3.23.85 \(\int \frac {3200000+157920000 x-8016000 x^2-50474400 x^3+3458500 x^4+5861095 x^5-382279 x^6-327075 x^7+16455 x^8+9020 x^9-250 x^{10}-100 x^{11}+(16000000+793600000 x+158320000 x^2-212152000 x^3-35721500 x^4+20295420 x^5+3157836 x^6-843100 x^7-128320 x^8+13000 x^9+2000 x^{10}) \log (2)+(36000000+1793600000 x+755020000 x^2-297522000 x^3-141278375 x^4+12506655 x^5+8945779 x^6+142825 x^7-200080 x^8-12750 x^9+500 x^{10}) \log ^2(2)+(48000000+2400800000 x+1473960000 x^2-87026000 x^3-189454000 x^4-19666000 x^5+6379600 x^6+1104800 x^7-20000 x^8-8000 x^9) \log ^3(2)+(42000000+2107700000 x+1641415000 x^2+218779750 x^3-110363750 x^4-31152250 x^5-132150 x^6+590100 x^7+37500 x^8-1000 x^9) \log ^4(2)+(25200000+1268120000 x+1161199000 x^2+303876600 x^3-12267000 x^4-16160200 x^5-1834080 x^6+46000 x^7+12000 x^8) \log ^5(2)+(10500000+529550000 x+542741250 x^2+190450250 x^3+20061750 x^4-2765350 x^5-724040 x^6-33500 x^7+1000 x^8) \log ^6(2)+(3000000+151550000 x+167710000 x^2+68994000 x^3+12198000 x^4+560000 x^5-84000 x^6-8000 x^7) \log ^7(2)+(562500+28446875 x+33026875 x^2+14815125 x^3+3162375 x^4+305000 x^5+6750 x^6-500 x^7) \log ^8(2)+(62500+3162500 x+3757500 x^2+1750500 x^3+400000 x^4+45000 x^5+2000 x^6) \log ^9(2)+(3125+158125 x+187875 x^2+87525 x^3+20000 x^4+2250 x^5+100 x^6) \log ^{10}(2)}{3200000-2080000 x-16000 x^2+245600 x^3-29500 x^4-9625 x^5+1625 x^6+125 x^7-25 x^8+(16000000-6400000 x-1680000 x^2+808000 x^3+54500 x^4-34500 x^5-500 x^6+500 x^7) \log (2)+(36000000-6400000 x-4980000 x^2+678000 x^3+241625 x^4-20625 x^5-4125 x^6+125 x^7) \log ^2(2)+(48000000+800000 x-6040000 x^2-226000 x^3+226000 x^4+10000 x^5-2000 x^6) \log ^3(2)+(42000000+7700000 x-3585000 x^2-670250 x^3+66250 x^4+11250 x^5-250 x^6) \log ^4(2)+(25200000+8120000 x-801000 x^2-413400 x^3-11000 x^4+3000 x^5) \log ^5(2)+(10500000+4550000 x+241250 x^2-107250 x^3-10250 x^4+250 x^5) \log ^6(2)+(3000000+1550000 x+210000 x^2-6000 x^3-2000 x^4) \log ^7(2)+(562500+321875 x+58125 x^2+2625 x^3-125 x^4) \log ^8(2)+(62500+37500 x+7500 x^2+500 x^3) \log ^9(2)+(3125+1875 x+375 x^2+25 x^3) \log ^{10}(2)} \, dx\) [2285]
Optimal. Leaf size=39 \[ x+\left (x+\frac {x^2}{5}\right )^2 \left (-5+\frac {x^2}{(5+x)^2 \left (x-(2+\log (2))^2\right )^2}\right )^2 \]
[Out]
x+(x^2/(x-(ln(2)+2)^2)^2/(5+x)^2-5)^2*(x+1/5*x^2)^2
________________________________________________________________________________________
Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(323\) vs. \(2(39)=78\).
time = 2.32, antiderivative size = 323, normalized size of antiderivative = 8.28, number of steps
used = 2, number of rules used = 1, integrand size = 844, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.001, Rules used = {2099}
\begin {gather*} x^4+10 x^3+\frac {123 x^2}{5}-\frac {1}{5} x \left (11+4 \log ^2(2)+16 \log (2)\right )-\frac {250 \left (17+3 \log ^2(2)+\log (4096)\right )}{(x+5) \left (9+\log ^2(2)+\log (16)\right )^5}+\frac {2 (2+\log (2))^{10} \left (23+2 \log ^2(2)+\log (256)\right )}{25 \left (9+\log ^2(2)+\log (16)\right )^3 \left (x-(2+\log (2))^2\right )^3}+\frac {(2+\log (2))^{12}}{25 \left (9+\log ^2(2)+\log (16)\right )^2 \left (x-(2+\log (2))^2\right )^4}+\frac {625}{(x+5)^2 \left (9+\log ^2(2)+\log (16)\right )^4}-\frac {(2+\log (2))^8 \left (64779+10 \log ^8(2)+160 \log ^7(2)+1320 \log ^6(2)+6880 \log ^5(2)+24694 \log ^4(2)+61872 \log ^3(2)+106686 \log ^2(2)+116088 \log (2)\right )}{25 \left (9+\log ^2(2)+\log (16)\right )^4 \left (x-(2+\log (2))^2\right )^2}-\frac {2 (2+\log (2))^6 \left (1177382+20 \log ^{10}(2)+400 \log ^9(2)+4100 \log ^8(2)+27200 \log ^7(2)+128198 \log ^6(2)+445256 \log ^5(2)+1153635 \log ^4(2)+2202520 \log ^3(2)+2986965 \log ^2(2)+2621076 \log (2)\right )}{25 \left (9+\log ^2(2)+\log (16)\right )^5 \left (x-(2+\log (2))^2\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
Int[(3200000 + 157920000*x - 8016000*x^2 - 50474400*x^3 + 3458500*x^4 + 5861095*x^5 - 382279*x^6 - 327075*x^7
+ 16455*x^8 + 9020*x^9 - 250*x^10 - 100*x^11 + (16000000 + 793600000*x + 158320000*x^2 - 212152000*x^3 - 35721
500*x^4 + 20295420*x^5 + 3157836*x^6 - 843100*x^7 - 128320*x^8 + 13000*x^9 + 2000*x^10)*Log[2] + (36000000 + 1
793600000*x + 755020000*x^2 - 297522000*x^3 - 141278375*x^4 + 12506655*x^5 + 8945779*x^6 + 142825*x^7 - 200080
*x^8 - 12750*x^9 + 500*x^10)*Log[2]^2 + (48000000 + 2400800000*x + 1473960000*x^2 - 87026000*x^3 - 189454000*x
^4 - 19666000*x^5 + 6379600*x^6 + 1104800*x^7 - 20000*x^8 - 8000*x^9)*Log[2]^3 + (42000000 + 2107700000*x + 16
41415000*x^2 + 218779750*x^3 - 110363750*x^4 - 31152250*x^5 - 132150*x^6 + 590100*x^7 + 37500*x^8 - 1000*x^9)*
Log[2]^4 + (25200000 + 1268120000*x + 1161199000*x^2 + 303876600*x^3 - 12267000*x^4 - 16160200*x^5 - 1834080*x
^6 + 46000*x^7 + 12000*x^8)*Log[2]^5 + (10500000 + 529550000*x + 542741250*x^2 + 190450250*x^3 + 20061750*x^4
- 2765350*x^5 - 724040*x^6 - 33500*x^7 + 1000*x^8)*Log[2]^6 + (3000000 + 151550000*x + 167710000*x^2 + 6899400
0*x^3 + 12198000*x^4 + 560000*x^5 - 84000*x^6 - 8000*x^7)*Log[2]^7 + (562500 + 28446875*x + 33026875*x^2 + 148
15125*x^3 + 3162375*x^4 + 305000*x^5 + 6750*x^6 - 500*x^7)*Log[2]^8 + (62500 + 3162500*x + 3757500*x^2 + 17505
00*x^3 + 400000*x^4 + 45000*x^5 + 2000*x^6)*Log[2]^9 + (3125 + 158125*x + 187875*x^2 + 87525*x^3 + 20000*x^4 +
2250*x^5 + 100*x^6)*Log[2]^10)/(3200000 - 2080000*x - 16000*x^2 + 245600*x^3 - 29500*x^4 - 9625*x^5 + 1625*x^
6 + 125*x^7 - 25*x^8 + (16000000 - 6400000*x - 1680000*x^2 + 808000*x^3 + 54500*x^4 - 34500*x^5 - 500*x^6 + 50
0*x^7)*Log[2] + (36000000 - 6400000*x - 4980000*x^2 + 678000*x^3 + 241625*x^4 - 20625*x^5 - 4125*x^6 + 125*x^7
)*Log[2]^2 + (48000000 + 800000*x - 6040000*x^2 - 226000*x^3 + 226000*x^4 + 10000*x^5 - 2000*x^6)*Log[2]^3 + (
42000000 + 7700000*x - 3585000*x^2 - 670250*x^3 + 66250*x^4 + 11250*x^5 - 250*x^6)*Log[2]^4 + (25200000 + 8120
000*x - 801000*x^2 - 413400*x^3 - 11000*x^4 + 3000*x^5)*Log[2]^5 + (10500000 + 4550000*x + 241250*x^2 - 107250
*x^3 - 10250*x^4 + 250*x^5)*Log[2]^6 + (3000000 + 1550000*x + 210000*x^2 - 6000*x^3 - 2000*x^4)*Log[2]^7 + (56
2500 + 321875*x + 58125*x^2 + 2625*x^3 - 125*x^4)*Log[2]^8 + (62500 + 37500*x + 7500*x^2 + 500*x^3)*Log[2]^9 +
(3125 + 1875*x + 375*x^2 + 25*x^3)*Log[2]^10),x]
[Out]
(123*x^2)/5 + 10*x^3 + x^4 - (x*(11 + 16*Log[2] + 4*Log[2]^2))/5 - (2*(2 + Log[2])^6*(1177382 + 2621076*Log[2]
+ 2986965*Log[2]^2 + 2202520*Log[2]^3 + 1153635*Log[2]^4 + 445256*Log[2]^5 + 128198*Log[2]^6 + 27200*Log[2]^7
+ 4100*Log[2]^8 + 400*Log[2]^9 + 20*Log[2]^10))/(25*(x - (2 + Log[2])^2)*(9 + Log[2]^2 + Log[16])^5) + 625/((
5 + x)^2*(9 + Log[2]^2 + Log[16])^4) - ((2 + Log[2])^8*(64779 + 116088*Log[2] + 106686*Log[2]^2 + 61872*Log[2]
^3 + 24694*Log[2]^4 + 6880*Log[2]^5 + 1320*Log[2]^6 + 160*Log[2]^7 + 10*Log[2]^8))/(25*(x - (2 + Log[2])^2)^2*
(9 + Log[2]^2 + Log[16])^4) + (2 + Log[2])^12/(25*(x - (2 + Log[2])^2)^4*(9 + Log[2]^2 + Log[16])^2) + (2*(2 +
Log[2])^10*(23 + 2*Log[2]^2 + Log[256]))/(25*(x - (2 + Log[2])^2)^3*(9 + Log[2]^2 + Log[16])^3) - (250*(17 +
3*Log[2]^2 + Log[4096]))/((5 + x)*(9 + Log[2]^2 + Log[16])^5)
Rule 2099
Int[(P_)^(p_)*(Q_)^(q_.), x_Symbol] :> With[{PP = Factor[P]}, Int[ExpandIntegrand[PP^p*Q^q, x], x] /; !SumQ[N
onfreeFactors[PP, x]]] /; FreeQ[q, x] && PolyQ[P, x] && PolyQ[Q, x] && IntegerQ[p] && NeQ[P, x]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(1272\) vs. \(2(39)=78\).
time = 0.62, size = 1272, normalized size = 32.62 \begin {gather*} \text {Too large to display} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(3200000 + 157920000*x - 8016000*x^2 - 50474400*x^3 + 3458500*x^4 + 5861095*x^5 - 382279*x^6 - 32707
5*x^7 + 16455*x^8 + 9020*x^9 - 250*x^10 - 100*x^11 + (16000000 + 793600000*x + 158320000*x^2 - 212152000*x^3 -
35721500*x^4 + 20295420*x^5 + 3157836*x^6 - 843100*x^7 - 128320*x^8 + 13000*x^9 + 2000*x^10)*Log[2] + (360000
00 + 1793600000*x + 755020000*x^2 - 297522000*x^3 - 141278375*x^4 + 12506655*x^5 + 8945779*x^6 + 142825*x^7 -
200080*x^8 - 12750*x^9 + 500*x^10)*Log[2]^2 + (48000000 + 2400800000*x + 1473960000*x^2 - 87026000*x^3 - 18945
4000*x^4 - 19666000*x^5 + 6379600*x^6 + 1104800*x^7 - 20000*x^8 - 8000*x^9)*Log[2]^3 + (42000000 + 2107700000*
x + 1641415000*x^2 + 218779750*x^3 - 110363750*x^4 - 31152250*x^5 - 132150*x^6 + 590100*x^7 + 37500*x^8 - 1000
*x^9)*Log[2]^4 + (25200000 + 1268120000*x + 1161199000*x^2 + 303876600*x^3 - 12267000*x^4 - 16160200*x^5 - 183
4080*x^6 + 46000*x^7 + 12000*x^8)*Log[2]^5 + (10500000 + 529550000*x + 542741250*x^2 + 190450250*x^3 + 2006175
0*x^4 - 2765350*x^5 - 724040*x^6 - 33500*x^7 + 1000*x^8)*Log[2]^6 + (3000000 + 151550000*x + 167710000*x^2 + 6
8994000*x^3 + 12198000*x^4 + 560000*x^5 - 84000*x^6 - 8000*x^7)*Log[2]^7 + (562500 + 28446875*x + 33026875*x^2
+ 14815125*x^3 + 3162375*x^4 + 305000*x^5 + 6750*x^6 - 500*x^7)*Log[2]^8 + (62500 + 3162500*x + 3757500*x^2 +
1750500*x^3 + 400000*x^4 + 45000*x^5 + 2000*x^6)*Log[2]^9 + (3125 + 158125*x + 187875*x^2 + 87525*x^3 + 20000
*x^4 + 2250*x^5 + 100*x^6)*Log[2]^10)/(3200000 - 2080000*x - 16000*x^2 + 245600*x^3 - 29500*x^4 - 9625*x^5 + 1
625*x^6 + 125*x^7 - 25*x^8 + (16000000 - 6400000*x - 1680000*x^2 + 808000*x^3 + 54500*x^4 - 34500*x^5 - 500*x^
6 + 500*x^7)*Log[2] + (36000000 - 6400000*x - 4980000*x^2 + 678000*x^3 + 241625*x^4 - 20625*x^5 - 4125*x^6 + 1
25*x^7)*Log[2]^2 + (48000000 + 800000*x - 6040000*x^2 - 226000*x^3 + 226000*x^4 + 10000*x^5 - 2000*x^6)*Log[2]
^3 + (42000000 + 7700000*x - 3585000*x^2 - 670250*x^3 + 66250*x^4 + 11250*x^5 - 250*x^6)*Log[2]^4 + (25200000
+ 8120000*x - 801000*x^2 - 413400*x^3 - 11000*x^4 + 3000*x^5)*Log[2]^5 + (10500000 + 4550000*x + 241250*x^2 -
107250*x^3 - 10250*x^4 + 250*x^5)*Log[2]^6 + (3000000 + 1550000*x + 210000*x^2 - 6000*x^3 - 2000*x^4)*Log[2]^7
+ (562500 + 321875*x + 58125*x^2 + 2625*x^3 - 125*x^4)*Log[2]^8 + (62500 + 37500*x + 7500*x^2 + 500*x^3)*Log[
2]^9 + (3125 + 1875*x + 375*x^2 + 25*x^3)*Log[2]^10),x]
[Out]
(-250*(5 + x)^3 + 25*(5 + x)^4 + (15625*(9 + 625004*Log[2] + Log[2]^2 - 78125*Log[256]))/((5 + x)^2*(9 + Log[2
]^2 + Log[16])^5) - (6250*(153 + 6250024*Log[2]^3 + 3*Log[2]^4 + Log[2]^2*(25000092 - 781250*Log[256]) + 22*Lo
g[256] - 390625*Log[256]^2))/((5 + x)*(9 + Log[2]^2 + Log[16])^6) + 5*(5 + x)^2*(123 + 1000*Log[2]^3 - 125*Log
[2]^2*(-32 + Log[256]) + 125*Log[256] - 500*Log[2]*(2 + Log[256])) + 5*(5 + x)*(9 + 6000*Log[2]^5 + Log[2]*(35
984 - 4000*Log[256]) - 750*Log[2]^4*(-64 + Log[256]) - 4500*Log[256] - 2000*Log[2]^3*(-52 + 3*Log[256]) - 4*Lo
g[2]^2*(-7999 + 3250*Log[256])) + (2*(105000*Log[2]^21 + Log[2]^4*(509505917395848 - 98362046137500*Log[256])
+ Log[2]^7*(840695768299472 - 77659718400000*Log[256]) + Log[2]^8*(621273003570269 - 47116825200000*Log[256])
+ Log[2]^9*(376932653146128 - 23752224800000*Log[256]) + Log[2]*(6609877814336 - 8077469600000*Log[256]) + Log
[2]^11*(80193792752104 - 3554974200000*Log[256]) + Log[2]^12*(28439749586863 - 1059551325000*Log[256]) + Log[2
]^14*(2115639525302 - 54839025000*Log[256]) + Log[2]^18*(1074599980 - 10381250*Log[256]) - 13125*Log[2]^20*(-3
20 + Log[256]) - 25000*Log[2]^19*(-3322 + 21*Log[256]) - 1080*Log[2]^17*(-9414791 + 124375*Log[256]) - 480*Log
[2]^15*(-913983438 + 19419125*Log[256]) - 15*Log[2]^16*(-4971295144 + 84733125*Log[256]) - 56*Log[2]^13*(-1513
64325331 + 4722412500*Log[256]) - 8*(84771504 + 103339429375*Log[256]) - 44*Log[2]^10*(-4318571213443 + 227823
810000*Log[256]) - 32*Log[2]^2*(-2019041042701 + 908512300000*Log[256]) - 72*Log[2]^5*(-10928821828189 + 15929
62560000*Log[256]) - 32*Log[2]^3*(-7267533124262 + 1990345134375*Log[256]) - 14*Log[2]^6*(-65537900426549 + 75
06297600000*Log[256])))/((x - (2 + Log[2])^2)*(9 + Log[2]^2 + Log[16])^6) + (2*(635904 + 133000*Log[2]^21 + Lo
g[2]^8*(724218502907652 - 55520407920000*Log[256]) + Log[2]^9*(444163263880884 - 28284058080000*Log[256]) + Lo
g[2]^10*(226272464756121 - 12056982344000*Log[256]) + Log[2]*(7440988091328 - 8904288160000*Log[256]) + Log[2]
^11*(96455858771272 - 4316127320000*Log[256]) + Log[2]^12*(34529018562259 - 1297536345000*Log[256]) + Log[2]^1
4*(2611015680006 - 68144640000*Log[256]) - 16625*Log[2]^20*(-320 + Log[256]) - 930123051000*Log[256] - 5000*Lo
g[2]^19*(-21006 + 133*Log[256]) - 3750*Log[2]^18*(-361376 + 3501*Log[256]) - 15000*Log[2]^17*(-851504 + 11293*
Log[256]) - 768000*Log[2]^15*(-709840 + 15171*Log[256]) - 6000*Log[2]^16*(-15535104 + 266095*Log[256]) - 168*L
og[2]^13*(-61787445001 + 1942720000*Log[256]) - 256*Log[2]^2*(-278259043661 + 125802197500*Log[256]) - 672*Log
[2]^6*(-1557438222589 + 180314520000*Log[256]) - 192*Log[2]^7*(-5048806584753 + 471496420000*Log[256]) - 96*Lo
g[2]^5*(-9251975900289 + 1362758432000*Log[256]) - 32*Log[2]^3*(-8051341151776 + 2224281774375*Log[256]) - 12*
Log[2]^4*(-47451346076512 + 9251975738125*Log[256])))/(3*(x - (2 + Log[2])^2)^3*(9 + Log[2]^2 + Log[16])^4) -
(-73728 - 34000*Log[2]^21 + 4250*Log[2]^20*(-320 + Log[256]) + 233038666750*Log[256] + 10000*Log[2]^19*(-2684
+ 17*Log[256]) + 5000*Log[2]^18*(-69216 + 671*Log[256]) + 30000*Log[2]^17*(-108631 + 1442*Log[256]) + 24000*Lo
g[2]^15*(-5781740 + 123731*Log[256]) + 750*Log[2]^16*(-31675136 + 543155*Log[256]) + 9472*Log[2]^2*(-188407234
6 + 852161875*Log[256]) + 2*Log[2]^14*(-331811520001 + 8672610000*Log[256]) + 8*Log[2]^13*(-329263766257 + 103
69110000*Log[256]) + 1536*Log[2]^7*(-158704085737 + 14839323125*Log[256]) + 1536*Log[2]^6*(-171164069386 + 198
38010625*Log[256]) + 16*Log[2]^11*(-1524742681379 + 68341169375*Log[256]) + 64*Log[2]^9*(-1749810909777 + 1115
96231875*Log[256]) + 16*Log[2]*(-116519363071 + 139421342500*Log[256]) + 96*Log[2]^8*(-1899433364829 + 1458175
75625*Log[256]) + 16*Log[2]^10*(-3571079422167 + 190592835125*Log[256]) + Log[2]^12*(-8747669680738 + 32926376
6250*Log[256]) + 8*Log[2]^3*(-8071677607168 + 2231255214375*Log[256]) + 8*Log[2]^5*(-27864031277351 + 41079376
32000*Log[256]) + Log[2]^4*(-142800337037248 + 27864030894375*Log[256]))/(2*(x - (2 + Log[2])^2)^4*(9 + Log[2]
^2 + Log[16])^3) - (149250816 - 189000*Log[2]^21 + 23625*Log[2]^20*(-320 + Log[256]) + 1377219520500*Log[256]
+ 15000*Log[2]^19*(-9956 + 63*Log[256]) + 2160*Log[2]^17*(-8428729 + 111625*Log[256]) + 10*Log[2]^18*(-1928879
99 + 1866750*Log[256]) + 160*Log[2]^15*(-4875830542 + 103985775*Log[256]) + 5*Log[2]^16*(-26620357126 + 455151
375*Log[256]) + 56*Log[2]^13*(-266638272293 + 8360730000*Log[256]) + 1536*Log[2]^2*(-68761673581 + 31044389375
*Log[256]) + Log[2]^14*(-3745606427906 + 97516620000*Log[256]) + 96*Log[2]*(-114758597503 + 137526942500*Log[2
56]) + 1008*Log[2]^6*(-1526489454811 + 176222040000*Log[256]) + 32*Log[2]^11*(-4362505361801 + 194596858125*Lo
g[256]) + 4*Log[2]^12*(-12454193899711 + 466617099375*Log[256]) + 144*Log[2]^3*(-2649085199408 + 730362938125*
Log[256]) + 112*Log[2]^5*(-11689969409567 + 1717306848000*Log[256]) + 16*Log[2]^7*(-88815685965221 + 826879572
0000*Log[256]) + Log[2]^10*(-328548217728871 + 17450031852000*Log[256]) + 6*Log[2]^4*(-140228528779024 + 27276
741294375*Log[256]) + Log[2]^9*(-64703797689268...
________________________________________________________________________________________
Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(531\) vs.
\(2(37)=74\).
time = 0.72, size = 532, normalized size = 13.64 Too large to display
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((100*x^6+2250*x^5+20000*x^4+87525*x^3+187875*x^2+158125*x+3125)*ln(2)^10+(2000*x^6+45000*x^5+400000*x^4+1
750500*x^3+3757500*x^2+3162500*x+62500)*ln(2)^9+(-500*x^7+6750*x^6+305000*x^5+3162375*x^4+14815125*x^3+3302687
5*x^2+28446875*x+562500)*ln(2)^8+(-8000*x^7-84000*x^6+560000*x^5+12198000*x^4+68994000*x^3+167710000*x^2+15155
0000*x+3000000)*ln(2)^7+(1000*x^8-33500*x^7-724040*x^6-2765350*x^5+20061750*x^4+190450250*x^3+542741250*x^2+52
9550000*x+10500000)*ln(2)^6+(12000*x^8+46000*x^7-1834080*x^6-16160200*x^5-12267000*x^4+303876600*x^3+116119900
0*x^2+1268120000*x+25200000)*ln(2)^5+(-1000*x^9+37500*x^8+590100*x^7-132150*x^6-31152250*x^5-110363750*x^4+218
779750*x^3+1641415000*x^2+2107700000*x+42000000)*ln(2)^4+(-8000*x^9-20000*x^8+1104800*x^7+6379600*x^6-19666000
*x^5-189454000*x^4-87026000*x^3+1473960000*x^2+2400800000*x+48000000)*ln(2)^3+(500*x^10-12750*x^9-200080*x^8+1
42825*x^7+8945779*x^6+12506655*x^5-141278375*x^4-297522000*x^3+755020000*x^2+1793600000*x+36000000)*ln(2)^2+(2
000*x^10+13000*x^9-128320*x^8-843100*x^7+3157836*x^6+20295420*x^5-35721500*x^4-212152000*x^3+158320000*x^2+793
600000*x+16000000)*ln(2)-100*x^11-250*x^10+9020*x^9+16455*x^8-327075*x^7-382279*x^6+5861095*x^5+3458500*x^4-50
474400*x^3-8016000*x^2+157920000*x+3200000)/((25*x^3+375*x^2+1875*x+3125)*ln(2)^10+(500*x^3+7500*x^2+37500*x+6
2500)*ln(2)^9+(-125*x^4+2625*x^3+58125*x^2+321875*x+562500)*ln(2)^8+(-2000*x^4-6000*x^3+210000*x^2+1550000*x+3
000000)*ln(2)^7+(250*x^5-10250*x^4-107250*x^3+241250*x^2+4550000*x+10500000)*ln(2)^6+(3000*x^5-11000*x^4-41340
0*x^3-801000*x^2+8120000*x+25200000)*ln(2)^5+(-250*x^6+11250*x^5+66250*x^4-670250*x^3-3585000*x^2+7700000*x+42
000000)*ln(2)^4+(-2000*x^6+10000*x^5+226000*x^4-226000*x^3-6040000*x^2+800000*x+48000000)*ln(2)^3+(125*x^7-412
5*x^6-20625*x^5+241625*x^4+678000*x^3-4980000*x^2-6400000*x+36000000)*ln(2)^2+(500*x^7-500*x^6-34500*x^5+54500
*x^4+808000*x^3-1680000*x^2-6400000*x+16000000)*ln(2)-25*x^8+125*x^7+1625*x^6-9625*x^5-29500*x^4+245600*x^3-16
000*x^2-2080000*x+3200000),x,method=_RETURNVERBOSE)
[Out]
x^4+10*x^3+123/5*x^2-4/5*x*ln(2)^2-16/5*x*ln(2)-11/5*x-1/75*(-12*ln(2)^12-288*ln(2)^11-3258*ln(2)^10-22920*ln(
2)^9-111240*ln(2)^8-390528*ln(2)^7-1012032*ln(2)^6-1942272*ln(2)^5-2730240*ln(2)^4-2734080*ln(2)^3-1847808*ln(
2)^2-755712*ln(2)-141312)/(ln(2)^2+4*ln(2)+9)^3/(-ln(2)^2-4*ln(2)+x-4)^3-1/100*(-4*ln(2)^12-96*ln(2)^11-1056*l
n(2)^10-7040*ln(2)^9-31680*ln(2)^8-101376*ln(2)^7-236544*ln(2)^6-405504*ln(2)^5-506880*ln(2)^4-450560*ln(2)^3-
270336*ln(2)^2-98304*ln(2)-16384)/(ln(2)^2+4*ln(2)+9)^2/(-ln(2)^2-4*ln(2)+x-4)^4-1/50*(20*ln(2)^16+640*ln(2)^1
5+10000*ln(2)^14+100800*ln(2)^13+730988*ln(2)^12+4032032*ln(2)^11+17455292*ln(2)^10+60367280*ln(2)^9+168215510
*ln(2)^8+378207072*ln(2)^7+682520608*ln(2)^6+976286848*ln(2)^5+1082884160*ln(2)^4+898398720*ln(2)^3+524539392*
ln(2)^2+192104448*ln(2)+33166848)/(ln(2)^2+4*ln(2)+9)^4/(-ln(2)^2-4*ln(2)+x-4)^2-1/25*(40*ln(2)^16+1280*ln(2)^
15+20200*ln(2)^14+207200*ln(2)^13+1538796*ln(2)^12+8742944*ln(2)^11+39205334*ln(2)^10+141227960*ln(2)^9+412257
170*ln(2)^8+976827424*ln(2)^7+1869635236*ln(2)^6+2855813296*ln(2)^5+3407206320*ln(2)^4+3063795840*ln(2)^3+1953
968064*ln(2)^2+787612416*ln(2)+150704896)/(ln(2)^2+4*ln(2)+9)^5/(-ln(2)^2-4*ln(2)+x-4)-1/25/(ln(2)^2+4*ln(2)+9
)^5*(18750*ln(2)^2+75000*ln(2)+106250)/(5+x)+625/(ln(2)^2+4*ln(2)+9)^4/(5+x)^2
________________________________________________________________________________________
Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 648 vs.
\(2 (38) = 76\).
time = 0.31, size = 648, normalized size = 16.62 \begin {gather*} x^{4} + 10 \, x^{3} - \frac {1}{5} \, {\left (4 \, \log \left (2\right )^{2} + 16 \, \log \left (2\right ) + 11\right )} x + \frac {123}{5} \, x^{2} + \frac {750 \, \log \left (2\right )^{12} + 18000 \, \log \left (2\right )^{11} + 198000 \, \log \left (2\right )^{10} + 1320000 \, \log \left (2\right )^{9} + 5939975 \, \log \left (2\right )^{8} + 19007600 \, \log \left (2\right )^{7} - 2 \, {\left (20 \, \log \left (2\right )^{6} + 240 \, \log \left (2\right )^{5} + 1200 \, \log \left (2\right )^{4} + 3200 \, \log \left (2\right )^{3} + 4798 \, \log \left (2\right )^{2} + 3832 \, \log \left (2\right ) + 1277\right )} x^{5} + 44349200 \, \log \left (2\right )^{6} + {\left (110 \, \log \left (2\right )^{8} + 1760 \, \log \left (2\right )^{7} + 11920 \, \log \left (2\right )^{6} + 44480 \, \log \left (2\right )^{5} + 99194 \, \log \left (2\right )^{4} + 133072 \, \log \left (2\right )^{3} + 101016 \, \log \left (2\right )^{2} + 35808 \, \log \left (2\right ) + 2599\right )} x^{4} + 76020800 \, \log \left (2\right )^{5} - 4 \, {\left (25 \, \log \left (2\right )^{10} + 500 \, \log \left (2\right )^{9} + 4225 \, \log \left (2\right )^{8} + 19600 \, \log \left (2\right )^{7} + 53449 \, \log \left (2\right )^{6} + 81388 \, \log \left (2\right )^{5} + 42955 \, \log \left (2\right )^{4} - 68840 \, \log \left (2\right )^{3} - 144705 \, \log \left (2\right )^{2} - 105412 \, \log \left (2\right ) - 28724\right )} x^{3} + 95012000 \, \log \left (2\right )^{4} + {\left (30 \, \log \left (2\right )^{12} + 720 \, \log \left (2\right )^{11} + 6920 \, \log \left (2\right )^{10} + 32800 \, \log \left (2\right )^{9} + 60349 \, \log \left (2\right )^{8} - 155696 \, \log \left (2\right )^{7} - 1277992 \, \log \left (2\right )^{6} - 3790688 \, \log \left (2\right )^{5} - 6557270 \, \log \left (2\right )^{4} - 7049392 \, \log \left (2\right )^{3} - 4560272 \, \log \left (2\right )^{2} - 1564864 \, \log \left (2\right ) - 197216\right )} x^{2} + 84435200 \, \log \left (2\right )^{3} + 10 \, {\left (30 \, \log \left (2\right )^{12} + 720 \, \log \left (2\right )^{11} + 7670 \, \log \left (2\right )^{10} + 47800 \, \log \left (2\right )^{9} + 192599 \, \log \left (2\right )^{8} + 520304 \, \log \left (2\right )^{7} + 933978 \, \log \left (2\right )^{6} + 1024952 \, \log \left (2\right )^{5} + 441080 \, \log \left (2\right )^{4} - 460992 \, \log \left (2\right )^{3} - 851872 \, \log \left (2\right )^{2} - 541824 \, \log \left (2\right ) - 132736\right )} x + 50643200 \, \log \left (2\right )^{2} + 18406400 \, \log \left (2\right ) + 3065600}{25 \, {\left (25 \, \log \left (2\right )^{8} + 400 \, \log \left (2\right )^{7} - 2 \, {\left (2 \, \log \left (2\right )^{2} + 8 \, \log \left (2\right ) + 3\right )} x^{5} + x^{6} + 2800 \, \log \left (2\right )^{6} + {\left (6 \, \log \left (2\right )^{4} + 48 \, \log \left (2\right )^{3} + 104 \, \log \left (2\right )^{2} + 32 \, \log \left (2\right ) - 39\right )} x^{4} + 11200 \, \log \left (2\right )^{5} - 4 \, {\left (\log \left (2\right )^{6} + 12 \, \log \left (2\right )^{5} + 45 \, \log \left (2\right )^{4} + 40 \, \log \left (2\right )^{3} - 95 \, \log \left (2\right )^{2} - 188 \, \log \left (2\right ) - 76\right )} x^{3} + 28000 \, \log \left (2\right )^{4} + {\left (\log \left (2\right )^{8} + 16 \, \log \left (2\right )^{7} + 72 \, \log \left (2\right )^{6} - 32 \, \log \left (2\right )^{5} - 1130 \, \log \left (2\right )^{4} - 3408 \, \log \left (2\right )^{3} - 4208 \, \log \left (2\right )^{2} - 1856 \, \log \left (2\right ) + 96\right )} x^{2} + 44800 \, \log \left (2\right )^{3} + 10 \, {\left (\log \left (2\right )^{8} + 16 \, \log \left (2\right )^{7} + 102 \, \log \left (2\right )^{6} + 328 \, \log \left (2\right )^{5} + 520 \, \log \left (2\right )^{4} + 192 \, \log \left (2\right )^{3} - 608 \, \log \left (2\right )^{2} - 896 \, \log \left (2\right ) - 384\right )} x + 44800 \, \log \left (2\right )^{2} + 25600 \, \log \left (2\right ) + 6400\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((100*x^6+2250*x^5+20000*x^4+87525*x^3+187875*x^2+158125*x+3125)*log(2)^10+(2000*x^6+45000*x^5+40000
0*x^4+1750500*x^3+3757500*x^2+3162500*x+62500)*log(2)^9+(-500*x^7+6750*x^6+305000*x^5+3162375*x^4+14815125*x^3
+33026875*x^2+28446875*x+562500)*log(2)^8+(-8000*x^7-84000*x^6+560000*x^5+12198000*x^4+68994000*x^3+167710000*
x^2+151550000*x+3000000)*log(2)^7+(1000*x^8-33500*x^7-724040*x^6-2765350*x^5+20061750*x^4+190450250*x^3+542741
250*x^2+529550000*x+10500000)*log(2)^6+(12000*x^8+46000*x^7-1834080*x^6-16160200*x^5-12267000*x^4+303876600*x^
3+1161199000*x^2+1268120000*x+25200000)*log(2)^5+(-1000*x^9+37500*x^8+590100*x^7-132150*x^6-31152250*x^5-11036
3750*x^4+218779750*x^3+1641415000*x^2+2107700000*x+42000000)*log(2)^4+(-8000*x^9-20000*x^8+1104800*x^7+6379600
*x^6-19666000*x^5-189454000*x^4-87026000*x^3+1473960000*x^2+2400800000*x+48000000)*log(2)^3+(500*x^10-12750*x^
9-200080*x^8+142825*x^7+8945779*x^6+12506655*x^5-141278375*x^4-297522000*x^3+755020000*x^2+1793600000*x+360000
00)*log(2)^2+(2000*x^10+13000*x^9-128320*x^8-843100*x^7+3157836*x^6+20295420*x^5-35721500*x^4-212152000*x^3+15
8320000*x^2+793600000*x+16000000)*log(2)-100*x^11-250*x^10+9020*x^9+16455*x^8-327075*x^7-382279*x^6+5861095*x^
5+3458500*x^4-50474400*x^3-8016000*x^2+157920000*x+3200000)/((25*x^3+375*x^2+1875*x+3125)*log(2)^10+(500*x^3+7
500*x^2+37500*x+62500)*log(2)^9+(-125*x^4+2625*x^3+58125*x^2+321875*x+562500)*log(2)^8+(-2000*x^4-6000*x^3+210
000*x^2+1550000*x+3000000)*log(2)^7+(250*x^5-10250*x^4-107250*x^3+241250*x^2+4550000*x+10500000)*log(2)^6+(300
0*x^5-11000*x^4-413400*x^3-801000*x^2+8120000*x+25200000)*log(2)^5+(-250*x^6+11250*x^5+66250*x^4-670250*x^3-35
85000*x^2+7700000*x+42000000)*log(2)^4+(-2000*x^6+10000*x^5+226000*x^4-226000*x^3-6040000*x^2+800000*x+4800000
0)*log(2)^3+(125*x^7-4125*x^6-20625*x^5+241625*x^4+678000*x^3-4980000*x^2-6400000*x+36000000)*log(2)^2+(500*x^
7-500*x^6-34500*x^5+54500*x^4+808000*x^3-1680000*x^2-6400000*x+16000000)*log(2)-25*x^8+125*x^7+1625*x^6-9625*x
^5-29500*x^4+245600*x^3-16000*x^2-2080000*x+3200000),x, algorithm="maxima")
[Out]
x^4 + 10*x^3 - 1/5*(4*log(2)^2 + 16*log(2) + 11)*x + 123/5*x^2 + 1/25*(750*log(2)^12 + 18000*log(2)^11 + 19800
0*log(2)^10 + 1320000*log(2)^9 + 5939975*log(2)^8 + 19007600*log(2)^7 - 2*(20*log(2)^6 + 240*log(2)^5 + 1200*l
og(2)^4 + 3200*log(2)^3 + 4798*log(2)^2 + 3832*log(2) + 1277)*x^5 + 44349200*log(2)^6 + (110*log(2)^8 + 1760*l
og(2)^7 + 11920*log(2)^6 + 44480*log(2)^5 + 99194*log(2)^4 + 133072*log(2)^3 + 101016*log(2)^2 + 35808*log(2)
+ 2599)*x^4 + 76020800*log(2)^5 - 4*(25*log(2)^10 + 500*log(2)^9 + 4225*log(2)^8 + 19600*log(2)^7 + 53449*log(
2)^6 + 81388*log(2)^5 + 42955*log(2)^4 - 68840*log(2)^3 - 144705*log(2)^2 - 105412*log(2) - 28724)*x^3 + 95012
000*log(2)^4 + (30*log(2)^12 + 720*log(2)^11 + 6920*log(2)^10 + 32800*log(2)^9 + 60349*log(2)^8 - 155696*log(2
)^7 - 1277992*log(2)^6 - 3790688*log(2)^5 - 6557270*log(2)^4 - 7049392*log(2)^3 - 4560272*log(2)^2 - 1564864*l
og(2) - 197216)*x^2 + 84435200*log(2)^3 + 10*(30*log(2)^12 + 720*log(2)^11 + 7670*log(2)^10 + 47800*log(2)^9 +
192599*log(2)^8 + 520304*log(2)^7 + 933978*log(2)^6 + 1024952*log(2)^5 + 441080*log(2)^4 - 460992*log(2)^3 -
851872*log(2)^2 - 541824*log(2) - 132736)*x + 50643200*log(2)^2 + 18406400*log(2) + 3065600)/(25*log(2)^8 + 40
0*log(2)^7 - 2*(2*log(2)^2 + 8*log(2) + 3)*x^5 + x^6 + 2800*log(2)^6 + (6*log(2)^4 + 48*log(2)^3 + 104*log(2)^
2 + 32*log(2) - 39)*x^4 + 11200*log(2)^5 - 4*(log(2)^6 + 12*log(2)^5 + 45*log(2)^4 + 40*log(2)^3 - 95*log(2)^2
- 188*log(2) - 76)*x^3 + 28000*log(2)^4 + (log(2)^8 + 16*log(2)^7 + 72*log(2)^6 - 32*log(2)^5 - 1130*log(2)^4
- 3408*log(2)^3 - 4208*log(2)^2 - 1856*log(2) + 96)*x^2 + 44800*log(2)^3 + 10*(log(2)^8 + 16*log(2)^7 + 102*l
og(2)^6 + 328*log(2)^5 + 520*log(2)^4 + 192*log(2)^3 - 608*log(2)^2 - 896*log(2) - 384)*x + 44800*log(2)^2 + 2
5600*log(2) + 6400)
________________________________________________________________________________________
Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 668 vs.
\(2 (38) = 76\).
time = 0.41, size = 668, normalized size = 17.13 \begin {gather*} \frac {30 \, {\left (x^{2} + 10 \, x + 25\right )} \log \left (2\right )^{12} + 720 \, {\left (x^{2} + 10 \, x + 25\right )} \log \left (2\right )^{11} - 120 \, {\left (x^{3} - 56 \, x^{2} - 635 \, x - 1650\right )} \log \left (2\right )^{10} + 25 \, x^{10} - 2400 \, {\left (x^{3} - 12 \, x^{2} - 195 \, x - 550\right )} \log \left (2\right )^{9} + 100 \, x^{9} + {\left (25 \, x^{6} + 500 \, x^{5} + 3930 \, x^{4} - 7275 \, x^{3} + 41974 \, x^{2} + 1836615 \, x + 5939975\right )} \log \left (2\right )^{8} - 1860 \, x^{8} + 16 \, {\left (25 \, x^{6} + 500 \, x^{5} + 3930 \, x^{4} + 7125 \, x^{3} - 4106 \, x^{2} + 295815 \, x + 1187975\right )} \log \left (2\right )^{7} - 5895 \, x^{7} - 4 \, {\left (25 \, x^{7} - 200 \, x^{6} - 10220 \, x^{5} - 97215 \, x^{4} - 283676 \, x^{3} - 5377 \, x^{2} - 1932445 \, x - 11087300\right )} \log \left (2\right )^{6} + 54745 \, x^{6} - 16 \, {\left (75 \, x^{7} + 800 \, x^{6} - 2660 \, x^{5} - 71565 \, x^{4} - 290748 \, x^{3} - 153907 \, x^{2} - 406095 \, x - 4751300\right )} \log \left (2\right )^{5} + 114551 \, x^{5} + 2 \, {\left (75 \, x^{8} - 1500 \, x^{7} - 34740 \, x^{6} - 135925 \, x^{5} + 709672 \, x^{4} + 5222565 \, x^{3} + 5172365 \, x^{2} - 804600 \, x + 47506000\right )} \log \left (2\right )^{4} - 755081 \, x^{4} + 16 \, {\left (75 \, x^{8} + 500 \, x^{7} - 5940 \, x^{6} - 57525 \, x^{5} - 24968 \, x^{4} + 826085 \, x^{3} + 1316413 \, x^{2} - 698120 \, x + 5277200\right )} \log \left (2\right )^{3} - 651984 \, x^{3} - 4 \, {\left (25 \, x^{9} - 400 \, x^{8} - 8255 \, x^{7} - 13845 \, x^{6} + 246849 \, x^{5} + 743511 \, x^{4} - 2104405 \, x^{3} - 6029932 \, x^{2} + 3289680 \, x - 12660800\right )} \log \left (2\right )^{2} + 3949984 \, x^{2} - 16 \, {\left (25 \, x^{9} + 200 \, x^{8} - 1055 \, x^{7} - 10165 \, x^{6} + 14489 \, x^{5} + 173207 \, x^{4} - 87853 \, x^{3} - 936196 \, x^{2} + 458640 \, x - 1150400\right )} \log \left (2\right ) - 1679360 \, x + 3065600}{25 \, {\left ({\left (x^{2} + 10 \, x + 25\right )} \log \left (2\right )^{8} + 16 \, {\left (x^{2} + 10 \, x + 25\right )} \log \left (2\right )^{7} - 4 \, {\left (x^{3} - 18 \, x^{2} - 255 \, x - 700\right )} \log \left (2\right )^{6} + x^{6} - 16 \, {\left (3 \, x^{3} + 2 \, x^{2} - 205 \, x - 700\right )} \log \left (2\right )^{5} - 6 \, x^{5} + 2 \, {\left (3 \, x^{4} - 90 \, x^{3} - 565 \, x^{2} + 2600 \, x + 14000\right )} \log \left (2\right )^{4} - 39 \, x^{4} + 16 \, {\left (3 \, x^{4} - 10 \, x^{3} - 213 \, x^{2} + 120 \, x + 2800\right )} \log \left (2\right )^{3} + 304 \, x^{3} - 4 \, {\left (x^{5} - 26 \, x^{4} - 95 \, x^{3} + 1052 \, x^{2} + 1520 \, x - 11200\right )} \log \left (2\right )^{2} + 96 \, x^{2} - 16 \, {\left (x^{5} - 2 \, x^{4} - 47 \, x^{3} + 116 \, x^{2} + 560 \, x - 1600\right )} \log \left (2\right ) - 3840 \, x + 6400\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((100*x^6+2250*x^5+20000*x^4+87525*x^3+187875*x^2+158125*x+3125)*log(2)^10+(2000*x^6+45000*x^5+40000
0*x^4+1750500*x^3+3757500*x^2+3162500*x+62500)*log(2)^9+(-500*x^7+6750*x^6+305000*x^5+3162375*x^4+14815125*x^3
+33026875*x^2+28446875*x+562500)*log(2)^8+(-8000*x^7-84000*x^6+560000*x^5+12198000*x^4+68994000*x^3+167710000*
x^2+151550000*x+3000000)*log(2)^7+(1000*x^8-33500*x^7-724040*x^6-2765350*x^5+20061750*x^4+190450250*x^3+542741
250*x^2+529550000*x+10500000)*log(2)^6+(12000*x^8+46000*x^7-1834080*x^6-16160200*x^5-12267000*x^4+303876600*x^
3+1161199000*x^2+1268120000*x+25200000)*log(2)^5+(-1000*x^9+37500*x^8+590100*x^7-132150*x^6-31152250*x^5-11036
3750*x^4+218779750*x^3+1641415000*x^2+2107700000*x+42000000)*log(2)^4+(-8000*x^9-20000*x^8+1104800*x^7+6379600
*x^6-19666000*x^5-189454000*x^4-87026000*x^3+1473960000*x^2+2400800000*x+48000000)*log(2)^3+(500*x^10-12750*x^
9-200080*x^8+142825*x^7+8945779*x^6+12506655*x^5-141278375*x^4-297522000*x^3+755020000*x^2+1793600000*x+360000
00)*log(2)^2+(2000*x^10+13000*x^9-128320*x^8-843100*x^7+3157836*x^6+20295420*x^5-35721500*x^4-212152000*x^3+15
8320000*x^2+793600000*x+16000000)*log(2)-100*x^11-250*x^10+9020*x^9+16455*x^8-327075*x^7-382279*x^6+5861095*x^
5+3458500*x^4-50474400*x^3-8016000*x^2+157920000*x+3200000)/((25*x^3+375*x^2+1875*x+3125)*log(2)^10+(500*x^3+7
500*x^2+37500*x+62500)*log(2)^9+(-125*x^4+2625*x^3+58125*x^2+321875*x+562500)*log(2)^8+(-2000*x^4-6000*x^3+210
000*x^2+1550000*x+3000000)*log(2)^7+(250*x^5-10250*x^4-107250*x^3+241250*x^2+4550000*x+10500000)*log(2)^6+(300
0*x^5-11000*x^4-413400*x^3-801000*x^2+8120000*x+25200000)*log(2)^5+(-250*x^6+11250*x^5+66250*x^4-670250*x^3-35
85000*x^2+7700000*x+42000000)*log(2)^4+(-2000*x^6+10000*x^5+226000*x^4-226000*x^3-6040000*x^2+800000*x+4800000
0)*log(2)^3+(125*x^7-4125*x^6-20625*x^5+241625*x^4+678000*x^3-4980000*x^2-6400000*x+36000000)*log(2)^2+(500*x^
7-500*x^6-34500*x^5+54500*x^4+808000*x^3-1680000*x^2-6400000*x+16000000)*log(2)-25*x^8+125*x^7+1625*x^6-9625*x
^5-29500*x^4+245600*x^3-16000*x^2-2080000*x+3200000),x, algorithm="fricas")
[Out]
1/25*(30*(x^2 + 10*x + 25)*log(2)^12 + 720*(x^2 + 10*x + 25)*log(2)^11 - 120*(x^3 - 56*x^2 - 635*x - 1650)*log
(2)^10 + 25*x^10 - 2400*(x^3 - 12*x^2 - 195*x - 550)*log(2)^9 + 100*x^9 + (25*x^6 + 500*x^5 + 3930*x^4 - 7275*
x^3 + 41974*x^2 + 1836615*x + 5939975)*log(2)^8 - 1860*x^8 + 16*(25*x^6 + 500*x^5 + 3930*x^4 + 7125*x^3 - 4106
*x^2 + 295815*x + 1187975)*log(2)^7 - 5895*x^7 - 4*(25*x^7 - 200*x^6 - 10220*x^5 - 97215*x^4 - 283676*x^3 - 53
77*x^2 - 1932445*x - 11087300)*log(2)^6 + 54745*x^6 - 16*(75*x^7 + 800*x^6 - 2660*x^5 - 71565*x^4 - 290748*x^3
- 153907*x^2 - 406095*x - 4751300)*log(2)^5 + 114551*x^5 + 2*(75*x^8 - 1500*x^7 - 34740*x^6 - 135925*x^5 + 70
9672*x^4 + 5222565*x^3 + 5172365*x^2 - 804600*x + 47506000)*log(2)^4 - 755081*x^4 + 16*(75*x^8 + 500*x^7 - 594
0*x^6 - 57525*x^5 - 24968*x^4 + 826085*x^3 + 1316413*x^2 - 698120*x + 5277200)*log(2)^3 - 651984*x^3 - 4*(25*x
^9 - 400*x^8 - 8255*x^7 - 13845*x^6 + 246849*x^5 + 743511*x^4 - 2104405*x^3 - 6029932*x^2 + 3289680*x - 126608
00)*log(2)^2 + 3949984*x^2 - 16*(25*x^9 + 200*x^8 - 1055*x^7 - 10165*x^6 + 14489*x^5 + 173207*x^4 - 87853*x^3
- 936196*x^2 + 458640*x - 1150400)*log(2) - 1679360*x + 3065600)/((x^2 + 10*x + 25)*log(2)^8 + 16*(x^2 + 10*x
+ 25)*log(2)^7 - 4*(x^3 - 18*x^2 - 255*x - 700)*log(2)^6 + x^6 - 16*(3*x^3 + 2*x^2 - 205*x - 700)*log(2)^5 - 6
*x^5 + 2*(3*x^4 - 90*x^3 - 565*x^2 + 2600*x + 14000)*log(2)^4 - 39*x^4 + 16*(3*x^4 - 10*x^3 - 213*x^2 + 120*x
+ 2800)*log(2)^3 + 304*x^3 - 4*(x^5 - 26*x^4 - 95*x^3 + 1052*x^2 + 1520*x - 11200)*log(2)^2 + 96*x^2 - 16*(x^5
- 2*x^4 - 47*x^3 + 116*x^2 + 560*x - 1600)*log(2) - 3840*x + 6400)
________________________________________________________________________________________
Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 728 vs.
\(2 (31) = 62\).
time = 26.86, size = 728, normalized size = 18.67 \begin {gather*} x^{4} + 10 x^{3} + \frac {123 x^{2}}{5} + x \left (- \frac {16 \log {\left (2 \right )}}{5} - \frac {11}{5} - \frac {4 \log {\left (2 \right )}^{2}}{5}\right ) + \frac {x^{5} \left (- 7664 \log {\left (2 \right )} - 9596 \log {\left (2 \right )}^{2} - 2554 - 6400 \log {\left (2 \right )}^{3} - 2400 \log {\left (2 \right )}^{4} - 480 \log {\left (2 \right )}^{5} - 40 \log {\left (2 \right )}^{6}\right ) + x^{4} \cdot \left (110 \log {\left (2 \right )}^{8} + 1760 \log {\left (2 \right )}^{7} + 11920 \log {\left (2 \right )}^{6} + 2599 + 44480 \log {\left (2 \right )}^{5} + 99194 \log {\left (2 \right )}^{4} + 35808 \log {\left (2 \right )} + 133072 \log {\left (2 \right )}^{3} + 101016 \log {\left (2 \right )}^{2}\right ) + x^{3} \left (- 325552 \log {\left (2 \right )}^{5} - 171820 \log {\left (2 \right )}^{4} - 213796 \log {\left (2 \right )}^{6} - 78400 \log {\left (2 \right )}^{7} - 16900 \log {\left (2 \right )}^{8} - 2000 \log {\left (2 \right )}^{9} - 100 \log {\left (2 \right )}^{10} + 275360 \log {\left (2 \right )}^{3} + 114896 + 578820 \log {\left (2 \right )}^{2} + 421648 \log {\left (2 \right )}\right ) + x^{2} \left (- 7049392 \log {\left (2 \right )}^{3} - 4560272 \log {\left (2 \right )}^{2} - 6557270 \log {\left (2 \right )}^{4} - 1564864 \log {\left (2 \right )} - 3790688 \log {\left (2 \right )}^{5} - 197216 - 1277992 \log {\left (2 \right )}^{6} - 155696 \log {\left (2 \right )}^{7} + 30 \log {\left (2 \right )}^{12} + 720 \log {\left (2 \right )}^{11} + 6920 \log {\left (2 \right )}^{10} + 32800 \log {\left (2 \right )}^{9} + 60349 \log {\left (2 \right )}^{8}\right ) + x \left (- 8518720 \log {\left (2 \right )}^{2} - 5418240 \log {\left (2 \right )} - 4609920 \log {\left (2 \right )}^{3} - 1327360 + 300 \log {\left (2 \right )}^{12} + 7200 \log {\left (2 \right )}^{11} + 76700 \log {\left (2 \right )}^{10} + 478000 \log {\left (2 \right )}^{9} + 1925990 \log {\left (2 \right )}^{8} + 5203040 \log {\left (2 \right )}^{7} + 4410800 \log {\left (2 \right )}^{4} + 9339780 \log {\left (2 \right )}^{6} + 10249520 \log {\left (2 \right )}^{5}\right ) + 750 \log {\left (2 \right )}^{12} + 18000 \log {\left (2 \right )}^{11} + 198000 \log {\left (2 \right )}^{10} + 1320000 \log {\left (2 \right )}^{9} + 5939975 \log {\left (2 \right )}^{8} + 19007600 \log {\left (2 \right )}^{7} + 3065600 + 44349200 \log {\left (2 \right )}^{6} + 76020800 \log {\left (2 \right )}^{5} + 18406400 \log {\left (2 \right )} + 95012000 \log {\left (2 \right )}^{4} + 50643200 \log {\left (2 \right )}^{2} + 84435200 \log {\left (2 \right )}^{3}}{25 x^{6} + x^{5} \left (- 400 \log {\left (2 \right )} - 150 - 100 \log {\left (2 \right )}^{2}\right ) + x^{4} \left (-975 + 150 \log {\left (2 \right )}^{4} + 1200 \log {\left (2 \right )}^{3} + 800 \log {\left (2 \right )} + 2600 \log {\left (2 \right )}^{2}\right ) + x^{3} \left (- 4000 \log {\left (2 \right )}^{3} - 4500 \log {\left (2 \right )}^{4} - 1200 \log {\left (2 \right )}^{5} - 100 \log {\left (2 \right )}^{6} + 9500 \log {\left (2 \right )}^{2} + 7600 + 18800 \log {\left (2 \right )}\right ) + x^{2} \left (- 105200 \log {\left (2 \right )}^{2} - 46400 \log {\left (2 \right )} - 85200 \log {\left (2 \right )}^{3} - 28250 \log {\left (2 \right )}^{4} - 800 \log {\left (2 \right )}^{5} + 25 \log {\left (2 \right )}^{8} + 400 \log {\left (2 \right )}^{7} + 1800 \log {\left (2 \right )}^{6} + 2400\right ) + x \left (- 224000 \log {\left (2 \right )} - 96000 - 152000 \log {\left (2 \right )}^{2} + 250 \log {\left (2 \right )}^{8} + 4000 \log {\left (2 \right )}^{7} + 25500 \log {\left (2 \right )}^{6} + 82000 \log {\left (2 \right )}^{5} + 48000 \log {\left (2 \right )}^{3} + 130000 \log {\left (2 \right )}^{4}\right ) + 625 \log {\left (2 \right )}^{8} + 10000 \log {\left (2 \right )}^{7} + 70000 \log {\left (2 \right )}^{6} + 280000 \log {\left (2 \right )}^{5} + 160000 + 700000 \log {\left (2 \right )}^{4} + 1120000 \log {\left (2 \right )}^{3} + 640000 \log {\left (2 \right )} + 1120000 \log {\left (2 \right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((100*x**6+2250*x**5+20000*x**4+87525*x**3+187875*x**2+158125*x+3125)*ln(2)**10+(2000*x**6+45000*x**
5+400000*x**4+1750500*x**3+3757500*x**2+3162500*x+62500)*ln(2)**9+(-500*x**7+6750*x**6+305000*x**5+3162375*x**
4+14815125*x**3+33026875*x**2+28446875*x+562500)*ln(2)**8+(-8000*x**7-84000*x**6+560000*x**5+12198000*x**4+689
94000*x**3+167710000*x**2+151550000*x+3000000)*ln(2)**7+(1000*x**8-33500*x**7-724040*x**6-2765350*x**5+2006175
0*x**4+190450250*x**3+542741250*x**2+529550000*x+10500000)*ln(2)**6+(12000*x**8+46000*x**7-1834080*x**6-161602
00*x**5-12267000*x**4+303876600*x**3+1161199000*x**2+1268120000*x+25200000)*ln(2)**5+(-1000*x**9+37500*x**8+59
0100*x**7-132150*x**6-31152250*x**5-110363750*x**4+218779750*x**3+1641415000*x**2+2107700000*x+42000000)*ln(2)
**4+(-8000*x**9-20000*x**8+1104800*x**7+6379600*x**6-19666000*x**5-189454000*x**4-87026000*x**3+1473960000*x**
2+2400800000*x+48000000)*ln(2)**3+(500*x**10-12750*x**9-200080*x**8+142825*x**7+8945779*x**6+12506655*x**5-141
278375*x**4-297522000*x**3+755020000*x**2+1793600000*x+36000000)*ln(2)**2+(2000*x**10+13000*x**9-128320*x**8-8
43100*x**7+3157836*x**6+20295420*x**5-35721500*x**4-212152000*x**3+158320000*x**2+793600000*x+16000000)*ln(2)-
100*x**11-250*x**10+9020*x**9+16455*x**8-327075*x**7-382279*x**6+5861095*x**5+3458500*x**4-50474400*x**3-80160
00*x**2+157920000*x+3200000)/((25*x**3+375*x**2+1875*x+3125)*ln(2)**10+(500*x**3+7500*x**2+37500*x+62500)*ln(2
)**9+(-125*x**4+2625*x**3+58125*x**2+321875*x+562500)*ln(2)**8+(-2000*x**4-6000*x**3+210000*x**2+1550000*x+300
0000)*ln(2)**7+(250*x**5-10250*x**4-107250*x**3+241250*x**2+4550000*x+10500000)*ln(2)**6+(3000*x**5-11000*x**4
-413400*x**3-801000*x**2+8120000*x+25200000)*ln(2)**5+(-250*x**6+11250*x**5+66250*x**4-670250*x**3-3585000*x**
2+7700000*x+42000000)*ln(2)**4+(-2000*x**6+10000*x**5+226000*x**4-226000*x**3-6040000*x**2+800000*x+48000000)*
ln(2)**3+(125*x**7-4125*x**6-20625*x**5+241625*x**4+678000*x**3-4980000*x**2-6400000*x+36000000)*ln(2)**2+(500
*x**7-500*x**6-34500*x**5+54500*x**4+808000*x**3-1680000*x**2-6400000*x+16000000)*ln(2)-25*x**8+125*x**7+1625*
x**6-9625*x**5-29500*x**4+245600*x**3-16000*x**2-2080000*x+3200000),x)
[Out]
x**4 + 10*x**3 + 123*x**2/5 + x*(-16*log(2)/5 - 11/5 - 4*log(2)**2/5) + (x**5*(-7664*log(2) - 9596*log(2)**2 -
2554 - 6400*log(2)**3 - 2400*log(2)**4 - 480*log(2)**5 - 40*log(2)**6) + x**4*(110*log(2)**8 + 1760*log(2)**7
+ 11920*log(2)**6 + 2599 + 44480*log(2)**5 + 99194*log(2)**4 + 35808*log(2) + 133072*log(2)**3 + 101016*log(2
)**2) + x**3*(-325552*log(2)**5 - 171820*log(2)**4 - 213796*log(2)**6 - 78400*log(2)**7 - 16900*log(2)**8 - 20
00*log(2)**9 - 100*log(2)**10 + 275360*log(2)**3 + 114896 + 578820*log(2)**2 + 421648*log(2)) + x**2*(-7049392
*log(2)**3 - 4560272*log(2)**2 - 6557270*log(2)**4 - 1564864*log(2) - 3790688*log(2)**5 - 197216 - 1277992*log
(2)**6 - 155696*log(2)**7 + 30*log(2)**12 + 720*log(2)**11 + 6920*log(2)**10 + 32800*log(2)**9 + 60349*log(2)*
*8) + x*(-8518720*log(2)**2 - 5418240*log(2) - 4609920*log(2)**3 - 1327360 + 300*log(2)**12 + 7200*log(2)**11
+ 76700*log(2)**10 + 478000*log(2)**9 + 1925990*log(2)**8 + 5203040*log(2)**7 + 4410800*log(2)**4 + 9339780*lo
g(2)**6 + 10249520*log(2)**5) + 750*log(2)**12 + 18000*log(2)**11 + 198000*log(2)**10 + 1320000*log(2)**9 + 59
39975*log(2)**8 + 19007600*log(2)**7 + 3065600 + 44349200*log(2)**6 + 76020800*log(2)**5 + 18406400*log(2) + 9
5012000*log(2)**4 + 50643200*log(2)**2 + 84435200*log(2)**3)/(25*x**6 + x**5*(-400*log(2) - 150 - 100*log(2)**
2) + x**4*(-975 + 150*log(2)**4 + 1200*log(2)**3 + 800*log(2) + 2600*log(2)**2) + x**3*(-4000*log(2)**3 - 4500
*log(2)**4 - 1200*log(2)**5 - 100*log(2)**6 + 9500*log(2)**2 + 7600 + 18800*log(2)) + x**2*(-105200*log(2)**2
- 46400*log(2) - 85200*log(2)**3 - 28250*log(2)**4 - 800*log(2)**5 + 25*log(2)**8 + 400*log(2)**7 + 1800*log(2
)**6 + 2400) + x*(-224000*log(2) - 96000 - 152000*log(2)**2 + 250*log(2)**8 + 4000*log(2)**7 + 25500*log(2)**6
+ 82000*log(2)**5 + 48000*log(2)**3 + 130000*log(2)**4) + 625*log(2)**8 + 10000*log(2)**7 + 70000*log(2)**6 +
280000*log(2)**5 + 160000 + 700000*log(2)**4 + 1120000*log(2)**3 + 640000*log(2) + 1120000*log(2)**2)
________________________________________________________________________________________
Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 785 vs.
\(2 (38) = 76\).
time = 0.45, size = 785, normalized size = 20.13 \begin {gather*} x^{4} + 10 \, x^{3} - \frac {4}{5} \, x \log \left (2\right )^{2} + \frac {123}{5} \, x^{2} - \frac {16}{5} \, x \log \left (2\right ) - \frac {11}{5} \, x - \frac {125 \, {\left (6 \, x \log \left (2\right )^{2} + 24 \, x \log \left (2\right ) + 25 \, \log \left (2\right )^{2} + 34 \, x + 100 \, \log \left (2\right ) + 125\right )}}{{\left (\log \left (2\right )^{10} + 20 \, \log \left (2\right )^{9} + 205 \, \log \left (2\right )^{8} + 1360 \, \log \left (2\right )^{7} + 6410 \, \log \left (2\right )^{6} + 22264 \, \log \left (2\right )^{5} + 57690 \, \log \left (2\right )^{4} + 110160 \, \log \left (2\right )^{3} + 149445 \, \log \left (2\right )^{2} + 131220 \, \log \left (2\right ) + 59049\right )} {\left (x + 5\right )}^{2}} + \frac {30 \, \log \left (2\right )^{22} - 100 \, x \log \left (2\right )^{20} + 1320 \, \log \left (2\right )^{21} + 110 \, x^{2} \log \left (2\right )^{18} - 4000 \, x \log \left (2\right )^{19} + 28470 \, \log \left (2\right )^{20} - 40 \, x^{3} \log \left (2\right )^{16} + 3960 \, x^{2} \log \left (2\right )^{17} - 78500 \, x \log \left (2\right )^{18} + 399600 \, \log \left (2\right )^{19} - 1280 \, x^{3} \log \left (2\right )^{15} + 70070 \, x^{2} \log \left (2\right )^{16} - 1002000 \, x \log \left (2\right )^{17} + 4088699 \, \log \left (2\right )^{18} - 20200 \, x^{3} \log \left (2\right )^{14} + 806080 \, x^{2} \log \left (2\right )^{15} - 9306996 \, x \log \left (2\right )^{16} + 32390604 \, \log \left (2\right )^{17} - 207200 \, x^{3} \log \left (2\right )^{13} + 6733094 \, x^{2} \log \left (2\right )^{14} - 66732672 \, x \log \left (2\right )^{15} + 206023823 \, \log \left (2\right )^{16} - 1538796 \, x^{3} \log \left (2\right )^{12} + 43249192 \, x^{2} \log \left (2\right )^{13} - 382586980 \, x \log \left (2\right )^{14} + 1077137632 \, \log \left (2\right )^{15} - 8742944 \, x^{3} \log \left (2\right )^{11} + 220915726 \, x^{2} \log \left (2\right )^{12} - 1793175280 \, x \log \left (2\right )^{13} + 4701546140 \, \log \left (2\right )^{14} - 39205334 \, x^{3} \log \left (2\right )^{10} + 915824848 \, x^{2} \log \left (2\right )^{11} - 6968730620 \, x \log \left (2\right )^{12} + 17308843024 \, \log \left (2\right )^{13} - 141227960 \, x^{3} \log \left (2\right )^{9} + 3118579909 \, x^{2} \log \left (2\right )^{10} - 22648257696 \, x \log \left (2\right )^{11} + 54086135524 \, \log \left (2\right )^{12} - 412257170 \, x^{3} \log \left (2\right )^{8} + 8775116516 \, x^{2} \log \left (2\right )^{9} - 61817826752 \, x \log \left (2\right )^{10} + 143897946208 \, \log \left (2\right )^{11} - 976827424 \, x^{3} \log \left (2\right )^{7} + 20423276593 \, x^{2} \log \left (2\right )^{8} - 141789944320 \, x \log \left (2\right )^{9} + 326084929632 \, \log \left (2\right )^{10} - 1869635236 \, x^{3} \log \left (2\right )^{6} + 39169875344 \, x^{2} \log \left (2\right )^{7} - 272499913920 \, x \log \left (2\right )^{8} + 627936581760 \, \log \left (2\right )^{9} - 2855813296 \, x^{3} \log \left (2\right )^{5} + 61361642832 \, x^{2} \log \left (2\right )^{6} - 435910241280 \, x \log \left (2\right )^{7} + 1022342006208 \, \log \left (2\right )^{8} - 3407206320 \, x^{3} \log \left (2\right )^{4} + 77339364416 \, x^{2} \log \left (2\right )^{5} - 574046610432 \, x \log \left (2\right )^{6} + 1395605982208 \, \log \left (2\right )^{7} - 3063795840 \, x^{3} \log \left (2\right )^{3} + 76581884256 \, x^{2} \log \left (2\right )^{4} - 611969798144 \, x \log \left (2\right )^{5} + 1577840132096 \, \log \left (2\right )^{6} - 1953968064 \, x^{3} \log \left (2\right )^{2} + 57388078848 \, x^{2} \log \left (2\right )^{3} - 515066270720 \, x \log \left (2\right )^{4} + 1451379318784 \, \log \left (2\right )^{5} - 787612416 \, x^{3} \log \left (2\right ) + 30589860864 \, x^{2} \log \left (2\right )^{2} - 329386270720 \, x \log \left (2\right )^{3} + 1058558581760 \, \log \left (2\right )^{4} - 150704896 \, x^{3} + 10329004032 \, x^{2} \log \left (2\right ) - 150347694080 \, x \log \left (2\right )^{2} + 588840230912 \, \log \left (2\right )^{3} + 1659207936 \, x^{2} - 43608834048 \, x \log \left (2\right ) + 234595868672 \, \log \left (2\right )^{2} - 6036013056 \, x + 59585101824 \, \log \left (2\right ) + 7244824576}{25 \, {\left (\log \left (2\right )^{10} + 20 \, \log \left (2\right )^{9} + 205 \, \log \left (2\right )^{8} + 1360 \, \log \left (2\right )^{7} + 6410 \, \log \left (2\right )^{6} + 22264 \, \log \left (2\right )^{5} + 57690 \, \log \left (2\right )^{4} + 110160 \, \log \left (2\right )^{3} + 149445 \, \log \left (2\right )^{2} + 131220 \, \log \left (2\right ) + 59049\right )} {\left (\log \left (2\right )^{2} - x + 4 \, \log \left (2\right ) + 4\right )}^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((100*x^6+2250*x^5+20000*x^4+87525*x^3+187875*x^2+158125*x+3125)*log(2)^10+(2000*x^6+45000*x^5+40000
0*x^4+1750500*x^3+3757500*x^2+3162500*x+62500)*log(2)^9+(-500*x^7+6750*x^6+305000*x^5+3162375*x^4+14815125*x^3
+33026875*x^2+28446875*x+562500)*log(2)^8+(-8000*x^7-84000*x^6+560000*x^5+12198000*x^4+68994000*x^3+167710000*
x^2+151550000*x+3000000)*log(2)^7+(1000*x^8-33500*x^7-724040*x^6-2765350*x^5+20061750*x^4+190450250*x^3+542741
250*x^2+529550000*x+10500000)*log(2)^6+(12000*x^8+46000*x^7-1834080*x^6-16160200*x^5-12267000*x^4+303876600*x^
3+1161199000*x^2+1268120000*x+25200000)*log(2)^5+(-1000*x^9+37500*x^8+590100*x^7-132150*x^6-31152250*x^5-11036
3750*x^4+218779750*x^3+1641415000*x^2+2107700000*x+42000000)*log(2)^4+(-8000*x^9-20000*x^8+1104800*x^7+6379600
*x^6-19666000*x^5-189454000*x^4-87026000*x^3+1473960000*x^2+2400800000*x+48000000)*log(2)^3+(500*x^10-12750*x^
9-200080*x^8+142825*x^7+8945779*x^6+12506655*x^5-141278375*x^4-297522000*x^3+755020000*x^2+1793600000*x+360000
00)*log(2)^2+(2000*x^10+13000*x^9-128320*x^8-843100*x^7+3157836*x^6+20295420*x^5-35721500*x^4-212152000*x^3+15
8320000*x^2+793600000*x+16000000)*log(2)-100*x^11-250*x^10+9020*x^9+16455*x^8-327075*x^7-382279*x^6+5861095*x^
5+3458500*x^4-50474400*x^3-8016000*x^2+157920000*x+3200000)/((25*x^3+375*x^2+1875*x+3125)*log(2)^10+(500*x^3+7
500*x^2+37500*x+62500)*log(2)^9+(-125*x^4+2625*x^3+58125*x^2+321875*x+562500)*log(2)^8+(-2000*x^4-6000*x^3+210
000*x^2+1550000*x+3000000)*log(2)^7+(250*x^5-10250*x^4-107250*x^3+241250*x^2+4550000*x+10500000)*log(2)^6+(300
0*x^5-11000*x^4-413400*x^3-801000*x^2+8120000*x+25200000)*log(2)^5+(-250*x^6+11250*x^5+66250*x^4-670250*x^3-35
85000*x^2+7700000*x+42000000)*log(2)^4+(-2000*x^6+10000*x^5+226000*x^4-226000*x^3-6040000*x^2+800000*x+4800000
0)*log(2)^3+(125*x^7-4125*x^6-20625*x^5+241625*x^4+678000*x^3-4980000*x^2-6400000*x+36000000)*log(2)^2+(500*x^
7-500*x^6-34500*x^5+54500*x^4+808000*x^3-1680000*x^2-6400000*x+16000000)*log(2)-25*x^8+125*x^7+1625*x^6-9625*x
^5-29500*x^4+245600*x^3-16000*x^2-2080000*x+3200000),x, algorithm="giac")
[Out]
x^4 + 10*x^3 - 4/5*x*log(2)^2 + 123/5*x^2 - 16/5*x*log(2) - 11/5*x - 125*(6*x*log(2)^2 + 24*x*log(2) + 25*log(
2)^2 + 34*x + 100*log(2) + 125)/((log(2)^10 + 20*log(2)^9 + 205*log(2)^8 + 1360*log(2)^7 + 6410*log(2)^6 + 222
64*log(2)^5 + 57690*log(2)^4 + 110160*log(2)^3 + 149445*log(2)^2 + 131220*log(2) + 59049)*(x + 5)^2) + 1/25*(3
0*log(2)^22 - 100*x*log(2)^20 + 1320*log(2)^21 + 110*x^2*log(2)^18 - 4000*x*log(2)^19 + 28470*log(2)^20 - 40*x
^3*log(2)^16 + 3960*x^2*log(2)^17 - 78500*x*log(2)^18 + 399600*log(2)^19 - 1280*x^3*log(2)^15 + 70070*x^2*log(
2)^16 - 1002000*x*log(2)^17 + 4088699*log(2)^18 - 20200*x^3*log(2)^14 + 806080*x^2*log(2)^15 - 9306996*x*log(2
)^16 + 32390604*log(2)^17 - 207200*x^3*log(2)^13 + 6733094*x^2*log(2)^14 - 66732672*x*log(2)^15 + 206023823*lo
g(2)^16 - 1538796*x^3*log(2)^12 + 43249192*x^2*log(2)^13 - 382586980*x*log(2)^14 + 1077137632*log(2)^15 - 8742
944*x^3*log(2)^11 + 220915726*x^2*log(2)^12 - 1793175280*x*log(2)^13 + 4701546140*log(2)^14 - 39205334*x^3*log
(2)^10 + 915824848*x^2*log(2)^11 - 6968730620*x*log(2)^12 + 17308843024*log(2)^13 - 141227960*x^3*log(2)^9 + 3
118579909*x^2*log(2)^10 - 22648257696*x*log(2)^11 + 54086135524*log(2)^12 - 412257170*x^3*log(2)^8 + 877511651
6*x^2*log(2)^9 - 61817826752*x*log(2)^10 + 143897946208*log(2)^11 - 976827424*x^3*log(2)^7 + 20423276593*x^2*l
og(2)^8 - 141789944320*x*log(2)^9 + 326084929632*log(2)^10 - 1869635236*x^3*log(2)^6 + 39169875344*x^2*log(2)^
7 - 272499913920*x*log(2)^8 + 627936581760*log(2)^9 - 2855813296*x^3*log(2)^5 + 61361642832*x^2*log(2)^6 - 435
910241280*x*log(2)^7 + 1022342006208*log(2)^8 - 3407206320*x^3*log(2)^4 + 77339364416*x^2*log(2)^5 - 574046610
432*x*log(2)^6 + 1395605982208*log(2)^7 - 3063795840*x^3*log(2)^3 + 76581884256*x^2*log(2)^4 - 611969798144*x*
log(2)^5 + 1577840132096*log(2)^6 - 1953968064*x^3*log(2)^2 + 57388078848*x^2*log(2)^3 - 515066270720*x*log(2)
^4 + 1451379318784*log(2)^5 - 787612416*x^3*log(2) + 30589860864*x^2*log(2)^2 - 329386270720*x*log(2)^3 + 1058
558581760*log(2)^4 - 150704896*x^3 + 10329004032*x^2*log(2) - 150347694080*x*log(2)^2 + 588840230912*log(2)^3
+ 1659207936*x^2 - 43608834048*x*log(2) + 234595868672*log(2)^2 - 6036013056*x + 59585101824*log(2) + 72448245
76)/((log(2)^10 + 20*log(2)^9 + 205*log(2)^8 + 1360*log(2)^7 + 6410*log(2)^6 + 22264*log(2)^5 + 57690*log(2)^4
+ 110160*log(2)^3 + 149445*log(2)^2 + 131220*log(2) + 59049)*(log(2)^2 - x + 4*log(2) + 4)^4)
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Mupad [B]
time = 2.56, size = 655, normalized size = 16.79 \begin {gather*} \frac {\left (-7664\,\ln \left (2\right )-9596\,{\ln \left (2\right )}^2-6400\,{\ln \left (2\right )}^3-2400\,{\ln \left (2\right )}^4-480\,{\ln \left (2\right )}^5-40\,{\ln \left (2\right )}^6-2554\right )\,x^5+\left (35808\,\ln \left (2\right )+101016\,{\ln \left (2\right )}^2+133072\,{\ln \left (2\right )}^3+99194\,{\ln \left (2\right )}^4+44480\,{\ln \left (2\right )}^5+11920\,{\ln \left (2\right )}^6+1760\,{\ln \left (2\right )}^7+110\,{\ln \left (2\right )}^8+2599\right )\,x^4+\left (421648\,\ln \left (2\right )+578820\,{\ln \left (2\right )}^2+275360\,{\ln \left (2\right )}^3-171820\,{\ln \left (2\right )}^4-325552\,{\ln \left (2\right )}^5-213796\,{\ln \left (2\right )}^6-78400\,{\ln \left (2\right )}^7-16900\,{\ln \left (2\right )}^8-2000\,{\ln \left (2\right )}^9-100\,{\ln \left (2\right )}^{10}+114896\right )\,x^3+\left (60349\,{\ln \left (2\right )}^8-4560272\,{\ln \left (2\right )}^2-7049392\,{\ln \left (2\right )}^3-6557270\,{\ln \left (2\right )}^4-3790688\,{\ln \left (2\right )}^5-1277992\,{\ln \left (2\right )}^6-155696\,{\ln \left (2\right )}^7-1564864\,\ln \left (2\right )+32800\,{\ln \left (2\right )}^9+6920\,{\ln \left (2\right )}^{10}+720\,{\ln \left (2\right )}^{11}+30\,{\ln \left (2\right )}^{12}-197216\right )\,x^2+\left (4410800\,{\ln \left (2\right )}^4-8518720\,{\ln \left (2\right )}^2-4609920\,{\ln \left (2\right )}^3-5418240\,\ln \left (2\right )+10249520\,{\ln \left (2\right )}^5+9339780\,{\ln \left (2\right )}^6+5203040\,{\ln \left (2\right )}^7+1925990\,{\ln \left (2\right )}^8+478000\,{\ln \left (2\right )}^9+76700\,{\ln \left (2\right )}^{10}+7200\,{\ln \left (2\right )}^{11}+300\,{\ln \left (2\right )}^{12}-1327360\right )\,x+18406400\,\ln \left (2\right )+50643200\,{\ln \left (2\right )}^2+84435200\,{\ln \left (2\right )}^3+95012000\,{\ln \left (2\right )}^4+76020800\,{\ln \left (2\right )}^5+44349200\,{\ln \left (2\right )}^6+19007600\,{\ln \left (2\right )}^7+5939975\,{\ln \left (2\right )}^8+1320000\,{\ln \left (2\right )}^9+198000\,{\ln \left (2\right )}^{10}+18000\,{\ln \left (2\right )}^{11}+750\,{\ln \left (2\right )}^{12}+3065600}{25\,x^6+\left (-400\,\ln \left (2\right )-100\,{\ln \left (2\right )}^2-150\right )\,x^5+\left (800\,\ln \left (2\right )+2600\,{\ln \left (2\right )}^2+1200\,{\ln \left (2\right )}^3+150\,{\ln \left (2\right )}^4-975\right )\,x^4+\left (18800\,\ln \left (2\right )+9500\,{\ln \left (2\right )}^2-4000\,{\ln \left (2\right )}^3-4500\,{\ln \left (2\right )}^4-1200\,{\ln \left (2\right )}^5-100\,{\ln \left (2\right )}^6+7600\right )\,x^3+\left (1800\,{\ln \left (2\right )}^6-105200\,{\ln \left (2\right )}^2-85200\,{\ln \left (2\right )}^3-28250\,{\ln \left (2\right )}^4-800\,{\ln \left (2\right )}^5-46400\,\ln \left (2\right )+400\,{\ln \left (2\right )}^7+25\,{\ln \left (2\right )}^8+2400\right )\,x^2+\left (48000\,{\ln \left (2\right )}^3-152000\,{\ln \left (2\right )}^2-224000\,\ln \left (2\right )+130000\,{\ln \left (2\right )}^4+82000\,{\ln \left (2\right )}^5+25500\,{\ln \left (2\right )}^6+4000\,{\ln \left (2\right )}^7+250\,{\ln \left (2\right )}^8-96000\right )\,x+640000\,\ln \left (2\right )+1120000\,{\ln \left (2\right )}^2+1120000\,{\ln \left (2\right )}^3+700000\,{\ln \left (2\right )}^4+280000\,{\ln \left (2\right )}^5+70000\,{\ln \left (2\right )}^6+10000\,{\ln \left (2\right )}^7+625\,{\ln \left (2\right )}^8+160000}-x\,\left (\frac {16\,\ln \left (2\right )}{5}+\frac {4\,{\ln \left (2\right )}^2}{5}+\frac {11}{5}\right )+\frac {123\,x^2}{5}+10\,x^3+x^4 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((157920000*x + log(2)^2*(1793600000*x + 755020000*x^2 - 297522000*x^3 - 141278375*x^4 + 12506655*x^5 + 894
5779*x^6 + 142825*x^7 - 200080*x^8 - 12750*x^9 + 500*x^10 + 36000000) + log(2)^4*(2107700000*x + 1641415000*x^
2 + 218779750*x^3 - 110363750*x^4 - 31152250*x^5 - 132150*x^6 + 590100*x^7 + 37500*x^8 - 1000*x^9 + 42000000)
+ log(2)^3*(2400800000*x + 1473960000*x^2 - 87026000*x^3 - 189454000*x^4 - 19666000*x^5 + 6379600*x^6 + 110480
0*x^7 - 20000*x^8 - 8000*x^9 + 48000000) + log(2)^6*(529550000*x + 542741250*x^2 + 190450250*x^3 + 20061750*x^
4 - 2765350*x^5 - 724040*x^6 - 33500*x^7 + 1000*x^8 + 10500000) + log(2)*(793600000*x + 158320000*x^2 - 212152
000*x^3 - 35721500*x^4 + 20295420*x^5 + 3157836*x^6 - 843100*x^7 - 128320*x^8 + 13000*x^9 + 2000*x^10 + 160000
00) + log(2)^10*(158125*x + 187875*x^2 + 87525*x^3 + 20000*x^4 + 2250*x^5 + 100*x^6 + 3125) + log(2)^9*(316250
0*x + 3757500*x^2 + 1750500*x^3 + 400000*x^4 + 45000*x^5 + 2000*x^6 + 62500) + log(2)^5*(1268120000*x + 116119
9000*x^2 + 303876600*x^3 - 12267000*x^4 - 16160200*x^5 - 1834080*x^6 + 46000*x^7 + 12000*x^8 + 25200000) + log
(2)^8*(28446875*x + 33026875*x^2 + 14815125*x^3 + 3162375*x^4 + 305000*x^5 + 6750*x^6 - 500*x^7 + 562500) + lo
g(2)^7*(151550000*x + 167710000*x^2 + 68994000*x^3 + 12198000*x^4 + 560000*x^5 - 84000*x^6 - 8000*x^7 + 300000
0) - 8016000*x^2 - 50474400*x^3 + 3458500*x^4 + 5861095*x^5 - 382279*x^6 - 327075*x^7 + 16455*x^8 + 9020*x^9 -
250*x^10 - 100*x^11 + 3200000)/(log(2)^8*(321875*x + 58125*x^2 + 2625*x^3 - 125*x^4 + 562500) - 2080000*x + l
og(2)^7*(1550000*x + 210000*x^2 - 6000*x^3 - 2000*x^4 + 3000000) + log(2)^6*(4550000*x + 241250*x^2 - 107250*x
^3 - 10250*x^4 + 250*x^5 + 10500000) + log(2)^5*(8120000*x - 801000*x^2 - 413400*x^3 - 11000*x^4 + 3000*x^5 +
25200000) - log(2)*(6400000*x + 1680000*x^2 - 808000*x^3 - 54500*x^4 + 34500*x^5 + 500*x^6 - 500*x^7 - 1600000
0) + log(2)^4*(7700000*x - 3585000*x^2 - 670250*x^3 + 66250*x^4 + 11250*x^5 - 250*x^6 + 42000000) + log(2)^3*(
800000*x - 6040000*x^2 - 226000*x^3 + 226000*x^4 + 10000*x^5 - 2000*x^6 + 48000000) - log(2)^2*(6400000*x + 49
80000*x^2 - 678000*x^3 - 241625*x^4 + 20625*x^5 + 4125*x^6 - 125*x^7 - 36000000) + log(2)^10*(1875*x + 375*x^2
+ 25*x^3 + 3125) + log(2)^9*(37500*x + 7500*x^2 + 500*x^3 + 62500) - 16000*x^2 + 245600*x^3 - 29500*x^4 - 962
5*x^5 + 1625*x^6 + 125*x^7 - 25*x^8 + 3200000),x)
[Out]
(18406400*log(2) - x^5*(7664*log(2) + 9596*log(2)^2 + 6400*log(2)^3 + 2400*log(2)^4 + 480*log(2)^5 + 40*log(2)
^6 + 2554) - x^2*(1564864*log(2) + 4560272*log(2)^2 + 7049392*log(2)^3 + 6557270*log(2)^4 + 3790688*log(2)^5 +
1277992*log(2)^6 + 155696*log(2)^7 - 60349*log(2)^8 - 32800*log(2)^9 - 6920*log(2)^10 - 720*log(2)^11 - 30*lo
g(2)^12 + 197216) + x^4*(35808*log(2) + 101016*log(2)^2 + 133072*log(2)^3 + 99194*log(2)^4 + 44480*log(2)^5 +
11920*log(2)^6 + 1760*log(2)^7 + 110*log(2)^8 + 2599) + 50643200*log(2)^2 + 84435200*log(2)^3 + 95012000*log(2
)^4 + 76020800*log(2)^5 + 44349200*log(2)^6 + 19007600*log(2)^7 + 5939975*log(2)^8 + 1320000*log(2)^9 + 198000
*log(2)^10 + 18000*log(2)^11 + 750*log(2)^12 + x*(4410800*log(2)^4 - 8518720*log(2)^2 - 4609920*log(2)^3 - 541
8240*log(2) + 10249520*log(2)^5 + 9339780*log(2)^6 + 5203040*log(2)^7 + 1925990*log(2)^8 + 478000*log(2)^9 + 7
6700*log(2)^10 + 7200*log(2)^11 + 300*log(2)^12 - 1327360) - x^3*(171820*log(2)^4 - 578820*log(2)^2 - 275360*l
og(2)^3 - 421648*log(2) + 325552*log(2)^5 + 213796*log(2)^6 + 78400*log(2)^7 + 16900*log(2)^8 + 2000*log(2)^9
+ 100*log(2)^10 - 114896) + 3065600)/(640000*log(2) + x*(48000*log(2)^3 - 152000*log(2)^2 - 224000*log(2) + 13
0000*log(2)^4 + 82000*log(2)^5 + 25500*log(2)^6 + 4000*log(2)^7 + 250*log(2)^8 - 96000) - x^3*(4000*log(2)^3 -
9500*log(2)^2 - 18800*log(2) + 4500*log(2)^4 + 1200*log(2)^5 + 100*log(2)^6 - 7600) - x^5*(400*log(2) + 100*l
og(2)^2 + 150) - x^2*(46400*log(2) + 105200*log(2)^2 + 85200*log(2)^3 + 28250*log(2)^4 + 800*log(2)^5 - 1800*l
og(2)^6 - 400*log(2)^7 - 25*log(2)^8 - 2400) + 1120000*log(2)^2 + 1120000*log(2)^3 + 700000*log(2)^4 + 280000*
log(2)^5 + 70000*log(2)^6 + 10000*log(2)^7 + 625*log(2)^8 + 25*x^6 + x^4*(800*log(2) + 2600*log(2)^2 + 1200*lo
g(2)^3 + 150*log(2)^4 - 975) + 160000) - x*((16*log(2))/5 + (4*log(2)^2)/5 + 11/5) + (123*x^2)/5 + 10*x^3 + x^
4
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