3.18.72 \(\int \frac {-107584-314880 x-314496 x^2-138240 x^3-25920 x^4+e^{5 e^x} (16+24 x^2+5 x^4)+(-275520-770560 x-844416 x^2-414720 x^3-95040 x^4) \log (5)+(-386320-935040 x-1083552 x^2-564480 x^3-162000 x^4) \log ^2(5)+(-373760-739840 x-901632 x^2-455680 x^3-168960 x^4) \log ^3(5)+(-263040-404800 x-551040 x^2-238720 x^3-119360 x^4) \log ^4(5)+(-138624-151040 x-259296 x^2-83200 x^3-59680 x^4) \log ^5(5)+(-54560-36480 x-93288 x^2-18880 x^3-21400 x^4) \log ^6(5)+(-15360-5120 x-24576 x^2-2560 x^3-5440 x^4) \log ^7(5)+(-2880-320 x-4416 x^2-160 x^3-940 x^4) \log ^8(5)+(-320-480 x^2-100 x^4) \log ^9(5)+(-16-24 x^2-5 x^4) \log ^{10}(5)+e^{4 e^x} (-320-320 x-576 x^2-160 x^3-140 x^4+e^x (160 x^2+32 x^3+40 x^4+8 x^5)+(-320-480 x^2-100 x^4) \log (5)+(-80-120 x^2-25 x^4) \log ^2(5))+e^{3 e^x} (3360+5760 x+7272 x^2+3520 x^3+1560 x^4+(5120+5120 x+9216 x^2+2560 x^3+2240 x^4) \log (5)+(3840+1280 x+6144 x^2+640 x^3+1360 x^4) \log ^2(5)+(1280+1920 x^2+400 x^4) \log ^3(5)+(160+240 x^2+50 x^4) \log ^4(5)+e^x (-1600 x-2560 x^2-1648 x^3-960 x^4-144 x^5+(-1920 x^2-384 x^3-480 x^4-96 x^5) \log (5)+(-480 x^2-96 x^3-120 x^4-24 x^5) \log ^2(5)))+e^{2 e^x} (-19840-46400 x-54528 x^2-28800 x^3-8640 x^4+(-40320-69120 x-87264 x^2-42240 x^3-18720 x^4) \log (5)+(-40800-48000 x-77112 x^2-25920 x^3-18120 x^4) \log ^2(5)+(-25600-15360 x-43008 x^2-7680 x^3-9920 x^4) \log ^3(5)+(-9600-1920 x-14976 x^2-960 x^3-3240 x^4) \log ^4(5)+(-1920-2880 x^2-600 x^4) \log ^5(5)+(-160-240 x^2-50 x^4) \log ^6(5)+e^x (12800 x+24800 x^2+18848 x^3+7200 x^4+864 x^5+(12800 x+20480 x^2+13184 x^3+7680 x^4+1152 x^5) \log (5)+(3200 x+12800 x^2+4832 x^3+3840 x^4+672 x^5) \log ^2(5)+(3840 x^2+768 x^3+960 x^4+192 x^5) \log ^3(5)+(480 x^2+96 x^3+120 x^4+24 x^5) \log ^4(5)))+e^{e^x} (68880+192640 x+211104 x^2+103680 x^3+23760 x^4+(158720+371200 x+436224 x^2+230400 x^3+69120 x^4) \log (5)+(200960+369280 x+458112 x^2+226560 x^3+92160 x^4) \log ^2(5)+(162560+220160 x+321984 x^2+125440 x^3+73280 x^4) \log ^3(5)+(92000+78720 x+163128 x^2+41280 x^3+37960 x^4) \log ^4(5)+(35840+15360 x+58368 x^2+7680 x^3+13120 x^4) \log ^5(5)+(8960+1280 x+13824 x^2+640 x^3+2960 x^4) \log ^6(5)+(1280+1920 x^2+400 x^4) \log ^7(5)+(80+120 x^2+25 x^4) \log ^8(5)+e^x (-65600 x-100480 x^2-60672 x^3-17280 x^4-1728 x^5+(-51200 x-99200 x^2-75392 x^3-28800 x^4-3456 x^5) \log (5)+(-38400 x-65760 x^2-45216 x^3-22560 x^4-3168 x^5) \log ^2(5)+(-12800 x-30720 x^2-15232 x^3-10240 x^4-1664 x^5) \log ^3(5)+(-1600 x-10240 x^2-3184 x^3-2880 x^4-528 x^5) \log ^4(5)+(-1920 x^2-384 x^3-480 x^4-96 x^5) \log ^5(5)+(-160 x^2-32 x^3-40 x^4-8 x^5) \log ^6(5)))}{-1024+e^{5 e^x}-5120 \log (5)-11520 \log ^2(5)-15360 \log ^3(5)-13440 \log ^4(5)-8064 \log ^5(5)-3360 \log ^6(5)-960 \log ^7(5)-180 \log ^8(5)-20 \log ^9(5)-\log ^{10}(5)+e^{4 e^x} (-20-20 \log (5)-5 \log ^2(5))+e^{3 e^x} (160+320 \log (5)+240 \log ^2(5)+80 \log ^3(5)+10 \log ^4(5))+e^{2 e^x} (-640-1920 \log (5)-2400 \log ^2(5)-1600 \log ^3(5)-600 \log ^4(5)-120 \log ^5(5)-10 \log ^6(5))+e^{e^x} (1280+5120 \log (5)+8960 \log ^2(5)+8960 \log ^3(5)+5600 \log ^4(5)+2240 \log ^5(5)+560 \log ^6(5)+80 \log ^7(5)+5 \log ^8(5))} \, dx\)

Optimal. Leaf size=33 \[ 3+x \left (4+\left (x-\frac {2 (5+x)}{e^{e^x}-(2+\log (5))^2}\right )^2\right )^2 \]

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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 {gather*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-107584 - 314880*x - 314496*x^2 - 138240*x^3 - 25920*x^4 + E^(5*E^x)*(16 + 24*x^2 + 5*x^4) + (-275520 - 7
70560*x - 844416*x^2 - 414720*x^3 - 95040*x^4)*Log[5] + (-386320 - 935040*x - 1083552*x^2 - 564480*x^3 - 16200
0*x^4)*Log[5]^2 + (-373760 - 739840*x - 901632*x^2 - 455680*x^3 - 168960*x^4)*Log[5]^3 + (-263040 - 404800*x -
551040*x^2 - 238720*x^3 - 119360*x^4)*Log[5]^4 + (-138624 - 151040*x - 259296*x^2 - 83200*x^3 - 59680*x^4)*Lo
g[5]^5 + (-54560 - 36480*x - 93288*x^2 - 18880*x^3 - 21400*x^4)*Log[5]^6 + (-15360 - 5120*x - 24576*x^2 - 2560
*x^3 - 5440*x^4)*Log[5]^7 + (-2880 - 320*x - 4416*x^2 - 160*x^3 - 940*x^4)*Log[5]^8 + (-320 - 480*x^2 - 100*x^
4)*Log[5]^9 + (-16 - 24*x^2 - 5*x^4)*Log[5]^10 + E^(4*E^x)*(-320 - 320*x - 576*x^2 - 160*x^3 - 140*x^4 + E^x*(
160*x^2 + 32*x^3 + 40*x^4 + 8*x^5) + (-320 - 480*x^2 - 100*x^4)*Log[5] + (-80 - 120*x^2 - 25*x^4)*Log[5]^2) +
E^(3*E^x)*(3360 + 5760*x + 7272*x^2 + 3520*x^3 + 1560*x^4 + (5120 + 5120*x + 9216*x^2 + 2560*x^3 + 2240*x^4)*L
og[5] + (3840 + 1280*x + 6144*x^2 + 640*x^3 + 1360*x^4)*Log[5]^2 + (1280 + 1920*x^2 + 400*x^4)*Log[5]^3 + (160
+ 240*x^2 + 50*x^4)*Log[5]^4 + E^x*(-1600*x - 2560*x^2 - 1648*x^3 - 960*x^4 - 144*x^5 + (-1920*x^2 - 384*x^3
- 480*x^4 - 96*x^5)*Log[5] + (-480*x^2 - 96*x^3 - 120*x^4 - 24*x^5)*Log[5]^2)) + E^(2*E^x)*(-19840 - 46400*x -
54528*x^2 - 28800*x^3 - 8640*x^4 + (-40320 - 69120*x - 87264*x^2 - 42240*x^3 - 18720*x^4)*Log[5] + (-40800 -
48000*x - 77112*x^2 - 25920*x^3 - 18120*x^4)*Log[5]^2 + (-25600 - 15360*x - 43008*x^2 - 7680*x^3 - 9920*x^4)*L
og[5]^3 + (-9600 - 1920*x - 14976*x^2 - 960*x^3 - 3240*x^4)*Log[5]^4 + (-1920 - 2880*x^2 - 600*x^4)*Log[5]^5 +
(-160 - 240*x^2 - 50*x^4)*Log[5]^6 + E^x*(12800*x + 24800*x^2 + 18848*x^3 + 7200*x^4 + 864*x^5 + (12800*x + 2
0480*x^2 + 13184*x^3 + 7680*x^4 + 1152*x^5)*Log[5] + (3200*x + 12800*x^2 + 4832*x^3 + 3840*x^4 + 672*x^5)*Log[
5]^2 + (3840*x^2 + 768*x^3 + 960*x^4 + 192*x^5)*Log[5]^3 + (480*x^2 + 96*x^3 + 120*x^4 + 24*x^5)*Log[5]^4)) +
E^E^x*(68880 + 192640*x + 211104*x^2 + 103680*x^3 + 23760*x^4 + (158720 + 371200*x + 436224*x^2 + 230400*x^3 +
69120*x^4)*Log[5] + (200960 + 369280*x + 458112*x^2 + 226560*x^3 + 92160*x^4)*Log[5]^2 + (162560 + 220160*x +
321984*x^2 + 125440*x^3 + 73280*x^4)*Log[5]^3 + (92000 + 78720*x + 163128*x^2 + 41280*x^3 + 37960*x^4)*Log[5]
^4 + (35840 + 15360*x + 58368*x^2 + 7680*x^3 + 13120*x^4)*Log[5]^5 + (8960 + 1280*x + 13824*x^2 + 640*x^3 + 29
60*x^4)*Log[5]^6 + (1280 + 1920*x^2 + 400*x^4)*Log[5]^7 + (80 + 120*x^2 + 25*x^4)*Log[5]^8 + E^x*(-65600*x - 1
00480*x^2 - 60672*x^3 - 17280*x^4 - 1728*x^5 + (-51200*x - 99200*x^2 - 75392*x^3 - 28800*x^4 - 3456*x^5)*Log[5
] + (-38400*x - 65760*x^2 - 45216*x^3 - 22560*x^4 - 3168*x^5)*Log[5]^2 + (-12800*x - 30720*x^2 - 15232*x^3 - 1
0240*x^4 - 1664*x^5)*Log[5]^3 + (-1600*x - 10240*x^2 - 3184*x^3 - 2880*x^4 - 528*x^5)*Log[5]^4 + (-1920*x^2 -
384*x^3 - 480*x^4 - 96*x^5)*Log[5]^5 + (-160*x^2 - 32*x^3 - 40*x^4 - 8*x^5)*Log[5]^6)))/(-1024 + E^(5*E^x) - 5
120*Log[5] - 11520*Log[5]^2 - 15360*Log[5]^3 - 13440*Log[5]^4 - 8064*Log[5]^5 - 3360*Log[5]^6 - 960*Log[5]^7 -
180*Log[5]^8 - 20*Log[5]^9 - Log[5]^10 + E^(4*E^x)*(-20 - 20*Log[5] - 5*Log[5]^2) + E^(3*E^x)*(160 + 320*Log[
5] + 240*Log[5]^2 + 80*Log[5]^3 + 10*Log[5]^4) + E^(2*E^x)*(-640 - 1920*Log[5] - 2400*Log[5]^2 - 1600*Log[5]^3
- 600*Log[5]^4 - 120*Log[5]^5 - 10*Log[5]^6) + E^E^x*(1280 + 5120*Log[5] + 8960*Log[5]^2 + 8960*Log[5]^3 + 56
00*Log[5]^4 + 2240*Log[5]^5 + 560*Log[5]^6 + 80*Log[5]^7 + 5*Log[5]^8)),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [B]  time = 3.16, size = 160, normalized size = 4.85 \begin {gather*} x \left (16+8 x^2+x^4+\frac {8 (5+x)^2 \left (4+3 x^2\right )}{\left (e^{e^x}-(2+\log (5))^2\right )^2}+\frac {32 x (5+x)^3}{\left (-e^{e^x}+(2+\log (5))^2\right )^3}+\frac {8 x \left (20+4 x+5 x^2+x^3\right )}{-e^{e^x}+(2+\log (5))^2}+\frac {e^{-x} (5+x)^2 \left (16 e^x (5+x)^2+x \left (-40 \log ^3(5)+5 \log ^2(625)+\log ^2(5) (-80+\log (9094947017729282379150390625))\right )\right )}{\left (e^{e^x}-(2+\log (5))^2\right )^4}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-107584 - 314880*x - 314496*x^2 - 138240*x^3 - 25920*x^4 + E^(5*E^x)*(16 + 24*x^2 + 5*x^4) + (-2755
20 - 770560*x - 844416*x^2 - 414720*x^3 - 95040*x^4)*Log[5] + (-386320 - 935040*x - 1083552*x^2 - 564480*x^3 -
162000*x^4)*Log[5]^2 + (-373760 - 739840*x - 901632*x^2 - 455680*x^3 - 168960*x^4)*Log[5]^3 + (-263040 - 4048
00*x - 551040*x^2 - 238720*x^3 - 119360*x^4)*Log[5]^4 + (-138624 - 151040*x - 259296*x^2 - 83200*x^3 - 59680*x
^4)*Log[5]^5 + (-54560 - 36480*x - 93288*x^2 - 18880*x^3 - 21400*x^4)*Log[5]^6 + (-15360 - 5120*x - 24576*x^2
- 2560*x^3 - 5440*x^4)*Log[5]^7 + (-2880 - 320*x - 4416*x^2 - 160*x^3 - 940*x^4)*Log[5]^8 + (-320 - 480*x^2 -
100*x^4)*Log[5]^9 + (-16 - 24*x^2 - 5*x^4)*Log[5]^10 + E^(4*E^x)*(-320 - 320*x - 576*x^2 - 160*x^3 - 140*x^4 +
E^x*(160*x^2 + 32*x^3 + 40*x^4 + 8*x^5) + (-320 - 480*x^2 - 100*x^4)*Log[5] + (-80 - 120*x^2 - 25*x^4)*Log[5]
^2) + E^(3*E^x)*(3360 + 5760*x + 7272*x^2 + 3520*x^3 + 1560*x^4 + (5120 + 5120*x + 9216*x^2 + 2560*x^3 + 2240*
x^4)*Log[5] + (3840 + 1280*x + 6144*x^2 + 640*x^3 + 1360*x^4)*Log[5]^2 + (1280 + 1920*x^2 + 400*x^4)*Log[5]^3
+ (160 + 240*x^2 + 50*x^4)*Log[5]^4 + E^x*(-1600*x - 2560*x^2 - 1648*x^3 - 960*x^4 - 144*x^5 + (-1920*x^2 - 38
4*x^3 - 480*x^4 - 96*x^5)*Log[5] + (-480*x^2 - 96*x^3 - 120*x^4 - 24*x^5)*Log[5]^2)) + E^(2*E^x)*(-19840 - 464
00*x - 54528*x^2 - 28800*x^3 - 8640*x^4 + (-40320 - 69120*x - 87264*x^2 - 42240*x^3 - 18720*x^4)*Log[5] + (-40
800 - 48000*x - 77112*x^2 - 25920*x^3 - 18120*x^4)*Log[5]^2 + (-25600 - 15360*x - 43008*x^2 - 7680*x^3 - 9920*
x^4)*Log[5]^3 + (-9600 - 1920*x - 14976*x^2 - 960*x^3 - 3240*x^4)*Log[5]^4 + (-1920 - 2880*x^2 - 600*x^4)*Log[
5]^5 + (-160 - 240*x^2 - 50*x^4)*Log[5]^6 + E^x*(12800*x + 24800*x^2 + 18848*x^3 + 7200*x^4 + 864*x^5 + (12800
*x + 20480*x^2 + 13184*x^3 + 7680*x^4 + 1152*x^5)*Log[5] + (3200*x + 12800*x^2 + 4832*x^3 + 3840*x^4 + 672*x^5
)*Log[5]^2 + (3840*x^2 + 768*x^3 + 960*x^4 + 192*x^5)*Log[5]^3 + (480*x^2 + 96*x^3 + 120*x^4 + 24*x^5)*Log[5]^
4)) + E^E^x*(68880 + 192640*x + 211104*x^2 + 103680*x^3 + 23760*x^4 + (158720 + 371200*x + 436224*x^2 + 230400
*x^3 + 69120*x^4)*Log[5] + (200960 + 369280*x + 458112*x^2 + 226560*x^3 + 92160*x^4)*Log[5]^2 + (162560 + 2201
60*x + 321984*x^2 + 125440*x^3 + 73280*x^4)*Log[5]^3 + (92000 + 78720*x + 163128*x^2 + 41280*x^3 + 37960*x^4)*
Log[5]^4 + (35840 + 15360*x + 58368*x^2 + 7680*x^3 + 13120*x^4)*Log[5]^5 + (8960 + 1280*x + 13824*x^2 + 640*x^
3 + 2960*x^4)*Log[5]^6 + (1280 + 1920*x^2 + 400*x^4)*Log[5]^7 + (80 + 120*x^2 + 25*x^4)*Log[5]^8 + E^x*(-65600
*x - 100480*x^2 - 60672*x^3 - 17280*x^4 - 1728*x^5 + (-51200*x - 99200*x^2 - 75392*x^3 - 28800*x^4 - 3456*x^5)
*Log[5] + (-38400*x - 65760*x^2 - 45216*x^3 - 22560*x^4 - 3168*x^5)*Log[5]^2 + (-12800*x - 30720*x^2 - 15232*x
^3 - 10240*x^4 - 1664*x^5)*Log[5]^3 + (-1600*x - 10240*x^2 - 3184*x^3 - 2880*x^4 - 528*x^5)*Log[5]^4 + (-1920*
x^2 - 384*x^3 - 480*x^4 - 96*x^5)*Log[5]^5 + (-160*x^2 - 32*x^3 - 40*x^4 - 8*x^5)*Log[5]^6)))/(-1024 + E^(5*E^
x) - 5120*Log[5] - 11520*Log[5]^2 - 15360*Log[5]^3 - 13440*Log[5]^4 - 8064*Log[5]^5 - 3360*Log[5]^6 - 960*Log[
5]^7 - 180*Log[5]^8 - 20*Log[5]^9 - Log[5]^10 + E^(4*E^x)*(-20 - 20*Log[5] - 5*Log[5]^2) + E^(3*E^x)*(160 + 32
0*Log[5] + 240*Log[5]^2 + 80*Log[5]^3 + 10*Log[5]^4) + E^(2*E^x)*(-640 - 1920*Log[5] - 2400*Log[5]^2 - 1600*Lo
g[5]^3 - 600*Log[5]^4 - 120*Log[5]^5 - 10*Log[5]^6) + E^E^x*(1280 + 5120*Log[5] + 8960*Log[5]^2 + 8960*Log[5]^
3 + 5600*Log[5]^4 + 2240*Log[5]^5 + 560*Log[5]^6 + 80*Log[5]^7 + 5*Log[5]^8)),x]

[Out]

x*(16 + 8*x^2 + x^4 + (8*(5 + x)^2*(4 + 3*x^2))/(E^E^x - (2 + Log[5])^2)^2 + (32*x*(5 + x)^3)/(-E^E^x + (2 + L
og[5])^2)^3 + (8*x*(20 + 4*x + 5*x^2 + x^3))/(-E^E^x + (2 + Log[5])^2) + ((5 + x)^2*(16*E^x*(5 + x)^2 + x*(-40
*Log[5]^3 + 5*Log[625]^2 + Log[5]^2*(-80 + Log[9094947017729282379150390625]))))/(E^x*(E^E^x - (2 + Log[5])^2)
^4))

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fricas [B]  time = 0.99, size = 765, normalized size = 23.18 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*x^4+24*x^2+16)*exp(exp(x))^5+((8*x^5+40*x^4+32*x^3+160*x^2)*exp(x)+(-25*x^4-120*x^2-80)*log(5)^2
+(-100*x^4-480*x^2-320)*log(5)-140*x^4-160*x^3-576*x^2-320*x-320)*exp(exp(x))^4+(((-24*x^5-120*x^4-96*x^3-480*
x^2)*log(5)^2+(-96*x^5-480*x^4-384*x^3-1920*x^2)*log(5)-144*x^5-960*x^4-1648*x^3-2560*x^2-1600*x)*exp(x)+(50*x
^4+240*x^2+160)*log(5)^4+(400*x^4+1920*x^2+1280)*log(5)^3+(1360*x^4+640*x^3+6144*x^2+1280*x+3840)*log(5)^2+(22
40*x^4+2560*x^3+9216*x^2+5120*x+5120)*log(5)+1560*x^4+3520*x^3+7272*x^2+5760*x+3360)*exp(exp(x))^3+(((24*x^5+1
20*x^4+96*x^3+480*x^2)*log(5)^4+(192*x^5+960*x^4+768*x^3+3840*x^2)*log(5)^3+(672*x^5+3840*x^4+4832*x^3+12800*x
^2+3200*x)*log(5)^2+(1152*x^5+7680*x^4+13184*x^3+20480*x^2+12800*x)*log(5)+864*x^5+7200*x^4+18848*x^3+24800*x^
2+12800*x)*exp(x)+(-50*x^4-240*x^2-160)*log(5)^6+(-600*x^4-2880*x^2-1920)*log(5)^5+(-3240*x^4-960*x^3-14976*x^
2-1920*x-9600)*log(5)^4+(-9920*x^4-7680*x^3-43008*x^2-15360*x-25600)*log(5)^3+(-18120*x^4-25920*x^3-77112*x^2-
48000*x-40800)*log(5)^2+(-18720*x^4-42240*x^3-87264*x^2-69120*x-40320)*log(5)-8640*x^4-28800*x^3-54528*x^2-464
00*x-19840)*exp(exp(x))^2+(((-8*x^5-40*x^4-32*x^3-160*x^2)*log(5)^6+(-96*x^5-480*x^4-384*x^3-1920*x^2)*log(5)^
5+(-528*x^5-2880*x^4-3184*x^3-10240*x^2-1600*x)*log(5)^4+(-1664*x^5-10240*x^4-15232*x^3-30720*x^2-12800*x)*log
(5)^3+(-3168*x^5-22560*x^4-45216*x^3-65760*x^2-38400*x)*log(5)^2+(-3456*x^5-28800*x^4-75392*x^3-99200*x^2-5120
0*x)*log(5)-1728*x^5-17280*x^4-60672*x^3-100480*x^2-65600*x)*exp(x)+(25*x^4+120*x^2+80)*log(5)^8+(400*x^4+1920
*x^2+1280)*log(5)^7+(2960*x^4+640*x^3+13824*x^2+1280*x+8960)*log(5)^6+(13120*x^4+7680*x^3+58368*x^2+15360*x+35
840)*log(5)^5+(37960*x^4+41280*x^3+163128*x^2+78720*x+92000)*log(5)^4+(73280*x^4+125440*x^3+321984*x^2+220160*
x+162560)*log(5)^3+(92160*x^4+226560*x^3+458112*x^2+369280*x+200960)*log(5)^2+(69120*x^4+230400*x^3+436224*x^2
+371200*x+158720)*log(5)+23760*x^4+103680*x^3+211104*x^2+192640*x+68880)*exp(exp(x))+(-5*x^4-24*x^2-16)*log(5)
^10+(-100*x^4-480*x^2-320)*log(5)^9+(-940*x^4-160*x^3-4416*x^2-320*x-2880)*log(5)^8+(-5440*x^4-2560*x^3-24576*
x^2-5120*x-15360)*log(5)^7+(-21400*x^4-18880*x^3-93288*x^2-36480*x-54560)*log(5)^6+(-59680*x^4-83200*x^3-25929
6*x^2-151040*x-138624)*log(5)^5+(-119360*x^4-238720*x^3-551040*x^2-404800*x-263040)*log(5)^4+(-168960*x^4-4556
80*x^3-901632*x^2-739840*x-373760)*log(5)^3+(-162000*x^4-564480*x^3-1083552*x^2-935040*x-386320)*log(5)^2+(-95
040*x^4-414720*x^3-844416*x^2-770560*x-275520)*log(5)-25920*x^4-138240*x^3-314496*x^2-314880*x-107584)/(exp(ex
p(x))^5+(-5*log(5)^2-20*log(5)-20)*exp(exp(x))^4+(10*log(5)^4+80*log(5)^3+240*log(5)^2+320*log(5)+160)*exp(exp
(x))^3+(-10*log(5)^6-120*log(5)^5-600*log(5)^4-1600*log(5)^3-2400*log(5)^2-1920*log(5)-640)*exp(exp(x))^2+(5*l
og(5)^8+80*log(5)^7+560*log(5)^6+2240*log(5)^5+5600*log(5)^4+8960*log(5)^3+8960*log(5)^2+5120*log(5)+1280)*exp
(exp(x))-log(5)^10-20*log(5)^9-180*log(5)^8-960*log(5)^7-3360*log(5)^6-8064*log(5)^5-13440*log(5)^4-15360*log(
5)^3-11520*log(5)^2-5120*log(5)-1024),x, algorithm="fricas")

[Out]

((x^5 + 8*x^3 + 16*x)*log(5)^8 + 16*(x^5 + 8*x^3 + 16*x)*log(5)^7 + 8*(15*x^5 + 5*x^4 + 116*x^3 + 20*x^2 + 224
*x)*log(5)^6 + 32*(17*x^5 + 15*x^4 + 124*x^3 + 60*x^2 + 224*x)*log(5)^5 + 1296*x^5 + 8*(203*x^5 + 330*x^4 + 14
39*x^3 + 1240*x^2 + 2340*x)*log(5)^4 + 8640*x^4 + 64*(51*x^5 + 130*x^4 + 383*x^3 + 440*x^2 + 548*x)*log(5)^3 +
26208*x^3 + 32*(135*x^5 + 495*x^4 + 1237*x^3 + 1565*x^2 + 1496*x)*log(5)^2 + 39360*x^2 + (x^5 + 8*x^3 + 16*x)
*e^(4*e^x) - 4*(6*x^5 + 10*x^4 + 40*x^3 + (x^5 + 8*x^3 + 16*x)*log(5)^2 + 40*x^2 + 4*(x^5 + 8*x^3 + 16*x)*log(
5) + 64*x)*e^(3*e^x) + 2*(108*x^5 + 3*(x^5 + 8*x^3 + 16*x)*log(5)^4 + 360*x^4 + 24*(x^5 + 8*x^3 + 16*x)*log(5)
^3 + 892*x^3 + 12*(7*x^5 + 5*x^4 + 52*x^3 + 20*x^2 + 96*x)*log(5)^2 + 1120*x^2 + 48*(3*x^5 + 5*x^4 + 20*x^3 +
20*x^2 + 32*x)*log(5) + 1168*x)*e^(2*e^x) - 4*((x^5 + 8*x^3 + 16*x)*log(5)^6 + 12*(x^5 + 8*x^3 + 16*x)*log(5)^
5 + 216*x^5 + 6*(11*x^5 + 5*x^4 + 84*x^3 + 20*x^2 + 160*x)*log(5)^4 + 1080*x^4 + 16*(13*x^5 + 15*x^4 + 92*x^3
+ 60*x^2 + 160*x)*log(5)^3 + 2760*x^3 + 4*(99*x^5 + 210*x^4 + 703*x^3 + 760*x^2 + 1060*x)*log(5)^2 + 3560*x^2
+ 16*(27*x^5 + 90*x^4 + 223*x^3 + 280*x^2 + 292*x)*log(5) + 2624*x)*e^(e^x) + 128*(27*x^5 + 135*x^4 + 345*x^3
+ 445*x^2 + 328*x)*log(5) + 26896*x)/(log(5)^8 + 16*log(5)^7 + 112*log(5)^6 + 448*log(5)^5 + 1120*log(5)^4 + 1
792*log(5)^3 - 4*(log(5)^2 + 4*log(5) + 4)*e^(3*e^x) + 6*(log(5)^4 + 8*log(5)^3 + 24*log(5)^2 + 32*log(5) + 16
)*e^(2*e^x) - 4*(log(5)^6 + 12*log(5)^5 + 60*log(5)^4 + 160*log(5)^3 + 240*log(5)^2 + 192*log(5) + 64)*e^(e^x)
+ 1792*log(5)^2 + e^(4*e^x) + 1024*log(5) + 256)

________________________________________________________________________________________

giac [B]  time = 2.17, size = 1239, normalized size = 37.55 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*x^4+24*x^2+16)*exp(exp(x))^5+((8*x^5+40*x^4+32*x^3+160*x^2)*exp(x)+(-25*x^4-120*x^2-80)*log(5)^2
+(-100*x^4-480*x^2-320)*log(5)-140*x^4-160*x^3-576*x^2-320*x-320)*exp(exp(x))^4+(((-24*x^5-120*x^4-96*x^3-480*
x^2)*log(5)^2+(-96*x^5-480*x^4-384*x^3-1920*x^2)*log(5)-144*x^5-960*x^4-1648*x^3-2560*x^2-1600*x)*exp(x)+(50*x
^4+240*x^2+160)*log(5)^4+(400*x^4+1920*x^2+1280)*log(5)^3+(1360*x^4+640*x^3+6144*x^2+1280*x+3840)*log(5)^2+(22
40*x^4+2560*x^3+9216*x^2+5120*x+5120)*log(5)+1560*x^4+3520*x^3+7272*x^2+5760*x+3360)*exp(exp(x))^3+(((24*x^5+1
20*x^4+96*x^3+480*x^2)*log(5)^4+(192*x^5+960*x^4+768*x^3+3840*x^2)*log(5)^3+(672*x^5+3840*x^4+4832*x^3+12800*x
^2+3200*x)*log(5)^2+(1152*x^5+7680*x^4+13184*x^3+20480*x^2+12800*x)*log(5)+864*x^5+7200*x^4+18848*x^3+24800*x^
2+12800*x)*exp(x)+(-50*x^4-240*x^2-160)*log(5)^6+(-600*x^4-2880*x^2-1920)*log(5)^5+(-3240*x^4-960*x^3-14976*x^
2-1920*x-9600)*log(5)^4+(-9920*x^4-7680*x^3-43008*x^2-15360*x-25600)*log(5)^3+(-18120*x^4-25920*x^3-77112*x^2-
48000*x-40800)*log(5)^2+(-18720*x^4-42240*x^3-87264*x^2-69120*x-40320)*log(5)-8640*x^4-28800*x^3-54528*x^2-464
00*x-19840)*exp(exp(x))^2+(((-8*x^5-40*x^4-32*x^3-160*x^2)*log(5)^6+(-96*x^5-480*x^4-384*x^3-1920*x^2)*log(5)^
5+(-528*x^5-2880*x^4-3184*x^3-10240*x^2-1600*x)*log(5)^4+(-1664*x^5-10240*x^4-15232*x^3-30720*x^2-12800*x)*log
(5)^3+(-3168*x^5-22560*x^4-45216*x^3-65760*x^2-38400*x)*log(5)^2+(-3456*x^5-28800*x^4-75392*x^3-99200*x^2-5120
0*x)*log(5)-1728*x^5-17280*x^4-60672*x^3-100480*x^2-65600*x)*exp(x)+(25*x^4+120*x^2+80)*log(5)^8+(400*x^4+1920
*x^2+1280)*log(5)^7+(2960*x^4+640*x^3+13824*x^2+1280*x+8960)*log(5)^6+(13120*x^4+7680*x^3+58368*x^2+15360*x+35
840)*log(5)^5+(37960*x^4+41280*x^3+163128*x^2+78720*x+92000)*log(5)^4+(73280*x^4+125440*x^3+321984*x^2+220160*
x+162560)*log(5)^3+(92160*x^4+226560*x^3+458112*x^2+369280*x+200960)*log(5)^2+(69120*x^4+230400*x^3+436224*x^2
+371200*x+158720)*log(5)+23760*x^4+103680*x^3+211104*x^2+192640*x+68880)*exp(exp(x))+(-5*x^4-24*x^2-16)*log(5)
^10+(-100*x^4-480*x^2-320)*log(5)^9+(-940*x^4-160*x^3-4416*x^2-320*x-2880)*log(5)^8+(-5440*x^4-2560*x^3-24576*
x^2-5120*x-15360)*log(5)^7+(-21400*x^4-18880*x^3-93288*x^2-36480*x-54560)*log(5)^6+(-59680*x^4-83200*x^3-25929
6*x^2-151040*x-138624)*log(5)^5+(-119360*x^4-238720*x^3-551040*x^2-404800*x-263040)*log(5)^4+(-168960*x^4-4556
80*x^3-901632*x^2-739840*x-373760)*log(5)^3+(-162000*x^4-564480*x^3-1083552*x^2-935040*x-386320)*log(5)^2+(-95
040*x^4-414720*x^3-844416*x^2-770560*x-275520)*log(5)-25920*x^4-138240*x^3-314496*x^2-314880*x-107584)/(exp(ex
p(x))^5+(-5*log(5)^2-20*log(5)-20)*exp(exp(x))^4+(10*log(5)^4+80*log(5)^3+240*log(5)^2+320*log(5)+160)*exp(exp
(x))^3+(-10*log(5)^6-120*log(5)^5-600*log(5)^4-1600*log(5)^3-2400*log(5)^2-1920*log(5)-640)*exp(exp(x))^2+(5*l
og(5)^8+80*log(5)^7+560*log(5)^6+2240*log(5)^5+5600*log(5)^4+8960*log(5)^3+8960*log(5)^2+5120*log(5)+1280)*exp
(exp(x))-log(5)^10-20*log(5)^9-180*log(5)^8-960*log(5)^7-3360*log(5)^6-8064*log(5)^5-13440*log(5)^4-15360*log(
5)^3-11520*log(5)^2-5120*log(5)-1024),x, algorithm="giac")

[Out]

(x^5*log(5)^8 - 4*x^5*e^(e^x)*log(5)^6 + 16*x^5*log(5)^7 - 48*x^5*e^(e^x)*log(5)^5 + 120*x^5*log(5)^6 + 8*x^3*
log(5)^8 + 6*x^5*e^(2*e^x)*log(5)^4 - 264*x^5*e^(e^x)*log(5)^4 + 544*x^5*log(5)^5 + 40*x^4*log(5)^6 - 32*x^3*e
^(e^x)*log(5)^6 + 128*x^3*log(5)^7 + 48*x^5*e^(2*e^x)*log(5)^3 - 832*x^5*e^(e^x)*log(5)^3 + 1624*x^5*log(5)^4
- 120*x^4*e^(e^x)*log(5)^4 + 480*x^4*log(5)^5 - 384*x^3*e^(e^x)*log(5)^5 + 928*x^3*log(5)^6 + 16*x*log(5)^8 -
4*x^5*e^(3*e^x)*log(5)^2 + 168*x^5*e^(2*e^x)*log(5)^2 - 1584*x^5*e^(e^x)*log(5)^2 + 3264*x^5*log(5)^3 - 960*x^
4*e^(e^x)*log(5)^3 + 2640*x^4*log(5)^4 + 48*x^3*e^(2*e^x)*log(5)^4 - 2016*x^3*e^(e^x)*log(5)^4 + 3968*x^3*log(
5)^5 + 160*x^2*log(5)^6 - 64*x*e^(e^x)*log(5)^6 + 256*x*log(5)^7 - 16*x^5*e^(3*e^x)*log(5) + 288*x^5*e^(2*e^x)
*log(5) - 1728*x^5*e^(e^x)*log(5) + 4320*x^5*log(5)^2 + 120*x^4*e^(2*e^x)*log(5)^2 - 3360*x^4*e^(e^x)*log(5)^2
+ 8320*x^4*log(5)^3 + 384*x^3*e^(2*e^x)*log(5)^3 - 5888*x^3*e^(e^x)*log(5)^3 + 11512*x^3*log(5)^4 - 480*x^2*e
^(e^x)*log(5)^4 + 1920*x^2*log(5)^5 - 768*x*e^(e^x)*log(5)^5 + 1792*x*log(5)^6 + x^5*e^(4*e^x) - 24*x^5*e^(3*e
^x) + 216*x^5*e^(2*e^x) - 864*x^5*e^(e^x) + 3456*x^5*log(5) + 480*x^4*e^(2*e^x)*log(5) - 5760*x^4*e^(e^x)*log(
5) + 15840*x^4*log(5)^2 - 32*x^3*e^(3*e^x)*log(5)^2 + 1248*x^3*e^(2*e^x)*log(5)^2 - 11248*x^3*e^(e^x)*log(5)^2
+ 24512*x^3*log(5)^3 - 3840*x^2*e^(e^x)*log(5)^3 + 9920*x^2*log(5)^4 + 96*x*e^(2*e^x)*log(5)^4 - 3840*x*e^(e^
x)*log(5)^4 + 7168*x*log(5)^5 + 1296*x^5 - 40*x^4*e^(3*e^x) + 720*x^4*e^(2*e^x) - 4320*x^4*e^(e^x) + 17280*x^4
*log(5) - 128*x^3*e^(3*e^x)*log(5) + 1920*x^3*e^(2*e^x)*log(5) - 14272*x^3*e^(e^x)*log(5) + 39584*x^3*log(5)^2
+ 480*x^2*e^(2*e^x)*log(5)^2 - 12160*x^2*e^(e^x)*log(5)^2 + 28160*x^2*log(5)^3 + 768*x*e^(2*e^x)*log(5)^3 - 1
0240*x*e^(e^x)*log(5)^3 + 18720*x*log(5)^4 + 8640*x^4 + 8*x^3*e^(4*e^x) - 160*x^3*e^(3*e^x) + 1784*x^3*e^(2*e^
x) - 11040*x^3*e^(e^x) + 44160*x^3*log(5) + 1920*x^2*e^(2*e^x)*log(5) - 17920*x^2*e^(e^x)*log(5) + 50080*x^2*l
og(5)^2 - 64*x*e^(3*e^x)*log(5)^2 + 2304*x*e^(2*e^x)*log(5)^2 - 16960*x*e^(e^x)*log(5)^2 + 35072*x*log(5)^3 +
26208*x^3 - 160*x^2*e^(3*e^x) + 2240*x^2*e^(2*e^x) - 14240*x^2*e^(e^x) + 56960*x^2*log(5) - 256*x*e^(3*e^x)*lo
g(5) + 3072*x*e^(2*e^x)*log(5) - 18688*x*e^(e^x)*log(5) + 47872*x*log(5)^2 + 39360*x^2 + 16*x*e^(4*e^x) - 256*
x*e^(3*e^x) + 2336*x*e^(2*e^x) - 10496*x*e^(e^x) + 41984*x*log(5) + 26896*x)/(log(5)^8 - 4*e^(e^x)*log(5)^6 +
16*log(5)^7 - 48*e^(e^x)*log(5)^5 + 112*log(5)^6 + 6*e^(2*e^x)*log(5)^4 - 240*e^(e^x)*log(5)^4 + 448*log(5)^5
+ 48*e^(2*e^x)*log(5)^3 - 640*e^(e^x)*log(5)^3 + 1120*log(5)^4 - 4*e^(3*e^x)*log(5)^2 + 144*e^(2*e^x)*log(5)^2
- 960*e^(e^x)*log(5)^2 + 1792*log(5)^3 - 16*e^(3*e^x)*log(5) + 192*e^(2*e^x)*log(5) - 768*e^(e^x)*log(5) + 17
92*log(5)^2 + e^(4*e^x) - 16*e^(3*e^x) + 96*e^(2*e^x) - 256*e^(e^x) + 1024*log(5) + 256)

________________________________________________________________________________________

maple [B]  time = 0.78, size = 680, normalized size = 20.61

method	result	size
risch	\(x^{5}+8 x^{3}+16 x +\frac {8 \left (2850+4920 x +1980 x^{3} \ln \relax (5)^{2}+63 x^{4} \ln \relax (5)^{4}+x^{4} \ln \relax (5)^{6}+12 x^{4} \ln \relax (5)^{5}-4 x^{2} {\mathrm e}^{3 \,{\mathrm e}^{x}}+4496 x^{2} \ln \relax (5)+48 x^{2} \ln \relax (5)^{5}+800 \ln \relax (5)^{3}+100 \ln \relax (5)^{4}+184 x^{4} \ln \relax (5)^{3}+3200 \ln \relax (5)+2400 \ln \relax (5)^{2}-800 \,{\mathrm e}^{{\mathrm e}^{x}}+130 x^{4}+1080 x^{3}+3020 x^{2}+20 x \ln \relax (5)^{6}-20 x \,{\mathrm e}^{3 \,{\mathrm e}^{x}}+1040 x^{3} \ln \relax (5)^{3}-{\mathrm e}^{3 \,{\mathrm e}^{x}} x^{4}-1124 \,{\mathrm e}^{{\mathrm e}^{x}} x^{2}+1240 x \ln \relax (5)^{4}+7120 x \ln \relax (5)+3156 x^{2} \ln \relax (5)^{2}-1780 x \,{\mathrm e}^{{\mathrm e}^{x}}-540 x^{3} {\mathrm e}^{{\mathrm e}^{x}}+2160 x^{3} \ln \relax (5)-76 x^{4} {\mathrm e}^{{\mathrm e}^{x}}+330 x^{3} \ln \relax (5)^{4}+100 \,{\mathrm e}^{2 \,{\mathrm e}^{x}}+5 x^{3} \ln \relax (5)^{6}+3520 \ln \relax (5)^{3} x +319 \ln \relax (5)^{4} x^{2}+316 x^{4} \ln \relax (5)^{2}+6260 x \ln \relax (5)^{2}+304 x^{4} \ln \relax (5)+1272 x^{2} \ln \relax (5)^{3}+60 \ln \relax (5) {\mathrm e}^{2 \,{\mathrm e}^{x}} x^{3}+60 \ln \relax (5)^{2} {\mathrm e}^{2 \,{\mathrm e}^{x}} x +48 \ln \relax (5) {\mathrm e}^{2 \,{\mathrm e}^{x}} x^{2}+15 \ln \relax (5)^{2} {\mathrm e}^{2 \,{\mathrm e}^{x}} x^{3}+12 \ln \relax (5)^{2} {\mathrm e}^{2 \,{\mathrm e}^{x}} x^{2}+4 \ln \relax (5)^{6} x^{2}+60 \ln \relax (5)^{5} x^{3}+240 \ln \relax (5)^{5} x -200 \ln \relax (5)^{2} {\mathrm e}^{{\mathrm e}^{x}}-800 \ln \relax (5) {\mathrm e}^{{\mathrm e}^{x}}-15 \ln \relax (5)^{4} {\mathrm e}^{{\mathrm e}^{x}} x^{3}-12 \ln \relax (5)^{4} {\mathrm e}^{{\mathrm e}^{x}} x^{2}-120 \ln \relax (5)^{3} {\mathrm e}^{{\mathrm e}^{x}} x^{3}-60 \ln \relax (5)^{4} {\mathrm e}^{{\mathrm e}^{x}} x -96 \ln \relax (5)^{3} {\mathrm e}^{{\mathrm e}^{x}} x^{2}-420 \ln \relax (5)^{2} {\mathrm e}^{{\mathrm e}^{x}} x^{3}-480 \ln \relax (5)^{3} {\mathrm e}^{{\mathrm e}^{x}} x -446 \ln \relax (5)^{2} {\mathrm e}^{{\mathrm e}^{x}} x^{2}-720 \ln \relax (5) {\mathrm e}^{{\mathrm e}^{x}} x^{3}-1520 \ln \relax (5)^{2} {\mathrm e}^{{\mathrm e}^{x}} x -1016 \ln \relax (5) {\mathrm e}^{{\mathrm e}^{x}} x^{2}-2240 \ln \relax (5) {\mathrm e}^{{\mathrm e}^{x}} x -3 \ln \relax (5)^{4} {\mathrm e}^{{\mathrm e}^{x}} x^{4}-24 \ln \relax (5)^{3} {\mathrm e}^{{\mathrm e}^{x}} x^{4}-78 \ln \relax (5)^{2} {\mathrm e}^{{\mathrm e}^{x}} x^{4}-120 \ln \relax (5) {\mathrm e}^{{\mathrm e}^{x}} x^{4}+127 x^{2} {\mathrm e}^{2 \,{\mathrm e}^{x}}+280 x \,{\mathrm e}^{2 \,{\mathrm e}^{x}}+90 x^{3} {\mathrm e}^{2 \,{\mathrm e}^{x}}+15 x^{4} {\mathrm e}^{2 \,{\mathrm e}^{x}}-5 \,{\mathrm e}^{3 \,{\mathrm e}^{x}} x^{3}+240 \ln \relax (5) {\mathrm e}^{2 \,{\mathrm e}^{x}} x +3 \ln \relax (5)^{2} {\mathrm e}^{2 \,{\mathrm e}^{x}} x^{4}+12 \ln \relax (5) {\mathrm e}^{2 \,{\mathrm e}^{x}} x^{4}\right ) x}{\left (\ln \relax (5)^{2}+4 \ln \relax (5)-{\mathrm e}^{{\mathrm e}^{x}}+4\right )^{4}}\)	\(680\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((5*x^4+24*x^2+16)*exp(exp(x))^5+((8*x^5+40*x^4+32*x^3+160*x^2)*exp(x)+(-25*x^4-120*x^2-80)*ln(5)^2+(-100*
x^4-480*x^2-320)*ln(5)-140*x^4-160*x^3-576*x^2-320*x-320)*exp(exp(x))^4+(((-24*x^5-120*x^4-96*x^3-480*x^2)*ln(
5)^2+(-96*x^5-480*x^4-384*x^3-1920*x^2)*ln(5)-144*x^5-960*x^4-1648*x^3-2560*x^2-1600*x)*exp(x)+(50*x^4+240*x^2
+160)*ln(5)^4+(400*x^4+1920*x^2+1280)*ln(5)^3+(1360*x^4+640*x^3+6144*x^2+1280*x+3840)*ln(5)^2+(2240*x^4+2560*x
^3+9216*x^2+5120*x+5120)*ln(5)+1560*x^4+3520*x^3+7272*x^2+5760*x+3360)*exp(exp(x))^3+(((24*x^5+120*x^4+96*x^3+
480*x^2)*ln(5)^4+(192*x^5+960*x^4+768*x^3+3840*x^2)*ln(5)^3+(672*x^5+3840*x^4+4832*x^3+12800*x^2+3200*x)*ln(5)
^2+(1152*x^5+7680*x^4+13184*x^3+20480*x^2+12800*x)*ln(5)+864*x^5+7200*x^4+18848*x^3+24800*x^2+12800*x)*exp(x)+
(-50*x^4-240*x^2-160)*ln(5)^6+(-600*x^4-2880*x^2-1920)*ln(5)^5+(-3240*x^4-960*x^3-14976*x^2-1920*x-9600)*ln(5)
^4+(-9920*x^4-7680*x^3-43008*x^2-15360*x-25600)*ln(5)^3+(-18120*x^4-25920*x^3-77112*x^2-48000*x-40800)*ln(5)^2
+(-18720*x^4-42240*x^3-87264*x^2-69120*x-40320)*ln(5)-8640*x^4-28800*x^3-54528*x^2-46400*x-19840)*exp(exp(x))^
2+(((-8*x^5-40*x^4-32*x^3-160*x^2)*ln(5)^6+(-96*x^5-480*x^4-384*x^3-1920*x^2)*ln(5)^5+(-528*x^5-2880*x^4-3184*
x^3-10240*x^2-1600*x)*ln(5)^4+(-1664*x^5-10240*x^4-15232*x^3-30720*x^2-12800*x)*ln(5)^3+(-3168*x^5-22560*x^4-4
5216*x^3-65760*x^2-38400*x)*ln(5)^2+(-3456*x^5-28800*x^4-75392*x^3-99200*x^2-51200*x)*ln(5)-1728*x^5-17280*x^4
-60672*x^3-100480*x^2-65600*x)*exp(x)+(25*x^4+120*x^2+80)*ln(5)^8+(400*x^4+1920*x^2+1280)*ln(5)^7+(2960*x^4+64
0*x^3+13824*x^2+1280*x+8960)*ln(5)^6+(13120*x^4+7680*x^3+58368*x^2+15360*x+35840)*ln(5)^5+(37960*x^4+41280*x^3
+163128*x^2+78720*x+92000)*ln(5)^4+(73280*x^4+125440*x^3+321984*x^2+220160*x+162560)*ln(5)^3+(92160*x^4+226560
*x^3+458112*x^2+369280*x+200960)*ln(5)^2+(69120*x^4+230400*x^3+436224*x^2+371200*x+158720)*ln(5)+23760*x^4+103
680*x^3+211104*x^2+192640*x+68880)*exp(exp(x))+(-5*x^4-24*x^2-16)*ln(5)^10+(-100*x^4-480*x^2-320)*ln(5)^9+(-94
0*x^4-160*x^3-4416*x^2-320*x-2880)*ln(5)^8+(-5440*x^4-2560*x^3-24576*x^2-5120*x-15360)*ln(5)^7+(-21400*x^4-188
80*x^3-93288*x^2-36480*x-54560)*ln(5)^6+(-59680*x^4-83200*x^3-259296*x^2-151040*x-138624)*ln(5)^5+(-119360*x^4
-238720*x^3-551040*x^2-404800*x-263040)*ln(5)^4+(-168960*x^4-455680*x^3-901632*x^2-739840*x-373760)*ln(5)^3+(-
162000*x^4-564480*x^3-1083552*x^2-935040*x-386320)*ln(5)^2+(-95040*x^4-414720*x^3-844416*x^2-770560*x-275520)*
ln(5)-25920*x^4-138240*x^3-314496*x^2-314880*x-107584)/(exp(exp(x))^5+(-5*ln(5)^2-20*ln(5)-20)*exp(exp(x))^4+(
10*ln(5)^4+80*ln(5)^3+240*ln(5)^2+320*ln(5)+160)*exp(exp(x))^3+(-10*ln(5)^6-120*ln(5)^5-600*ln(5)^4-1600*ln(5)
^3-2400*ln(5)^2-1920*ln(5)-640)*exp(exp(x))^2+(5*ln(5)^8+80*ln(5)^7+560*ln(5)^6+2240*ln(5)^5+5600*ln(5)^4+8960
*ln(5)^3+8960*ln(5)^2+5120*ln(5)+1280)*exp(exp(x))-ln(5)^10-20*ln(5)^9-180*ln(5)^8-960*ln(5)^7-3360*ln(5)^6-80
64*ln(5)^5-13440*ln(5)^4-15360*ln(5)^3-11520*ln(5)^2-5120*ln(5)-1024),x,method=_RETURNVERBOSE)

[Out]

x^5+8*x^3+16*x+8*(2850+4920*x+1980*x^3*ln(5)^2+63*x^4*ln(5)^4+x^4*ln(5)^6+12*x^4*ln(5)^5-4*x^2*exp(3*exp(x))+4
496*x^2*ln(5)+48*x^2*ln(5)^5+800*ln(5)^3+100*ln(5)^4+184*x^4*ln(5)^3+3200*ln(5)+2400*ln(5)^2-800*exp(exp(x))+1
30*x^4+1080*x^3+3020*x^2+20*x*ln(5)^6-20*x*exp(3*exp(x))+1040*x^3*ln(5)^3-exp(3*exp(x))*x^4-1124*exp(exp(x))*x
^2+1240*x*ln(5)^4+7120*x*ln(5)+3156*x^2*ln(5)^2-1780*x*exp(exp(x))-540*x^3*exp(exp(x))+2160*x^3*ln(5)-76*x^4*e
xp(exp(x))+330*x^3*ln(5)^4+100*exp(2*exp(x))+5*x^3*ln(5)^6+3520*ln(5)^3*x+319*ln(5)^4*x^2+316*x^4*ln(5)^2+6260
*x*ln(5)^2+304*x^4*ln(5)+1272*x^2*ln(5)^3+60*ln(5)*exp(2*exp(x))*x^3+60*ln(5)^2*exp(2*exp(x))*x+48*ln(5)*exp(2
*exp(x))*x^2+15*ln(5)^2*exp(2*exp(x))*x^3+12*ln(5)^2*exp(2*exp(x))*x^2+4*ln(5)^6*x^2+60*ln(5)^5*x^3+240*ln(5)^
5*x-200*ln(5)^2*exp(exp(x))-800*ln(5)*exp(exp(x))-15*ln(5)^4*exp(exp(x))*x^3-12*ln(5)^4*exp(exp(x))*x^2-120*ln
(5)^3*exp(exp(x))*x^3-60*ln(5)^4*exp(exp(x))*x-96*ln(5)^3*exp(exp(x))*x^2-420*ln(5)^2*exp(exp(x))*x^3-480*ln(5
)^3*exp(exp(x))*x-446*ln(5)^2*exp(exp(x))*x^2-720*ln(5)*exp(exp(x))*x^3-1520*ln(5)^2*exp(exp(x))*x-1016*ln(5)*
exp(exp(x))*x^2-2240*ln(5)*exp(exp(x))*x-3*ln(5)^4*exp(exp(x))*x^4-24*ln(5)^3*exp(exp(x))*x^4-78*ln(5)^2*exp(e
xp(x))*x^4-120*ln(5)*exp(exp(x))*x^4+127*x^2*exp(2*exp(x))+280*x*exp(2*exp(x))+90*x^3*exp(2*exp(x))+15*x^4*exp
(2*exp(x))-5*exp(3*exp(x))*x^3+240*ln(5)*exp(2*exp(x))*x+3*ln(5)^2*exp(2*exp(x))*x^4+12*ln(5)*exp(2*exp(x))*x^
4)*x/(ln(5)^2+4*ln(5)-exp(exp(x))+4)^4

________________________________________________________________________________________

maxima [B]  time = 1.35, size = 747, normalized size = 22.64 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*x^4+24*x^2+16)*exp(exp(x))^5+((8*x^5+40*x^4+32*x^3+160*x^2)*exp(x)+(-25*x^4-120*x^2-80)*log(5)^2
+(-100*x^4-480*x^2-320)*log(5)-140*x^4-160*x^3-576*x^2-320*x-320)*exp(exp(x))^4+(((-24*x^5-120*x^4-96*x^3-480*
x^2)*log(5)^2+(-96*x^5-480*x^4-384*x^3-1920*x^2)*log(5)-144*x^5-960*x^4-1648*x^3-2560*x^2-1600*x)*exp(x)+(50*x
^4+240*x^2+160)*log(5)^4+(400*x^4+1920*x^2+1280)*log(5)^3+(1360*x^4+640*x^3+6144*x^2+1280*x+3840)*log(5)^2+(22
40*x^4+2560*x^3+9216*x^2+5120*x+5120)*log(5)+1560*x^4+3520*x^3+7272*x^2+5760*x+3360)*exp(exp(x))^3+(((24*x^5+1
20*x^4+96*x^3+480*x^2)*log(5)^4+(192*x^5+960*x^4+768*x^3+3840*x^2)*log(5)^3+(672*x^5+3840*x^4+4832*x^3+12800*x
^2+3200*x)*log(5)^2+(1152*x^5+7680*x^4+13184*x^3+20480*x^2+12800*x)*log(5)+864*x^5+7200*x^4+18848*x^3+24800*x^
2+12800*x)*exp(x)+(-50*x^4-240*x^2-160)*log(5)^6+(-600*x^4-2880*x^2-1920)*log(5)^5+(-3240*x^4-960*x^3-14976*x^
2-1920*x-9600)*log(5)^4+(-9920*x^4-7680*x^3-43008*x^2-15360*x-25600)*log(5)^3+(-18120*x^4-25920*x^3-77112*x^2-
48000*x-40800)*log(5)^2+(-18720*x^4-42240*x^3-87264*x^2-69120*x-40320)*log(5)-8640*x^4-28800*x^3-54528*x^2-464
00*x-19840)*exp(exp(x))^2+(((-8*x^5-40*x^4-32*x^3-160*x^2)*log(5)^6+(-96*x^5-480*x^4-384*x^3-1920*x^2)*log(5)^
5+(-528*x^5-2880*x^4-3184*x^3-10240*x^2-1600*x)*log(5)^4+(-1664*x^5-10240*x^4-15232*x^3-30720*x^2-12800*x)*log
(5)^3+(-3168*x^5-22560*x^4-45216*x^3-65760*x^2-38400*x)*log(5)^2+(-3456*x^5-28800*x^4-75392*x^3-99200*x^2-5120
0*x)*log(5)-1728*x^5-17280*x^4-60672*x^3-100480*x^2-65600*x)*exp(x)+(25*x^4+120*x^2+80)*log(5)^8+(400*x^4+1920
*x^2+1280)*log(5)^7+(2960*x^4+640*x^3+13824*x^2+1280*x+8960)*log(5)^6+(13120*x^4+7680*x^3+58368*x^2+15360*x+35
840)*log(5)^5+(37960*x^4+41280*x^3+163128*x^2+78720*x+92000)*log(5)^4+(73280*x^4+125440*x^3+321984*x^2+220160*
x+162560)*log(5)^3+(92160*x^4+226560*x^3+458112*x^2+369280*x+200960)*log(5)^2+(69120*x^4+230400*x^3+436224*x^2
+371200*x+158720)*log(5)+23760*x^4+103680*x^3+211104*x^2+192640*x+68880)*exp(exp(x))+(-5*x^4-24*x^2-16)*log(5)
^10+(-100*x^4-480*x^2-320)*log(5)^9+(-940*x^4-160*x^3-4416*x^2-320*x-2880)*log(5)^8+(-5440*x^4-2560*x^3-24576*
x^2-5120*x-15360)*log(5)^7+(-21400*x^4-18880*x^3-93288*x^2-36480*x-54560)*log(5)^6+(-59680*x^4-83200*x^3-25929
6*x^2-151040*x-138624)*log(5)^5+(-119360*x^4-238720*x^3-551040*x^2-404800*x-263040)*log(5)^4+(-168960*x^4-4556
80*x^3-901632*x^2-739840*x-373760)*log(5)^3+(-162000*x^4-564480*x^3-1083552*x^2-935040*x-386320)*log(5)^2+(-95
040*x^4-414720*x^3-844416*x^2-770560*x-275520)*log(5)-25920*x^4-138240*x^3-314496*x^2-314880*x-107584)/(exp(ex
p(x))^5+(-5*log(5)^2-20*log(5)-20)*exp(exp(x))^4+(10*log(5)^4+80*log(5)^3+240*log(5)^2+320*log(5)+160)*exp(exp
(x))^3+(-10*log(5)^6-120*log(5)^5-600*log(5)^4-1600*log(5)^3-2400*log(5)^2-1920*log(5)-640)*exp(exp(x))^2+(5*l
og(5)^8+80*log(5)^7+560*log(5)^6+2240*log(5)^5+5600*log(5)^4+8960*log(5)^3+8960*log(5)^2+5120*log(5)+1280)*exp
(exp(x))-log(5)^10-20*log(5)^9-180*log(5)^8-960*log(5)^7-3360*log(5)^6-8064*log(5)^5-13440*log(5)^4-15360*log(
5)^3-11520*log(5)^2-5120*log(5)-1024),x, algorithm="maxima")

[Out]

((log(5)^8 + 16*log(5)^7 + 120*log(5)^6 + 544*log(5)^5 + 1624*log(5)^4 + 3264*log(5)^3 + 4320*log(5)^2 + 3456*
log(5) + 1296)*x^5 + 40*(log(5)^6 + 12*log(5)^5 + 66*log(5)^4 + 208*log(5)^3 + 396*log(5)^2 + 432*log(5) + 216
)*x^4 + 8*(log(5)^8 + 16*log(5)^7 + 116*log(5)^6 + 496*log(5)^5 + 1439*log(5)^4 + 3064*log(5)^3 + 4948*log(5)^
2 + 5520*log(5) + 3276)*x^3 + 160*(log(5)^6 + 12*log(5)^5 + 62*log(5)^4 + 176*log(5)^3 + 313*log(5)^2 + 356*lo
g(5) + 246)*x^2 + 16*(log(5)^8 + 16*log(5)^7 + 112*log(5)^6 + 448*log(5)^5 + 1170*log(5)^4 + 2192*log(5)^3 + 2
992*log(5)^2 + 2624*log(5) + 1681)*x + (x^5 + 8*x^3 + 16*x)*e^(4*e^x) - 4*((log(5)^2 + 4*log(5) + 6)*x^5 + 8*(
log(5)^2 + 4*log(5) + 5)*x^3 + 10*x^4 + 16*(log(5)^2 + 4*log(5) + 4)*x + 40*x^2)*e^(3*e^x) + 2*(3*(log(5)^4 +
8*log(5)^3 + 28*log(5)^2 + 48*log(5) + 36)*x^5 + 60*(log(5)^2 + 4*log(5) + 6)*x^4 + 4*(6*log(5)^4 + 48*log(5)^
3 + 156*log(5)^2 + 240*log(5) + 223)*x^3 + 80*(3*log(5)^2 + 12*log(5) + 14)*x^2 + 16*(3*log(5)^4 + 24*log(5)^3
+ 72*log(5)^2 + 96*log(5) + 73)*x)*e^(2*e^x) - 4*((log(5)^6 + 12*log(5)^5 + 66*log(5)^4 + 208*log(5)^3 + 396*
log(5)^2 + 432*log(5) + 216)*x^5 + 30*(log(5)^4 + 8*log(5)^3 + 28*log(5)^2 + 48*log(5) + 36)*x^4 + 4*(2*log(5)
^6 + 24*log(5)^5 + 126*log(5)^4 + 368*log(5)^3 + 703*log(5)^2 + 892*log(5) + 690)*x^3 + 40*(3*log(5)^4 + 24*lo
g(5)^3 + 76*log(5)^2 + 112*log(5) + 89)*x^2 + 16*(log(5)^6 + 12*log(5)^5 + 60*log(5)^4 + 160*log(5)^3 + 265*lo
g(5)^2 + 292*log(5) + 164)*x)*e^(e^x))/(log(5)^8 + 16*log(5)^7 + 112*log(5)^6 + 448*log(5)^5 + 1120*log(5)^4 +
1792*log(5)^3 - 4*(log(5)^2 + 4*log(5) + 4)*e^(3*e^x) + 6*(log(5)^4 + 8*log(5)^3 + 24*log(5)^2 + 32*log(5) +
16)*e^(2*e^x) - 4*(log(5)^6 + 12*log(5)^5 + 60*log(5)^4 + 160*log(5)^3 + 240*log(5)^2 + 192*log(5) + 64)*e^(e^
x) + 1792*log(5)^2 + e^(4*e^x) + 1024*log(5) + 256)

________________________________________________________________________________________

mupad [F]  time = 0.00, size = -1, normalized size = -0.03 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((314880*x + log(5)^8*(320*x + 4416*x^2 + 160*x^3 + 940*x^4 + 2880) + log(5)^7*(5120*x + 24576*x^2 + 2560*x
^3 + 5440*x^4 + 15360) + log(5)^6*(36480*x + 93288*x^2 + 18880*x^3 + 21400*x^4 + 54560) + log(5)^5*(151040*x +
259296*x^2 + 83200*x^3 + 59680*x^4 + 138624) + log(5)^4*(404800*x + 551040*x^2 + 238720*x^3 + 119360*x^4 + 26
3040) + log(5)^3*(739840*x + 901632*x^2 + 455680*x^3 + 168960*x^4 + 373760) + log(5)^2*(935040*x + 1083552*x^2
+ 564480*x^3 + 162000*x^4 + 386320) - exp(3*exp(x))*(5760*x + log(5)^2*(1280*x + 6144*x^2 + 640*x^3 + 1360*x^
4 + 3840) + log(5)*(5120*x + 9216*x^2 + 2560*x^3 + 2240*x^4 + 5120) - exp(x)*(1600*x + log(5)*(1920*x^2 + 384*
x^3 + 480*x^4 + 96*x^5) + log(5)^2*(480*x^2 + 96*x^3 + 120*x^4 + 24*x^5) + 2560*x^2 + 1648*x^3 + 960*x^4 + 144
*x^5) + 7272*x^2 + 3520*x^3 + 1560*x^4 + log(5)^4*(240*x^2 + 50*x^4 + 160) + log(5)^3*(1920*x^2 + 400*x^4 + 12
80) + 3360) + log(5)*(770560*x + 844416*x^2 + 414720*x^3 + 95040*x^4 + 275520) + exp(2*exp(x))*(46400*x + log(
5)^4*(1920*x + 14976*x^2 + 960*x^3 + 3240*x^4 + 9600) + log(5)^3*(15360*x + 43008*x^2 + 7680*x^3 + 9920*x^4 +
25600) + log(5)^2*(48000*x + 77112*x^2 + 25920*x^3 + 18120*x^4 + 40800) - exp(x)*(12800*x + log(5)^2*(3200*x +
12800*x^2 + 4832*x^3 + 3840*x^4 + 672*x^5) + log(5)^4*(480*x^2 + 96*x^3 + 120*x^4 + 24*x^5) + log(5)^3*(3840*
x^2 + 768*x^3 + 960*x^4 + 192*x^5) + 24800*x^2 + 18848*x^3 + 7200*x^4 + 864*x^5 + log(5)*(12800*x + 20480*x^2
+ 13184*x^3 + 7680*x^4 + 1152*x^5)) + log(5)*(69120*x + 87264*x^2 + 42240*x^3 + 18720*x^4 + 40320) + 54528*x^2
+ 28800*x^3 + 8640*x^4 + log(5)^6*(240*x^2 + 50*x^4 + 160) + log(5)^5*(2880*x^2 + 600*x^4 + 1920) + 19840) -
exp(5*exp(x))*(24*x^2 + 5*x^4 + 16) + 314496*x^2 + 138240*x^3 + 25920*x^4 + exp(4*exp(x))*(320*x - exp(x)*(160
*x^2 + 32*x^3 + 40*x^4 + 8*x^5) + log(5)*(480*x^2 + 100*x^4 + 320) + 576*x^2 + 160*x^3 + 140*x^4 + log(5)^2*(1
20*x^2 + 25*x^4 + 80) + 320) - exp(exp(x))*(192640*x + log(5)^6*(1280*x + 13824*x^2 + 640*x^3 + 2960*x^4 + 896
0) + log(5)^5*(15360*x + 58368*x^2 + 7680*x^3 + 13120*x^4 + 35840) + log(5)^4*(78720*x + 163128*x^2 + 41280*x^
3 + 37960*x^4 + 92000) + log(5)^3*(220160*x + 321984*x^2 + 125440*x^3 + 73280*x^4 + 162560) + log(5)^2*(369280
*x + 458112*x^2 + 226560*x^3 + 92160*x^4 + 200960) + log(5)*(371200*x + 436224*x^2 + 230400*x^3 + 69120*x^4 +
158720) - exp(x)*(65600*x + log(5)^4*(1600*x + 10240*x^2 + 3184*x^3 + 2880*x^4 + 528*x^5) + log(5)^3*(12800*x
+ 30720*x^2 + 15232*x^3 + 10240*x^4 + 1664*x^5) + log(5)^2*(38400*x + 65760*x^2 + 45216*x^3 + 22560*x^4 + 3168
*x^5) + log(5)^6*(160*x^2 + 32*x^3 + 40*x^4 + 8*x^5) + log(5)^5*(1920*x^2 + 384*x^3 + 480*x^4 + 96*x^5) + 1004
80*x^2 + 60672*x^3 + 17280*x^4 + 1728*x^5 + log(5)*(51200*x + 99200*x^2 + 75392*x^3 + 28800*x^4 + 3456*x^5)) +
211104*x^2 + 103680*x^3 + 23760*x^4 + log(5)^8*(120*x^2 + 25*x^4 + 80) + log(5)^7*(1920*x^2 + 400*x^4 + 1280)
+ 68880) + log(5)^10*(24*x^2 + 5*x^4 + 16) + log(5)^9*(480*x^2 + 100*x^4 + 320) + 107584)/(5120*log(5) - exp(
5*exp(x)) + exp(2*exp(x))*(1920*log(5) + 2400*log(5)^2 + 1600*log(5)^3 + 600*log(5)^4 + 120*log(5)^5 + 10*log(
5)^6 + 640) + exp(4*exp(x))*(20*log(5) + 5*log(5)^2 + 20) - exp(3*exp(x))*(320*log(5) + 240*log(5)^2 + 80*log(
5)^3 + 10*log(5)^4 + 160) + 11520*log(5)^2 + 15360*log(5)^3 + 13440*log(5)^4 + 8064*log(5)^5 + 3360*log(5)^6 +
960*log(5)^7 + 180*log(5)^8 + 20*log(5)^9 + log(5)^10 - exp(exp(x))*(5120*log(5) + 8960*log(5)^2 + 8960*log(5
)^3 + 5600*log(5)^4 + 2240*log(5)^5 + 560*log(5)^6 + 80*log(5)^7 + 5*log(5)^8 + 1280) + 1024),x)

[Out]

int((314880*x + log(5)^8*(320*x + 4416*x^2 + 160*x^3 + 940*x^4 + 2880) + log(5)^7*(5120*x + 24576*x^2 + 2560*x
^3 + 5440*x^4 + 15360) + log(5)^6*(36480*x + 93288*x^2 + 18880*x^3 + 21400*x^4 + 54560) + log(5)^5*(151040*x +
259296*x^2 + 83200*x^3 + 59680*x^4 + 138624) + log(5)^4*(404800*x + 551040*x^2 + 238720*x^3 + 119360*x^4 + 26
3040) + log(5)^3*(739840*x + 901632*x^2 + 455680*x^3 + 168960*x^4 + 373760) + log(5)^2*(935040*x + 1083552*x^2
+ 564480*x^3 + 162000*x^4 + 386320) - exp(3*exp(x))*(5760*x + log(5)^2*(1280*x + 6144*x^2 + 640*x^3 + 1360*x^
4 + 3840) + log(5)*(5120*x + 9216*x^2 + 2560*x^3 + 2240*x^4 + 5120) - exp(x)*(1600*x + log(5)*(1920*x^2 + 384*
x^3 + 480*x^4 + 96*x^5) + log(5)^2*(480*x^2 + 96*x^3 + 120*x^4 + 24*x^5) + 2560*x^2 + 1648*x^3 + 960*x^4 + 144
*x^5) + 7272*x^2 + 3520*x^3 + 1560*x^4 + log(5)^4*(240*x^2 + 50*x^4 + 160) + log(5)^3*(1920*x^2 + 400*x^4 + 12
80) + 3360) + log(5)*(770560*x + 844416*x^2 + 414720*x^3 + 95040*x^4 + 275520) + exp(2*exp(x))*(46400*x + log(
5)^4*(1920*x + 14976*x^2 + 960*x^3 + 3240*x^4 + 9600) + log(5)^3*(15360*x + 43008*x^2 + 7680*x^3 + 9920*x^4 +
25600) + log(5)^2*(48000*x + 77112*x^2 + 25920*x^3 + 18120*x^4 + 40800) - exp(x)*(12800*x + log(5)^2*(3200*x +
12800*x^2 + 4832*x^3 + 3840*x^4 + 672*x^5) + log(5)^4*(480*x^2 + 96*x^3 + 120*x^4 + 24*x^5) + log(5)^3*(3840*
x^2 + 768*x^3 + 960*x^4 + 192*x^5) + 24800*x^2 + 18848*x^3 + 7200*x^4 + 864*x^5 + log(5)*(12800*x + 20480*x^2
+ 13184*x^3 + 7680*x^4 + 1152*x^5)) + log(5)*(69120*x + 87264*x^2 + 42240*x^3 + 18720*x^4 + 40320) + 54528*x^2
+ 28800*x^3 + 8640*x^4 + log(5)^6*(240*x^2 + 50*x^4 + 160) + log(5)^5*(2880*x^2 + 600*x^4 + 1920) + 19840) -
exp(5*exp(x))*(24*x^2 + 5*x^4 + 16) + 314496*x^2 + 138240*x^3 + 25920*x^4 + exp(4*exp(x))*(320*x - exp(x)*(160
*x^2 + 32*x^3 + 40*x^4 + 8*x^5) + log(5)*(480*x^2 + 100*x^4 + 320) + 576*x^2 + 160*x^3 + 140*x^4 + log(5)^2*(1
20*x^2 + 25*x^4 + 80) + 320) - exp(exp(x))*(192640*x + log(5)^6*(1280*x + 13824*x^2 + 640*x^3 + 2960*x^4 + 896
0) + log(5)^5*(15360*x + 58368*x^2 + 7680*x^3 + 13120*x^4 + 35840) + log(5)^4*(78720*x + 163128*x^2 + 41280*x^
3 + 37960*x^4 + 92000) + log(5)^3*(220160*x + 321984*x^2 + 125440*x^3 + 73280*x^4 + 162560) + log(5)^2*(369280
*x + 458112*x^2 + 226560*x^3 + 92160*x^4 + 200960) + log(5)*(371200*x + 436224*x^2 + 230400*x^3 + 69120*x^4 +
158720) - exp(x)*(65600*x + log(5)^4*(1600*x + 10240*x^2 + 3184*x^3 + 2880*x^4 + 528*x^5) + log(5)^3*(12800*x
+ 30720*x^2 + 15232*x^3 + 10240*x^4 + 1664*x^5) + log(5)^2*(38400*x + 65760*x^2 + 45216*x^3 + 22560*x^4 + 3168
*x^5) + log(5)^6*(160*x^2 + 32*x^3 + 40*x^4 + 8*x^5) + log(5)^5*(1920*x^2 + 384*x^3 + 480*x^4 + 96*x^5) + 1004
80*x^2 + 60672*x^3 + 17280*x^4 + 1728*x^5 + log(5)*(51200*x + 99200*x^2 + 75392*x^3 + 28800*x^4 + 3456*x^5)) +
211104*x^2 + 103680*x^3 + 23760*x^4 + log(5)^8*(120*x^2 + 25*x^4 + 80) + log(5)^7*(1920*x^2 + 400*x^4 + 1280)
+ 68880) + log(5)^10*(24*x^2 + 5*x^4 + 16) + log(5)^9*(480*x^2 + 100*x^4 + 320) + 107584)/(5120*log(5) - exp(
5*exp(x)) + exp(2*exp(x))*(1920*log(5) + 2400*log(5)^2 + 1600*log(5)^3 + 600*log(5)^4 + 120*log(5)^5 + 10*log(
5)^6 + 640) + exp(4*exp(x))*(20*log(5) + 5*log(5)^2 + 20) - exp(3*exp(x))*(320*log(5) + 240*log(5)^2 + 80*log(
5)^3 + 10*log(5)^4 + 160) + 11520*log(5)^2 + 15360*log(5)^3 + 13440*log(5)^4 + 8064*log(5)^5 + 3360*log(5)^6 +
960*log(5)^7 + 180*log(5)^8 + 20*log(5)^9 + log(5)^10 - exp(exp(x))*(5120*log(5) + 8960*log(5)^2 + 8960*log(5
)^3 + 5600*log(5)^4 + 2240*log(5)^5 + 560*log(5)^6 + 80*log(5)^7 + 5*log(5)^8 + 1280) + 1024), x)

________________________________________________________________________________________

sympy [B]  time = 5.81, size = 804, normalized size = 24.36 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*x**4+24*x**2+16)*exp(exp(x))**5+((8*x**5+40*x**4+32*x**3+160*x**2)*exp(x)+(-25*x**4-120*x**2-80)
*ln(5)**2+(-100*x**4-480*x**2-320)*ln(5)-140*x**4-160*x**3-576*x**2-320*x-320)*exp(exp(x))**4+(((-24*x**5-120*
x**4-96*x**3-480*x**2)*ln(5)**2+(-96*x**5-480*x**4-384*x**3-1920*x**2)*ln(5)-144*x**5-960*x**4-1648*x**3-2560*
x**2-1600*x)*exp(x)+(50*x**4+240*x**2+160)*ln(5)**4+(400*x**4+1920*x**2+1280)*ln(5)**3+(1360*x**4+640*x**3+614
4*x**2+1280*x+3840)*ln(5)**2+(2240*x**4+2560*x**3+9216*x**2+5120*x+5120)*ln(5)+1560*x**4+3520*x**3+7272*x**2+5
760*x+3360)*exp(exp(x))**3+(((24*x**5+120*x**4+96*x**3+480*x**2)*ln(5)**4+(192*x**5+960*x**4+768*x**3+3840*x**
2)*ln(5)**3+(672*x**5+3840*x**4+4832*x**3+12800*x**2+3200*x)*ln(5)**2+(1152*x**5+7680*x**4+13184*x**3+20480*x*
*2+12800*x)*ln(5)+864*x**5+7200*x**4+18848*x**3+24800*x**2+12800*x)*exp(x)+(-50*x**4-240*x**2-160)*ln(5)**6+(-
600*x**4-2880*x**2-1920)*ln(5)**5+(-3240*x**4-960*x**3-14976*x**2-1920*x-9600)*ln(5)**4+(-9920*x**4-7680*x**3-
43008*x**2-15360*x-25600)*ln(5)**3+(-18120*x**4-25920*x**3-77112*x**2-48000*x-40800)*ln(5)**2+(-18720*x**4-422
40*x**3-87264*x**2-69120*x-40320)*ln(5)-8640*x**4-28800*x**3-54528*x**2-46400*x-19840)*exp(exp(x))**2+(((-8*x*
*5-40*x**4-32*x**3-160*x**2)*ln(5)**6+(-96*x**5-480*x**4-384*x**3-1920*x**2)*ln(5)**5+(-528*x**5-2880*x**4-318
4*x**3-10240*x**2-1600*x)*ln(5)**4+(-1664*x**5-10240*x**4-15232*x**3-30720*x**2-12800*x)*ln(5)**3+(-3168*x**5-
22560*x**4-45216*x**3-65760*x**2-38400*x)*ln(5)**2+(-3456*x**5-28800*x**4-75392*x**3-99200*x**2-51200*x)*ln(5)
-1728*x**5-17280*x**4-60672*x**3-100480*x**2-65600*x)*exp(x)+(25*x**4+120*x**2+80)*ln(5)**8+(400*x**4+1920*x**
2+1280)*ln(5)**7+(2960*x**4+640*x**3+13824*x**2+1280*x+8960)*ln(5)**6+(13120*x**4+7680*x**3+58368*x**2+15360*x
+35840)*ln(5)**5+(37960*x**4+41280*x**3+163128*x**2+78720*x+92000)*ln(5)**4+(73280*x**4+125440*x**3+321984*x**
2+220160*x+162560)*ln(5)**3+(92160*x**4+226560*x**3+458112*x**2+369280*x+200960)*ln(5)**2+(69120*x**4+230400*x
**3+436224*x**2+371200*x+158720)*ln(5)+23760*x**4+103680*x**3+211104*x**2+192640*x+68880)*exp(exp(x))+(-5*x**4
-24*x**2-16)*ln(5)**10+(-100*x**4-480*x**2-320)*ln(5)**9+(-940*x**4-160*x**3-4416*x**2-320*x-2880)*ln(5)**8+(-
5440*x**4-2560*x**3-24576*x**2-5120*x-15360)*ln(5)**7+(-21400*x**4-18880*x**3-93288*x**2-36480*x-54560)*ln(5)*
*6+(-59680*x**4-83200*x**3-259296*x**2-151040*x-138624)*ln(5)**5+(-119360*x**4-238720*x**3-551040*x**2-404800*
x-263040)*ln(5)**4+(-168960*x**4-455680*x**3-901632*x**2-739840*x-373760)*ln(5)**3+(-162000*x**4-564480*x**3-1
083552*x**2-935040*x-386320)*ln(5)**2+(-95040*x**4-414720*x**3-844416*x**2-770560*x-275520)*ln(5)-25920*x**4-1
38240*x**3-314496*x**2-314880*x-107584)/(exp(exp(x))**5+(-5*ln(5)**2-20*ln(5)-20)*exp(exp(x))**4+(10*ln(5)**4+
80*ln(5)**3+240*ln(5)**2+320*ln(5)+160)*exp(exp(x))**3+(-10*ln(5)**6-120*ln(5)**5-600*ln(5)**4-1600*ln(5)**3-2
400*ln(5)**2-1920*ln(5)-640)*exp(exp(x))**2+(5*ln(5)**8+80*ln(5)**7+560*ln(5)**6+2240*ln(5)**5+5600*ln(5)**4+8
960*ln(5)**3+8960*ln(5)**2+5120*ln(5)+1280)*exp(exp(x))-ln(5)**10-20*ln(5)**9-180*ln(5)**8-960*ln(5)**7-3360*l
n(5)**6-8064*ln(5)**5-13440*ln(5)**4-15360*ln(5)**3-11520*ln(5)**2-5120*ln(5)-1024),x)

[Out]

x**5 + 8*x**3 + 16*x + (8*x**5*log(5)**6 + 96*x**5*log(5)**5 + 1040*x**5 + 504*x**5*log(5)**4 + 2432*x**5*log(
5) + 1472*x**5*log(5)**3 + 2528*x**5*log(5)**2 + 40*x**4*log(5)**6 + 480*x**4*log(5)**5 + 8640*x**4 + 2640*x**
4*log(5)**4 + 17280*x**4*log(5) + 8320*x**4*log(5)**3 + 15840*x**4*log(5)**2 + 32*x**3*log(5)**6 + 384*x**3*lo
g(5)**5 + 2552*x**3*log(5)**4 + 24160*x**3 + 10176*x**3*log(5)**3 + 35968*x**3*log(5) + 25248*x**3*log(5)**2 +
160*x**2*log(5)**6 + 1920*x**2*log(5)**5 + 39360*x**2 + 9920*x**2*log(5)**4 + 56960*x**2*log(5) + 28160*x**2*
log(5)**3 + 50080*x**2*log(5)**2 + 800*x*log(5)**4 + 22800*x + 6400*x*log(5)**3 + 25600*x*log(5) + 19200*x*log
(5)**2 + (-8*x**5 - 40*x**4 - 32*x**3 - 160*x**2)*exp(3*exp(x)) + (24*x**5*log(5)**2 + 120*x**5 + 96*x**5*log(
5) + 120*x**4*log(5)**2 + 720*x**4 + 480*x**4*log(5) + 96*x**3*log(5)**2 + 384*x**3*log(5) + 1016*x**3 + 480*x
**2*log(5)**2 + 2240*x**2 + 1920*x**2*log(5) + 800*x)*exp(2*exp(x)) + (-624*x**5*log(5)**2 - 960*x**5*log(5) -
192*x**5*log(5)**3 - 608*x**5 - 24*x**5*log(5)**4 - 5760*x**4*log(5) - 3360*x**4*log(5)**2 - 4320*x**4 - 960*
x**4*log(5)**3 - 120*x**4*log(5)**4 - 8128*x**3*log(5) - 3568*x**3*log(5)**2 - 8992*x**3 - 768*x**3*log(5)**3
- 96*x**3*log(5)**4 - 12160*x**2*log(5)**2 - 17920*x**2*log(5) - 3840*x**2*log(5)**3 - 14240*x**2 - 480*x**2*l
og(5)**4 - 6400*x*log(5) - 6400*x - 1600*x*log(5)**2)*exp(exp(x)))/(exp(4*exp(x)) + (-16*log(5) - 16 - 4*log(5
)**2)*exp(3*exp(x)) + (6*log(5)**4 + 96 + 48*log(5)**3 + 192*log(5) + 144*log(5)**2)*exp(2*exp(x)) + (-640*log
(5)**3 - 960*log(5)**2 - 240*log(5)**4 - 768*log(5) - 48*log(5)**5 - 256 - 4*log(5)**6)*exp(exp(x)) + log(5)**
8 + 256 + 16*log(5)**7 + 1024*log(5) + 112*log(5)**6 + 1792*log(5)**2 + 448*log(5)**5 + 1792*log(5)**3 + 1120*
log(5)**4)

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