm{e}}^{x{\mathrm{e}}^x}(-4x^8+(\frac{388}{5}-4\ln (2))x^7+(\frac{388\ln (2)}{5}-\frac{11436}{25})x^6+(\frac{63852}{125}-\frac{11436\ln (2)}{25})x^5+(\frac{63852\ln (2)}{125}+\frac{1032576}{625})x^4+(\frac{1032576\ln (2)}{625}+\frac{730464}{625})x^3+(\frac{730464\ln (2)}{625}+\frac{210112}{625})x^2+(\frac{210112\ln (2)}{625}+\frac{21952}{625})x+\frac{21952\ln (2)}{625})+{\mathrm{e}}^{4x{\mathrm{e}}^x}(x^5+(\ln (2)+\frac{8}{5})x^4+(\frac{8\ln (2)}{5}+\frac{24}{25})x^3+(\frac{24\ln (2)}{25}+\frac{32}{125})x^2+(\frac{32\ln (2)}{125}+\frac{16}{625})x+\frac{16\ln (2)}{625})+x^8(\frac{\ln \left(256\right)}{8}-\frac{132}{5})-x^7(\frac{132\ln (2)}{5}-\frac{6254}{25})+x^6(\frac{6254\ln (2)}{25}-\frac{116028}{125})-x^5(\frac{116028\ln (2)}{125}-\frac{300561}{625})+x^2(\frac{1225784\ln (2)}{625}+\frac{362208}{625})+x^4(\frac{300561\ln (2)}{625}+\frac{1624392}{625})+x^3(\frac{1624392\ln (2)}{625}+\frac{1225784}{625})-{\mathrm{e}}^{3x{\mathrm{e}}^x}(-4x^6+(\frac{108}{5}-4\ln (2))x^5+(\frac{108\ln (2)}{5}+\frac{1024}{25})x^4+(\frac{1024\ln (2)}{25}+\frac{3232}{125})x^3+(\frac{3232\ln (2)}{125}+\frac{4416}{625})x^2+(\frac{4416\ln (2)}{625}+\frac{448}{625})x+\frac{448\ln (2)}{625})+{\mathrm{e}}^{2x{\mathrm{e}}^x}(6x^7+(6\ln (2)-\frac{372}{5})x^6+(\frac{4134}{25}-\frac{372\ln (2)}{5})x^5+(\frac{4134\ln (2)}{25}+\frac{48912}{125})x^4+(\frac{48912\ln (2)}{125}+\frac{163056}{625})x^3+(\frac{163056\ln (2)}{625}+\frac{45696}{625})x^2+(\frac{45696\ln (2)}{625}+\frac{4704}{625})x+\frac{4704\ln (2)}{625})+x^9\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((724416*x)/625 - (exp(3*x*exp(x))*(8832*x + log(2)*(32320*x + 76800*x^2 + 54000*x^3 - 12500*x^4 + 4416) +
exp(x)*(1344*x + log(2)*(14592*x + 61728*x^2 + 125280*x^3 + 117300*x^4 + 33000*x^5 - 7500*x^6 + 1344) + 14592*
x^2 + 61728*x^3 + 125280*x^4 + 117300*x^5 + 33000*x^6 - 7500*x^7) + 48480*x^2 + 102400*x^3 + 67500*x^4 - 15000
*x^5 + 448))/625 + (exp(4*x*exp(x))*(320*x + exp(x)*(64*x + 704*x^2 + 3040*x^3 + 6400*x^4 + 6500*x^5 + 2500*x^
6 + log(2)*(704*x + 3040*x^2 + 6400*x^3 + 6500*x^4 + 2500*x^5 + 64)) + log(2)*(1200*x + 3000*x^2 + 2500*x^3 +
160) + 1800*x^2 + 4000*x^3 + 3125*x^4 + 16))/625 + (log(2)*(2451568*x + 4873176*x^2 + 1202244*x^3 - 2900700*x^
4 + 938100*x^5 - 115500*x^6 + 5000*x^7 + 362208))/625 - (exp(x*exp(x))*(420224*x + log(2)*(1460928*x + 3097728
*x^2 + 1277040*x^3 - 1429500*x^4 + 291000*x^5 - 17500*x^6 + 210112) + exp(x)*(21952*x + log(2)*(232064*x + 940
576*x^2 + 1763040*x^3 + 1351836*x^4 + 33360*x^5 - 237400*x^6 + 46000*x^7 - 2500*x^8 + 21952) + 232064*x^2 + 94
0576*x^3 + 1763040*x^4 + 1351836*x^5 + 33360*x^6 - 237400*x^7 + 46000*x^8 - 2500*x^9) + 2191392*x^2 + 4130304*
x^3 + 1596300*x^4 - 1715400*x^5 + 339500*x^6 - 20000*x^7 + 21952))/625 + (3677352*x^2)/625 + (6497568*x^3)/625
+ (300561*x^4)/125 - (696168*x^5)/125 + (43778*x^6)/25 - (1056*x^7)/5 + 9*x^8 + (exp(2*x*exp(x))*(91392*x + e
xp(x)*(9408*x + log(2)*(100800*x + 417504*x^2 + 815232*x^3 + 695820*x^4 + 113700*x^5 - 85500*x^6 + 7500*x^7 +
9408) + 100800*x^2 + 417504*x^3 + 815232*x^4 + 695820*x^5 + 113700*x^6 - 85500*x^7 + 7500*x^8) + 489168*x^2 +
978240*x^3 + 516750*x^4 - 279000*x^5 + 26250*x^6 + log(2)*(326112*x + 733680*x^2 + 413400*x^3 - 232500*x^4 + 2
2500*x^5 + 45696) + 4704))/625 + 38416/625,x)

[Out]

x*((362208*log(2))/625 + 38416/625) - exp(x*exp(x))*((21952*log(2))/625 + x*((210112*log(2))/625 + 21952/625)
- x^7*(4*log(2) - 388/5) + x^6*((388*log(2))/5 - 11436/25) - x^5*((11436*log(2))/25 - 63852/125) + x^2*((73046
4*log(2))/625 + 210112/625) + x^4*((63852*log(2))/125 + 1032576/625) + x^3*((1032576*log(2))/625 + 730464/625)
- 4*x^8) + exp(4*x*exp(x))*((16*log(2))/625 + x*((32*log(2))/125 + 16/625) + x^4*(log(2) + 8/5) + x^3*((8*log
(2))/5 + 24/25) + x^2*((24*log(2))/25 + 32/125) + x^5) + x^8*(log(256)/8 - 132/5) - x^7*((132*log(2))/5 - 6254
/25) + x^6*((6254*log(2))/25 - 116028/125) - x^5*((116028*log(2))/125 - 300561/625) + x^2*((1225784*log(2))/62
5 + 362208/625) + x^4*((300561*log(2))/625 + 1624392/625) + x^3*((1624392*log(2))/625 + 1225784/625) - exp(3*x
*exp(x))*((448*log(2))/625 + x*((4416*log(2))/625 + 448/625) - x^5*(4*log(2) - 108/5) + x^4*((108*log(2))/5 +
1024/25) + x^3*((1024*log(2))/25 + 3232/125) + x^2*((3232*log(2))/125 + 4416/625) - 4*x^6) + exp(2*x*exp(x))*(
(4704*log(2))/625 + x*((45696*log(2))/625 + 4704/625) + x^6*(6*log(2) - 372/5) - x^5*((372*log(2))/5 - 4134/25
) + x^4*((4134*log(2))/25 + 48912/125) + x^2*((163056*log(2))/625 + 45696/625) + x^3*((48912*log(2))/125 + 163
056/625) + 6*x^7) + x^9

________________________________________________________________________________________

sympy [B]  time = 1.45, size = 471, normalized size = 16.82 $$\begin{array}{c}{x}^9+x^8(-\frac{132}{5}+\log (2))+x^7(\frac{6254}{25}-\frac{132\log (2)}{5})+x^6(-\frac{116028}{125}+\frac{6254\log (2)}{25})+x^5(\frac{300561}{625}-\frac{116028\log (2)}{125})+x^4(\frac{300561\log (2)}{625}+\frac{1624392}{625})+x^3(\frac{1624392\log (2)}{625}+\frac{1225784}{625})+x^2(\frac{362208}{625}+\frac{1225784\log (2)}{625})+x(\frac{38416}{625}+\frac{362208\log (2)}{625})+\frac{(152587890625x^5+152587890625x^4\log (2)[phone]\mathrm{}{x}^4+146484375000x^3+244140625000x^3\log (2)[phone]\mathrm{}{x}^2+146484375000x^2\log (2)[phone]\mathrm{}x+39062500000x\log (2)[phone]\mathrm{}\log (2))e^{4x{e}^x}}{152587890625}+\frac{(610351562500x^6-3295898437500x^5+610351562500x^5\log (2)-6250000000000x^4-3295898437500x^4\log (2)-6250000000000x^3\log (2)-3945312500000x^3-3945312500000x^2\log (2)-1078125000000x^2-1078125000000x\log (2)-109375000000x-109375000000\log (2))e^{3x{e}^x}}{152587890625}+\frac{(915527343750x^7-11352539062500x^6+915527343750x^6\log (2)-11352539062500x^5\log (2)[phone]\mathrm{}{x}^5+25231933593750x^4\log (2)[phone]\mathrm{}{x}^4+39808593750000x^3+59707031250000x^3\log (2)[phone]\mathrm{}{x}^2+39808593750000x^2\log (2)[phone]\mathrm{}x+11156250000000x\log (2)[phone]\mathrm{}\log (2))e^{2x{e}^x}}{152587890625}+\frac{(610351562500x^8-11840820312500x^7+610351562500x^7\log (2)-11840820312500x^6\log (2)[phone]\mathrm{}{x}^6-77944335937500x^5+69799804687500x^5\log (2)-252093750000000x^4-77944335937500x^4\log (2)-178335937500000x^3-252093750000000x^3\log (2)-178335937500000x^2\log (2)-51296875000000x^2-51296875000000x\log (2)-5359375000000x-5359375000000\log (2))e^{x{e}^x}}{152587890625}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/625*(((2500*x**5+6500*x**4+6400*x**3+3040*x**2+704*x+64)*ln(2)+2500*x**6+6500*x**5+6400*x**4+3040*
x**3+704*x**2+64*x)*exp(x)+(2500*x**3+3000*x**2+1200*x+160)*ln(2)+3125*x**4+4000*x**3+1800*x**2+320*x+16)*exp(
exp(x)*x)**4+1/625*(((7500*x**6-33000*x**5-117300*x**4-125280*x**3-61728*x**2-14592*x-1344)*ln(2)+7500*x**7-33
000*x**6-117300*x**5-125280*x**4-61728*x**3-14592*x**2-1344*x)*exp(x)+(12500*x**4-54000*x**3-76800*x**2-32320*
x-4416)*ln(2)+15000*x**5-67500*x**4-102400*x**3-48480*x**2-8832*x-448)*exp(exp(x)*x)**3+1/625*(((7500*x**7-855
00*x**6+113700*x**5+695820*x**4+815232*x**3+417504*x**2+100800*x+9408)*ln(2)+7500*x**8-85500*x**7+113700*x**6+
695820*x**5+815232*x**4+417504*x**3+100800*x**2+9408*x)*exp(x)+(22500*x**5-232500*x**4+413400*x**3+733680*x**2
+326112*x+45696)*ln(2)+26250*x**6-279000*x**5+516750*x**4+978240*x**3+489168*x**2+91392*x+4704)*exp(exp(x)*x)*
*2+1/625*(((2500*x**8-46000*x**7+237400*x**6-33360*x**5-1351836*x**4-1763040*x**3-940576*x**2-232064*x-21952)*
ln(2)+2500*x**9-46000*x**8+237400*x**7-33360*x**6-1351836*x**5-1763040*x**4-940576*x**3-232064*x**2-21952*x)*e
xp(x)+(17500*x**6-291000*x**5+1429500*x**4-1277040*x**3-3097728*x**2-1460928*x-210112)*ln(2)+20000*x**7-339500
*x**6+1715400*x**5-1596300*x**4-4130304*x**3-2191392*x**2-420224*x-21952)*exp(exp(x)*x)+1/625*(5000*x**7-11550
0*x**6+938100*x**5-2900700*x**4+1202244*x**3+4873176*x**2+2451568*x+362208)*ln(2)+9*x**8-1056/5*x**7+43778/25*
x**6-696168/125*x**5+300561/125*x**4+6497568/625*x**3+3677352/625*x**2+724416/625*x+38416/625,x)

[Out]

x**9 + x**8*(-132/5 + log(2)) + x**7*(6254/25 - 132*log(2)/5) + x**6*(-116028/125 + 6254*log(2)/25) + x**5*(30
0561/625 - 116028*log(2)/125) + x**4*(300561*log(2)/625 + 1624392/625) + x**3*(1624392*log(2)/625 + 1225784/62
5) + x**2*(362208/625 + 1225784*log(2)/625) + x*(38416/625 + 362208*log(2)/625) + (152587890625*x**5 + 1525878
90625*x**4*log(2) + 244140625000*x**4 + 146484375000*x**3 + 244140625000*x**3*log(2) + 39062500000*x**2 + 1464
84375000*x**2*log(2) + 3906250000*x + 39062500000*x*log(2) + 3906250000*log(2))*exp(4*x*exp(x))/152587890625 +
(610351562500*x**6 - 3295898437500*x**5 + 610351562500*x**5*log(2) - 6250000000000*x**4 - 3295898437500*x**4*
log(2) - 6250000000000*x**3*log(2) - 3945312500000*x**3 - 3945312500000*x**2*log(2) - 1078125000000*x**2 - 107
8125000000*x*log(2) - 109375000000*x - 109375000000*log(2))*exp(3*x*exp(x))/152587890625 + (915527343750*x**7
- 11352539062500*x**6 + 915527343750*x**6*log(2) - 11352539062500*x**5*log(2) + 25231933593750*x**5 + 25231933
593750*x**4*log(2) + 59707031250000*x**4 + 39808593750000*x**3 + 59707031250000*x**3*log(2) + 11156250000000*x
**2 + 39808593750000*x**2*log(2) + 1148437500000*x + 11156250000000*x*log(2) + 1148437500000*log(2))*exp(2*x*e
xp(x))/152587890625 + (610351562500*x**8 - 11840820312500*x**7 + 610351562500*x**7*log(2) - 11840820312500*x**
6*log(2) + 69799804687500*x**6 - 77944335937500*x**5 + 69799804687500*x**5*log(2) - 252093750000000*x**4 - 779
44335937500*x**4*log(2) - 178335937500000*x**3 - 252093750000000*x**3*log(2) - 178335937500000*x**2*log(2) - 5
1296875000000*x**2 - 51296875000000*x*log(2) - 5359375000000*x - 5359375000000*log(2))*exp(x*exp(x))/152587890
625

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