\(\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 result

Integrand size = 844, antiderivative size = 39 \[ \text {the integral} =x+\left (x+\frac {x^2}{5}\right )^2 \left (-5+\frac {x^2}{(5+x)^2 \left (x-(2+\log (2))^2\right )^2}\right )^2 \] Output:

x+(x^2/(x-(ln(2)+2)^2)^2/(5+x)^2-5)^2*(x+1/5*x^2)^2
                                                                                    
                                                                                    
 

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(1272\) vs. \(2(39)=78\).

Time = 0.87 (sec) , antiderivative size = 1272, normalized size of antiderivative = 32.62 \[ \text {the integral} =\text {Too large to display} \] Input:

Integrate[(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^1 
0 - 100*x^11 + (16000000 + 793600000*x + 158320000*x^2 - 212152000*x^3 - 3 
5721500*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 - 2975 
22000*x^3 - 141278375*x^4 + 12506655*x^5 + 8945779*x^6 + 142825*x^7 - 2000 
80*x^8 - 12750*x^9 + 500*x^10)*Log[2]^2 + (48000000 + 2400800000*x + 14739 
60000*x^2 - 87026000*x^3 - 189454000*x^4 - 19666000*x^5 + 6379600*x^6 + 11 
04800*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 + 68994000*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 + 675 
0*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 - 2 
080000*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 - 498000 
0*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 + 8120000*x - 8010 
00*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]
 

Output:

(-250*(5 + x)^3 + 25*(5 + x)^4 + (15625*(9 + 625004*Log[2] + Log[2]^2 - 78 
125*Log[256]))/((5 + x)^2*(9 + Log[2]^2 + Log[16])^5) - (6250*(153 + 62500 
24*Log[2]^3 + 3*Log[2]^4 + Log[2]^2*(25000092 - 781250*Log[256]) + 22*Log[ 
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]*(35984 
- 4000*Log[256]) - 750*Log[2]^4*(-64 + Log[256]) - 4500*Log[256] - 2000*Lo 
g[2]^3*(-52 + 3*Log[256]) - 4*Log[2]^2*(-7999 + 3250*Log[256])) + (2*(1050 
00*Log[2]^21 + Log[2]^4*(509505917395848 - 98362046137500*Log[256]) + Log[ 
2]^7*(840695768299472 - 77659718400000*Log[256]) + Log[2]^8*(6212730035702 
69 - 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 - 105 
9551325000*Log[256]) + Log[2]^14*(2115639525302 - 54839025000*Log[256]) + 
Log[2]^18*(1074599980 - 10381250*Log[256]) - 13125*Log[2]^20*(-320 + Log[2 
56]) - 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*(-151364325331 + 4 
722412500*Log[256]) - 8*(84771504 + 103339429375*Log[256]) - 44*Log[2]^10* 
(-4318571213443 + 227823810000*Log[256]) - 32*Log[2]^2*(-2019041042701 ...
 

Rubi [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(323\) vs. \(2(39)=78\).

Time = 3.06 (sec) , antiderivative size = 323, normalized size of antiderivative = 8.28, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.002, Rules used = {2462, 2009}

Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.

\(\displaystyle \int \frac {-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+\left (100 x^6+2250 x^5+20000 x^4+87525 x^3+187875 x^2+158125 x+3125\right ) \log ^{10}(2)+\left (2000 x^6+45000 x^5+400000 x^4+1750500 x^3+3757500 x^2+3162500 x+62500\right ) \log ^9(2)+\left (-500 x^7+6750 x^6+305000 x^5+3162375 x^4+14815125 x^3+33026875 x^2+28446875 x+562500\right ) \log ^8(2)+\left (-8000 x^7-84000 x^6+560000 x^5+12198000 x^4+68994000 x^3+167710000 x^2+151550000 x+3000000\right ) \log ^7(2)+\left (1000 x^8-33500 x^7-724040 x^6-2765350 x^5+20061750 x^4+190450250 x^3+542741250 x^2+529550000 x+10500000\right ) \log ^6(2)+\left (12000 x^8+46000 x^7-1834080 x^6-16160200 x^5-12267000 x^4+303876600 x^3+1161199000 x^2+1268120000 x+25200000\right ) \log ^5(2)+\left (-1000 x^9+37500 x^8+590100 x^7-132150 x^6-31152250 x^5-110363750 x^4+218779750 x^3+1641415000 x^2+2107700000 x+42000000\right ) \log ^4(2)+\left (-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\right ) \log ^3(2)+\left (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+36000000\right ) \log ^2(2)+\left (2000 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+793600000 x+16000000\right ) \log (2)+3200000}{-25 x^8+125 x^7+1625 x^6-9625 x^5-29500 x^4+245600 x^3-16000 x^2-2080000 x+\left (25 x^3+375 x^2+1875 x+3125\right ) \log ^{10}(2)+\left (500 x^3+7500 x^2+37500 x+62500\right ) \log ^9(2)+\left (-125 x^4+2625 x^3+58125 x^2+321875 x+562500\right ) \log ^8(2)+\left (-2000 x^4-6000 x^3+210000 x^2+1550000 x+3000000\right ) \log ^7(2)+\left (250 x^5-10250 x^4-107250 x^3+241250 x^2+4550000 x+10500000\right ) \log ^6(2)+\left (3000 x^5-11000 x^4-413400 x^3-801000 x^2+8120000 x+25200000\right ) \log ^5(2)+\left (-250 x^6+11250 x^5+66250 x^4-670250 x^3-3585000 x^2+7700000 x+42000000\right ) \log ^4(2)+\left (-2000 x^6+10000 x^5+226000 x^4-226000 x^3-6040000 x^2+800000 x+48000000\right ) \log ^3(2)+\left (125 x^7-4125 x^6-20625 x^5+241625 x^4+678000 x^3-4980000 x^2-6400000 x+36000000\right ) \log ^2(2)+\left (500 x^7-500 x^6-34500 x^5+54500 x^4+808000 x^3-1680000 x^2-6400000 x+16000000\right ) \log (2)+3200000} \, dx\)

\(\Big \downarrow \) 2462

\(\displaystyle \int \left (4 x^3+30 x^2+\frac {246 x}{5}+\frac {250 \left (17+3 \log ^2(2)+\log (4096)\right )}{(x+5)^2 \left (9+\log ^2(2)+\log (16)\right )^5}-\frac {6 (2+\log (2))^{10} \left (23+2 \log ^2(2)+\log (256)\right )}{25 \left (9+\log ^2(2)+\log (16)\right )^3 \left (-x+4+\log ^2(2)+4 \log (2)\right )^4}+\frac {4 (2+\log (2))^{12}}{25 \left (9+\log ^2(2)+\log (16)\right )^2 \left (-x+4+\log ^2(2)+4 \log (2)\right )^5}-\frac {1250}{(x+5)^3 \left (9+\log ^2(2)+\log (16)\right )^4}-\frac {2 (2+\log (2))^8 \left (64779+10 \log ^8(2)+160 \log ^7(2)+1320 \log ^6(2)+6880 \log ^5(2)+24694 \log ^4(2)+61872 \log ^3(2)+106686 \log ^2(2)+116088 \log (2)\right )}{25 \left (9+\log ^2(2)+\log (16)\right )^4 \left (-x+4+\log ^2(2)+4 \log (2)\right )^3}+\frac {2 (2+\log (2))^6 \left (1177382+20 \log ^{10}(2)+400 \log ^9(2)+4100 \log ^8(2)+27200 \log ^7(2)+128198 \log ^6(2)+445256 \log ^5(2)+1153635 \log ^4(2)+2202520 \log ^3(2)+2986965 \log ^2(2)+2621076 \log (2)\right )}{25 \left (9+\log ^2(2)+\log (16)\right )^5 \left (-x+4+\log ^2(2)+4 \log (2)\right )^2}+\frac {1}{5} \left (-11-4 \log ^2(2)-16 \log (2)\right )\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle x^4+10 x^3+\frac {123 x^2}{5}-\frac {1}{5} x \left (11+4 \log ^2(2)+16 \log (2)\right )-\frac {250 \left (17+3 \log ^2(2)+\log (4096)\right )}{(x+5) \left (9+\log ^2(2)+\log (16)\right )^5}+\frac {2 (2+\log (2))^{10} \left (23+2 \log ^2(2)+\log (256)\right )}{25 \left (9+\log ^2(2)+\log (16)\right )^3 \left (x-(2+\log (2))^2\right )^3}+\frac {(2+\log (2))^{12}}{25 \left (9+\log ^2(2)+\log (16)\right )^2 \left (x-(2+\log (2))^2\right )^4}+\frac {625}{(x+5)^2 \left (9+\log ^2(2)+\log (16)\right )^4}-\frac {(2+\log (2))^8 \left (64779+10 \log ^8(2)+160 \log ^7(2)+1320 \log ^6(2)+6880 \log ^5(2)+24694 \log ^4(2)+61872 \log ^3(2)+106686 \log ^2(2)+116088 \log (2)\right )}{25 \left (9+\log ^2(2)+\log (16)\right )^4 \left (x-(2+\log (2))^2\right )^2}-\frac {2 (2+\log (2))^6 \left (1177382+20 \log ^{10}(2)+400 \log ^9(2)+4100 \log ^8(2)+27200 \log ^7(2)+128198 \log ^6(2)+445256 \log ^5(2)+1153635 \log ^4(2)+2202520 \log ^3(2)+2986965 \log ^2(2)+2621076 \log (2)\right )}{25 \left (9+\log ^2(2)+\log (16)\right )^5 \left (x-(2+\log (2))^2\right )}\)

Input:

Int[(3200000 + 157920000*x - 8016000*x^2 - 50474400*x^3 + 3458500*x^4 + 58 
61095*x^5 - 382279*x^6 - 327075*x^7 + 16455*x^8 + 9020*x^9 - 250*x^10 - 10 
0*x^11 + (16000000 + 793600000*x + 158320000*x^2 - 212152000*x^3 - 3572150 
0*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[2]^3 + (42000000 + 2107700000*x + 16414150 
00*x^2 + 218779750*x^3 - 110363750*x^4 - 31152250*x^5 - 132150*x^6 + 59010 
0*x^7 + 37500*x^8 - 1000*x^9)*Log[2]^4 + (25200000 + 1268120000*x + 116119 
9000*x^2 + 303876600*x^3 - 12267000*x^4 - 16160200*x^5 - 1834080*x^6 + 460 
00*x^7 + 12000*x^8)*Log[2]^5 + (10500000 + 529550000*x + 542741250*x^2 + 1 
90450250*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 + 68994000*x^3 + 12 
198000*x^4 + 560000*x^5 - 84000*x^6 - 8000*x^7)*Log[2]^7 + (562500 + 28446 
875*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 + 400 
000*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 - 34 
500*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 + (48 
000000 + 800000*x - 6040000*x^2 - 226000*x^3 + 226000*x^4 + 10000*x^5 - 20 
00*x^6)*Log[2]^3 + (42000000 + 7700000*x - 3585000*x^2 - 670250*x^3 + 6625 
0*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 + 2 
41250*x^2 - 107250*x^3 - 10250*x^4 + 250*x^5)*Log[2]^6 + (3000000 + 155000 
0*x + 210000*x^2 - 6000*x^3 - 2000*x^4)*Log[2]^7 + (562500 + 321875*x + 58 
125*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]
 

Output:

(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)
 

Defintions of rubi rules used

rule 2009

Int[u_, x_Symbol] :> Simp[IntSum[u, x], x] /; SumQ[u]
 

rule 2462

Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{Qx = Factor[Px]}, Int[ExpandIntegr 
and[u*Qx^p, x], x] /;  !SumQ[NonfreeFactors[Qx, x]]] /; PolyQ[Px, x] && GtQ 
[Expon[Px, x], 2] &&  !BinomialQ[Px, x] &&  !TrinomialQ[Px, x] && ILtQ[p, 0 
] && RationalFunctionQ[u, x]
 

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(531\) vs. \(2(37)=74\).

Time = 1.63 (sec) , antiderivative size = 532, normalized size of antiderivative = 13.64

method	result	size
default	\(x^{4}+10 x^{3}+\frac {123 x^{2}}{5}-\frac {4 x \ln \left (2\right )^{2}}{5}-\frac {16 x \ln \left (2\right )}{5}-\frac {11 x}{5}-\frac {18750 \ln \left (2\right )^{2}+75000 \ln \left (2\right )+106250}{25 \left (\ln \left (2\right )^{2}+4 \ln \left (2\right )+9\right )^{5} \left (5+x \right )}+\frac {625}{\left (\ln \left (2\right )^{2}+4 \ln \left (2\right )+9\right )^{4} \left (5+x \right )^{2}}-\frac {-12 \ln \left (2\right )^{12}-288 \ln \left (2\right )^{11}-3258 \ln \left (2\right )^{10}-22920 \ln \left (2\right )^{9}-111240 \ln \left (2\right )^{8}-390528 \ln \left (2\right )^{7}-1012032 \ln \left (2\right )^{6}-1942272 \ln \left (2\right )^{5}-2730240 \ln \left (2\right )^{4}-2734080 \ln \left (2\right )^{3}-1847808 \ln \left (2\right )^{2}-755712 \ln \left (2\right )-141312}{75 \left (\ln \left (2\right )^{2}+4 \ln \left (2\right )+9\right )^{3} \left (-\ln \left (2\right )^{2}-4 \ln \left (2\right )+x -4\right )^{3}}-\frac {-4 \ln \left (2\right )^{12}-96 \ln \left (2\right )^{11}-1056 \ln \left (2\right )^{10}-7040 \ln \left (2\right )^{9}-31680 \ln \left (2\right )^{8}-101376 \ln \left (2\right )^{7}-236544 \ln \left (2\right )^{6}-405504 \ln \left (2\right )^{5}-506880 \ln \left (2\right )^{4}-450560 \ln \left (2\right )^{3}-270336 \ln \left (2\right )^{2}-98304 \ln \left (2\right )-16384}{100 \left (\ln \left (2\right )^{2}+4 \ln \left (2\right )+9\right )^{2} \left (-\ln \left (2\right )^{2}-4 \ln \left (2\right )+x -4\right )^{4}}-\frac {20 \ln \left (2\right )^{16}+640 \ln \left (2\right )^{15}+10000 \ln \left (2\right )^{14}+100800 \ln \left (2\right )^{13}+730988 \ln \left (2\right )^{12}+4032032 \ln \left (2\right )^{11}[phone] \ln \left (2\right )^{10}[phone] \ln \left (2\right )^{9}[phone] \ln \left (2\right )^{8}[phone] \ln \left (2\right )^{7}[phone] \ln \left (2\right )^{6}[phone] \ln \left (2\right )^{5}[phone] \ln \left (2\right )^{4}[phone] \ln \left (2\right )^{3}[phone] \ln \left (2\right )^{2}[phone] \ln \left (2\right )[phone]}{50 \left (\ln \left (2\right )^{2}+4 \ln \left (2\right )+9\right )^{4} \left (-\ln \left (2\right )^{2}-4 \ln \left (2\right )+x -4\right )^{2}}-\frac {40 \ln \left (2\right )^{16}+1280 \ln \left (2\right )^{15}+20200 \ln \left (2\right )^{14}+207200 \ln \left (2\right )^{13}+1538796 \ln \left (2\right )^{12}+8742944 \ln \left (2\right )^{11}[phone] \ln \left (2\right )^{10}[phone] \ln \left (2\right )^{9}[phone] \ln \left (2\right )^{8}[phone] \ln \left (2\right )^{7}[phone] \ln \left (2\right )^{6}[phone] \ln \left (2\right )^{5}[phone] \ln \left (2\right )^{4}[phone] \ln \left (2\right )^{3}[phone] \ln \left (2\right )^{2}[phone] \ln \left (2\right )[phone]}{25 \left (\ln \left (2\right )^{2}+4 \ln \left (2\right )+9\right )^{5} \left (-\ln \left (2\right )^{2}-4 \ln \left (2\right )+x -4\right )}\)	\(532\)
norman	\(\text {Expression too large to display}\)	\(631\)
risch	\(\text {Expression too large to display}\)	\(715\)
gosper	\(\text {Expression too large to display}\)	\(1115\)
parallelrisch	\(\text {Expression too large to display}\)	\(1115\)

Input:

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+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+68994000*x^3+167710000*x^2+151550000*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+529550 
000*x[phone])*ln(2)^6+(12000*x^8+46000*x^7-1834080*x^6-16160200*x^5-1226 
7000*x^4+303876600*x^3+1161199000*x^2+1268120000*x[phone])*ln(2)^5+(-100 
0*x^9+37500*x^8+590100*x^7-132150*x^6-31152250*x^5-110363750*x^4+218779750 
*x^3+1641415000*x^2+2107700000*x[phone])*ln(2)^4+(-8000*x^9-20000*x^8+11 
04800*x^7+6379600*x^6-19666000*x^5-189454000*x^4-87026000*x^3+1473960000*x 
^2+2400800000*x[phone])*ln(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+17936 
00000*x[phone])*ln(2)^2+(2000*x^10+13000*x^9-128320*x^8-843100*x^7+31578 
36*x^6+20295420*x^5-35721500*x^4-212152000*x^3+158320000*x^2+793600000*x+1 
6000000)*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^3-8016000*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+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+3000000)*ln(2)^7+(250*x^5-10250*x^4-107250*x^3+2412 
50*x^2+4550000*x[phone])*ln(2)^6+(3000*x^5-11000*x^4-413400*x^3-801000*x 
^2+8120000*x[phone])*ln(2)^5+(-250*x^6+11250*x^5+66250*x^4-670250*x^3-35 
85000*x^2+7700000*x[phone])*ln(2)^4+(-2000*x^6+10000*x^5+226000*x^4-2260 
00*x^3-6040000*x^2+800000*x[phone])*ln(2)^3+(125*x^7-4125*x^6-20625*x^5+ 
241625*x^4+678000*x^3-4980000*x^2-6400000*x[phone])*ln(2)^2+(500*x^7-500 
*x^6-34500*x^5+54500*x^4+808000*x^3-1680000*x^2-6400000*x[phone])*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,method=_RETURNVERBOSE)
 

Output:

x^4+10*x^3+123/5*x^2-4/5*x*ln(2)^2-16/5*x*ln(2)-11/5*x-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)^2-1/75*(-12*ln(2)^12-288*ln(2)^11-3258*ln(2)^10-22920*ln(2)^9-11124 
0*ln(2)^8-390528*ln(2)^7-1012032*ln(2)^6-1942272*ln(2)^5-2730240*ln(2)^4-2 
734080*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*ln(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)^15+10000*ln(2)^ 
14+100800*ln(2)^13+730988*ln(2)^12+4032032*ln(2)^11+17455292*ln(2)^10+6036 
7280*ln(2)^9+168215510*ln(2)^8+378207072*ln(2)^7+682520608*ln(2)^6+9762868 
48*ln(2)^5+1082884160*ln(2)^4+898398720*ln(2)^3+524539392*ln(2)^2+19210444 
8*ln(2)[phone])/(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+874 
2944*ln(2)^11+39205334*ln(2)^10+141227960*ln(2)^9+412257170*ln(2)^8+976827 
424*ln(2)^7+1869635236*ln(2)^6+2855813296*ln(2)^5+3407206320*ln(2)^4+30637 
95840*ln(2)^3+1953968064*ln(2)^2+787612416*ln(2)[phone])/(ln(2)^2+4*ln( 
2)+9)^5/(-ln(2)^2-4*ln(2)+x-4)
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 668 vs. \(2 (38) = 76\).

Time = 0.08 (sec) , antiderivative size = 668, normalized size of antiderivative = 17.13 \[ \text {the integral} =\text {Too large to display} \] Input:

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+400000*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+3 
3026875*x^2+28446875*x+562500)*log(2)^8+(-8000*x^7-84000*x^6+560000*x^5+12 
198000*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+542741250* 
x^2+529550000*x[phone])*log(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[phone])*lo 
g(2)^5+(-1000*x^9+37500*x^8+590100*x^7-132150*x^6-31152250*x^5-110363750*x 
^4+218779750*x^3+1641415000*x^2+2107700000*x[phone])*log(2)^4+(-8000*x^9 
-20000*x^8+1104800*x^7+6379600*x^6-19666000*x^5-189454000*x^4-87026000*x^3 
[phone]*x^2+2400800000*x[phone])*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+75502 
0000*x^2+1793600000*x[phone])*log(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[phone])*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+7500*x^2+3750 
0*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+210000*x^2+1550000*x+3000000)*log(2)^7+(250*x^5-10250 
*x^4-107250*x^3+241250*x^2+4550000*x[phone])*log(2)^6+(3000*x^5-11000*x^ 
4-413400*x^3-801000*x^2+8120000*x[phone])*log(2)^5+(-250*x^6+11250*x^5+6 
6250*x^4-670250*x^3-3585000*x^2+7700000*x[phone])*log(2)^4+(-2000*x^6+10 
000*x^5+226000*x^4-226000*x^3-6040000*x^2+800000*x[phone])*log(2)^3+(125 
*x^7-4125*x^6-20625*x^5+241625*x^4+678000*x^3-4980000*x^2-6400000*x+360000 
00)*log(2)^2+(500*x^7-500*x^6-34500*x^5+54500*x^4+808000*x^3-1680000*x^2-6 
400000*x[phone])*log(2)-25*x^8+125*x^7+1625*x^6-9625*x^5-29500*x^4+24560 
0*x^3-16000*x^2-2080000*x+3200000),x, algorithm="fricas")
 

Output:

1/25*(30*(x^2 + 10*x + 25)*log(2)^12 + 720*(x^2 + 10*x + 25)*log(2)^11 - 1 
20*(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 + 50 
0*x^5 + 3930*x^4 + 7125*x^3 - 4106*x^2 + 295815*x + 1187975)*log(2)^7 - 58 
95*x^7 - 4*(25*x^7 - 200*x^6 - 10220*x^5 - 97215*x^4 - 283676*x^3 - 5377*x 
^2 - 1932445*x - 11087300)*log(2)^6 + 54745*x^6 - 16*(75*x^7 + 800*x^6 - 2 
660*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 + 709672*x 
^4 + 5222565*x^3 + 5172365*x^2 - 804600*x + 47506000)*log(2)^4 - 755081*x^ 
4 + 16*(75*x^8 + 500*x^7 - 5940*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 - 6029 
932*x^2 + 3289680*x - 12660800)*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 - 1 
0*x^3 - 213*x^2 + 120*x + 2800)*log(2)^3 + 304*x^3 - 4*(x^5 - 26*x^4 - ...
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 728 vs. \(2 (31) = 62\).

Time = 30.21 (sec) , antiderivative size = 728, normalized size of antiderivative = 18.67 \[ \text {the integral} =\text {Too large to display} \] Input:

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+68994000*x**3+167710000*x**2+151550000*x+30 
00000)*ln(2)**7+(1000*x**8-33500*x**7-724040*x**6-2765350*x**5+20061750*x* 
*4+190450250*x**3+542741250*x**2+529550000*x[phone])*ln(2)**6+(12000*x** 
8+46000*x**7-1834080*x**6-16160200*x**5-12267000*x**4+303876600*x**3+11611 
99000*x**2+1268120000*x[phone])*ln(2)**5+(-1000*x**9+37500*x**8+590100*x 
**7-132150*x**6-31152250*x**5-110363750*x**4+218779750*x**3+1641415000*x** 
2+2107700000*x[phone])*ln(2)**4+(-8000*x**9-20000*x**8+1104800*x**7+6379 
600*x**6-19666000*x**5-189454000*x**4-87026000*x**3+1473960000*x**2+240080 
0000*x[phone])*ln(2)**3+(500*x**10-12750*x**9-200080*x**8+142825*x**7+89 
45779*x**6+12506655*x**5-141278375*x**4-297522000*x**3+755020000*x**2+1793 
600000*x[phone])*ln(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+158320000*x**2+79 
3600000*x[phone])*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**3-8016000*x**2+1579 
20000*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+5625 
00)*ln(2)**8+(-2000*x**4-6000*x**3+210000*x**2+1550000*x+3000000)*ln(2)**7 
+(250*x**5-10250*x**4-107250*x**3+241250*x**2+4550000*x[phone])*ln(2)**6 
+(3000*x**5-11000*x**4-413400*x**3-801000*x**2+8120000*x[phone])*ln(2)** 
5+(-250*x**6+11250*x**5+66250*x**4-670250*x**3-3585000*x**2+7700000*x+4200 
0000)*ln(2)**4+(-2000*x**6+10000*x**5+226000*x**4-226000*x**3-6040000*x**2 
+800000*x[phone])*ln(2)**3+(125*x**7-4125*x**6-20625*x**5+241625*x**4+67 
8000*x**3-4980000*x**2-6400000*x[phone])*ln(2)**2+(500*x**7-500*x**6-345 
00*x**5+54500*x**4+808000*x**3-1680000*x**2-6400000*x[phone])*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)
 

Output:

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 - 2000*l 
og(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*l 
og(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 + 3 
2800*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 + 44 
10800*log(2)**4 + 9339780*log(2)**6 + 10249520*log(2)**5) + 750*log(2)**12 
 + 18000*log(2)**11 + 198000*log(2)**10 + 1320000*log(2)**9 + 5939975*log( 
2)**8 + 19007600*log(2)**7 + 3065600 + 44349200*log(2)**6 + 76020800*log(2 
)**5 + 18406400*log(2) + 95012000*log(2)**4 + 50643200*log(2)**2 + 8443520 
0*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 + 9...
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 648 vs. \(2 (38) = 76\).

Time = 0.07 (sec) , antiderivative size = 648, normalized size of antiderivative = 16.62 \[ \text {the integral} =\text {Too large to display} \] Input:

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+400000*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+3 
3026875*x^2+28446875*x+562500)*log(2)^8+(-8000*x^7-84000*x^6+560000*x^5+12 
198000*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+542741250* 
x^2+529550000*x[phone])*log(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[phone])*lo 
g(2)^5+(-1000*x^9+37500*x^8+590100*x^7-132150*x^6-31152250*x^5-110363750*x 
^4+218779750*x^3+1641415000*x^2+2107700000*x[phone])*log(2)^4+(-8000*x^9 
-20000*x^8+1104800*x^7+6379600*x^6-19666000*x^5-189454000*x^4-87026000*x^3 
[phone]*x^2+2400800000*x[phone])*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+75502 
0000*x^2+1793600000*x[phone])*log(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[phone])*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+7500*x^2+3750 
0*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+210000*x^2+1550000*x+3000000)*log(2)^7+(250*x^5-10250 
*x^4-107250*x^3+241250*x^2+4550000*x[phone])*log(2)^6+(3000*x^5-11000*x^ 
4-413400*x^3-801000*x^2+8120000*x[phone])*log(2)^5+(-250*x^6+11250*x^5+6 
6250*x^4-670250*x^3-3585000*x^2+7700000*x[phone])*log(2)^4+(-2000*x^6+10 
000*x^5+226000*x^4-226000*x^3-6040000*x^2+800000*x[phone])*log(2)^3+(125 
*x^7-4125*x^6-20625*x^5+241625*x^4+678000*x^3-4980000*x^2-6400000*x+360000 
00)*log(2)^2+(500*x^7-500*x^6-34500*x^5+54500*x^4+808000*x^3-1680000*x^2-6 
400000*x[phone])*log(2)-25*x^8+125*x^7+1625*x^6-9625*x^5-29500*x^4+24560 
0*x^3-16000*x^2-2080000*x+3200000),x, algorithm="maxima")
 

Output:

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 + 198000*log(2)^10 + 1320000*log(2)^9 + 59399 
75*log(2)^8 + 19007600*log(2)^7 - 2*(20*log(2)^6 + 240*log(2)^5 + 1200*log 
(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*log(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) + 25 
99)*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 - 6 
8840*log(2)^3 - 144705*log(2)^2 - 105412*log(2) - 28724)*x^3 + 95012000*lo 
g(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*log(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*lo 
g(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 + 400*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 + 4 
0*log(2)^3 - 95*log(2)^2 - 188*log(2) - 76)*x^3 + 28000*log(2)^4 + (log...
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 785 vs. \(2 (38) = 76\).

Time = 0.16 (sec) , antiderivative size = 785, normalized size of antiderivative = 20.13 \[ \text {the integral} =\text {Too large to display} \] Input:

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+400000*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+3 
3026875*x^2+28446875*x+562500)*log(2)^8+(-8000*x^7-84000*x^6+560000*x^5+12 
198000*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+542741250* 
x^2+529550000*x[phone])*log(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[phone])*lo 
g(2)^5+(-1000*x^9+37500*x^8+590100*x^7-132150*x^6-31152250*x^5-110363750*x 
^4+218779750*x^3+1641415000*x^2+2107700000*x[phone])*log(2)^4+(-8000*x^9 
-20000*x^8+1104800*x^7+6379600*x^6-19666000*x^5-189454000*x^4-87026000*x^3 
[phone]*x^2+2400800000*x[phone])*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+75502 
0000*x^2+1793600000*x[phone])*log(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[phone])*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+7500*x^2+3750 
0*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+210000*x^2+1550000*x+3000000)*log(2)^7+(250*x^5-10250 
*x^4-107250*x^3+241250*x^2+4550000*x[phone])*log(2)^6+(3000*x^5-11000*x^ 
4-413400*x^3-801000*x^2+8120000*x[phone])*log(2)^5+(-250*x^6+11250*x^5+6 
6250*x^4-670250*x^3-3585000*x^2+7700000*x[phone])*log(2)^4+(-2000*x^6+10 
000*x^5+226000*x^4-226000*x^3-6040000*x^2+800000*x[phone])*log(2)^3+(125 
*x^7-4125*x^6-20625*x^5+241625*x^4+678000*x^3-4980000*x^2-6400000*x+360000 
00)*log(2)^2+(500*x^7-500*x^6-34500*x^5+54500*x^4+808000*x^3-1680000*x^2-6 
400000*x[phone])*log(2)-25*x^8+125*x^7+1625*x^6-9625*x^5-29500*x^4+24560 
0*x^3-16000*x^2-2080000*x+3200000),x, algorithm="giac")
 

Output:

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 + 22264 
*log(2)^5 + 57690*log(2)^4 + 110160*log(2)^3 + 149445*log(2)^2 + 131220*lo 
g(2) + 59049)*(x + 5)^2) + 1/25*(30*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*l 
og(2)^16 + 3960*x^2*log(2)^17 - 78500*x*log(2)^18 + 399600*log(2)^19 - 128 
0*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 - 66732 
672*x*log(2)^15 + 206023823*log(2)^16 - 1538796*x^3*log(2)^12 + 43249192*x 
^2*log(2)^13 - 382586980*x*log(2)^14 + 1077137632*log(2)^15 - 8742944*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 + 3118579909* 
x^2*log(2)^10 - 22648257696*x*log(2)^11 + 54086135524*log(2)^12 - 41225717 
0*x^3*log(2)^8 + 8775116516*x^2*log(2)^9 - 61817826752*x*log(2)^10 + 14389 
7946208*log(2)^11 - 976827424*x^3*log(2)^7 + 20423276593*x^2*log(2)^8 - 14 
1789944320*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(...
 

Mupad [B] (verification not implemented)

Time = 3.24 (sec) , antiderivative size = 655, normalized size of antiderivative = 16.79 \[ \text {the integral} =\text {Too large to display} \] Input:

int((157920000*x + log(2)^2*(1793600000*x + 755020000*x^2 - 297522000*x^3 
- 141278375*x^4 + 12506655*x^5 + 8945779*x^6 + 142825*x^7 - 200080*x^8 - 1 
2750*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 + 1104800*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 - 212152000*x^ 
3 - 35721500*x^4 + 20295420*x^5 + 3157836*x^6 - 843100*x^7 - 128320*x^8 + 
13000*x^9 + 2000*x^10 + 16000000) + log(2)^10*(158125*x + 187875*x^2 + 875 
25*x^3 + 20000*x^4 + 2250*x^5 + 100*x^6 + 3125) + log(2)^9*(3162500*x + 37 
57500*x^2 + 1750500*x^3 + 400000*x^4 + 45000*x^5 + 2000*x^6 + 62500) + log 
(2)^5*(1268120000*x + 1161199000*x^2 + 303876600*x^3 - 12267000*x^4 - 1616 
0200*x^5 - 1834080*x^6 + 46000*x^7 + 12000*x^8 + 25200000) + log(2)^8*(284 
46875*x + 33026875*x^2 + 14815125*x^3 + 3162375*x^4 + 305000*x^5 + 6750*x^ 
6 - 500*x^7 + 562500) + log(2)^7*(151550000*x + 167710000*x^2 + 68994000*x 
^3 + 12198000*x^4 + 560000*x^5 - 84000*x^6 - 8000*x^7 + 3000000) - 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 + log(2)^7*(15500 
00*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*(812 
0000*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 - 16000000) + 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 + 4980000*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 - 9625*x^5 + 1625*x^6 + 125*x^7 - 25*x^8 + 3200000),x)
 

Output:

(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) + 456 
0272*log(2)^2 + 7049392*log(2)^3 + 6557270*log(2)^4 + 3790688*log(2)^5 + 1 
277992*log(2)^6 + 155696*log(2)^7 - 60349*log(2)^8 - 32800*log(2)^9 - 6920 
*log(2)^10 - 720*log(2)^11 - 30*log(2)^12 + 197216) + x^4*(35808*log(2) + 
101016*log(2)^2 + 133072*log(2)^3 + 99194*log(2)^4 + 44480*log(2)^5 + 1192 
0*log(2)^6 + 1760*log(2)^7 + 110*log(2)^8 + 2599) + 50643200*log(2)^2 + 84 
435200*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 - 5418240*log(2) + 10249520*log(2)^5 + 9339780*lo 
g(2)^6 + 5203040*log(2)^7 + 1925990*log(2)^8 + 478000*log(2)^9 + 76700*log 
(2)^10 + 7200*log(2)^11 + 300*log(2)^12 - 1327360) - x^3*(171820*log(2)^4 
- 578820*log(2)^2 - 275360*log(2)^3 - 421648*log(2) + 325552*log(2)^5 + 21 
3796*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) + 130000*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*log(2)^2 + 150) - x^2*(46400*log(2) + 105200*log...
 

Reduce [B] (verification not implemented)

Time = 2.19 (sec) , antiderivative size = 1300, normalized size of antiderivative = 33.33 \[ \text {the integral} =\text {Too large to display} \] Input:

int(((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+400000*x^4+1750500*x^3+3757500*x^2+3162500*x+6250 
0)*log(2)^9+(-500*x^7+6750*x^6+305000*x^5+3162375*x^4+14815125*x^3+3302687 
5*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^8-33 
500*x^7-724040*x^6-2765350*x^5+20061750*x^4+190450250*x^3+542741250*x^2+52 
9550000*x[phone])*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[phone])*log(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[phone])*log(2)^4+(-8000*x^9-20000 
*x^8+1104800*x^7+6379600*x^6-19666000*x^5-189454000*x^4-87026000*x^3+14739 
60000*x^2+2400800000*x[phone])*log(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[phone])*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+158320000*x^2+7936 
00000*x[phone])*log(2)-100*x^11-250*x^10+9020*x^9+16455*x^8-327075*x^7-3 
82279*x^6+5861095*x^5+3458500*x^4-50474400*x^3-8016000*x^2+157920000*x+320 
0000)/((25*x^3+375*x^2+1875*x+3125)*log(2)^10+(500*x^3+7500*x^2+37500*x+62 
500)*log(2)^9+(-125*x^4+2625*x^3+58125*x^2+321875*x+562500)*log(2)^8+(-200 
0*x^4-6000*x^3+210000*x^2+1550000*x+3000000)*log(2)^7+(250*x^5-10250*x^4-1 
07250*x^3+241250*x^2+4550000*x[phone])*log(2)^6+(3000*x^5-11000*x^4-4134 
00*x^3-801000*x^2+8120000*x[phone])*log(2)^5+(-250*x^6+11250*x^5+66250*x 
^4-670250*x^3-3585000*x^2+7700000*x[phone])*log(2)^4+(-2000*x^6+10000*x^ 
5+226000*x^4-226000*x^3-6040000*x^2+800000*x[phone])*log(2)^3+(125*x^7-4 
125*x^6-20625*x^5+241625*x^4+678000*x^3-4980000*x^2-6400000*x[phone])*lo 
g(2)^2+(500*x^7-500*x^6-34500*x^5+54500*x^4+808000*x^3-1680000*x^2-6400000 
*x[phone])*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)
 

Output:

(500*log(2)**16*x**2 + 5000*log(2)**16*x + 12500*log(2)**16 + 16000*log(2) 
**15*x**2 + 160000*log(2)**15*x + 400000*log(2)**15 - 2000*log(2)**14*x**3 
 + 205000*log(2)**14*x**2 + 2200000*log(2)**14*x + 5625000*log(2)**14 - 56 
000*log(2)**13*x**3 + 1260000*log(2)**13*x**2 + 16800000*log(2)**13*x + 45 
500000*log(2)**13 + 3000*log(2)**12*x**4 - 638000*log(2)**12*x**3 + 257005 
0*log(2)**12*x**2 + 75050500*log(2)**12*x + 229376250*log(2)**12 + 72000*l 
og(2)**11*x**4 - 3664000*log(2)**11*x**3 - 14030800*log(2)**11*x**2 + 1704 
92000*log(2)**11*x + 700230000*log(2)**11 + 100*log(2)**10*x**6 + 697000*l 
og(2)**10*x**4 - 9472100*log(2)**10*x**3 - 111542300*log(2)**10*x**2 - 546 
40500*log(2)**10*x + 894155000*log(2)**10 + 2000*log(2)**9*x**6 + 3380000* 
log(2)**9*x**4 + 6270000*log(2)**9*x**3 - 295022000*log(2)**9*x**2 - 16929 
70000*log(2)**9*x - 2449300000*log(2)**9 - 400*log(2)**8*x**7 + 10250*log( 
2)**8*x**6 + 7484900*log(2)**8*x**4 + 118273750*log(2)**8*x**3 - 70624625* 
log(2)**8*x**2 - 5598390000*log(2)**8*x - 16311584375*log(2)**8 - 6400*log 
(2)**7*x**7 - 28000*log(2)**7*x**6 - 1969600*log(2)**7*x**4 + 344284000*lo 
g(2)**7*x**3 + 1738857200*log(2)**7*x**2 - 9242528000*log(2)**7*x - 454800 
70000*log(2)**7 + 600*log(2)**6*x**8 - 31800*log(2)**6*x**7 - 437040*log(2 
)**6*x**6 - 52277200*log(2)**6*x**4 + 399814500*log(2)**6*x**3 + 541793280 
0*log(2)**6*x**2 - 6286734500*log(2)**6*x - 80121930000*log(2)**6 + 7200*l 
og(2)**5*x**8 - 23200*log(2)**5*x**7 - 1526080*log(2)**5*x**6 - 1268848...