Integrand size = 214, antiderivative size = 19 \[ \int \frac {-25600000000-61440000000 x-64511808000 x^2-38707027200 x^3-14515148160 x^4-3483642816 x^5-522547200 x^6-44789760 x^7-1679616 x^8+\left (25600000000+61440000000 x+64512000000 x^2+38707200000 x^3+14515200000 x^4+3483648000 x^5+522547200 x^6+44789760 x^7+1679616 x^8\right ) \log (3)}{25600000000+61439680000 x+64511616001 x^2+38707027200 x^3+14515165440 x^4+3483645408 x^5+522547200 x^6+44789760 x^7+1679616 x^8+\left (-51200000000-122879680000 x-129023616000 x^2-77414227200 x^3-29030365440 x^4-6967293408 x^5-1045094400 x^6-89579520 x^7-3359232 x^8\right ) \log (3)+\left (25600000000+61440000000 x+64512000000 x^2+38707200000 x^3+14515200000 x^4+3483648000 x^5+522547200 x^6+44789760 x^7+1679616 x^8\right ) \log ^2(3)} \, dx=\frac {x}{-1+\frac {x}{(x+5 (4+x))^4}+\log (3)} \] Output:
x/(ln(3)+x/(6*x+20)^4-1)
Leaf count is larger than twice the leaf count of optimal. \(46\) vs. \(2(19)=38\).
Time = 0.05 (sec) , antiderivative size = 46, normalized size of antiderivative = 2.42 \[ \int \frac {-25600000000-61440000000 x-64511808000 x^2-38707027200 x^3-14515148160 x^4-3483642816 x^5-522547200 x^6-44789760 x^7-1679616 x^8+\left (25600000000+61440000000 x+64512000000 x^2+38707200000 x^3+14515200000 x^4+3483648000 x^5+522547200 x^6+44789760 x^7+1679616 x^8\right ) \log (3)}{25600000000+61439680000 x+64511616001 x^2+38707027200 x^3+14515165440 x^4+3483645408 x^5+522547200 x^6+44789760 x^7+1679616 x^8+\left (-51200000000-122879680000 x-129023616000 x^2-77414227200 x^3-29030365440 x^4-6967293408 x^5-1045094400 x^6-89579520 x^7-3359232 x^8\right ) \log (3)+\left (25600000000+61440000000 x+64512000000 x^2+38707200000 x^3+14515200000 x^4+3483648000 x^5+522547200 x^6+44789760 x^7+1679616 x^8\right ) \log ^2(3)} \, dx=\frac {10+3 x-\frac {9 x^2}{3 x-48 (10+3 x)^4+48 (10+3 x)^4 \log (3)}}{3 (-1+\log (3))} \] Input:
Integrate[(-25600000000 - 61440000000*x - 64511808000*x^2 - 38707027200*x^ 3 - 14515148160*x^4 - 3483642816*x^5 - 522547200*x^6 - 44789760*x^7 - 1679 616*x^8 + (25600000000 + 61440000000*x + 64512000000*x^2 + 38707200000*x^3 + 14515200000*x^4 + 3483648000*x^5 + 522547200*x^6 + 44789760*x^7 + 16796 16*x^8)*Log[3])/(25600000000 + 61439680000*x + 64511616001*x^2 + 387070272 00*x^3 + 14515165440*x^4 + 3483645408*x^5 + 522547200*x^6 + 44789760*x^7 + 1679616*x^8 + (-51200000000 - 122879680000*x - 129023616000*x^2 - 7741422 7200*x^3 - 29030365440*x^4 - 6967293408*x^5 - 1045094400*x^6 - 89579520*x^ 7 - 3359232*x^8)*Log[3] + (25600000000 + 61440000000*x + 64512000000*x^2 + 38707200000*x^3 + 14515200000*x^4 + 3483648000*x^5 + 522547200*x^6 + 4478 9760*x^7 + 1679616*x^8)*Log[3]^2),x]
Output:
(10 + 3*x - (9*x^2)/(3*x - 48*(10 + 3*x)^4 + 48*(10 + 3*x)^4*Log[3]))/(3*( -1 + Log[3]))
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.
| \(\displaystyle \int \frac {-1679616 x^8-44789760 x^7-522547200 x^6-3483642816 x^5-14515148160 x^4-38707027200 x^3-64511808000 x^2+\left (1679616 x^8+44789760 x^7+522547200 x^6+3483648000 x^5+14515200000 x^4+38707200000 x^3+64512000000 x^2+61440000000 x+25600000000\right ) \log (3)-61440000000 x-25600000000}{1679616 x^8+44789760 x^7+522547200 x^6+3483645408 x^5+14515165440 x^4+38707027200 x^3+64511616001 x^2+\left (1679616 x^8+44789760 x^7+522547200 x^6+3483648000 x^5+14515200000 x^4+38707200000 x^3+64512000000 x^2+61440000000 x+25600000000\right ) \log ^2(3)+\left (-3359232 x^8-89579520 x^7-1045094400 x^6-6967293408 x^5-29030365440 x^4-77414227200 x^3-129023616000 x^2-122879680000 x-51200000000\right ) \log (3)+61439680000 x+25600000000} \, dx\) |
| \(\Big \downarrow \) 2462 |
| \(\displaystyle \int \left (\frac {2 (3 x-20)}{3 (1-\log (3)) \left (1296 x^4 (1-\log (3))+17280 x^3 (1-\log (3))+86400 x^2 (1-\log (3))+x (191999-192000 \log (3))+160000 (1-\log (3))\right )}+\frac {172800 x^3 (1-\log (3))+9 x^2 (192001-192000 \log (3))+40 x (143999-144000 \log (3))+6400000 (1-\log (3))}{3 (1-\log (3)) \left (1296 x^4 (1-\log (3))+17280 x^3 (1-\log (3))+86400 x^2 (1-\log (3))+x (191999-192000 \log (3))+160000 (1-\log (3))\right )^2}+\frac {1}{\log (3)-1}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {40 \int \frac {1}{-1296 (1-\log (3)) x^4-17280 (1-\log (3)) x^3-86400 (1-\log (3)) x^2-(191999-192000 \log (3)) x-160000 (1-\log (3))}dx}{3 (1-\log (3))}+\frac {100 \int \frac {1}{\left (1296 (1-\log (3)) x^4+17280 (1-\log (3)) x^3+86400 (1-\log (3)) x^2+(191999-192000 \log (3)) x+160000 (1-\log (3))\right )^2}dx}{9 (1-\log (3))}-\frac {40 \int \frac {x}{\left (1296 (1-\log (3)) x^4+17280 (1-\log (3)) x^3+86400 (1-\log (3)) x^2+(191999-192000 \log (3)) x+160000 (1-\log (3))\right )^2}dx}{3 (1-\log (3))}+\frac {3 \int \frac {x^2}{\left (1296 (1-\log (3)) x^4+17280 (1-\log (3)) x^3+86400 (1-\log (3)) x^2+(191999-192000 \log (3)) x+160000 (1-\log (3))\right )^2}dx}{1-\log (3)}+\frac {2 \int \frac {x}{1296 (1-\log (3)) x^4+17280 (1-\log (3)) x^3+86400 (1-\log (3)) x^2+(191999-192000 \log (3)) x+160000 (1-\log (3))}dx}{1-\log (3)}-\frac {100}{9 (1-\log (3)) \left (1296 x^4 (1-\log (3))+17280 x^3 (1-\log (3))+86400 x^2 (1-\log (3))+x (191999-192000 \log (3))+160000 (1-\log (3))\right )}-\frac {x}{1-\log (3)}\) |
Input:
Int[(-25600000000 - 61440000000*x - 64511808000*x^2 - 38707027200*x^3 - 14 515148160*x^4 - 3483642816*x^5 - 522547200*x^6 - 44789760*x^7 - 1679616*x^ 8 + (25600000000 + 61440000000*x + 64512000000*x^2 + 38707200000*x^3 + 145 15200000*x^4 + 3483648000*x^5 + 522547200*x^6 + 44789760*x^7 + 1679616*x^8 )*Log[3])/(25600000000 + 61439680000*x + 64511616001*x^2 + 38707027200*x^3 + 14515165440*x^4 + 3483645408*x^5 + 522547200*x^6 + 44789760*x^7 + 16796 16*x^8 + (-51200000000 - 122879680000*x - 129023616000*x^2 - 77414227200*x ^3 - 29030365440*x^4 - 6967293408*x^5 - 1045094400*x^6 - 89579520*x^7 - 33 59232*x^8)*Log[3] + (25600000000 + 61440000000*x + 64512000000*x^2 + 38707 200000*x^3 + 14515200000*x^4 + 3483648000*x^5 + 522547200*x^6 + 44789760*x ^7 + 1679616*x^8)*Log[3]^2),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(71\) vs. \(2(17)=34\).
Time = 0.34 (sec) , antiderivative size = 72, normalized size of antiderivative = 3.79
| method | result | size |
| default | \(\frac {x}{\ln \left (3\right )-1}-\frac {x^{2}}{1296 \left (\ln \left (3\right )-1\right ) \left (x^{4} \ln \left (3\right )+\frac {40 x^{3} \ln \left (3\right )}{3}-x^{4}+\frac {200 x^{2} \ln \left (3\right )}{3}-\frac {40 x^{3}}{3}+\frac {4000 x \ln \left (3\right )}{27}-\frac {200 x^{2}}{3}+\frac {10000 \ln \left (3\right )}{81}-\frac {191999 x}{1296}-\frac {10000}{81}\right )}\) | \(72\) |
| risch | \(\frac {x}{\ln \left (3\right )-1}-\frac {x^{2}}{1296 \left (\ln \left (3\right )-1\right ) \left (x^{4} \ln \left (3\right )+\frac {40 x^{3} \ln \left (3\right )}{3}-x^{4}+\frac {200 x^{2} \ln \left (3\right )}{3}-\frac {40 x^{3}}{3}+\frac {4000 x \ln \left (3\right )}{27}-\frac {200 x^{2}}{3}+\frac {10000 \ln \left (3\right )}{81}-\frac {191999 x}{1296}-\frac {10000}{81}\right )}\) | \(72\) |
| norman | \(\frac {-960000 x^{2}-144000 x^{3}-\frac {40 \left (-179999+180000 \ln \left (3\right )\right ) x}{3 \left (\ln \left (3\right )-1\right )}+1296 x^{5}-\frac {6400000}{3}}{1296 x^{4} \ln \left (3\right )+17280 x^{3} \ln \left (3\right )-1296 x^{4}+86400 x^{2} \ln \left (3\right )-17280 x^{3}+192000 x \ln \left (3\right )-86400 x^{2}+160000 \ln \left (3\right )-191999 x -160000}\) | \(86\) |
| gosper | \(\frac {1296 x^{5} \ln \left (3\right )-1296 x^{5}-144000 x^{3} \ln \left (3\right )-960000 x^{2} \ln \left (3\right )+144000 x^{3}-2400000 x \ln \left (3\right )+960000 x^{2}-\frac {6400000 \ln \left (3\right )}{3}+\frac {7199960 x}{3}+\frac {6400000}{3}}{\left (1296 x^{4} \ln \left (3\right )+17280 x^{3} \ln \left (3\right )-1296 x^{4}+86400 x^{2} \ln \left (3\right )-17280 x^{3}+192000 x \ln \left (3\right )-86400 x^{2}+160000 \ln \left (3\right )-191999 x -160000\right ) \left (\ln \left (3\right )-1\right )}\) | \(111\) |
| parallelrisch | \(\frac {1679616 x^{5} \ln \left (3\right )+2764800000-1679616 x^{5}-186624000 x^{3} \ln \left (3\right )-1244160000 x^{2} \ln \left (3\right )+186624000 x^{3}-3110400000 x \ln \left (3\right )+1244160000 x^{2}-2764800000 \ln \left (3\right )+3110382720 x}{1296 \left (\ln \left (3\right )-1\right ) \left (1296 x^{4} \ln \left (3\right )+17280 x^{3} \ln \left (3\right )-1296 x^{4}+86400 x^{2} \ln \left (3\right )-17280 x^{3}+192000 x \ln \left (3\right )-86400 x^{2}+160000 \ln \left (3\right )-191999 x -160000\right )}\) | \(111\) |
Input:
int(((1679616*x^8+44789760*x^7+522547200*x^6+3483648000*x^5+14515200000*x^ 4+38707200000*x^3+64512000000*x^2+61440000000*x+25600000000)*ln(3)-1679616 *x^8-44789760*x^7-522547200*x^6-3483642816*x^5-14515148160*x^4-38707027200 *x^3-64511808000*x^2-61440000000*x-25600000000)/((1679616*x^8+44789760*x^7 +522547200*x^6+3483648000*x^5+14515200000*x^4+38707200000*x^3+64512000000* x^2+61440000000*x+25600000000)*ln(3)^2+(-3359232*x^8-89579520*x^7-10450944 00*x^6-6967293408*x^5-29030365440*x^4-77414227200*x^3-129023616000*x^2-122 879680000*x-51200000000)*ln(3)+1679616*x^8+44789760*x^7+522547200*x^6+3483 645408*x^5+14515165440*x^4+38707027200*x^3+64511616001*x^2+61439680000*x+2 5600000000),x,method=_RETURNVERBOSE)
Output:
x/(ln(3)-1)-1/1296/(ln(3)-1)*x^2/(x^4*ln(3)+40/3*x^3*ln(3)-x^4+200/3*x^2*l n(3)-40/3*x^3+4000/27*x*ln(3)-200/3*x^2+10000/81*ln(3)-191999/1296*x-10000 /81)
Leaf count of result is larger than twice the leaf count of optimal. 72 vs. \(2 (20) = 40\).
Time = 0.11 (sec) , antiderivative size = 72, normalized size of antiderivative = 3.79 \[ \int \frac {-25600000000-61440000000 x-64511808000 x^2-38707027200 x^3-14515148160 x^4-3483642816 x^5-522547200 x^6-44789760 x^7-1679616 x^8+\left (25600000000+61440000000 x+64512000000 x^2+38707200000 x^3+14515200000 x^4+3483648000 x^5+522547200 x^6+44789760 x^7+1679616 x^8\right ) \log (3)}{25600000000+61439680000 x+64511616001 x^2+38707027200 x^3+14515165440 x^4+3483645408 x^5+522547200 x^6+44789760 x^7+1679616 x^8+\left (-51200000000-122879680000 x-129023616000 x^2-77414227200 x^3-29030365440 x^4-6967293408 x^5-1045094400 x^6-89579520 x^7-3359232 x^8\right ) \log (3)+\left (25600000000+61440000000 x+64512000000 x^2+38707200000 x^3+14515200000 x^4+3483648000 x^5+522547200 x^6+44789760 x^7+1679616 x^8\right ) \log ^2(3)} \, dx=-\frac {16 \, {\left (81 \, x^{5} + 1080 \, x^{4} + 5400 \, x^{3} + 12000 \, x^{2} + 10000 \, x\right )}}{1296 \, x^{4} + 17280 \, x^{3} + 86400 \, x^{2} - 16 \, {\left (81 \, x^{4} + 1080 \, x^{3} + 5400 \, x^{2} + 12000 \, x + 10000\right )} \log \left (3\right ) + 191999 \, x + 160000} \] Input:
integrate(((1679616*x^8+44789760*x^7+522547200*x^6+3483648000*x^5+14515200 000*x^4+38707200000*x^3+64512000000*x^2+61440000000*x+25600000000)*log(3)- 1679616*x^8-44789760*x^7-522547200*x^6-3483642816*x^5-14515148160*x^4-3870 7027200*x^3-64511808000*x^2-61440000000*x-25600000000)/((1679616*x^8+44789 760*x^7+522547200*x^6+3483648000*x^5+14515200000*x^4+38707200000*x^3+64512 000000*x^2+61440000000*x+25600000000)*log(3)^2+(-3359232*x^8-89579520*x^7- 1045094400*x^6-6967293408*x^5-29030365440*x^4-77414227200*x^3-129023616000 *x^2-122879680000*x-51200000000)*log(3)+1679616*x^8+44789760*x^7+522547200 *x^6+3483645408*x^5+14515165440*x^4+38707027200*x^3+64511616001*x^2+614396 80000*x+25600000000),x, algorithm="fricas")
Output:
-16*(81*x^5 + 1080*x^4 + 5400*x^3 + 12000*x^2 + 10000*x)/(1296*x^4 + 17280 *x^3 + 86400*x^2 - 16*(81*x^4 + 1080*x^3 + 5400*x^2 + 12000*x + 10000)*log (3) + 191999*x + 160000)
Leaf count of result is larger than twice the leaf count of optimal. 88 vs. \(2 (14) = 28\).
Time = 4.92 (sec) , antiderivative size = 88, normalized size of antiderivative = 4.63 \[ \int \frac {-25600000000-61440000000 x-64511808000 x^2-38707027200 x^3-14515148160 x^4-3483642816 x^5-522547200 x^6-44789760 x^7-1679616 x^8+\left (25600000000+61440000000 x+64512000000 x^2+38707200000 x^3+14515200000 x^4+3483648000 x^5+522547200 x^6+44789760 x^7+1679616 x^8\right ) \log (3)}{25600000000+61439680000 x+64511616001 x^2+38707027200 x^3+14515165440 x^4+3483645408 x^5+522547200 x^6+44789760 x^7+1679616 x^8+\left (-51200000000-122879680000 x-129023616000 x^2-77414227200 x^3-29030365440 x^4-6967293408 x^5-1045094400 x^6-89579520 x^7-3359232 x^8\right ) \log (3)+\left (25600000000+61440000000 x+64512000000 x^2+38707200000 x^3+14515200000 x^4+3483648000 x^5+522547200 x^6+44789760 x^7+1679616 x^8\right ) \log ^2(3)} \, dx=- \frac {x^{2}}{x^{4} \left (- 2592 \log {\left (3 \right )} + 1296 + 1296 \log {\left (3 \right )}^{2}\right ) + x^{3} \left (- 34560 \log {\left (3 \right )} + 17280 + 17280 \log {\left (3 \right )}^{2}\right ) + x^{2} \left (- 172800 \log {\left (3 \right )} + 86400 + 86400 \log {\left (3 \right )}^{2}\right ) + x \left (- 383999 \log {\left (3 \right )} + 191999 + 192000 \log {\left (3 \right )}^{2}\right ) - 320000 \log {\left (3 \right )} + 160000 + 160000 \log {\left (3 \right )}^{2}} + \frac {x}{-1 + \log {\left (3 \right )}} \] Input:
integrate(((1679616*x**8+44789760*x**7+522547200*x**6+3483648000*x**5+1451 5200000*x**4+38707200000*x**3+64512000000*x**2+61440000000*x+25600000000)* ln(3)-1679616*x**8-44789760*x**7-522547200*x**6-3483642816*x**5-1451514816 0*x**4-38707027200*x**3-64511808000*x**2-61440000000*x-25600000000)/((1679 616*x**8+44789760*x**7+522547200*x**6+3483648000*x**5+14515200000*x**4+387 07200000*x**3+64512000000*x**2+61440000000*x+25600000000)*ln(3)**2+(-33592 32*x**8-89579520*x**7-1045094400*x**6-6967293408*x**5-29030365440*x**4-774 14227200*x**3-129023616000*x**2-122879680000*x-51200000000)*ln(3)+1679616* x**8+44789760*x**7+522547200*x**6+3483645408*x**5+14515165440*x**4+3870702 7200*x**3+64511616001*x**2+61439680000*x+25600000000),x)
Output:
-x**2/(x**4*(-2592*log(3) + 1296 + 1296*log(3)**2) + x**3*(-34560*log(3) + 17280 + 17280*log(3)**2) + x**2*(-172800*log(3) + 86400 + 86400*log(3)**2 ) + x*(-383999*log(3) + 191999 + 192000*log(3)**2) - 320000*log(3) + 16000 0 + 160000*log(3)**2) + x/(-1 + log(3))
Leaf count of result is larger than twice the leaf count of optimal. 87 vs. \(2 (20) = 40\).
Time = 0.04 (sec) , antiderivative size = 87, normalized size of antiderivative = 4.58 \[ \int \frac {-25600000000-61440000000 x-64511808000 x^2-38707027200 x^3-14515148160 x^4-3483642816 x^5-522547200 x^6-44789760 x^7-1679616 x^8+\left (25600000000+61440000000 x+64512000000 x^2+38707200000 x^3+14515200000 x^4+3483648000 x^5+522547200 x^6+44789760 x^7+1679616 x^8\right ) \log (3)}{25600000000+61439680000 x+64511616001 x^2+38707027200 x^3+14515165440 x^4+3483645408 x^5+522547200 x^6+44789760 x^7+1679616 x^8+\left (-51200000000-122879680000 x-129023616000 x^2-77414227200 x^3-29030365440 x^4-6967293408 x^5-1045094400 x^6-89579520 x^7-3359232 x^8\right ) \log (3)+\left (25600000000+61440000000 x+64512000000 x^2+38707200000 x^3+14515200000 x^4+3483648000 x^5+522547200 x^6+44789760 x^7+1679616 x^8\right ) \log ^2(3)} \, dx=-\frac {x^{2}}{1296 \, {\left (\log \left (3\right )^{2} - 2 \, \log \left (3\right ) + 1\right )} x^{4} + 17280 \, {\left (\log \left (3\right )^{2} - 2 \, \log \left (3\right ) + 1\right )} x^{3} + 86400 \, {\left (\log \left (3\right )^{2} - 2 \, \log \left (3\right ) + 1\right )} x^{2} + {\left (192000 \, \log \left (3\right )^{2} - 383999 \, \log \left (3\right ) + 191999\right )} x + 160000 \, \log \left (3\right )^{2} - 320000 \, \log \left (3\right ) + 160000} + \frac {x}{\log \left (3\right ) - 1} \] Input:
integrate(((1679616*x^8+44789760*x^7+522547200*x^6+3483648000*x^5+14515200 000*x^4+38707200000*x^3+64512000000*x^2+61440000000*x+25600000000)*log(3)- 1679616*x^8-44789760*x^7-522547200*x^6-3483642816*x^5-14515148160*x^4-3870 7027200*x^3-64511808000*x^2-61440000000*x-25600000000)/((1679616*x^8+44789 760*x^7+522547200*x^6+3483648000*x^5+14515200000*x^4+38707200000*x^3+64512 000000*x^2+61440000000*x+25600000000)*log(3)^2+(-3359232*x^8-89579520*x^7- 1045094400*x^6-6967293408*x^5-29030365440*x^4-77414227200*x^3-129023616000 *x^2-122879680000*x-51200000000)*log(3)+1679616*x^8+44789760*x^7+522547200 *x^6+3483645408*x^5+14515165440*x^4+38707027200*x^3+64511616001*x^2+614396 80000*x+25600000000),x, algorithm="maxima")
Output:
-x^2/(1296*(log(3)^2 - 2*log(3) + 1)*x^4 + 17280*(log(3)^2 - 2*log(3) + 1) *x^3 + 86400*(log(3)^2 - 2*log(3) + 1)*x^2 + (192000*log(3)^2 - 383999*log (3) + 191999)*x + 160000*log(3)^2 - 320000*log(3) + 160000) + x/(log(3) - 1)
Leaf count of result is larger than twice the leaf count of optimal. 85 vs. \(2 (20) = 40\).
Time = 0.13 (sec) , antiderivative size = 85, normalized size of antiderivative = 4.47 \[ \int \frac {-25600000000-61440000000 x-64511808000 x^2-38707027200 x^3-14515148160 x^4-3483642816 x^5-522547200 x^6-44789760 x^7-1679616 x^8+\left (25600000000+61440000000 x+64512000000 x^2+38707200000 x^3+14515200000 x^4+3483648000 x^5+522547200 x^6+44789760 x^7+1679616 x^8\right ) \log (3)}{25600000000+61439680000 x+64511616001 x^2+38707027200 x^3+14515165440 x^4+3483645408 x^5+522547200 x^6+44789760 x^7+1679616 x^8+\left (-51200000000-122879680000 x-129023616000 x^2-77414227200 x^3-29030365440 x^4-6967293408 x^5-1045094400 x^6-89579520 x^7-3359232 x^8\right ) \log (3)+\left (25600000000+61440000000 x+64512000000 x^2+38707200000 x^3+14515200000 x^4+3483648000 x^5+522547200 x^6+44789760 x^7+1679616 x^8\right ) \log ^2(3)} \, dx=\frac {x \log \left (3\right ) - x}{\log \left (3\right )^{2} - 2 \, \log \left (3\right ) + 1} - \frac {x^{2}}{{\left (1296 \, x^{4} \log \left (3\right ) - 1296 \, x^{4} + 17280 \, x^{3} \log \left (3\right ) - 17280 \, x^{3} + 86400 \, x^{2} \log \left (3\right ) - 86400 \, x^{2} + 192000 \, x \log \left (3\right ) - 191999 \, x + 160000 \, \log \left (3\right ) - 160000\right )} {\left (\log \left (3\right ) - 1\right )}} \] Input:
integrate(((1679616*x^8+44789760*x^7+522547200*x^6+3483648000*x^5+14515200 000*x^4+38707200000*x^3+64512000000*x^2+61440000000*x+25600000000)*log(3)- 1679616*x^8-44789760*x^7-522547200*x^6-3483642816*x^5-14515148160*x^4-3870 7027200*x^3-64511808000*x^2-61440000000*x-25600000000)/((1679616*x^8+44789 760*x^7+522547200*x^6+3483648000*x^5+14515200000*x^4+38707200000*x^3+64512 000000*x^2+61440000000*x+25600000000)*log(3)^2+(-3359232*x^8-89579520*x^7- 1045094400*x^6-6967293408*x^5-29030365440*x^4-77414227200*x^3-129023616000 *x^2-122879680000*x-51200000000)*log(3)+1679616*x^8+44789760*x^7+522547200 *x^6+3483645408*x^5+14515165440*x^4+38707027200*x^3+64511616001*x^2+614396 80000*x+25600000000),x, algorithm="giac")
Output:
(x*log(3) - x)/(log(3)^2 - 2*log(3) + 1) - x^2/((1296*x^4*log(3) - 1296*x^ 4 + 17280*x^3*log(3) - 17280*x^3 + 86400*x^2*log(3) - 86400*x^2 + 192000*x *log(3) - 191999*x + 160000*log(3) - 160000)*(log(3) - 1))
Time = 3.31 (sec) , antiderivative size = 66, normalized size of antiderivative = 3.47 \[ \int \frac {-25600000000-61440000000 x-64511808000 x^2-38707027200 x^3-14515148160 x^4-3483642816 x^5-522547200 x^6-44789760 x^7-1679616 x^8+\left (25600000000+61440000000 x+64512000000 x^2+38707200000 x^3+14515200000 x^4+3483648000 x^5+522547200 x^6+44789760 x^7+1679616 x^8\right ) \log (3)}{25600000000+61439680000 x+64511616001 x^2+38707027200 x^3+14515165440 x^4+3483645408 x^5+522547200 x^6+44789760 x^7+1679616 x^8+\left (-51200000000-122879680000 x-129023616000 x^2-77414227200 x^3-29030365440 x^4-6967293408 x^5-1045094400 x^6-89579520 x^7-3359232 x^8\right ) \log (3)+\left (25600000000+61440000000 x+64512000000 x^2+38707200000 x^3+14515200000 x^4+3483648000 x^5+522547200 x^6+44789760 x^7+1679616 x^8\right ) \log ^2(3)} \, dx=\frac {x}{\ln \left (3\right )-1}-\frac {x^2}{\left (\ln \left (3\right )-1\right )\,\left (\left (1296\,\ln \left (3\right )-1296\right )\,x^4+\left (17280\,\ln \left (3\right )-17280\right )\,x^3+\left (86400\,\ln \left (3\right )-86400\right )\,x^2+\left (192000\,\ln \left (3\right )-191999\right )\,x+160000\,\ln \left (3\right )-160000\right )} \] Input:
int(-(61440000000*x - log(3)*(61440000000*x + 64512000000*x^2 + 3870720000 0*x^3 + 14515200000*x^4 + 3483648000*x^5 + 522547200*x^6 + 44789760*x^7 + 1679616*x^8 + 25600000000) + 64511808000*x^2 + 38707027200*x^3 + 145151481 60*x^4 + 3483642816*x^5 + 522547200*x^6 + 44789760*x^7 + 1679616*x^8 + 256 00000000)/(61439680000*x + log(3)^2*(61440000000*x + 64512000000*x^2 + 387 07200000*x^3 + 14515200000*x^4 + 3483648000*x^5 + 522547200*x^6 + 44789760 *x^7 + 1679616*x^8 + 25600000000) - log(3)*(122879680000*x + 129023616000* x^2 + 77414227200*x^3 + 29030365440*x^4 + 6967293408*x^5 + 1045094400*x^6 + 89579520*x^7 + 3359232*x^8 + 51200000000) + 64511616001*x^2 + 3870702720 0*x^3 + 14515165440*x^4 + 3483645408*x^5 + 522547200*x^6 + 44789760*x^7 + 1679616*x^8 + 25600000000),x)
Output:
x/(log(3) - 1) - x^2/((log(3) - 1)*(160000*log(3) + x*(192000*log(3) - 191 999) + x^4*(1296*log(3) - 1296) + x^3*(17280*log(3) - 17280) + x^2*(86400* log(3) - 86400) - 160000))
Time = 0.19 (sec) , antiderivative size = 143, normalized size of antiderivative = 7.53 \[ \int \frac {-25600000000-61440000000 x-64511808000 x^2-38707027200 x^3-14515148160 x^4-3483642816 x^5-522547200 x^6-44789760 x^7-1679616 x^8+\left (25600000000+61440000000 x+64512000000 x^2+38707200000 x^3+14515200000 x^4+3483648000 x^5+522547200 x^6+44789760 x^7+1679616 x^8\right ) \log (3)}{25600000000+61439680000 x+64511616001 x^2+38707027200 x^3+14515165440 x^4+3483645408 x^5+522547200 x^6+44789760 x^7+1679616 x^8+\left (-51200000000-122879680000 x-129023616000 x^2-77414227200 x^3-29030365440 x^4-6967293408 x^5-1045094400 x^6-89579520 x^7-3359232 x^8\right ) \log (3)+\left (25600000000+61440000000 x+64512000000 x^2+38707200000 x^3+14515200000 x^4+3483648000 x^5+522547200 x^6+44789760 x^7+1679616 x^8\right ) \log ^2(3)} \, dx=\frac {1296 \,\mathrm {log}\left (3\right ) x^{5}+10800 \,\mathrm {log}\left (3\right ) x^{4}-240000 \,\mathrm {log}\left (3\right ) x^{2}-800000 \,\mathrm {log}\left (3\right ) x -800000 \,\mathrm {log}\left (3\right )-1296 x^{5}-10800 x^{4}+240000 x^{2}+799995 x +800000}{1296 x^{4} \mathrm {log}\left (3\right )^{2}+17280 \mathrm {log}\left (3\right )^{2} x^{3}+86400 \mathrm {log}\left (3\right )^{2} x^{2}+192000 \mathrm {log}\left (3\right )^{2} x +160000 \mathrm {log}\left (3\right )^{2}-2592 \,\mathrm {log}\left (3\right ) x^{4}-34560 \,\mathrm {log}\left (3\right ) x^{3}-172800 \,\mathrm {log}\left (3\right ) x^{2}-383999 \,\mathrm {log}\left (3\right ) x -320000 \,\mathrm {log}\left (3\right )+1296 x^{4}+17280 x^{3}+86400 x^{2}+191999 x +160000} \] Input:
int(((1679616*x^8+44789760*x^7+522547200*x^6+3483648000*x^5+14515200000*x^ 4+38707200000*x^3+64512000000*x^2+61440000000*x+25600000000)*log(3)-167961 6*x^8-44789760*x^7-522547200*x^6-3483642816*x^5-14515148160*x^4-3870702720 0*x^3-64511808000*x^2-61440000000*x-25600000000)/((1679616*x^8+44789760*x^ 7+522547200*x^6+3483648000*x^5+14515200000*x^4+38707200000*x^3+64512000000 *x^2+61440000000*x+25600000000)*log(3)^2+(-3359232*x^8-89579520*x^7-104509 4400*x^6-6967293408*x^5-29030365440*x^4-77414227200*x^3-129023616000*x^2-1 22879680000*x-51200000000)*log(3)+1679616*x^8+44789760*x^7+522547200*x^6+3 483645408*x^5+14515165440*x^4+38707027200*x^3+64511616001*x^2+61439680000* x+25600000000),x)
Output:
(1296*log(3)*x**5 + 10800*log(3)*x**4 - 240000*log(3)*x**2 - 800000*log(3) *x - 800000*log(3) - 1296*x**5 - 10800*x**4 + 240000*x**2 + 799995*x + 800 000)/(1296*log(3)**2*x**4 + 17280*log(3)**2*x**3 + 86400*log(3)**2*x**2 + 192000*log(3)**2*x + 160000*log(3)**2 - 2592*log(3)*x**4 - 34560*log(3)*x* *3 - 172800*log(3)*x**2 - 383999*log(3)*x - 320000*log(3) + 1296*x**4 + 17 280*x**3 + 86400*x**2 + 191999*x + 160000)