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

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

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

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Mathematica [B]  time = 0.07, size = 46, normalized size = 2.42 $$\begin{array}{c}\frac{10+3x-\frac{9x^2}{3x-48(10+3x{)}^4+48(10+3x{)}^4\log (3)}}{3(-1+\log (3))}\end{array}$$

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 $$\begin{array}{c}-\frac{16(81x^5+1080x^4+5400x^3+12000x^2+10000x)}{1296x^4+17280x^3+86400x^2-16(81x^4+1080x^3+5400x^2+12000x+10000)\log (3)+191999x+160000}\end{array}$$

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 $$\begin{array}{c}\frac{x\log (3)-x}{\log (3{)}^2-2\log (3)+1}-\frac{x^2}{(1296x^4\log (3)-1296x^4+17280x^3\log (3)-17280x^3+86400x^2\log (3)-86400x^2+192000x\log (3)-191999x+160000\log (3)-160000)(\log (3)-1)}\end{array}$$

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

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 $$\begin{array}{c}-\frac{x^2}{1296(\log (3{)}^2-2\log (3)+1)x^4+17280(\log (3{)}^2-2\log (3)+1)x^3+86400(\log (3{)}^2-2\log (3)+1)x^2+(192000\log (3{)}^2-383999\log (3)+191999)x+160000\log (3{)}^2-320000\log (3)+160000}+\frac{x}{\log (3)-1}\end{array}$$

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 $$\begin{array}{c}\frac{x}{\ln (3)-1}-\frac{x^2}{(\ln (3)-1)((1296\ln (3)-1296)x^4+(17280\ln (3)-17280)x^3+(86400\ln (3)-86400)x^2+(192000\ln (3)-191999)x+160000\ln (3)-160000)}\end{array}$$

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 $$\begin{array}{c}-\frac{x^2}{x^4(-2592\log (3)+1296+1296\log {(3)}^2)+x^3(-34560\log (3)+17280+17280\log {(3)}^2)+x^2(-172800\log (3)+86400+86400\log {(3)}^2)+x(-383999\log (3)+191999+192000\log {(3)}^2)-320000\log (3)+160000+160000\log {(3)}^2}+\frac{x}{-1+\log (3)}\end{array}$$

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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