3.73.84 \(\int \frac {-25600000000-61440000000 x-64511808000 x^2-38707027200 x^3-14515148160 x^4-3483642816 x^5-522547200 x^6-44789760 x^7-1679616 x^8+(25600000000+61440000000 x+64512000000 x^2+38707200000 x^3+14515200000 x^4+3483648000 x^5+522547200 x^6+44789760 x^7+1679616 x^8) \log (3)}{25600000000+61439680000 x+64511616001 x^2+38707027200 x^3+14515165440 x^4+3483645408 x^5+522547200 x^6+44789760 x^7+1679616 x^8+(-51200000000-122879680000 x-129023616000 x^2-77414227200 x^3-29030365440 x^4-6967293408 x^5-1045094400 x^6-89579520 x^7-3359232 x^8) \log (3)+(25600000000+61440000000 x+64512000000 x^2+38707200000 x^3+14515200000 x^4+3483648000 x^5+522547200 x^6+44789760 x^7+1679616 x^8) \log ^2(3)} \, dx\)

Optimal. Leaf size=19 \[ \frac {x}{-1+\frac {x}{(x+5 (4+x))^4}+\log (3)} \]

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Rubi [F]  time = 1.76, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \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 \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-25600000000 - 61440000000*x - 64511808000*x^2 - 38707027200*x^3 - 14515148160*x^4 - 3483642816*x^5 - 522
547200*x^6 - 44789760*x^7 - 1679616*x^8 + (25600000000 + 61440000000*x + 64512000000*x^2 + 38707200000*x^3 + 1
4515200000*x^4 + 3483648000*x^5 + 522547200*x^6 + 44789760*x^7 + 1679616*x^8)*Log[3])/(25600000000 + 614396800
00*x + 64511616001*x^2 + 38707027200*x^3 + 14515165440*x^4 + 3483645408*x^5 + 522547200*x^6 + 44789760*x^7 + 1
679616*x^8 + (-51200000000 - 122879680000*x - 129023616000*x^2 - 77414227200*x^3 - 29030365440*x^4 - 696729340
8*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 + 44789760*x^7 + 1679616*x^8)*Log[3]^2),x]

[Out]

-(x/(1 - Log[3])) - 100/(9*(x*(191999 - 192000*Log[3]) + 160000*(1 - Log[3]) + 86400*x^2*(1 - Log[3]) + 17280*
x^3*(1 - Log[3]) + 1296*x^4*(1 - Log[3]))*(1 - Log[3])) + (40*Defer[Int][(-(x*(191999 - 192000*Log[3])) - 1600
00*(1 - Log[3]) - 86400*x^2*(1 - Log[3]) - 17280*x^3*(1 - Log[3]) - 1296*x^4*(1 - Log[3]))^(-1), x])/(3*(1 - L
og[3])) + (100*Defer[Int][(x*(191999 - 192000*Log[3]) + 160000*(1 - Log[3]) + 86400*x^2*(1 - Log[3]) + 17280*x
^3*(1 - Log[3]) + 1296*x^4*(1 - Log[3]))^(-2), x])/(9*(1 - Log[3])) - (40*Defer[Int][x/(x*(191999 - 192000*Log
[3]) + 160000*(1 - Log[3]) + 86400*x^2*(1 - Log[3]) + 17280*x^3*(1 - Log[3]) + 1296*x^4*(1 - Log[3]))^2, x])/(
3*(1 - Log[3])) + (3*Defer[Int][x^2/(x*(191999 - 192000*Log[3]) + 160000*(1 - Log[3]) + 86400*x^2*(1 - Log[3])
+ 17280*x^3*(1 - Log[3]) + 1296*x^4*(1 - Log[3]))^2, x])/(1 - Log[3]) + (2*Defer[Int][x/(x*(191999 - 192000*L
og[3]) + 160000*(1 - Log[3]) + 86400*x^2*(1 - Log[3]) + 17280*x^3*(1 - Log[3]) + 1296*x^4*(1 - Log[3])), x])/(
1 - Log[3])

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {9 x^2 (192001-192000 \log (3))+40 x (143999-144000 \log (3))+6400000 (1-\log (3))+172800 x^3 (1-\log (3))}{3 \left (x (191999-192000 \log (3))+160000 (1-\log (3))+86400 x^2 (1-\log (3))+17280 x^3 (1-\log (3))+1296 x^4 (1-\log (3))\right )^2 (1-\log (3))}+\frac {2 (-20+3 x)}{3 \left (x (191999-192000 \log (3))+160000 (1-\log (3))+86400 x^2 (1-\log (3))+17280 x^3 (1-\log (3))+1296 x^4 (1-\log (3))\right ) (1-\log (3))}+\frac {1}{-1+\log (3)}\right ) \, dx\\ &=-\frac {x}{1-\log (3)}+\frac {\int \frac {9 x^2 (192001-192000 \log (3))+40 x (143999-144000 \log (3))+6400000 (1-\log (3))+172800 x^3 (1-\log (3))}{\left (x (191999-192000 \log (3))+160000 (1-\log (3))+86400 x^2 (1-\log (3))+17280 x^3 (1-\log (3))+1296 x^4 (1-\log (3))\right )^2} \, dx}{3 (1-\log (3))}+\frac {2 \int \frac {-20+3 x}{x (191999-192000 \log (3))+160000 (1-\log (3))+86400 x^2 (1-\log (3))+17280 x^3 (1-\log (3))+1296 x^4 (1-\log (3))} \, dx}{3 (1-\log (3))}\\ &=-\frac {x}{1-\log (3)}-\frac {100}{9 \left (x (191999-192000 \log (3))+160000 (1-\log (3))+86400 x^2 (1-\log (3))+17280 x^3 (1-\log (3))+1296 x^4 (1-\log (3))\right ) (1-\log (3))}+\frac {\int \frac {172800 (1-\log (3))-207360 x (1-\log (3))+46656 x^2 (1-\log (3))}{\left (x (191999-192000 \log (3))+160000 (1-\log (3))+86400 x^2 (1-\log (3))+17280 x^3 (1-\log (3))+1296 x^4 (1-\log (3))\right )^2} \, dx}{15552 (1-\log (3))^2}+\frac {2 \int \left (\frac {20}{-x (191999-192000 \log (3))-160000 (1-\log (3))-86400 x^2 (1-\log (3))-17280 x^3 (1-\log (3))-1296 x^4 (1-\log (3))}+\frac {3 x}{x (191999-192000 \log (3))+160000 (1-\log (3))+86400 x^2 (1-\log (3))+17280 x^3 (1-\log (3))+1296 x^4 (1-\log (3))}\right ) \, dx}{3 (1-\log (3))}\\ &=-\frac {x}{1-\log (3)}-\frac {100}{9 \left (x (191999-192000 \log (3))+160000 (1-\log (3))+86400 x^2 (1-\log (3))+17280 x^3 (1-\log (3))+1296 x^4 (1-\log (3))\right ) (1-\log (3))}+\frac {\int \frac {1728 \left (100-120 x+27 x^2\right ) (1-\log (3))}{\left (x (191999-192000 \log (3))+160000 (1-\log (3))+86400 x^2 (1-\log (3))+17280 x^3 (1-\log (3))+1296 x^4 (1-\log (3))\right )^2} \, dx}{15552 (1-\log (3))^2}+\frac {2 \int \frac {x}{x (191999-192000 \log (3))+160000 (1-\log (3))+86400 x^2 (1-\log (3))+17280 x^3 (1-\log (3))+1296 x^4 (1-\log (3))} \, dx}{1-\log (3)}+\frac {40 \int \frac {1}{-x (191999-192000 \log (3))-160000 (1-\log (3))-86400 x^2 (1-\log (3))-17280 x^3 (1-\log (3))-1296 x^4 (1-\log (3))} \, dx}{3 (1-\log (3))}\\ &=-\frac {x}{1-\log (3)}-\frac {100}{9 \left (x (191999-192000 \log (3))+160000 (1-\log (3))+86400 x^2 (1-\log (3))+17280 x^3 (1-\log (3))+1296 x^4 (1-\log (3))\right ) (1-\log (3))}+\frac {\int \frac {100-120 x+27 x^2}{\left (x (191999-192000 \log (3))+160000 (1-\log (3))+86400 x^2 (1-\log (3))+17280 x^3 (1-\log (3))+1296 x^4 (1-\log (3))\right )^2} \, dx}{9 (1-\log (3))}+\frac {2 \int \frac {x}{x (191999-192000 \log (3))+160000 (1-\log (3))+86400 x^2 (1-\log (3))+17280 x^3 (1-\log (3))+1296 x^4 (1-\log (3))} \, dx}{1-\log (3)}+\frac {40 \int \frac {1}{-x (191999-192000 \log (3))-160000 (1-\log (3))-86400 x^2 (1-\log (3))-17280 x^3 (1-\log (3))-1296 x^4 (1-\log (3))} \, dx}{3 (1-\log (3))}\\ &=-\frac {x}{1-\log (3)}-\frac {100}{9 \left (x (191999-192000 \log (3))+160000 (1-\log (3))+86400 x^2 (1-\log (3))+17280 x^3 (1-\log (3))+1296 x^4 (1-\log (3))\right ) (1-\log (3))}+\frac {\int \left (\frac {100}{\left (x (191999-192000 \log (3))+160000 (1-\log (3))+86400 x^2 (1-\log (3))+17280 x^3 (1-\log (3))+1296 x^4 (1-\log (3))\right )^2}-\frac {120 x}{\left (x (191999-192000 \log (3))+160000 (1-\log (3))+86400 x^2 (1-\log (3))+17280 x^3 (1-\log (3))+1296 x^4 (1-\log (3))\right )^2}+\frac {27 x^2}{\left (x (191999-192000 \log (3))+160000 (1-\log (3))+86400 x^2 (1-\log (3))+17280 x^3 (1-\log (3))+1296 x^4 (1-\log (3))\right )^2}\right ) \, dx}{9 (1-\log (3))}+\frac {2 \int \frac {x}{x (191999-192000 \log (3))+160000 (1-\log (3))+86400 x^2 (1-\log (3))+17280 x^3 (1-\log (3))+1296 x^4 (1-\log (3))} \, dx}{1-\log (3)}+\frac {40 \int \frac {1}{-x (191999-192000 \log (3))-160000 (1-\log (3))-86400 x^2 (1-\log (3))-17280 x^3 (1-\log (3))-1296 x^4 (1-\log (3))} \, dx}{3 (1-\log (3))}\\ &=-\frac {x}{1-\log (3)}-\frac {100}{9 \left (x (191999-192000 \log (3))+160000 (1-\log (3))+86400 x^2 (1-\log (3))+17280 x^3 (1-\log (3))+1296 x^4 (1-\log (3))\right ) (1-\log (3))}+\frac {2 \int \frac {x}{x (191999-192000 \log (3))+160000 (1-\log (3))+86400 x^2 (1-\log (3))+17280 x^3 (1-\log (3))+1296 x^4 (1-\log (3))} \, dx}{1-\log (3)}+\frac {3 \int \frac {x^2}{\left (x (191999-192000 \log (3))+160000 (1-\log (3))+86400 x^2 (1-\log (3))+17280 x^3 (1-\log (3))+1296 x^4 (1-\log (3))\right )^2} \, dx}{1-\log (3)}+\frac {100 \int \frac {1}{\left (x (191999-192000 \log (3))+160000 (1-\log (3))+86400 x^2 (1-\log (3))+17280 x^3 (1-\log (3))+1296 x^4 (1-\log (3))\right )^2} \, dx}{9 (1-\log (3))}+\frac {40 \int \frac {1}{-x (191999-192000 \log (3))-160000 (1-\log (3))-86400 x^2 (1-\log (3))-17280 x^3 (1-\log (3))-1296 x^4 (1-\log (3))} \, dx}{3 (1-\log (3))}-\frac {40 \int \frac {x}{\left (x (191999-192000 \log (3))+160000 (1-\log (3))+86400 x^2 (1-\log (3))+17280 x^3 (1-\log (3))+1296 x^4 (1-\log (3))\right )^2} \, dx}{3 (1-\log (3))}\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.07, size = 46, normalized size = 2.42 \begin {gather*} \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))} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-25600000000 - 61440000000*x - 64511808000*x^2 - 38707027200*x^3 - 14515148160*x^4 - 3483642816*x^5
- 522547200*x^6 - 44789760*x^7 - 1679616*x^8 + (25600000000 + 61440000000*x + 64512000000*x^2 + 38707200000*x
^3 + 14515200000*x^4 + 3483648000*x^5 + 522547200*x^6 + 44789760*x^7 + 1679616*x^8)*Log[3])/(25600000000 + 614
39680000*x + 64511616001*x^2 + 38707027200*x^3 + 14515165440*x^4 + 3483645408*x^5 + 522547200*x^6 + 44789760*x
^7 + 1679616*x^8 + (-51200000000 - 122879680000*x - 129023616000*x^2 - 77414227200*x^3 - 29030365440*x^4 - 696
7293408*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 + 44789760*x^7 + 1679616*x^8)*Log[3]
^2),x]

[Out]

(10 + 3*x - (9*x^2)/(3*x - 48*(10 + 3*x)^4 + 48*(10 + 3*x)^4*Log[3]))/(3*(-1 + Log[3]))

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fricas [B]  time = 0.53, size = 72, normalized size = 3.79 \begin {gather*} -\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 \relax (3) + 191999 \, x + 160000} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((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)-1679616*x^8-44789760*x^7-522547200*x^6-3483642816*x^5-14515148160*x^4-38
707027200*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^7-1045094400*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+
61439680000*x+25600000000),x, algorithm="fricas")

[Out]

-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)

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giac [B]  time = 0.29, size = 85, normalized size = 4.47 \begin {gather*} \frac {x \log \relax (3) - x}{\log \relax (3)^{2} - 2 \, \log \relax (3) + 1} - \frac {x^{2}}{{\left (1296 \, x^{4} \log \relax (3) - 1296 \, x^{4} + 17280 \, x^{3} \log \relax (3) - 17280 \, x^{3} + 86400 \, x^{2} \log \relax (3) - 86400 \, x^{2} + 192000 \, x \log \relax (3) - 191999 \, x + 160000 \, \log \relax (3) - 160000\right )} {\left (\log \relax (3) - 1\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((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)-1679616*x^8-44789760*x^7-522547200*x^6-3483642816*x^5-14515148160*x^4-38
707027200*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^7-1045094400*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+
61439680000*x+25600000000),x, algorithm="giac")

[Out]

(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 + 8
6400*x^2*log(3) - 86400*x^2 + 192000*x*log(3) - 191999*x + 160000*log(3) - 160000)*(log(3) - 1))

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maple [B]  time = 0.26, size = 72, normalized size = 3.79

method	result	size
default	\(\frac {x}{\ln \relax (3)-1}-\frac {x^{2}}{1296 \left (\ln \relax (3)-1\right ) \left (x^{4} \ln \relax (3)+\frac {40 x^{3} \ln \relax (3)}{3}-x^{4}+\frac {200 x^{2} \ln \relax (3)}{3}-\frac {40 x^{3}}{3}+\frac {4000 x \ln \relax (3)}{27}-\frac {200 x^{2}}{3}+\frac {10000 \ln \relax (3)}{81}-\frac {191999 x}{1296}-\frac {10000}{81}\right )}\)	\(72\)
risch	\(\frac {x}{\ln \relax (3)-1}-\frac {x^{2}}{1296 \left (\ln \relax (3)-1\right ) \left (x^{4} \ln \relax (3)+\frac {40 x^{3} \ln \relax (3)}{3}-x^{4}+\frac {200 x^{2} \ln \relax (3)}{3}-\frac {40 x^{3}}{3}+\frac {4000 x \ln \relax (3)}{27}-\frac {200 x^{2}}{3}+\frac {10000 \ln \relax (3)}{81}-\frac {191999 x}{1296}-\frac {10000}{81}\right )}\)	\(72\)
norman	\(\frac {-960000 x^{2}-144000 x^{3}-\frac {40 \left (-179999+180000 \ln \relax (3)\right ) x}{3 \left (\ln \relax (3)-1\right )}+1296 x^{5}-\frac {6400000}{3}}{1296 x^{4} \ln \relax (3)+17280 x^{3} \ln \relax (3)-1296 x^{4}+86400 x^{2} \ln \relax (3)-17280 x^{3}+192000 x \ln \relax (3)-86400 x^{2}+160000 \ln \relax (3)-191999 x -160000}\)	\(86\)
gosper	\(\frac {1296 x^{5} \ln \relax (3)-1296 x^{5}-144000 x^{3} \ln \relax (3)-960000 x^{2} \ln \relax (3)+144000 x^{3}-2400000 x \ln \relax (3)+960000 x^{2}-\frac {6400000 \ln \relax (3)}{3}+\frac {7199960 x}{3}+\frac {6400000}{3}}{\left (1296 x^{4} \ln \relax (3)+17280 x^{3} \ln \relax (3)-1296 x^{4}+86400 x^{2} \ln \relax (3)-17280 x^{3}+192000 x \ln \relax (3)-86400 x^{2}+160000 \ln \relax (3)-191999 x -160000\right ) \left (\ln \relax (3)-1\right )}\)	\(111\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((1679616*x^8+44789760*x^7+522547200*x^6+3483648000*x^5+14515200000*x^4+38707200000*x^3+64512000000*x^2+61
440000000*x+25600000000)*ln(3)-1679616*x^8-44789760*x^7-522547200*x^6-3483642816*x^5-14515148160*x^4-387070272
00*x^3-64511808000*x^2-61440000000*x-25600000000)/((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)^2+(-3359232*x^8-89579520*x^7-1045
094400*x^6-6967293408*x^5-29030365440*x^4-77414227200*x^3-129023616000*x^2-122879680000*x-51200000000)*ln(3)+1
679616*x^8+44789760*x^7+522547200*x^6+3483645408*x^5+14515165440*x^4+38707027200*x^3+64511616001*x^2+614396800
00*x+25600000000),x,method=_RETURNVERBOSE)

[Out]

1/(ln(3)-1)*x-1/1296/(ln(3)-1)*x^2/(x^4*ln(3)+40/3*x^3*ln(3)-x^4+200/3*x^2*ln(3)-40/3*x^3+4000/27*x*ln(3)-200/
3*x^2+10000/81*ln(3)-191999/1296*x-10000/81)

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maxima [B]  time = 0.36, size = 87, normalized size = 4.58 \begin {gather*} -\frac {x^{2}}{1296 \, {\left (\log \relax (3)^{2} - 2 \, \log \relax (3) + 1\right )} x^{4} + 17280 \, {\left (\log \relax (3)^{2} - 2 \, \log \relax (3) + 1\right )} x^{3} + 86400 \, {\left (\log \relax (3)^{2} - 2 \, \log \relax (3) + 1\right )} x^{2} + {\left (192000 \, \log \relax (3)^{2} - 383999 \, \log \relax (3) + 191999\right )} x + 160000 \, \log \relax (3)^{2} - 320000 \, \log \relax (3) + 160000} + \frac {x}{\log \relax (3) - 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((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)-1679616*x^8-44789760*x^7-522547200*x^6-3483642816*x^5-14515148160*x^4-38
707027200*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^7-1045094400*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+
61439680000*x+25600000000),x, algorithm="maxima")

[Out]

-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)

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mupad [B]  time = 4.74, size = 66, normalized size = 3.47 \begin {gather*} \frac {x}{\ln \relax (3)-1}-\frac {x^2}{\left (\ln \relax (3)-1\right )\,\left (\left (1296\,\ln \relax (3)-1296\right )\,x^4+\left (17280\,\ln \relax (3)-17280\right )\,x^3+\left (86400\,\ln \relax (3)-86400\right )\,x^2+\left (192000\,\ln \relax (3)-191999\right )\,x+160000\,\ln \relax (3)-160000\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(61440000000*x - log(3)*(61440000000*x + 64512000000*x^2 + 38707200000*x^3 + 14515200000*x^4 + 3483648000
*x^5 + 522547200*x^6 + 44789760*x^7 + 1679616*x^8 + 25600000000) + 64511808000*x^2 + 38707027200*x^3 + 1451514
8160*x^4 + 3483642816*x^5 + 522547200*x^6 + 44789760*x^7 + 1679616*x^8 + 25600000000)/(61439680000*x + log(3)^
2*(61440000000*x + 64512000000*x^2 + 38707200000*x^3 + 14515200000*x^4 + 3483648000*x^5 + 522547200*x^6 + 4478
9760*x^7 + 1679616*x^8 + 25600000000) - log(3)*(122879680000*x + 129023616000*x^2 + 77414227200*x^3 + 29030365
440*x^4 + 6967293408*x^5 + 1045094400*x^6 + 89579520*x^7 + 3359232*x^8 + 51200000000) + 64511616001*x^2 + 3870
7027200*x^3 + 14515165440*x^4 + 3483645408*x^5 + 522547200*x^6 + 44789760*x^7 + 1679616*x^8 + 25600000000),x)

[Out]

x/(log(3) - 1) - x^2/((log(3) - 1)*(160000*log(3) + x*(192000*log(3) - 191999) + x^4*(1296*log(3) - 1296) + x^
3*(17280*log(3) - 17280) + x^2*(86400*log(3) - 86400) - 160000))

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sympy [B]  time = 8.04, size = 88, normalized size = 4.63 \begin {gather*} - \frac {x^{2}}{x^{4} \left (- 2592 \log {\relax (3 )} + 1296 + 1296 \log {\relax (3 )}^{2}\right ) + x^{3} \left (- 34560 \log {\relax (3 )} + 17280 + 17280 \log {\relax (3 )}^{2}\right ) + x^{2} \left (- 172800 \log {\relax (3 )} + 86400 + 86400 \log {\relax (3 )}^{2}\right ) + x \left (- 383999 \log {\relax (3 )} + 191999 + 192000 \log {\relax (3 )}^{2}\right ) - 320000 \log {\relax (3 )} + 160000 + 160000 \log {\relax (3 )}^{2}} + \frac {x}{-1 + \log {\relax (3 )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((1679616*x**8+44789760*x**7+522547200*x**6+3483648000*x**5+14515200000*x**4+38707200000*x**3+645120
00000*x**2+61440000000*x+25600000000)*ln(3)-1679616*x**8-44789760*x**7-522547200*x**6-3483642816*x**5-14515148
160*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+(-3
359232*x**8-89579520*x**7-1045094400*x**6-6967293408*x**5-29030365440*x**4-77414227200*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+3
8707027200*x**3+64511616001*x**2+61439680000*x+25600000000),x)

[Out]

-x**2/(x**4*(-2592*log(3) + 1296 + 1296*log(3)**2) + x**3*(-34560*log(3) + 17280 + 17280*log(3)**2) + x**2*(-1
72800*log(3) + 86400 + 86400*log(3)**2) + x*(-383999*log(3) + 191999 + 192000*log(3)**2) - 320000*log(3) + 160
000 + 160000*log(3)**2) + x/(-1 + log(3))

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