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

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

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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 {gather*} x^9-\frac {132 x^8}{5}+x^8 \log (2)+\frac {6254 x^7}{25}-\frac {132}{5} x^7 \log (2)-\frac {116028 x^6}{125}+\frac {6254}{25} x^6 \log (2)+\frac {300561 x^5}{625}-\frac {116028}{125} x^5 \log (2)+\frac {1624392 x^4}{625}+\frac {300561}{625} x^4 \log (2)+\frac {1225784 x^3}{625}+\frac {1624392}{625} x^3 \log (2)+\frac {362208 x^2}{625}+\frac {1225784}{625} x^2 \log (2)+\frac {e^{4 e^x x+x} \left (625 x^6+1625 x^5+1600 x^4+760 x^3+176 x^2+\left (625 x^5+1625 x^4+1600 x^3+760 x^2+176 x+16\right ) \log (2)+16 x\right )}{625 \left (e^x x+e^x\right )}-\frac {4 e^{3 e^x x+x} \left (-625 x^7+2750 x^6+9775 x^5+10440 x^4+5144 x^3+1216 x^2+\left (-625 x^6+2750 x^5+9775 x^4+10440 x^3+5144 x^2+1216 x+112\right ) \log (2)+112 x\right )}{625 \left (e^x x+e^x\right )}+\frac {6 e^{2 e^x x+x} \left (625 x^8-7125 x^7+9475 x^6+57985 x^5+67936 x^4+34792 x^3+8400 x^2+\left (625 x^7-7125 x^6+9475 x^5+57985 x^4+67936 x^3+34792 x^2+8400 x+784\right ) \log (2)+784 x\right )}{625 \left (e^x x+e^x\right )}-\frac {4 e^{e^x x+x} \left (-625 x^9+11500 x^8-59350 x^7+8340 x^6+337959 x^5+440760 x^4+235144 x^3+58016 x^2+\left (-625 x^8+11500 x^7-59350 x^6+8340 x^5+337959 x^4+440760 x^3+235144 x^2+58016 x+5488\right ) \log (2)+5488 x\right )}{625 \left (e^x x+e^x\right )}+\frac {38416 x}{625}+\frac {362208}{625} x \log (2) \end {gather*}

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

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

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 {gather*} 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} \, {\left (625 \, x^{5} + 1000 \, x^{4} + 600 \, x^{3} + 160 \, x^{2} + {\left (625 \, x^{4} + 1000 \, x^{3} + 600 \, x^{2} + 160 \, x + 16\right )} \log \relax (2) + 16 \, x\right )} e^{\left (4 \, x e^{x}\right )} + \frac {4}{625} \, {\left (625 \, x^{6} - 3375 \, x^{5} - 6400 \, x^{4} - 4040 \, x^{3} - 1104 \, x^{2} + {\left (625 \, x^{5} - 3375 \, x^{4} - 6400 \, x^{3} - 4040 \, x^{2} - 1104 \, x - 112\right )} \log \relax (2) - 112 \, x\right )} e^{\left (3 \, x e^{x}\right )} + \frac {6}{625} \, {\left (625 \, x^{7} - 7750 \, x^{6} + 17225 \, x^{5} + 40760 \, x^{4} + 27176 \, x^{3} + 7616 \, x^{2} + {\left (625 \, x^{6} - 7750 \, x^{5} + 17225 \, x^{4} + 40760 \, x^{3} + 27176 \, x^{2} + 7616 \, x + 784\right )} \log \relax (2) + 784 \, x\right )} e^{\left (2 \, x e^{x}\right )} + \frac {4}{625} \, {\left (625 \, x^{8} - 12125 \, x^{7} + 71475 \, x^{6} - 79815 \, x^{5} - 258144 \, x^{4} - 182616 \, x^{3} - 52528 \, x^{2} + {\left (625 \, x^{7} - 12125 \, x^{6} + 71475 \, x^{5} - 79815 \, x^{4} - 258144 \, x^{3} - 182616 \, x^{2} - 52528 \, x - 5488\right )} \log \relax (2) - 5488 \, x\right )} e^{\left (x e^{x}\right )} + \frac {1}{625} \, {\left (625 \, x^{8} - 16500 \, x^{7} + 156350 \, x^{6} - 580140 \, x^{5} + 300561 \, x^{4} + 1624392 \, x^{3} + 1225784 \, x^{2} + 362208 \, x\right )} \log \relax (2) + \frac {38416}{625} \, x \end {gather*}

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

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

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maxima [B]  time = 0.82, size = 390, normalized size = 13.93 \begin {gather*} 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} \, {\left (625 \, x^{5} + 125 \, x^{4} {\left (5 \, \log \relax (2) + 8\right )} + 200 \, x^{3} {\left (5 \, \log \relax (2) + 3\right )} + 40 \, x^{2} {\left (15 \, \log \relax (2) + 4\right )} + 16 \, x {\left (10 \, \log \relax (2) + 1\right )} + 16 \, \log \relax (2)\right )} e^{\left (4 \, x e^{x}\right )} + \frac {4}{625} \, {\left (625 \, x^{6} + 125 \, x^{5} {\left (5 \, \log \relax (2) - 27\right )} - 25 \, x^{4} {\left (135 \, \log \relax (2) + 256\right )} - 40 \, x^{3} {\left (160 \, \log \relax (2) + 101\right )} - 8 \, x^{2} {\left (505 \, \log \relax (2) + 138\right )} - 16 \, x {\left (69 \, \log \relax (2) + 7\right )} - 112 \, \log \relax (2)\right )} e^{\left (3 \, x e^{x}\right )} + \frac {6}{625} \, {\left (625 \, x^{7} + 125 \, x^{6} {\left (5 \, \log \relax (2) - 62\right )} - 25 \, x^{5} {\left (310 \, \log \relax (2) - 689\right )} + 5 \, x^{4} {\left (3445 \, \log \relax (2) + 8152\right )} + 8 \, x^{3} {\left (5095 \, \log \relax (2) + 3397\right )} + 8 \, x^{2} {\left (3397 \, \log \relax (2) + 952\right )} + 112 \, x {\left (68 \, \log \relax (2) + 7\right )} + 784 \, \log \relax (2)\right )} e^{\left (2 \, x e^{x}\right )} + \frac {4}{625} \, {\left (625 \, x^{8} + 125 \, x^{7} {\left (5 \, \log \relax (2) - 97\right )} - 25 \, x^{6} {\left (485 \, \log \relax (2) - 2859\right )} + 15 \, x^{5} {\left (4765 \, \log \relax (2) - 5321\right )} - 3 \, x^{4} {\left (26605 \, \log \relax (2) + 86048\right )} - 24 \, x^{3} {\left (10756 \, \log \relax (2) + 7609\right )} - 56 \, x^{2} {\left (3261 \, \log \relax (2) + 938\right )} - 784 \, x {\left (67 \, \log \relax (2) + 7\right )} - 5488 \, \log \relax (2)\right )} e^{\left (x e^{x}\right )} + \frac {1}{625} \, {\left (625 \, x^{8} - 16500 \, x^{7} + 156350 \, x^{6} - 580140 \, x^{5} + 300561 \, x^{4} + 1624392 \, x^{3} + 1225784 \, x^{2} + 362208 \, x\right )} \log \relax (2) + \frac {38416}{625} \, x \end {gather*}

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

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

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

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sympy [B]  time = 1.45, size = 471, normalized size = 16.82 \begin {gather*} x^{9} + x^{8} \left (- \frac {132}{5} + \log {\relax (2 )}\right ) + x^{7} \left (\frac {6254}{25} - \frac {132 \log {\relax (2 )}}{5}\right ) + x^{6} \left (- \frac {116028}{125} + \frac {6254 \log {\relax (2 )}}{25}\right ) + x^{5} \left (\frac {300561}{625} - \frac {116028 \log {\relax (2 )}}{125}\right ) + x^{4} \left (\frac {300561 \log {\relax (2 )}}{625} + \frac {1624392}{625}\right ) + x^{3} \left (\frac {1624392 \log {\relax (2 )}}{625} + \frac {1225784}{625}\right ) + x^{2} \left (\frac {362208}{625} + \frac {1225784 \log {\relax (2 )}}{625}\right ) + x \left (\frac {38416}{625} + \frac {362208 \log {\relax (2 )}}{625}\right ) + \frac {\left (152587890625 x^{5} + 152587890625 x^{4} \log {\relax (2 )} + 244140625000 x^{4} + 146484375000 x^{3} + 244140625000 x^{3} \log {\relax (2 )} + 39062500000 x^{2} + 146484375000 x^{2} \log {\relax (2 )} + 3906250000 x + 39062500000 x \log {\relax (2 )} + 3906250000 \log {\relax (2 )}\right ) e^{4 x e^{x}}}{152587890625} + \frac {\left (610351562500 x^{6} - 3295898437500 x^{5} + 610351562500 x^{5} \log {\relax (2 )} - 6250000000000 x^{4} - 3295898437500 x^{4} \log {\relax (2 )} - 6250000000000 x^{3} \log {\relax (2 )} - 3945312500000 x^{3} - 3945312500000 x^{2} \log {\relax (2 )} - 1078125000000 x^{2} - 1078125000000 x \log {\relax (2 )} - 109375000000 x - 109375000000 \log {\relax (2 )}\right ) e^{3 x e^{x}}}{152587890625} + \frac {\left (915527343750 x^{7} - 11352539062500 x^{6} + 915527343750 x^{6} \log {\relax (2 )} - 11352539062500 x^{5} \log {\relax (2 )} + 25231933593750 x^{5} + 25231933593750 x^{4} \log {\relax (2 )} + 59707031250000 x^{4} + 39808593750000 x^{3} + 59707031250000 x^{3} \log {\relax (2 )} + 11156250000000 x^{2} + 39808593750000 x^{2} \log {\relax (2 )} + 1148437500000 x + 11156250000000 x \log {\relax (2 )} + 1148437500000 \log {\relax (2 )}\right ) e^{2 x e^{x}}}{152587890625} + \frac {\left (610351562500 x^{8} - 11840820312500 x^{7} + 610351562500 x^{7} \log {\relax (2 )} - 11840820312500 x^{6} \log {\relax (2 )} + 69799804687500 x^{6} - 77944335937500 x^{5} + 69799804687500 x^{5} \log {\relax (2 )} - 252093750000000 x^{4} - 77944335937500 x^{4} \log {\relax (2 )} - 178335937500000 x^{3} - 252093750000000 x^{3} \log {\relax (2 )} - 178335937500000 x^{2} \log {\relax (2 )} - 51296875000000 x^{2} - 51296875000000 x \log {\relax (2 )} - 5359375000000 x - 5359375000000 \log {\relax (2 )}\right ) e^{x e^{x}}}{152587890625} \end {gather*}

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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