3.85.9 \(\int \frac {-36 x^2-12 x^3-18 x^2 \log (5)+e^{80} x^{40} (492+240 x+246 \log (5))}{4+4 x+x^2+(4+2 x) \log (5)+\log ^2(5)} \, dx\)
Optimal. Leaf size=24 \[ \frac {6 x \left (e^{40 (2+\log (x))}-x^2\right )}{2+x+\log (5)} \]
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Rubi [B] time = 33.91, antiderivative size = 1080, normalized size of antiderivative = 45.00,
number of steps used = 5, number of rules used = 4, integrand size = 57, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.070, Rules used =
{6, 1986, 27, 1850}
result too large to display
Antiderivative was successfully verified.
[In]
Int[(-36*x^2 - 12*x^3 - 18*x^2*Log[5] + E^80*x^40*(492 + 240*x + 246*Log[5]))/(4 + 4*x + x^2 + (4 + 2*x)*Log[5
] + Log[5]^2),x]
[Out]
-607620*E^80*(2 + Log[5])^37*(2 + x + Log[5])^3 + 4496388*E^80*(2 + Log[5])^36*(2 + x + Log[5])^4 - 26978328*E
^80*(2 + Log[5])^35*(2 + x + Log[5])^5 + 134891640*E^80*(2 + Log[5])^34*(2 + x + Log[5])^6 - 573289470*E^80*(2
+ Log[5])^33*(2 + x + Log[5])^7 + 2102061390*E^80*(2 + Log[5])^32*(2 + x + Log[5])^8 - 6726596448*E^80*(2 + L
og[5])^31*(2 + x + Log[5])^9 + 18956771808*E^80*(2 + Log[5])^30*(2 + x + Log[5])^10 - 47391929520*E^80*(2 + Lo
g[5])^29*(2 + x + Log[5])^11 + 105720458160*E^80*(2 + Log[5])^28*(2 + x + Log[5])^12 - 211440916320*E^80*(2 +
Log[5])^27*(2 + x + Log[5])^13 + 380593649376*E^80*(2 + Log[5])^26*(2 + x + Log[5])^14 - 618464680236*E^80*(2
+ Log[5])^25*(2 + x + Log[5])^15 + 909506882700*E^80*(2 + Log[5])^24*(2 + x + Log[5])^16 - 1212675843600*E^80*
(2 + Log[5])^23*(2 + x + Log[5])^17 + 1467976021200*E^80*(2 + Log[5])^22*(2 + x + Log[5])^18 - 1614773623320*E
^80*(2 + Log[5])^21*(2 + x + Log[5])^19 + 1614773623320*E^80*(2 + Log[5])^20*(2 + x + Log[5])^20 - 14679760212
00*E^80*(2 + Log[5])^19*(2 + x + Log[5])^21 + 1212675843600*E^80*(2 + Log[5])^18*(2 + x + Log[5])^22 - 9095068
82700*E^80*(2 + Log[5])^17*(2 + x + Log[5])^23 + 618464680236*E^80*(2 + Log[5])^16*(2 + x + Log[5])^24 - 38059
3649376*E^80*(2 + Log[5])^15*(2 + x + Log[5])^25 + 211440916320*E^80*(2 + Log[5])^14*(2 + x + Log[5])^26 - 105
720458160*E^80*(2 + Log[5])^13*(2 + x + Log[5])^27 + 47391929520*E^80*(2 + Log[5])^12*(2 + x + Log[5])^28 - 18
956771808*E^80*(2 + Log[5])^11*(2 + x + Log[5])^29 + 6726596448*E^80*(2 + Log[5])^10*(2 + x + Log[5])^30 - 210
2061390*E^80*(2 + Log[5])^9*(2 + x + Log[5])^31 + 573289470*E^80*(2 + Log[5])^8*(2 + x + Log[5])^32 - 13489164
0*E^80*(2 + Log[5])^7*(2 + x + Log[5])^33 + 26978328*E^80*(2 + Log[5])^6*(2 + x + Log[5])^34 - 4496388*E^80*(2
+ Log[5])^5*(2 + x + Log[5])^35 + 607620*E^80*(2 + Log[5])^4*(2 + x + Log[5])^36 - 63960*E^80*(2 + Log[5])^3*
(2 + x + Log[5])^37 + 4920*E^80*(2 + Log[5])^2*(2 + x + Log[5])^38 - 246*E^80*(2 + Log[5])*(2 + x + Log[5])^39
+ 6*E^80*(2 + x + Log[5])^40 - (6*(2 + Log[5])^3*(-1 + 274877906944*E^80 + 5222680231936*E^80*Log[5] + 483097
92145408*E^80*Log[5]^2 + 289858752872448*E^80*Log[5]^3 + 1268132043816960*E^80*Log[5]^4 + 4311648948977664*E^8
0*Log[5]^5 + 11857034609688576*E^80*Log[5]^6 + 27101793393573888*E^80*Log[5]^7 + 52509724700049408*E^80*Log[5]
^8 + 87516207833415680*E^80*Log[5]^9 + 126898501358452736*E^80*Log[5]^10 + 161507183547121664*E^80*Log[5]^11 +
181695581490511872*E^80*Log[5]^12 + 181695581490511872*E^80*Log[5]^13 + 162228197759385600*E^80*Log[5]^14 + 1
29782558207508480*E^80*Log[5]^15 + 93281213711646720*E^80*Log[5]^16 + 60358432401653760*E^80*Log[5]^17 + 35209
085567631360*E^80*Log[5]^18 + 18531097667174400*E^80*Log[5]^19 + 8802271391907840*E^80*Log[5]^20 + 37724020251
03360*E^80*Log[5]^21 + 1457518964244480*E^80*Log[5]^22 + 506963117998080*E^80*Log[5]^23 + 158425974374400*E^80
*Log[5]^24 + 44359272824832*E^80*Log[5]^25 + 11089818206208*E^80*Log[5]^26 + 2464404045824*E^80*Log[5]^27 + 48
4079366144*E^80*Log[5]^28 + 83461959680*E^80*Log[5]^29 + 12519293952*E^80*Log[5]^30 + 1615392768*E^80*Log[5]^3
1 + 176683584*E^80*Log[5]^32 + 16062144*E^80*Log[5]^33 + 1181040*E^80*Log[5]^34 + 67488*E^80*Log[5]^35 + 2812*
E^80*Log[5]^36 + 76*E^80*Log[5]^37 + E^80*Log[5]^38))/(2 + x + Log[5]) - 6*(2 + x + Log[5])^2*(1 - 10660*E^80*
(2 + Log[5])^38) + 6*x*(2 + Log[5])*(3 - 820*E^80*(2 + Log[5])^38)
Rule 6
Int[(u_.)*((w_.) + (a_.)*(v_) + (b_.)*(v_))^(p_.), x_Symbol] :> Int[u*((a + b)*v + w)^p, x] /; FreeQ[{a, b}, x
] && !FreeQ[v, x]
Rule 27
Int[(u_.)*((a_) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> Int[u*Cancel[(b/2 + c*x)^(2*p)/c^p], x] /; Fr
eeQ[{a, b, c}, x] && EqQ[b^2 - 4*a*c, 0] && IntegerQ[p]
Rule 1850
Int[(Pq_)*((a_) + (b_.)*(x_)^(n_.))^(p_.), x_Symbol] :> Int[ExpandIntegrand[Pq*(a + b*x^n)^p, x], x] /; FreeQ[
{a, b, n}, x] && PolyQ[Pq, x] && (IGtQ[p, 0] || EqQ[n, 1])
Rule 1986
Int[(Pq_)*(u_)^(p_.), x_Symbol] :> Int[Pq*ExpandToSum[u, x]^p, x] /; FreeQ[p, x] && PolyQ[Pq, x] && QuadraticQ
[u, x] && !QuadraticMatchQ[u, x]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-12 x^3+x^2 (-36-18 \log (5))+e^{80} x^{40} (492+240 x+246 \log (5))}{4+4 x+x^2+(4+2 x) \log (5)+\log ^2(5)} \, dx\\ &=\int \frac {-12 x^3+x^2 (-36-18 \log (5))+e^{80} x^{40} (492+240 x+246 \log (5))}{x^2+2 x (2+\log (5))+(2+\log (5))^2} \, dx\\ &=\int \frac {-12 x^3+x^2 (-36-18 \log (5))+e^{80} x^{40} (492+240 x+246 \log (5))}{(2+x+\log (5))^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [B] time = 0.50, size = 54, normalized size = 2.25 \begin {gather*} \frac {6 \left (-x^3+x (2+\log (5))^2+(2+\log (5))^3+e^{80} \left (x^{41}-x (2+\log (5))^{40}-(2+\log (5))^{41}\right )\right )}{2+x+\log (5)} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(-36*x^2 - 12*x^3 - 18*x^2*Log[5] + E^80*x^40*(492 + 240*x + 246*Log[5]))/(4 + 4*x + x^2 + (4 + 2*x)
*Log[5] + Log[5]^2),x]
[Out]
(6*(-x^3 + x*(2 + Log[5])^2 + (2 + Log[5])^3 + E^80*(x^41 - x*(2 + Log[5])^40 - (2 + Log[5])^41)))/(2 + x + Lo
g[5])
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fricas [B] time = 0.94, size = 565, normalized size = 23.54 result too large to
display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((246*log(5)+240*x+492)*exp(40*log(x)+80)-18*x^2*log(5)-12*x^3-36*x^2)/(log(5)^2+(2*x+4)*log(5)+x^2+
4*x+4),x, algorithm="fricas")
[Out]
-6*((x + 82)*e^80*log(5)^40 + e^80*log(5)^41 + 80*(x + 41)*e^80*log(5)^39 + 1040*(3*x + 82)*e^80*log(5)^38 + 3
9520*(2*x + 41)*e^80*log(5)^37 + 292448*(5*x + 82)*e^80*log(5)^36 + 7018752*(3*x + 41)*e^80*log(5)^35 + 350937
60*(7*x + 82)*e^80*log(5)^34 + 596593920*(4*x + 41)*e^80*log(5)^33 + 2187511040*(9*x + 82)*e^80*log(5)^32 + 28
000141312*(5*x + 41)*e^80*log(5)^31 + 78909489152*(11*x + 82)*e^80*log(5)^30 + 789094891520*(6*x + 41)*e^80*lo
g(5)^29 + 1760288604160*(13*x + 82)*e^80*log(5)^28 + 14082308833280*(7*x + 41)*e^80*log(5)^27 + 25348155899904
*(15*x + 82)*e^80*log(5)^26 + 164763013349376*(8*x + 41)*e^80*log(5)^25 + 242298549043200*(17*x + 82)*e^80*log
(5)^24 + 1292258928230400*(9*x + 41)*e^80*log(5)^23 + 1564313439436800*(19*x + 82)*e^80*log(5)^22 + 6882979133
521920*(10*x + 41)*e^80*log(5)^21 + 6882979133521920*(21*x + 82)*e^80*log(5)^20 + 25029015030988800*(11*x + 41
)*e^80*log(5)^19 + 20676142851686400*(23*x + 82)*e^80*log(5)^18 + 62028428555059200*(12*x + 41)*e^80*log(5)^17
+ 42179331417440256*(25*x + 82)*e^80*log(5)^16 + 103826046566006784*(13*x + 41)*e^80*log(5)^15 + 576811369811
14880*(27*x + 82)*e^80*log(5)^14 + 115362273962229760*(14*x + 41)*e^80*log(5)^13 + 51714122810654720*(29*x + 8
2)*e^80*log(5)^12 + 82742596497047552*(15*x + 41)*e^80*log(5)^11 + 29360276176371712*(31*x + 82)*e^80*log(5)^1
0 + 36700345220464640*(16*x + 41)*e^80*log(5)^9 + 10009185060126720*(33*x + 82)*e^80*log(5)^8 + 94204094683545
60*(17*x + 41)*e^80*log(5)^7 + 1884081893670912*(35*x + 82)*e^80*log(5)^6 + 1256054595780608*(18*x + 41)*e^80*
log(5)^5 + 169737107537920*(37*x + 82)*e^80*log(5)^4 + (71468255805440*(19*x + 41)*e^80 - 1)*log(5)^3 + x^3 +
(5497558138880*(39*x + 82)*e^80 - x - 6)*log(5)^2 - (x^41 - 1099511627776*x - 2199023255552)*e^80 + 4*(2748779
06944*(20*x + 41)*e^80 - x - 3)*log(5) - 4*x - 8)/(x + log(5) + 2)
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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((246*log(5)+240*x+492)*exp(40*log(x)+80)-18*x^2*log(5)-12*x^3-36*x^2)/(log(5)^2+(2*x+4)*log(5)+x^2+
4*x+4),x, algorithm="giac")
[Out]
Timed out
________________________________________________________________________________________
maple [B] time = 0.68, size = 9387, normalized size = 391.12
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result |
size |
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| default |
\(\text {Expression too large to display}\) |
\(9387\) |
| risch |
\(\text {Expression too large to display}\) |
\(9387\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((246*ln(5)+240*x+492)*exp(40*ln(x)+80)-18*x^2*ln(5)-12*x^3-36*x^2)/(ln(5)^2+(2*x+4)*ln(5)+x^2+4*x+4),x,me
thod=_RETURNVERBOSE)
[Out]
result too large to display
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maxima [B] time = 0.48, size = 6875, normalized size = 286.46 result too large to
display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((246*log(5)+240*x+492)*exp(40*log(x)+80)-18*x^2*log(5)-12*x^3-36*x^2)/(log(5)^2+(2*x+4)*log(5)+x^2+
4*x+4),x, algorithm="maxima")
[Out]
6*x^40*e^80 - 6*(e^80*log(5) + 2*e^80)*x^39 + 6*(e^80*log(5)^2 + 4*e^80*log(5) + 4*e^80)*x^38 - 6*(e^80*log(5)
^3 + 6*e^80*log(5)^2 + 12*e^80*log(5) + 8*e^80)*x^37 + 6*(e^80*log(5)^4 + 8*e^80*log(5)^3 + 24*e^80*log(5)^2 +
32*e^80*log(5) + 16*e^80)*x^36 - 6*(e^80*log(5)^5 + 10*e^80*log(5)^4 + 40*e^80*log(5)^3 + 80*e^80*log(5)^2 +
80*e^80*log(5) + 32*e^80)*x^35 + 6*(e^80*log(5)^6 + 12*e^80*log(5)^5 + 60*e^80*log(5)^4 + 160*e^80*log(5)^3 +
240*e^80*log(5)^2 + 192*e^80*log(5) + 64*e^80)*x^34 - 6*(e^80*log(5)^7 + 14*e^80*log(5)^6 + 84*e^80*log(5)^5 +
280*e^80*log(5)^4 + 560*e^80*log(5)^3 + 672*e^80*log(5)^2 + 448*e^80*log(5) + 128*e^80)*x^33 + 6*(e^80*log(5)
^8 + 16*e^80*log(5)^7 + 112*e^80*log(5)^6 + 448*e^80*log(5)^5 + 1120*e^80*log(5)^4 + 1792*e^80*log(5)^3 + 1792
*e^80*log(5)^2 + 1024*e^80*log(5) + 256*e^80)*x^32 - 6*(e^80*log(5)^9 + 18*e^80*log(5)^8 + 144*e^80*log(5)^7 +
672*e^80*log(5)^6 + 2016*e^80*log(5)^5 + 4032*e^80*log(5)^4 + 5376*e^80*log(5)^3 + 4608*e^80*log(5)^2 + 2304*
e^80*log(5) + 512*e^80)*x^31 + 6*(e^80*log(5)^10 + 20*e^80*log(5)^9 + 180*e^80*log(5)^8 + 960*e^80*log(5)^7 +
3360*e^80*log(5)^6 + 8064*e^80*log(5)^5 + 13440*e^80*log(5)^4 + 15360*e^80*log(5)^3 + 11520*e^80*log(5)^2 + 51
20*e^80*log(5) + 1024*e^80)*x^30 - 6*(e^80*log(5)^11 + 22*e^80*log(5)^10 + 220*e^80*log(5)^9 + 1320*e^80*log(5
)^8 + 5280*e^80*log(5)^7 + 14784*e^80*log(5)^6 + 29568*e^80*log(5)^5 + 42240*e^80*log(5)^4 + 42240*e^80*log(5)
^3 + 28160*e^80*log(5)^2 + 11264*e^80*log(5) + 2048*e^80)*x^29 + 6*(e^80*log(5)^12 + 24*e^80*log(5)^11 + 264*e
^80*log(5)^10 + 1760*e^80*log(5)^9 + 7920*e^80*log(5)^8 + 25344*e^80*log(5)^7 + 59136*e^80*log(5)^6 + 101376*e
^80*log(5)^5 + 126720*e^80*log(5)^4 + 112640*e^80*log(5)^3 + 67584*e^80*log(5)^2 + 24576*e^80*log(5) + 4096*e^
80)*x^28 - 6*(e^80*log(5)^13 + 26*e^80*log(5)^12 + 312*e^80*log(5)^11 + 2288*e^80*log(5)^10 + 11440*e^80*log(5
)^9 + 41184*e^80*log(5)^8 + 109824*e^80*log(5)^7 + 219648*e^80*log(5)^6 + 329472*e^80*log(5)^5 + 366080*e^80*l
og(5)^4 + 292864*e^80*log(5)^3 + 159744*e^80*log(5)^2 + 53248*e^80*log(5) + 8192*e^80)*x^27 + 6*(e^80*log(5)^1
4 + 28*e^80*log(5)^13 + 364*e^80*log(5)^12 + 2912*e^80*log(5)^11 + 16016*e^80*log(5)^10 + 64064*e^80*log(5)^9
+ 192192*e^80*log(5)^8 + 439296*e^80*log(5)^7 + 768768*e^80*log(5)^6 + 1025024*e^80*log(5)^5 + 1025024*e^80*lo
g(5)^4 + 745472*e^80*log(5)^3 + 372736*e^80*log(5)^2 + 114688*e^80*log(5) + 16384*e^80)*x^26 - 6*(e^80*log(5)^
15 + 30*e^80*log(5)^14 + 420*e^80*log(5)^13 + 3640*e^80*log(5)^12 + 21840*e^80*log(5)^11 + 96096*e^80*log(5)^1
0 + 320320*e^80*log(5)^9 + 823680*e^80*log(5)^8 + 1647360*e^80*log(5)^7 + 2562560*e^80*log(5)^6 + 3075072*e^80
*log(5)^5 + 2795520*e^80*log(5)^4 + 1863680*e^80*log(5)^3 + 860160*e^80*log(5)^2 + 245760*e^80*log(5) + 32768*
e^80)*x^25 + 6*(e^80*log(5)^16 + 32*e^80*log(5)^15 + 480*e^80*log(5)^14 + 4480*e^80*log(5)^13 + 29120*e^80*log
(5)^12 + 139776*e^80*log(5)^11 + 512512*e^80*log(5)^10 + 1464320*e^80*log(5)^9 + 3294720*e^80*log(5)^8 + 58572
80*e^80*log(5)^7 + 8200192*e^80*log(5)^6 + 8945664*e^80*log(5)^5 + 7454720*e^80*log(5)^4 + 4587520*e^80*log(5)
^3 + 1966080*e^80*log(5)^2 + 524288*e^80*log(5) + 65536*e^80)*x^24 - 6*(e^80*log(5)^17 + 34*e^80*log(5)^16 + 5
44*e^80*log(5)^15 + 5440*e^80*log(5)^14 + 38080*e^80*log(5)^13 + 198016*e^80*log(5)^12 + 792064*e^80*log(5)^11
+ 2489344*e^80*log(5)^10 + 6223360*e^80*log(5)^9 + 12446720*e^80*log(5)^8 + 19914752*e^80*log(5)^7 + 25346048
*e^80*log(5)^6 + 25346048*e^80*log(5)^5 + 19496960*e^80*log(5)^4 + 11141120*e^80*log(5)^3 + 4456448*e^80*log(5
)^2 + 1114112*e^80*log(5) + 131072*e^80)*x^23 + 6*(e^80*log(5)^18 + 36*e^80*log(5)^17 + 612*e^80*log(5)^16 + 6
528*e^80*log(5)^15 + 48960*e^80*log(5)^14 + 274176*e^80*log(5)^13 + 1188096*e^80*log(5)^12 + 4073472*e^80*log(
5)^11 + 11202048*e^80*log(5)^10 + 24893440*e^80*log(5)^9 + 44808192*e^80*log(5)^8 + 65175552*e^80*log(5)^7 + 7
6038144*e^80*log(5)^6 + 70189056*e^80*log(5)^5 + 50135040*e^80*log(5)^4 + 26738688*e^80*log(5)^3 + 10027008*e^
80*log(5)^2 + 2359296*e^80*log(5) + 262144*e^80)*x^22 - 6*(e^80*log(5)^19 + 38*e^80*log(5)^18 + 684*e^80*log(5
)^17 + 7752*e^80*log(5)^16 + 62016*e^80*log(5)^15 + 372096*e^80*log(5)^14 + 1736448*e^80*log(5)^13 + 6449664*e
^80*log(5)^12 + 19348992*e^80*log(5)^11 + 47297536*e^80*log(5)^10 + 94595072*e^80*log(5)^9 + 154791936*e^80*lo
g(5)^8 + 206389248*e^80*log(5)^7 + 222265344*e^80*log(5)^6 + 190513152*e^80*log(5)^5 + 127008768*e^80*log(5)^4
+ 63504384*e^80*log(5)^3 + 22413312*e^80*log(5)^2 + 4980736*e^80*log(5) + 524288*e^80)*x^21 + 6*(e^80*log(5)^
20 + 40*e^80*log(5)^19 + 760*e^80*log(5)^18 + 9120*e^80*log(5)^17 + 77520*e^80*log(5)^16 + 496128*e^80*log(5)^
15 + 2480640*e^80*log(5)^14 + 9922560*e^80*log(5)^13 + 32248320*e^80*log(5)^12 + 85995520*e^80*log(5)^11 + 189
190144*e^80*log(5)^10 + 343982080*e^80*log(5)^9 + 515973120*e^80*log(5)^8 + 635043840*e^80*log(5)^7 + 63504384
0*e^80*log(5)^6 + 508035072*e^80*log(5)^5 + 317521920*e^80*log(5)^4 + 149422080*e^80*log(5)^3 + 49807360*e^80*
log(5)^2 + 10485760*e^80*log(5) + 1048576*e^80)*x^20 - 6*(e^80*log(5)^21 + 42*e^80*log(5)^20 + 840*e^80*log(5)
^19 + 10640*e^80*log(5)^18 + 95760*e^80*log(5)^17 + 651168*e^80*log(5)^16 + 3472896*e^80*log(5)^15 + 14883840*
e^80*log(5)^14 + 52093440*e^80*log(5)^13 + 150492160*e^80*log(5)^12 + 361181184*e^80*log(5)^11 + 722362368*e^8
0*log(5)^10 + 1203937280*e^80*log(5)^9 + 1666990080*e^80*log(5)^8 + 1905131520*e^80*log(5)^7 + 1778122752*e^80
*log(5)^6 + 1333592064*e^80*log(5)^5 + 784465920*e^80*log(5)^4 + 348651520*e^80*log(5)^3 + 110100480*e^80*log(
5)^2 + 22020096*e^80*log(5) + 2097152*e^80)*x^19 + 6*(e^80*log(5)^22 + 44*e^80*log(5)^21 + 924*e^80*log(5)^20
+ 12320*e^80*log(5)^19 + 117040*e^80*log(5)^18 + 842688*e^80*log(5)^17 + 4775232*e^80*log(5)^16 + 21829632*e^8
0*log(5)^15 + 81861120*e^80*log(5)^14 + 254679040*e^80*log(5)^13 + 662165504*e^80*log(5)^12 + 1444724736*e^80*
log(5)^11 + 2648662016*e^80*log(5)^10 + 4074864640*e^80*log(5)^9 + 5239111680*e^80*log(5)^8 + 5588385792*e^80*
log(5)^7 + 4889837568*e^80*log(5)^6 + 3451650048*e^80*log(5)^5 + 1917583360*e^80*log(5)^4 + 807403520*e^80*log
(5)^3 + 242221056*e^80*log(5)^2 + 46137344*e^80*log(5) + 4194304*e^80)*x^18 - 6*(e^80*log(5)^23 + 46*e^80*log(
5)^22 + 1012*e^80*log(5)^21 + 14168*e^80*log(5)^20 + 141680*e^80*log(5)^19 + 1076768*e^80*log(5)^18 + 6460608*
e^80*log(5)^17 + 31380096*e^80*log(5)^16 + 125520384*e^80*log(5)^15 + 418401280*e^80*log(5)^14 + 1171523584*e^
80*log(5)^13 + 2769055744*e^80*log(5)^12 + 5538111488*e^80*log(5)^11 + 9372188672*e^80*log(5)^10 + 13388840960
*e^80*log(5)^9 + 16066609152*e^80*log(5)^8 + 16066609152*e^80*log(5)^7 + 13231325184*e^80*log(5)^6 + 882088345
6*e^80*log(5)^5 + 4642570240*e^80*log(5)^4 + 1857028096*e^80*log(5)^3 + 530579456*e^80*log(5)^2 + 96468992*e^8
0*log(5) + 8388608*e^80)*x^17 + 6*(e^80*log(5)^24 + 48*e^80*log(5)^23 + 1104*e^80*log(5)^22 + 16192*e^80*log(5
)^21 + 170016*e^80*log(5)^20 + 1360128*e^80*log(5)^19 + 8614144*e^80*log(5)^18 + 44301312*e^80*log(5)^17 + 188
280576*e^80*log(5)^16 + 669442048*e^80*log(5)^15 + 2008326144*e^80*log(5)^14 + 5112102912*e^80*log(5)^13 + 110
76222976*e^80*log(5)^12 + 20448411648*e^80*log(5)^11 + 32133218304*e^80*log(5)^10 + 42844291072*e^80*log(5)^9
+ 48199827456*e^80*log(5)^8 + 45364543488*e^80*log(5)^7 + 35283533824*e^80*log(5)^6 + 22284337152*e^80*log(5)^
5 + 11142168576*e^80*log(5)^4 + 4244635648*e^80*log(5)^3 + 1157627904*e^80*log(5)^2 + 201326592*e^80*log(5) +
16777216*e^80)*x^16 - 6*(e^80*log(5)^25 + 50*e^80*log(5)^24 + 1200*e^80*log(5)^23 + 18400*e^80*log(5)^22 + 202
400*e^80*log(5)^21 + 1700160*e^80*log(5)^20 + 11334400*e^80*log(5)^19 + 61529600*e^80*log(5)^18 + 276883200*e^
80*log(5)^17 + 1046003200*e^80*log(5)^16 + 3347210240*e^80*log(5)^15 + 9128755200*e^80*log(5)^14 + 21300428800
*e^80*log(5)^13 + 42600857600*e^80*log(5)^12 + 73030041600*e^80*log(5)^11 + 107110727680*e^80*log(5)^10 + 1338
88409600*e^80*log(5)^9 + 141764198400*e^80*log(5)^8 + 126012620800*e^80*log(5)^7 + 92851404800*e^80*log(5)^6 +
55710842880*e^80*log(5)^5 + 26528972800*e^80*log(5)^4 + 9646899200*e^80*log(5)^3 + 2516582400*e^80*log(5)^2 +
419430400*e^80*log(5) + 33554432*e^80)*x^15 + 6*(e^80*log(5)^26 + 52*e^80*log(5)^25 + 1300*e^80*log(5)^24 + 2
0800*e^80*log(5)^23 + 239200*e^80*log(5)^22 + 2104960*e^80*log(5)^21 + 14734720*e^80*log(5)^20 + 84198400*e^80
*log(5)^19 + 399942400*e^80*log(5)^18 + 1599769600*e^80*log(5)^17 + 5439216640*e^80*log(5)^16 + 15823175680*e^
80*log(5)^15 + 39557939200*e^80*log(5)^14 + 85201715200*e^80*log(5)^13 + 158231756800*e^80*log(5)^12 + 2531708
10880*e^80*log(5)^11 + 348109864960*e^80*log(5)^10 + 409541017600*e^80*log(5)^9 + 409541017600*e^80*log(5)^8 +
344876646400*e^80*log(5)^7 + 241413652480*e^80*log(5)^6 + 137950658560*e^80*log(5)^5 + 62704844800*e^80*log(5
)^4 + 21810380800*e^80*log(5)^3 + 5452595200*e^80*log(5)^2 + 872415232*e^80*log(5) + 67108864*e^80)*x^14 - 6*(
e^80*log(5)^27 + 54*e^80*log(5)^26 + 1404*e^80*log(5)^25 + 23400*e^80*log(5)^24 + 280800*e^80*log(5)^23 + 2583
360*e^80*log(5)^22 + 18944640*e^80*log(5)^21 + 113667840*e^80*log(5)^20 + 568339200*e^80*log(5)^19 + 239965440
0*e^80*log(5)^18 + 8638755840*e^80*log(5)^17 + 26701608960*e^80*log(5)^16 + 71204290560*e^80*log(5)^15 + 16431
7593600*e^80*log(5)^14 + 328635187200*e^80*log(5)^13 + 569634324480*e^80*log(5)^12 + 854451486720*e^80*log(5)^
11 + 1105760747520*e^80*log(5)^10 + 1228623052800*e^80*log(5)^9 + 1163958681600*e^80*log(5)^8 + 931166945280*e
^80*log(5)^7 + 620777963520*e^80*log(5)^6 + 338606161920*e^80*log(5)^5 + 147220070400*e^80*log(5)^4 + 49073356
800*e^80*log(5)^3 + 11777605632*e^80*log(5)^2 + 1811939328*e^80*log(5) + 134217728*e^80)*x^13 + 6*(e^80*log(5)
^28 + 56*e^80*log(5)^27 + 1512*e^80*log(5)^26 + 26208*e^80*log(5)^25 + 327600*e^80*log(5)^24 + 3144960*e^80*lo
g(5)^23 + 24111360*e^80*log(5)^22 + 151557120*e^80*log(5)^21 + 795674880*e^80*log(5)^20 + 3536332800*e^80*log(
5)^19 + 13438064640*e^80*log(5)^18 + 43979120640*e^80*log(5)^17 + 124607508480*e^80*log(5)^16 + 306726174720*e
^80*log(5)^15 + 657270374400*e^80*log(5)^14 + 1226904698880*e^80*log(5)^13 + 1993720135680*e^80*log(5)^12 + 28
14663720960*e^80*log(5)^11 + 3440144547840*e^80*log(5)^10 + 3621204787200*e^80*log(5)^9 + 3259084308480*e^80*l
og(5)^8 + 2483111854080*e^80*log(5)^7 + 1580162088960*e^80*log(5)^6 + 824432394240*e^80*log(5)^5 + 34351349760
0*e^80*log(5)^4 + 109924319232*e^80*log(5)^3 + 25367150592*e^80*log(5)^2 + 3758096384*e^80*log(5) + 268435456*
e^80)*x^12 - 6*(e^80*log(5)^29 + 58*e^80*log(5)^28 + 1624*e^80*log(5)^27 + 29232*e^80*log(5)^26 + 380016*e^80*
log(5)^25 + 3800160*e^80*log(5)^24 + 30401280*e^80*log(5)^23 + 199779840*e^80*log(5)^22 + 1098789120*e^80*log(
5)^21 + 5127682560*e^80*log(5)^20 + 20510730240*e^80*log(5)^19 + 70855249920*e^80*log(5)^18 + 212565749760*e^8
0*log(5)^17 + 555941191680*e^80*log(5)^16 + 1270722723840*e^80*log(5)^15 + 2541445447680*e^80*log(5)^14 + 4447
529533440*e^80*log(5)^13 + 6802103992320*e^80*log(5)^12 + 9069471989760*e^80*log(5)^11 + 10501493882880*e^80*l
og(5)^10 + 10501493882880*e^80*log(5)^9 + 9001280471040*e^80*log(5)^8 + 6546385797120*e^80*log(5)^7 + 39847565
72160*e^80*log(5)^6 + 1992378286080*e^80*log(5)^5 + 796951314432*e^80*log(5)^4 + 245215789056*e^80*log(5)^3 +
54492397568*e^80*log(5)^2 + 7784628224*e^80*log(5) + 536870912*e^80)*x^11 + 6*(e^80*log(5)^30 + 60*e^80*log(5)
^29 + 1740*e^80*log(5)^28 + 32480*e^80*log(5)^27 + 438480*e^80*log(5)^26 + 4560192*e^80*log(5)^25 + 38001600*e
^80*log(5)^24 + 260582400*e^80*log(5)^23 + 1498348800*e^80*log(5)^22 + 7325260800*e^80*log(5)^21 + 30766095360
*e^80*log(5)^20 + 111876710400*e^80*log(5)^19 + 354276249600*e^80*log(5)^18 + 981072691200*e^80*log(5)^17 + 23
82605107200*e^80*log(5)^16 + 5082890895360*e^80*log(5)^15 + 9530420428800*e^80*log(5)^14 + 15697163059200*e^80
*log(5)^13 + 22673679974400*e^80*log(5)^12 + 28640437862400*e^80*log(5)^11 + 31504481648640*e^80*log(5)^10 + 3
0004268236800*e^80*log(5)^9 + 24548946739200*e^80*log(5)^8 + 17077528166400*e^80*log(5)^7 + 9961891430400*e^80
*log(5)^6 + 4781707886592*e^80*log(5)^5 + 1839118417920*e^80*log(5)^4 + 544923975680*e^80*log(5)^3 + 116769423
360*e^80*log(5)^2 + 16106127360*e^80*log(5) + 1073741824*e^80)*x^10 - 6*(e^80*log(5)^31 + 62*e^80*log(5)^30 +
1860*e^80*log(5)^29 + 35960*e^80*log(5)^28 + 503440*e^80*log(5)^27 + 5437152*e^80*log(5)^26 + 47121984*e^80*lo
g(5)^25 + 336585600*e^80*log(5)^24 + 2019513600*e^80*log(5)^23 + 10321958400*e^80*log(5)^22 + 45416616960*e^80
*log(5)^21 + 173408901120*e^80*log(5)^20 + 578029670400*e^80*log(5)^19 + 1689625190400*e^80*log(5)^18 + 434475
0489600*e^80*log(5)^17 + 9848101109760*e^80*log(5)^16 + 19696202219520*e^80*log(5)^15 + 34758003916800*e^80*lo
g(5)^14 + 54068006092800*e^80*log(5)^13 + 73987797811200*e^80*log(5)^12 + 88785357373440*e^80*log(5)^11 + 9301
3231534080*e^80*log(5)^10 + 84557483212800*e^80*log(5)^9 + 66175421644800*e^80*log(5)^8 + 44116947763200*e^80*
log(5)^7 + 24705490747392*e^80*log(5)^6 + 11402534191104*e^80*log(5)^5 + 4223160811520*e^80*log(5)^4 + 1206617
374720*e^80*log(5)^3 + 249644974080*e^80*log(5)^2 + 33285996544*e^80*log(5) + 2147483648*e^80)*x^9 + 6*(e^80*l
og(5)^32 + 64*e^80*log(5)^31 + 1984*e^80*log(5)^30 + 39680*e^80*log(5)^29 + 575360*e^80*log(5)^28 + 6444032*e^
80*log(5)^27 + 57996288*e^80*log(5)^26 + 430829568*e^80*log(5)^25 + 2692684800*e^80*log(5)^24 + 14360985600*e^
80*log(5)^23 + 66060533760*e^80*log(5)^22 + 264242135040*e^80*log(5)^21 + 924847472640*e^80*log(5)^20 + 284568
4531200*e^80*log(5)^19 + 7724000870400*e^80*log(5)^18 + 18537602088960*e^80*log(5)^17 + 39392404439040*e^80*lo
g(5)^16 + 74150408355840*e^80*log(5)^15 + 123584013926400*e^80*log(5)^14 + 182123809996800*e^80*log(5)^13 + 23
6760952995840*e^80*log(5)^12 + 270583946280960*e^80*log(5)^11 + 270583946280960*e^80*log(5)^10 + 2352903880704
00*e^80*log(5)^9 + 176467791052800*e^80*log(5)^8 + 112939386273792*e^80*log(5)^7 + 60813515685888*e^80*log(5)^
6 + 27028229193728*e^80*log(5)^5 + 9652938997760*e^80*log(5)^4 + 2662879723520*e^80*log(5)^3 + 532575944704*e^
80*log(5)^2 + 68719476736*e^80*log(5) + 4294967296*e^80)*x^8 - 6*(e^80*log(5)^33 + 66*e^80*log(5)^32 + 2112*e^
80*log(5)^31 + 43648*e^80*log(5)^30 + 654720*e^80*log(5)^29 + 7594752*e^80*log(5)^28 + 70884352*e^80*log(5)^27
+ 546822144*e^80*log(5)^26 + 3554343936*e^80*log(5)^25 + 19746355200*e^80*log(5)^24 + 94782504960*e^80*log(5)
^23 + 396363202560*e^80*log(5)^22 + 1453331742720*e^80*log(5)^21 + 4695379476480*e^80*log(5)^20 + 134153699328
00*e^80*log(5)^19 + 33985603829760*e^80*log(5)^18 + 76467608616960*e^80*log(5)^17 + 152935217233920*e^80*log(5
)^16 + 271884830638080*e^80*log(5)^15 + 429291837849600*e^80*log(5)^14 + 601008572989440*e^80*log(5)^13 + 7441
05852272640*e^80*log(5)^12 + 811751838842880*e^80*log(5)^11 + 776458280632320*e^80*log(5)^10 + 647048567193600
*e^80*log(5)^9 + 465874968379392*e^80*log(5)^8 + 286692288233472*e^80*log(5)^7 + 148655260565504*e^80*log(5)^6
+ 63709397385216*e^80*log(5)^5 + 21968757719040*e^80*log(5)^4 + 5858335391744*e^80*log(5)^3 + 1133871366144*e
^80*log(5)^2 + 141733920768*e^80*log(5) + 8589934592*e^80)*x^7 + 6*(e^80*log(5)^34 + 68*e^80*log(5)^33 + 2244*
e^80*log(5)^32 + 47872*e^80*log(5)^31 + 742016*e^80*log(5)^30 + 8904192*e^80*log(5)^29 + 86073856*e^80*log(5)^
28 + 688590848*e^80*log(5)^27 + 4647988224*e^80*log(5)^26 + 26855043072*e^80*log(5)^25 + 134275215360*e^80*log
(5)^24 + 585928212480*e^80*log(5)^23 + 2246058147840*e^80*log(5)^22 + 7602042961920*e^80*log(5)^21 + 228061288
85760*e^80*log(5)^20 + 60816343695360*e^80*log(5)^19 + 144438816276480*e^80*log(5)^18 + 305870434467840*e^80*l
og(5)^17 + 577755265105920*e^80*log(5)^16 + 973061499125760*e^80*log(5)^15 + 1459592248688640*e^80*log(5)^14 +
1946122998251520*e^80*log(5)^13 + 2299963543388160*e^80*log(5)^12 + 2399961958318080*e^80*log(5)^11 + 2199965
128458240*e^80*log(5)^10 + 1759972102766592*e^80*log(5)^9 + 1218442224992256*e^80*log(5)^8 + 722039837032448*e
^80*log(5)^7 + 361019918516224*e^80*log(5)^6 + 149387552489472*e^80*log(5)^5 + 49795850829824*e^80*log(5)^4 +
12850542149632*e^80*log(5)^3 + 2409476653056*e^80*log(5)^2 + 292057776128*e^80*log(5) + 17179869184*e^80)*x^6
- 6*(e^80*log(5)^35 + 70*e^80*log(5)^34 + 2380*e^80*log(5)^33 + 52360*e^80*log(5)^32 + 837760*e^80*log(5)^31 +
10388224*e^80*log(5)^30 + 103882240*e^80*log(5)^29 + 860738560*e^80*log(5)^28 + 6025169920*e^80*log(5)^27 + 3
6151019520*e^80*log(5)^26 + 187985301504*e^80*log(5)^25 + 854478643200*e^80*log(5)^24 + 3417914572800*e^80*log
(5)^23 + 12094159257600*e^80*log(5)^22 + 38010214809600*e^80*log(5)^21 + 106428601466880*e^80*log(5)^20 + 2660
71503667200*e^80*log(5)^19 + 594748067020800*e^80*log(5)^18 + 1189496134041600*e^80*log(5)^17 + 21285720293376
00*e^80*log(5)^16 + 3405715246940160*e^80*log(5)^15 + 4865307495628800*e^80*log(5)^14 + 6192209539891200*e^80*
log(5)^13 + 6999889045094400*e^80*log(5)^12 + 6999889045094400*e^80*log(5)^11 + 6159902359683072*e^80*log(5)^1
0 + 4738386430525440*e^80*log(5)^9 + 3158924287016960*e^80*log(5)^8 + 1805099592581120*e^80*log(5)^7 + 8714273
89521920*e^80*log(5)^6 + 348570955808768*e^80*log(5)^5 + 112442243809280*e^80*log(5)^4 + 28110560952320*e^80*l
og(5)^3 + 5111011082240*e^80*log(5)^2 + 601295421440*e^80*log(5) + 34359738368*e^80)*x^5 + 6*(e^80*log(5)^36 +
72*e^80*log(5)^35 + 2520*e^80*log(5)^34 + 57120*e^80*log(5)^33 + 942480*e^80*log(5)^32 + 12063744*e^80*log(5)
^31 + 124658688*e^80*log(5)^30 + 1068503040*e^80*log(5)^29 + 7746647040*e^80*log(5)^28 + 48201359360*e^80*log(
5)^27 + 260287340544*e^80*log(5)^26 + 1230449246208*e^80*log(5)^25 + 5126871859200*e^80*log(5)^24 + 1892998840
3200*e^80*log(5)^23 + 62198533324800*e^80*log(5)^22 + 182449031086080*e^80*log(5)^21 + 478928706600960*e^80*lo
g(5)^20 + 1126891074355200*e^80*log(5)^19 + 2378992268083200*e^80*log(5)^18 + 4507564297420800*e^80*log(5)^17
+ 7662859305615360*e^80*log(5)^16 + 11676737989509120*e^80*log(5)^15 + 15922824531148800*e^80*log(5)^14 + 1938
4308124876800*e^80*log(5)^13 + 20999667135283200*e^80*log(5)^12 + 20159680449871872*e^80*log(5)^11 + 170581911
49891584*e^80*log(5)^10 + 12635697148067840*e^80*log(5)^9 + 8122948166615040*e^80*log(5)^8 + 4481626574684160*
e^80*log(5)^7 + 2091425734852608*e^80*log(5)^6 + 809584155426816*e^80*log(5)^5 + 252995048570880*e^80*log(5)^4
+ 61332132986880*e^80*log(5)^3 + 10823317585920*e^80*log(5)^2 + 1236950581248*e^80*log(5) + 68719476736*e^80)
*x^4 - 6*(e^80*log(5)^37 + 74*e^80*log(5)^36 + 2664*e^80*log(5)^35 + 62160*e^80*log(5)^34 + 1056720*e^80*log(5
)^33 + 13948704*e^80*log(5)^32 + 148786176*e^80*log(5)^31 + 1317820416*e^80*log(5)^30 + 9883653120*e^80*log(5)
^29 + 63694653440*e^80*log(5)^28 + 356690059264*e^80*log(5)^27 + 1751023927296*e^80*log(5)^26 + 7587770351616*
e^80*log(5)^25 + 29183732121600*e^80*log(5)^24 + 100058510131200*e^80*log(5)^23 + 306846097735680*e^80*log(5)^
22 + 843826768773120*e^80*log(5)^21 + 2084748487557120*e^80*log(5)^20 + 4632774416793600*e^80*log(5)^19 + 9265
548833587200*e^80*log(5)^18 + 16677987900456960*e^80*log(5)^17 + 27002456600739840*e^80*log(5)^16 + 3927630051
0167040*e^80*log(5)^15 + 51229957187174400*e^80*log(5)^14 + 59768283385036800*e^80*log(5)^13 + 621590147204382
72*e^80*log(5)^12 + 57377552049635328*e^80*log(5)^11 + 46752079447851008*e^80*log(5)^10 + 33394342462750720*e^
80*log(5)^9 + 20727522907914240*e^80*log(5)^8 + 11054678884220928*e^80*log(5)^7 + 4992435625132032*e^80*log(5)
^6 + 1872163359424512*e^80*log(5)^5 + 567322230128640*e^80*log(5)^4 + 133487583559680*e^80*log(5)^3 + 22883585
753088*e^80*log(5)^2 + 2542620639232*e^80*log(5) + 137438953472*e^80)*x^3 + 6*(e^80*log(5)^38 + 76*e^80*log(5)
^37 + 2812*e^80*log(5)^36 + 67488*e^80*log(5)^35 + 1181040*e^80*log(5)^34 + 16062144*e^80*log(5)^33 + 17668358
4*e^80*log(5)^32 + 1615392768*e^80*log(5)^31 + 12519293952*e^80*log(5)^30 + 83461959680*e^80*log(5)^29 + 48407
9366144*e^80*log(5)^28 + 2464404045824*e^80*log(5)^27 + 11089818206208*e^80*log(5)^26 + 44359272824832*e^80*lo
g(5)^25 + 158425974374400*e^80*log(5)^24 + 506963117998080*e^80*log(5)^23 + 1457518964244480*e^80*log(5)^22 +
3772402025103360*e^80*log(5)^21 + 8802271391907840*e^80*log(5)^20 + 18531097667174400*e^80*log(5)^19 + 3520908
5567631360*e^80*log(5)^18 + 60358432401653760*e^80*log(5)^17 + 93281213711646720*e^80*log(5)^16 + 129782558207
508480*e^80*log(5)^15 + 162228197759385600*e^80*log(5)^14 + 181695581490511872*e^80*log(5)^13 + 18169558149051
1872*e^80*log(5)^12 + 161507183547121664*e^80*log(5)^11 + 126898501358452736*e^80*log(5)^10 + 8751620783341568
0*e^80*log(5)^9 + 52509724700049408*e^80*log(5)^8 + 27101793393573888*e^80*log(5)^7 + 11857034609688576*e^80*l
og(5)^6 + 4311648948977664*e^80*log(5)^5 + 1268132043816960*e^80*log(5)^4 + 289858752872448*e^80*log(5)^3 + 48
309792145408*e^80*log(5)^2 + 5222680231936*e^80*log(5) + 274877906944*e^80 - 1)*x^2 - 6*(e^80*log(5)^39 + 78*e
^80*log(5)^38 + 2964*e^80*log(5)^37 + 73112*e^80*log(5)^36 + 1316016*e^80*log(5)^35 + 18424224*e^80*log(5)^34
+ 208807872*e^80*log(5)^33 + 1968759936*e^80*log(5)^32 + 15750079488*e^80*log(5)^31 + 108500547584*e^80*log(5)
^30 + 651003285504*e^80*log(5)^29 + 3432562778112*e^80*log(5)^28 + 16018626297856*e^80*log(5)^27 + 66538909237
248*e^80*log(5)^26 + 247144520024064*e^80*log(5)^25 + 823815066746880*e^80*log(5)^24 + 2471445200240640*e^80*l
og(5)^23 + 6687439953592320*e^80*log(5)^22 + 16347075442114560*e^80*log(5)^21 + 36135640450990080*e^80*log(5)^
20 + 72271280901980160*e^80*log(5)^19 + 130776603536916480*e^80*log(5)^18 + 213998078514954240*e^80*log(5)^17
+ 316344985630801920*e^80*log(5)^16 + 421793314174402560*e^80*log(5)^15 + 506151977009283072*e^80*log(5)^14 +
545086744471535616*e^80*log(5)^13 + 524898346528145408*e^80*log(5)^12 + 449912868452696064*e^80*log(5)^11 + 34
1313210550321152*e^80*log(5)^10 + 227542140366880768*e^80*log(5)^9 + 132121242793672704*e^80*log(5)^8 + 660606
21396836352*e^80*log(5)^7 + 28025718168354816*e^80*log(5)^6 + 9891429941772288*e^80*log(5)^5 + 282612284050636
8*e^80*log(5)^4 + 628027297890304*e^80*log(5)^3 + 101842264522752*e^80*log(5)^2 + (10720238370816*e^80 - 1)*lo
g(5) + 549755813888*e^80 - 2)*x - 6*(e^80*log(5)^41 + 82*e^80*log(5)^40 + 3280*e^80*log(5)^39 + 85280*e^80*log
(5)^38 + 1620320*e^80*log(5)^37 + 23980736*e^80*log(5)^36 + 287768832*e^80*log(5)^35 + 2877688320*e^80*log(5)^
34 + 24460350720*e^80*log(5)^33 + 179375905280*e^80*log(5)^32 + 1148005793792*e^80*log(5)^31 + 6470578110464*e
^80*log(5)^30 + 32352890552320*e^80*log(5)^29 + 144343665541120*e^80*log(5)^28 + 577374662164480*e^80*log(5)^2
7 + 2078548783792128*e^80*log(5)^26 + 6755283547324416*e^80*log(5)^25 + 19868481021542400*e^80*log(5)^24 + 529
82616057446400*e^80*log(5)^23 + 128273702033817600*e^80*log(5)^22 + 282202144474398720*e^80*log(5)^21 + 564404
288948797440*e^80*log(5)^20 + 1026189616270540800*e^80*log(5)^19 + 1695443713838284800*e^80*log(5)^18 + 254316
5570757427200*e^80*log(5)^17 + 3458705176230100992*e^80*log(5)^16 + 4256867909206278144*e^80*log(5)^15 + 47298
53232451420160*e^80*log(5)^14 + 4729853232451420160*e^80*log(5)^13 + 4240558070473687040*e^80*log(5)^12 + 3392
446456378949632*e^80*log(5)^11 + 2407542646462480384*e^80*log(5)^10 + 1504714154039050240*e^80*log(5)^9 + 8207
53174930391040*e^80*log(5)^8 + 386236788202536960*e^80*log(5)^7 + 154494715281014784*e^80*log(5)^6 + 514982384
27004928*e^80*log(5)^5 + 13918442818109440*e^80*log(5)^4 + (2930198488023040*e^80 - 1)*log(5)^3 + 2*(225399883
694080*e^80 - 3)*log(5)^2 + 4*(11269994184704*e^80 - 3)*log(5) + 2199023255552*e^80 - 8)/(x + log(5) + 2)
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mupad [B] time = 5.89, size = 20, normalized size = 0.83 \begin {gather*} \frac {6\,x^3\,\left (x^{38}\,{\mathrm {e}}^{80}-1\right )}{x+\ln \relax (5)+2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(-(18*x^2*log(5) - exp(40*log(x) + 80)*(240*x + 246*log(5) + 492) + 36*x^2 + 12*x^3)/(4*x + log(5)*(2*x + 4
) + log(5)^2 + x^2 + 4),x)
[Out]
(6*x^3*(x^38*exp(80) - 1))/(x + log(5) + 2)
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((246*ln(5)+240*x+492)*exp(40*ln(x)+80)-18*x**2*ln(5)-12*x**3-36*x**2)/(ln(5)**2+(2*x+4)*ln(5)+x**2+
4*x+4),x)
[Out]
Timed out
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