3.17.74 $\int \frac{300x^3+300x^4+(-3600x^2-4500x^3-900x^4)\log (\frac{1+x}{3})+(14400x+21600x^2+8100x^3+900x^4){\log }^2(\frac{1+x}{3})+(-19200-33600x-18000x^2-3900x^3-300x^4){\log }^3(\frac{1+x}{3})+{\log }^2(x^2)(-30x^4+(120x^3+30x^4)\log (\frac{1+x}{3})+(120x^2+120x^3){\log }^2(\frac{1+x}{3})+(-480x-600x^2-120x^3){\log }^3(\frac{1+x}{3}))+{\log }^3(x^2)(-6x^4\log (\frac{1+x}{3})+(24x^2+24x^3){\log }^3(\frac{1+x}{3}))+\log (x^2)((60x^3+60x^4)\log (\frac{1+x}{3})+(-480x^2-600x^3-120x^4){\log }^2(\frac{1+x}{3})+(960x+1440x^2+540x^3+60x^4){\log }^3(\frac{1+x}{3}))}{{\log }^3(x^2)(-5x^4-5x^5+(60x^3+75x^4+15x^5)\log (\frac{1+x}{3})+(-240x^2-360x^3-135x^4-15x^5){\log }^2(\frac{1+x}{3})+(320x+560x^2+300x^3+65x^4+5x^5){\log }^3(\frac{1+x}{3}))}dx$

Optimal. Leaf size=40 $$3(1+\frac{1}{5}{(\frac{5}{\log \left(x^2\right)}+\frac{x}{-4-x+\frac{x}{\log \left(\frac{1+x}{3}\right)}})}^2)$$

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Rubi [F]  time = 50.26, 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 = {} $$\begin{array}{c}\int \frac{300x^3+300x^4+(-3600x^2-4500x^3-900x^4)\log \left(\frac{1+x}{3}\right)+(14400x+21600x^2+8100x^3+900x^4){\log }^2\left(\frac{1+x}{3}\right)+(-19200-33600x-18000x^2-3900x^3-300x^4){\log }^3\left(\frac{1+x}{3}\right)+{\log }^2\left(x^2\right)(-30x^4+(120x^3+30x^4)\log \left(\frac{1+x}{3}\right)+(120x^2+120x^3){\log }^2\left(\frac{1+x}{3}\right)+(-480x-600x^2-120x^3){\log }^3\left(\frac{1+x}{3}\right))+{\log }^3\left(x^2\right)(-6x^4\log \left(\frac{1+x}{3}\right)+(24x^2+24x^3){\log }^3\left(\frac{1+x}{3}\right))+\log \left(x^2\right)((60x^3+60x^4)\log \left(\frac{1+x}{3}\right)+(-480x^2-600x^3-120x^4){\log }^2\left(\frac{1+x}{3}\right)+(960x+1440x^2+540x^3+60x^4){\log }^3\left(\frac{1+x}{3}\right))}{{\log }^3\left(x^2\right)(-5x^4-5x^5+(60x^3+75x^4+15x^5)\log \left(\frac{1+x}{3}\right)+(-240x^2-360x^3-135x^4-15x^5){\log }^2\left(\frac{1+x}{3}\right)+(320x+560x^2+300x^3+65x^4+5x^5){\log }^3\left(\frac{1+x}{3}\right))}dx\end{array}$$

Verification is not applicable to the result.

[In]

Int[(300*x^3 + 300*x^4 + (-3600*x^2 - 4500*x^3 - 900*x^4)*Log[(1 + x)/3] + (14400*x + 21600*x^2 + 8100*x^3 + 9
00*x^4)*Log[(1 + x)/3]^2 + (-19200 - 33600*x - 18000*x^2 - 3900*x^3 - 300*x^4)*Log[(1 + x)/3]^3 + Log[x^2]^2*(
-30*x^4 + (120*x^3 + 30*x^4)*Log[(1 + x)/3] + (120*x^2 + 120*x^3)*Log[(1 + x)/3]^2 + (-480*x - 600*x^2 - 120*x
^3)*Log[(1 + x)/3]^3) + Log[x^2]^3*(-6*x^4*Log[(1 + x)/3] + (24*x^2 + 24*x^3)*Log[(1 + x)/3]^3) + Log[x^2]*((6
0*x^3 + 60*x^4)*Log[(1 + x)/3] + (-480*x^2 - 600*x^3 - 120*x^4)*Log[(1 + x)/3]^2 + (960*x + 1440*x^2 + 540*x^3
+ 60*x^4)*Log[(1 + x)/3]^3))/(Log[x^2]^3*(-5*x^4 - 5*x^5 + (60*x^3 + 75*x^4 + 15*x^5)*Log[(1 + x)/3] + (-240*
x^2 - 360*x^3 - 135*x^4 - 15*x^5)*Log[(1 + x)/3]^2 + (320*x + 560*x^2 + 300*x^3 + 65*x^4 + 5*x^5)*Log[(1 + x)/
3]^3)),x]

[Out]

(3*x^2)/(5*(4 + x)^2) + 15/Log[x^2]^2 + 12*Defer[Int][1/((4 + x)*Log[x^2]^2), x] - 24*Defer[Int][1/((4 + x)^2*
Log[x^2]), x] - (2*Defer[Int][1/((1 + x)*(-x + 4*Log[(1 + x)/3] + x*Log[(1 + x)/3])^3), x])/5 + (6144*Defer[In
t][1/((4 + x)^3*(-x + 4*Log[(1 + x)/3] + x*Log[(1 + x)/3])^3), x])/5 + (2816*Defer[Int][1/((4 + x)*(-x + 4*Log
[(1 + x)/3] + x*Log[(1 + x)/3])^3), x])/5 + (1152*Defer[Int][1/((4 + x)^3*(-x + 4*Log[(1 + x)/3] + x*Log[(1 +
x)/3])), x])/5 + (72*Defer[Int][1/((4 + x)*(-x + 4*Log[(1 + x)/3] + x*Log[(1 + x)/3])), x])/5 - 48*Defer[Int][
1/((4 + x)*Log[x^2]^2*(-x + 4*Log[(1 + x)/3] + x*Log[(1 + x)/3])), x] - 48*Defer[Int][1/((4 + x)*Log[x^2]*(-x
+ 4*Log[(1 + x)/3] + x*Log[(1 + x)/3])), x] + (102*Defer[Int][(x - (4 + x)*Log[(1 + x)/3])^(-2), x])/5 - (6*De
fer[Int][x/(x - (4 + x)*Log[(1 + x)/3])^2, x])/5 + (2*Defer[Int][1/((1 + x)*(x - (4 + x)*Log[(1 + x)/3])^2), x
])/5 - (4608*Defer[Int][1/((4 + x)^3*(x - (4 + x)*Log[(1 + x)/3])^2), x])/5 + (3456*Defer[Int][1/((4 + x)^2*(x
- (4 + x)*Log[(1 + x)/3])^2), x])/5 - (992*Defer[Int][1/((4 + x)*(x - (4 + x)*Log[(1 + x)/3])^2), x])/5 - 30*
Defer[Int][1/(Log[x^2]*(x - (4 + x)*Log[(1 + x)/3])^2), x] + 6*Defer[Int][x/(Log[x^2]*(x - (4 + x)*Log[(1 + x)
/3])^2), x] + 6*Defer[Int][1/((1 + x)*Log[x^2]*(x - (4 + x)*Log[(1 + x)/3])^2), x] - 384*Defer[Int][1/((4 + x)
^2*Log[x^2]*(x - (4 + x)*Log[(1 + x)/3])^2), x] + 192*Defer[Int][1/((4 + x)*Log[x^2]*(x - (4 + x)*Log[(1 + x)/
3])^2), x] - (414*Defer[Int][(-x + (4 + x)*Log[(1 + x)/3])^(-3), x])/5 + (54*Defer[Int][x/(-x + (4 + x)*Log[(1
+ x)/3])^3, x])/5 - (6*Defer[Int][x^2/(-x + (4 + x)*Log[(1 + x)/3])^3, x])/5 - (6144*Defer[Int][1/((4 + x)^2*
(-x + (4 + x)*Log[(1 + x)/3])^3), x])/5 - (576*Defer[Int][1/((4 + x)^2*(-x + (4 + x)*Log[(1 + x)/3])), x])/5 +
12*Defer[Int][1/(Log[x^2]^2*(-x + (4 + x)*Log[(1 + x)/3])), x] + 192*Defer[Int][1/((4 + x)^2*Log[x^2]*(-x + (
4 + x)*Log[(1 + x)/3])), x]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int \frac{6(-10x(1+x)\log \left(x^2\right)\log \left(\frac{1+x}{3}\right){(x-(4+x)\log \left(\frac{1+x}{3}\right))}^2+50(1+x){(-x+(4+x)\log \left(\frac{1+x}{3}\right))}^3+x^2{\log }^3\left(x^2\right)\log \left(\frac{1+x}{3}\right)(x^2-4(1+x){\log }^2\left(\frac{1+x}{3}\right))-5x{\log }^2\left(x^2\right)(-x^3+x^2(4+x)\log \left(\frac{1+x}{3}\right)+4x(1+x){\log }^2\left(\frac{1+x}{3}\right)-4(4+5x+x^2){\log }^3\left(\frac{1+x}{3}\right)))}{5x(1+x){\log }^3\left(x^2\right){(x-(4+x)\log \left(\frac{1+x}{3}\right))}^3}dx\\ & =\frac{6}{5}\int \frac{-10x(1+x)\log \left(x^2\right)\log \left(\frac{1+x}{3}\right){(x-(4+x)\log \left(\frac{1+x}{3}\right))}^2+50(1+x){(-x+(4+x)\log \left(\frac{1+x}{3}\right))}^3+x^2{\log }^3\left(x^2\right)\log \left(\frac{1+x}{3}\right)(x^2-4(1+x){\log }^2\left(\frac{1+x}{3}\right))-5x{\log }^2\left(x^2\right)(-x^3+x^2(4+x)\log \left(\frac{1+x}{3}\right)+4x(1+x){\log }^2\left(\frac{1+x}{3}\right)-4(4+5x+x^2){\log }^3\left(\frac{1+x}{3}\right))}{x(1+x){\log }^3\left(x^2\right){(x-(4+x)\log \left(\frac{1+x}{3}\right))}^3}dx\\ & =\frac{6}{5}\int (\frac{2(-1600-1200x-300x^2-25x^3+80x\log \left(x^2\right)+40x^2\log \left(x^2\right)+5x^3\log \left(x^2\right)-40x{\log }^2\left(x^2\right)-10x^2{\log }^2\left(x^2\right)+2x^2{\log }^3\left(x^2\right))}{x(4+x{)}^3{\log }^3\left(x^2\right)}-\frac{x^4(12+4x+x^2)}{(1+x)(4+x{)}^3{(-x+4\log \left(\frac{1+x}{3}\right)+x\log \left(\frac{1+x}{3}\right))}^3}-\frac{x^2(-240-140x-40x^2-5x^3+4x\log \left(x^2\right)-4x^2\log \left(x^2\right)+x^3\log \left(x^2\right))}{(1+x)(4+x{)}^3\log \left(x^2\right){(-x+4\log \left(\frac{1+x}{3}\right)+x\log \left(\frac{1+x}{3}\right))}^2}+\frac{2x(80+40x+5x^2-80\log \left(x^2\right)-20x\log \left(x^2\right)+6x{\log }^2\left(x^2\right))}{(4+x{)}^3{\log }^2\left(x^2\right)(-x+4\log \left(\frac{1+x}{3}\right)+x\log \left(\frac{1+x}{3}\right))})dx\\ & =-(\frac{6}{5}\int \frac{x^4(12+4x+x^2)}{(1+x)(4+x{)}^3{(-x+4\log \left(\frac{1+x}{3}\right)+x\log \left(\frac{1+x}{3}\right))}^3}dx)-\frac{6}{5}\int \frac{x^2(-240-140x-40x^2-5x^3+4x\log \left(x^2\right)-4x^2\log \left(x^2\right)+x^3\log \left(x^2\right))}{(1+x)(4+x{)}^3\log \left(x^2\right){(-x+4\log \left(\frac{1+x}{3}\right)+x\log \left(\frac{1+x}{3}\right))}^2}dx+\frac{12}{5}\int \frac{-1600-1200x-300x^2-25x^3+80x\log \left(x^2\right)+40x^2\log \left(x^2\right)+5x^3\log \left(x^2\right)-40x{\log }^2\left(x^2\right)-10x^2{\log }^2\left(x^2\right)+2x^2{\log }^3\left(x^2\right)}{x(4+x{)}^3{\log }^3\left(x^2\right)}dx+\frac{12}{5}\int \frac{x(80+40x+5x^2-80\log \left(x^2\right)-20x\log \left(x^2\right)+6x{\log }^2\left(x^2\right))}{(4+x{)}^3{\log }^2\left(x^2\right)(-x+4\log \left(\frac{1+x}{3}\right)+x\log \left(\frac{1+x}{3}\right))}dx\\ & =-(\frac{6}{5}\int \frac{x^2(-5(48+28x+8x^2+x^3)+(-2+x{)}^{2}x\log \left(x^2\right))}{(1+x)(4+x{)}^3\log \left(x^2\right){(x-(4+x)\log \left(\frac{1+x}{3}\right))}^2}dx)-\frac{6}{5}\int (\frac{69}{{(-x+4\log \left(\frac{1+x}{3}\right)+x\log \left(\frac{1+x}{3}\right))}^3}-\frac{9x}{{(-x+4\log \left(\frac{1+x}{3}\right)+x\log \left(\frac{1+x}{3}\right))}^3}+\frac{x^2}{{(-x+4\log \left(\frac{1+x}{3}\right)+x\log \left(\frac{1+x}{3}\right))}^3}+\frac{1}{3(1+x){(-x+4\log \left(\frac{1+x}{3}\right)+x\log \left(\frac{1+x}{3}\right))}^3}-\frac{1024}{(4+x{)}^3{(-x+4\log \left(\frac{1+x}{3}\right)+x\log \left(\frac{1+x}{3}\right))}^3}+\frac{1024}{(4+x{)}^2{(-x+4\log \left(\frac{1+x}{3}\right)+x\log \left(\frac{1+x}{3}\right))}^3}-\frac{1408}{3(4+x){(-x+4\log \left(\frac{1+x}{3}\right)+x\log \left(\frac{1+x}{3}\right))}^3})dx+\frac{12}{5}\int (\frac{2x}{(4+x{)}^3}-\frac{25}{x{\log }^3\left(x^2\right)}+\frac{5}{(4+x){\log }^2\left(x^2\right)}-\frac{10}{(4+x{)}^2\log \left(x^2\right)})dx+\frac{12}{5}\int \frac{x(-5(4+x{)}^2+20(4+x)\log \left(x^2\right)-6x{\log }^2\left(x^2\right))}{(4+x{)}^3{\log }^2\left(x^2\right)(x-(4+x)\log \left(\frac{1+x}{3}\right))}dx\\ & =\text{Rest of rules removed due to large latex content}\end{array}\end{array}$$

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Mathematica [B]  time = 0.33, size = 104, normalized size = 2.60 $$\begin{array}{c}-\frac{6}{5}(-\frac{25}{2{\log }^2\left(x^2\right)}+\frac{5x\log \left(\frac{1+x}{3}\right)}{\log \left(x^2\right)(-x+(4+x)\log \left(\frac{1+x}{3}\right))}+\frac{x^2-2x(4+x)\log \left(\frac{1+x}{3}\right)+8(2+x){\log }^2\left(\frac{1+x}{3}\right)}{2{(x-(4+x)\log \left(\frac{1+x}{3}\right))}^2})\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(300*x^3 + 300*x^4 + (-3600*x^2 - 4500*x^3 - 900*x^4)*Log[(1 + x)/3] + (14400*x + 21600*x^2 + 8100*x
^3 + 900*x^4)*Log[(1 + x)/3]^2 + (-19200 - 33600*x - 18000*x^2 - 3900*x^3 - 300*x^4)*Log[(1 + x)/3]^3 + Log[x^
2]^2*(-30*x^4 + (120*x^3 + 30*x^4)*Log[(1 + x)/3] + (120*x^2 + 120*x^3)*Log[(1 + x)/3]^2 + (-480*x - 600*x^2 -
120*x^3)*Log[(1 + x)/3]^3) + Log[x^2]^3*(-6*x^4*Log[(1 + x)/3] + (24*x^2 + 24*x^3)*Log[(1 + x)/3]^3) + Log[x^
2]*((60*x^3 + 60*x^4)*Log[(1 + x)/3] + (-480*x^2 - 600*x^3 - 120*x^4)*Log[(1 + x)/3]^2 + (960*x + 1440*x^2 + 5
40*x^3 + 60*x^4)*Log[(1 + x)/3]^3))/(Log[x^2]^3*(-5*x^4 - 5*x^5 + (60*x^3 + 75*x^4 + 15*x^5)*Log[(1 + x)/3] +
(-240*x^2 - 360*x^3 - 135*x^4 - 15*x^5)*Log[(1 + x)/3]^2 + (320*x + 560*x^2 + 300*x^3 + 65*x^4 + 5*x^5)*Log[(1
+ x)/3]^3)),x]

[Out]

(-6*(-25/(2*Log[x^2]^2) + (5*x*Log[(1 + x)/3])/(Log[x^2]*(-x + (4 + x)*Log[(1 + x)/3])) + (x^2 - 2*x*(4 + x)*L
og[(1 + x)/3] + 8*(2 + x)*Log[(1 + x)/3]^2)/(2*(x - (4 + x)*Log[(1 + x)/3])^2)))/5

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fricas [B]  time = 0.92, size = 158, normalized size = 3.95 $$\begin{array}{c}-\frac{3((8(x+2)\log {(\frac{1}{3}x+\frac{1}{3})}^2+x^2-2(x^2+4x)\log (\frac{1}{3}x+\frac{1}{3}))\log {\left(x^2\right)}^2-25(x^2+8x+16)\log {(\frac{1}{3}x+\frac{1}{3})}^2-25x^2-10(x^2\log (\frac{1}{3}x+\frac{1}{3})-(x^2+4x)\log {(\frac{1}{3}x+\frac{1}{3})}^2)\log \left(x^2\right)+50(x^2+4x)\log (\frac{1}{3}x+\frac{1}{3}))}{5((x^2+8x+16)\log {(\frac{1}{3}x+\frac{1}{3})}^2+x^2-2(x^2+4x)\log (\frac{1}{3}x+\frac{1}{3}))\log {\left(x^2\right)}^2}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((24*x^3+24*x^2)*log(1/3*x+1/3)^3-6*x^4*log(1/3*x+1/3))*log(x^2)^3+((-120*x^3-600*x^2-480*x)*log(1/
3*x+1/3)^3+(120*x^3+120*x^2)*log(1/3*x+1/3)^2+(30*x^4+120*x^3)*log(1/3*x+1/3)-30*x^4)*log(x^2)^2+((60*x^4+540*
x^3+1440*x^2+960*x)*log(1/3*x+1/3)^3+(-120*x^4-600*x^3-480*x^2)*log(1/3*x+1/3)^2+(60*x^4+60*x^3)*log(1/3*x+1/3
))*log(x^2)+(-300*x^4-3900*x^3-18000*x^2-33600*x-19200)*log(1/3*x+1/3)^3+(900*x^4+8100*x^3+21600*x^2+14400*x)*
log(1/3*x+1/3)^2+(-900*x^4-4500*x^3-3600*x^2)*log(1/3*x+1/3)+300*x^4+300*x^3)/((5*x^5+65*x^4+300*x^3+560*x^2+3
20*x)*log(1/3*x+1/3)^3+(-15*x^5-135*x^4-360*x^3-240*x^2)*log(1/3*x+1/3)^2+(15*x^5+75*x^4+60*x^3)*log(1/3*x+1/3
)-5*x^5-5*x^4)/log(x^2)^3,x, algorithm="fricas")

[Out]

-3/5*((8*(x + 2)*log(1/3*x + 1/3)^2 + x^2 - 2*(x^2 + 4*x)*log(1/3*x + 1/3))*log(x^2)^2 - 25*(x^2 + 8*x + 16)*l
og(1/3*x + 1/3)^2 - 25*x^2 - 10*(x^2*log(1/3*x + 1/3) - (x^2 + 4*x)*log(1/3*x + 1/3)^2)*log(x^2) + 50*(x^2 + 4
*x)*log(1/3*x + 1/3))/(((x^2 + 8*x + 16)*log(1/3*x + 1/3)^2 + x^2 - 2*(x^2 + 4*x)*log(1/3*x + 1/3))*log(x^2)^2
)

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giac [B]  time = 1.23, size = 485, normalized size = 12.12 $$\begin{array}{c}-\frac{3(2x^4\log (3)\log \left(x^2\right)-2x^4\log \left(x^2\right)\log (x+1)-10x^4\log (3)+x^4\log \left(x^2\right)+8x^3\log (3)\log \left(x^2\right)+10x^4\log (x+1)-8x^3\log \left(x^2\right)\log (x+1)-10x^4-80x^3\log (3)+80x^3\log (x+1)-40x^3-160x^2\log (3)+160x^2\log (x+1))}{5(x^4\log (3{)}^2\log \left(x^2\right)-2x^4\log (3)\log \left(x^2\right)\log (x+1)+x^4\log \left(x^2\right)\log {(x+1)}^2+2x^4\log (3)\log \left(x^2\right)+16x^3\log (3{)}^2\log \left(x^2\right)-2x^4\log \left(x^2\right)\log (x+1)-32x^3\log (3)\log \left(x^2\right)\log (x+1)+16x^3\log \left(x^2\right)\log {(x+1)}^2+x^4\log \left(x^2\right)+24x^3\log (3)\log \left(x^2\right)+96x^2\log (3{)}^2\log \left(x^2\right)-24x^3\log \left(x^2\right)\log (x+1)-192x^2\log (3)\log \left(x^2\right)\log (x+1)+96x^2\log \left(x^2\right)\log {(x+1)}^2+8x^3\log \left(x^2\right)+96x^2\log (3)\log \left(x^2\right)+256x\log (3{)}^2\log \left(x^2\right)-96x^2\log \left(x^2\right)\log (x+1)-512x\log (3)\log \left(x^2\right)\log (x+1)+256x\log \left(x^2\right)\log {(x+1)}^2+16x^2\log \left(x^2\right)+128x\log (3)\log \left(x^2\right)+256\log (3{)}^2\log \left(x^2\right)-128x\log \left(x^2\right)\log (x+1)-512\log (3)\log \left(x^2\right)\log (x+1)+256\log \left(x^2\right)\log {(x+1)}^2)}-\frac{3(2x\log \left(x^2\right)-5x-20)}{x\log {\left(x^2\right)}^2+4\log {\left(x^2\right)}^2}-\frac{24(x+2)}{5(x^2+8x+16)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((24*x^3+24*x^2)*log(1/3*x+1/3)^3-6*x^4*log(1/3*x+1/3))*log(x^2)^3+((-120*x^3-600*x^2-480*x)*log(1/
3*x+1/3)^3+(120*x^3+120*x^2)*log(1/3*x+1/3)^2+(30*x^4+120*x^3)*log(1/3*x+1/3)-30*x^4)*log(x^2)^2+((60*x^4+540*
x^3+1440*x^2+960*x)*log(1/3*x+1/3)^3+(-120*x^4-600*x^3-480*x^2)*log(1/3*x+1/3)^2+(60*x^4+60*x^3)*log(1/3*x+1/3
))*log(x^2)+(-300*x^4-3900*x^3-18000*x^2-33600*x-19200)*log(1/3*x+1/3)^3+(900*x^4+8100*x^3+21600*x^2+14400*x)*
log(1/3*x+1/3)^2+(-900*x^4-4500*x^3-3600*x^2)*log(1/3*x+1/3)+300*x^4+300*x^3)/((5*x^5+65*x^4+300*x^3+560*x^2+3
20*x)*log(1/3*x+1/3)^3+(-15*x^5-135*x^4-360*x^3-240*x^2)*log(1/3*x+1/3)^2+(15*x^5+75*x^4+60*x^3)*log(1/3*x+1/3
)-5*x^5-5*x^4)/log(x^2)^3,x, algorithm="giac")

[Out]

-3/5*(2*x^4*log(3)*log(x^2) - 2*x^4*log(x^2)*log(x + 1) - 10*x^4*log(3) + x^4*log(x^2) + 8*x^3*log(3)*log(x^2)
+ 10*x^4*log(x + 1) - 8*x^3*log(x^2)*log(x + 1) - 10*x^4 - 80*x^3*log(3) + 80*x^3*log(x + 1) - 40*x^3 - 160*x
^2*log(3) + 160*x^2*log(x + 1))/(x^4*log(3)^2*log(x^2) - 2*x^4*log(3)*log(x^2)*log(x + 1) + x^4*log(x^2)*log(x
+ 1)^2 + 2*x^4*log(3)*log(x^2) + 16*x^3*log(3)^2*log(x^2) - 2*x^4*log(x^2)*log(x + 1) - 32*x^3*log(3)*log(x^2
)*log(x + 1) + 16*x^3*log(x^2)*log(x + 1)^2 + x^4*log(x^2) + 24*x^3*log(3)*log(x^2) + 96*x^2*log(3)^2*log(x^2)
- 24*x^3*log(x^2)*log(x + 1) - 192*x^2*log(3)*log(x^2)*log(x + 1) + 96*x^2*log(x^2)*log(x + 1)^2 + 8*x^3*log(
x^2) + 96*x^2*log(3)*log(x^2) + 256*x*log(3)^2*log(x^2) - 96*x^2*log(x^2)*log(x + 1) - 512*x*log(3)*log(x^2)*l
og(x + 1) + 256*x*log(x^2)*log(x + 1)^2 + 16*x^2*log(x^2) + 128*x*log(3)*log(x^2) + 256*log(3)^2*log(x^2) - 12
8*x*log(x^2)*log(x + 1) - 512*log(3)*log(x^2)*log(x + 1) + 256*log(x^2)*log(x + 1)^2) - 3*(2*x*log(x^2) - 5*x
- 20)/(x*log(x^2)^2 + 4*log(x^2)^2) - 24/5*(x + 2)/(x^2 + 8*x + 16)

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maple [C]  time = 2.21, size = 892, normalized size = 22.30

method	result	size
risch	$-\frac{12(-400-200x+20x^2\ln (x)+64\ln (x{)}^2-25x^2+32x\ln (x{)}^2+80x\ln (x)-20i\pi x\mathrm{csgn}{\left(i{x}^2\right)}^3-4{\pi }^2\mathrm{csgn}{\left(i{x}^2\right)}^6-32i\ln (x)\pi \mathrm{csgn}{\left(i{x}^2\right)}^3-4{\pi }^2\mathrm{csgn}{\left(ix\right)}^4\mathrm{csgn}{\left(i{x}^2\right)}^2+16{\pi }^2\mathrm{csgn}{\left(ix\right)}^3\mathrm{csgn}{\left(i{x}^2\right)}^3-24{\pi }^2\mathrm{csgn}{\left(ix\right)}^2\mathrm{csgn}{\left(i{x}^2\right)}^4+16{\pi }^2\mathrm{csgn}\left(ix\right)\mathrm{csgn}{\left(i{x}^2\right)}^5-20i\pi x\mathrm{csgn}{\left(ix\right)}^2\mathrm{csgn}\left(i{x}^2\right)+40i\pi x\mathrm{csgn}\left(ix\right)\mathrm{csgn}{\left(i{x}^2\right)}^2-5i\pi x^2\mathrm{csgn}{\left(ix\right)}^2\mathrm{csgn}\left(i{x}^2\right)+10i\pi x^2\mathrm{csgn}\left(ix\right)\mathrm{csgn}{\left(i{x}^2\right)}^2+64i\ln (x)\pi \mathrm{csgn}\left(ix\right)\mathrm{csgn}{\left(i{x}^2\right)}^2-32i\ln (x)\pi \mathrm{csgn}{\left(ix\right)}^2\mathrm{csgn}\left(i{x}^2\right)-16i\pi x\mathrm{csgn}{\left(i{x}^2\right)}^3\ln (x)-2{\pi }^{2}x\mathrm{csgn}{\left(ix\right)}^4\mathrm{csgn}{\left(i{x}^2\right)}^2+8{\pi }^{2}x\mathrm{csgn}{\left(ix\right)}^3\mathrm{csgn}{\left(i{x}^2\right)}^3-12{\pi }^{2}x\mathrm{csgn}{\left(ix\right)}^2\mathrm{csgn}{\left(i{x}^2\right)}^4+8{\pi }^{2}x\mathrm{csgn}\left(ix\right)\mathrm{csgn}{\left(i{x}^2\right)}^5-5i\pi x^2\mathrm{csgn}{\left(i{x}^2\right)}^3-2{\pi }^{2}x\mathrm{csgn}{\left(i{x}^2\right)}^6-16i\pi x\mathrm{csgn}{\left(ix\right)}^2\mathrm{csgn}\left(i{x}^2\right)\ln (x)+32i\pi x\mathrm{csgn}\left(ix\right)\mathrm{csgn}{\left(i{x}^2\right)}^2\ln (x))}{5{(4+x)}^2{(4\ln (x)-i\pi \mathrm{csgn}\left(i{x}^2\right)\mathrm{csgn}{\left(ix\right)}^2+2i\pi \mathrm{csgn}{\left(i{x}^2\right)}^2\mathrm{csgn}\left(ix\right)-i\pi \mathrm{csgn}{\left(i{x}^2\right)}^3)}^2}+\frac{\frac{6\pi x^4\mathrm{csgn}{\left(ix\right)}^2\mathrm{csgn}\left(i{x}^2\right)\ln (\frac{x}{3}+\frac{1}{3})}{5}-\frac{12\pi x^4\mathrm{csgn}\left(ix\right)\mathrm{csgn}{\left(i{x}^2\right)}^2\ln (\frac{x}{3}+\frac{1}{3})}{5}+\frac{6\pi x^4\mathrm{csgn}{\left(i{x}^2\right)}^3\ln (\frac{x}{3}+\frac{1}{3})}{5}-\frac{3\pi x^4\mathrm{csgn}{\left(ix\right)}^2\mathrm{csgn}\left(i{x}^2\right)}{5}+\frac{6\pi x^4\mathrm{csgn}\left(ix\right)\mathrm{csgn}{\left(i{x}^2\right)}^2}{5}-\frac{3\pi x^4\mathrm{csgn}{\left(i{x}^2\right)}^3}{5}+\frac{24\pi x^3\mathrm{csgn}{\left(ix\right)}^2\mathrm{csgn}\left(i{x}^2\right)\ln (\frac{x}{3}+\frac{1}{3})}{5}-\frac{48\pi x^3\mathrm{csgn}\left(ix\right)\mathrm{csgn}{\left(i{x}^2\right)}^2\ln (\frac{x}{3}+\frac{1}{3})}{5}+\frac{24\pi x^3\mathrm{csgn}{\left(i{x}^2\right)}^3\ln (\frac{x}{3}+\frac{1}{3})}{5}+\frac{24i{x}^4\ln (x)\ln (\frac{x}{3}+\frac{1}{3})}{5}+48i{x}^3-192i{x}^2\ln (\frac{x}{3}+\frac{1}{3})+\frac{96i{x}^3\ln (x)\ln (\frac{x}{3}+\frac{1}{3})}{5}-12i{x}^4\ln (\frac{x}{3}+\frac{1}{3})-96i{x}^3\ln (\frac{x}{3}+\frac{1}{3})-\frac{12i{x}^4\ln (x)}{5}+12i{x}^4}{{(x\ln (\frac{x}{3}+\frac{1}{3})-x+4\ln (\frac{x}{3}+\frac{1}{3}))}^2(\pi \mathrm{csgn}{\left(ix\right)}^2\mathrm{csgn}\left(i{x}^2\right)-2\pi \mathrm{csgn}\left(ix\right)\mathrm{csgn}{\left(i{x}^2\right)}^2+\pi \mathrm{csgn}{\left(i{x}^2\right)}^3+4i\ln (x))(x^2+8x+16)}$	$892$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((24*x^3+24*x^2)*ln(1/3*x+1/3)^3-6*x^4*ln(1/3*x+1/3))*ln(x^2)^3+((-120*x^3-600*x^2-480*x)*ln(1/3*x+1/3)^3
+(120*x^3+120*x^2)*ln(1/3*x+1/3)^2+(30*x^4+120*x^3)*ln(1/3*x+1/3)-30*x^4)*ln(x^2)^2+((60*x^4+540*x^3+1440*x^2+
960*x)*ln(1/3*x+1/3)^3+(-120*x^4-600*x^3-480*x^2)*ln(1/3*x+1/3)^2+(60*x^4+60*x^3)*ln(1/3*x+1/3))*ln(x^2)+(-300
*x^4-3900*x^3-18000*x^2-33600*x-19200)*ln(1/3*x+1/3)^3+(900*x^4+8100*x^3+21600*x^2+14400*x)*ln(1/3*x+1/3)^2+(-
900*x^4-4500*x^3-3600*x^2)*ln(1/3*x+1/3)+300*x^4+300*x^3)/((5*x^5+65*x^4+300*x^3+560*x^2+320*x)*ln(1/3*x+1/3)^
3+(-15*x^5-135*x^4-360*x^3-240*x^2)*ln(1/3*x+1/3)^2+(15*x^5+75*x^4+60*x^3)*ln(1/3*x+1/3)-5*x^5-5*x^4)/ln(x^2)^
3,x,method=_RETURNVERBOSE)

[Out]

-12/5*(-400-200*x+20*x^2*ln(x)+64*ln(x)^2-25*x^2+32*x*ln(x)^2+80*x*ln(x)-4*Pi^2*csgn(I*x^2)^6-4*Pi^2*csgn(I*x)
^4*csgn(I*x^2)^2+16*Pi^2*csgn(I*x)^3*csgn(I*x^2)^3-24*Pi^2*csgn(I*x)^2*csgn(I*x^2)^4+16*Pi^2*csgn(I*x)*csgn(I*
x^2)^5-16*I*Pi*x*csgn(I*x)^2*csgn(I*x^2)*ln(x)+32*I*Pi*x*csgn(I*x)*csgn(I*x^2)^2*ln(x)-2*Pi^2*x*csgn(I*x^2)^6-
2*Pi^2*x*csgn(I*x)^4*csgn(I*x^2)^2+8*Pi^2*x*csgn(I*x)^3*csgn(I*x^2)^3-12*Pi^2*x*csgn(I*x)^2*csgn(I*x^2)^4+8*Pi
^2*x*csgn(I*x)*csgn(I*x^2)^5-5*I*Pi*x^2*csgn(I*x^2)^3-20*I*Pi*x*csgn(I*x^2)^3-32*I*ln(x)*Pi*csgn(I*x^2)^3-5*I*
Pi*x^2*csgn(I*x)^2*csgn(I*x^2)+10*I*Pi*x^2*csgn(I*x)*csgn(I*x^2)^2-20*I*Pi*x*csgn(I*x)^2*csgn(I*x^2)+64*I*ln(x
)*Pi*csgn(I*x)*csgn(I*x^2)^2+40*I*Pi*x*csgn(I*x)*csgn(I*x^2)^2-32*I*ln(x)*Pi*csgn(I*x)^2*csgn(I*x^2)-16*I*Pi*x
*csgn(I*x^2)^3*ln(x))/(4+x)^2/(4*ln(x)-I*Pi*csgn(I*x^2)*csgn(I*x)^2+2*I*Pi*csgn(I*x^2)^2*csgn(I*x)-I*Pi*csgn(I
*x^2)^3)^2+3/5*(2*Pi*x^4*csgn(I*x)^2*csgn(I*x^2)*ln(1/3*x+1/3)-4*Pi*x^4*csgn(I*x)*csgn(I*x^2)^2*ln(1/3*x+1/3)+
2*Pi*x^4*csgn(I*x^2)^3*ln(1/3*x+1/3)-Pi*x^4*csgn(I*x)^2*csgn(I*x^2)+2*Pi*x^4*csgn(I*x)*csgn(I*x^2)^2-Pi*x^4*cs
gn(I*x^2)^3+8*Pi*x^3*csgn(I*x)^2*csgn(I*x^2)*ln(1/3*x+1/3)-16*Pi*x^3*csgn(I*x)*csgn(I*x^2)^2*ln(1/3*x+1/3)+8*P
i*x^3*csgn(I*x^2)^3*ln(1/3*x+1/3)+8*I*x^4*ln(x)*ln(1/3*x+1/3)+80*I*x^3-320*I*x^2*ln(1/3*x+1/3)+32*I*x^3*ln(x)*
ln(1/3*x+1/3)-20*I*x^4*ln(1/3*x+1/3)-160*I*x^3*ln(1/3*x+1/3)-4*I*x^4*ln(x)+20*I*x^4)/(x*ln(1/3*x+1/3)-x+4*ln(1
/3*x+1/3))^2/(Pi*csgn(I*x)^2*csgn(I*x^2)-2*Pi*csgn(I*x)*csgn(I*x^2)^2+Pi*csgn(I*x^2)^3+4*I*ln(x))/(x^2+8*x+16)

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maxima [B]  time = 0.81, size = 290, normalized size = 7.25 $$\begin{array}{c}\frac{3(25(\log (3{)}^2+2\log (3)+1)x^2-(32(x+2)\log (x{)}^2-25x^2+20(x^2+4x)\log (x)-200x-400)\log {(x+1)}^2-4(x^2(2\log (3)+1)+8(\log (3{)}^2+\log (3))x+16\log (3{)}^2)\log (x{)}^2+200(\log (3{)}^2+\log (3))x+400\log (3{)}^2-2(25x^2(\log (3)+1)-4(x^2+4x(2\log (3)+1)+16\log (3))\log (x{)}^2+100x(2\log (3)+1)-10(x^2(2\log (3)+1)+8x\log (3))\log (x)+400\log (3))\log (x+1)-20((\log (3{)}^2+\log (3))x^2+4x\log (3{)}^2)\log (x))}{20((x^2+8x+16)\log {(x+1)}^2\log (x{)}^2-2(x^2(\log (3)+1)+4x(2\log (3)+1)+16\log (3))\log (x+1)\log (x{)}^2+((\log (3{)}^2+2\log (3)+1)x^2+8(\log (3{)}^2+\log (3))x+16\log (3{)}^2)\log (x{)}^2)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((24*x^3+24*x^2)*log(1/3*x+1/3)^3-6*x^4*log(1/3*x+1/3))*log(x^2)^3+((-120*x^3-600*x^2-480*x)*log(1/
3*x+1/3)^3+(120*x^3+120*x^2)*log(1/3*x+1/3)^2+(30*x^4+120*x^3)*log(1/3*x+1/3)-30*x^4)*log(x^2)^2+((60*x^4+540*
x^3+1440*x^2+960*x)*log(1/3*x+1/3)^3+(-120*x^4-600*x^3-480*x^2)*log(1/3*x+1/3)^2+(60*x^4+60*x^3)*log(1/3*x+1/3
))*log(x^2)+(-300*x^4-3900*x^3-18000*x^2-33600*x-19200)*log(1/3*x+1/3)^3+(900*x^4+8100*x^3+21600*x^2+14400*x)*
log(1/3*x+1/3)^2+(-900*x^4-4500*x^3-3600*x^2)*log(1/3*x+1/3)+300*x^4+300*x^3)/((5*x^5+65*x^4+300*x^3+560*x^2+3
20*x)*log(1/3*x+1/3)^3+(-15*x^5-135*x^4-360*x^3-240*x^2)*log(1/3*x+1/3)^2+(15*x^5+75*x^4+60*x^3)*log(1/3*x+1/3
)-5*x^5-5*x^4)/log(x^2)^3,x, algorithm="maxima")

[Out]

3/20*(25*(log(3)^2 + 2*log(3) + 1)*x^2 - (32*(x + 2)*log(x)^2 - 25*x^2 + 20*(x^2 + 4*x)*log(x) - 200*x - 400)*
log(x + 1)^2 - 4*(x^2*(2*log(3) + 1) + 8*(log(3)^2 + log(3))*x + 16*log(3)^2)*log(x)^2 + 200*(log(3)^2 + log(3
))*x + 400*log(3)^2 - 2*(25*x^2*(log(3) + 1) - 4*(x^2 + 4*x*(2*log(3) + 1) + 16*log(3))*log(x)^2 + 100*x*(2*lo
g(3) + 1) - 10*(x^2*(2*log(3) + 1) + 8*x*log(3))*log(x) + 400*log(3))*log(x + 1) - 20*((log(3)^2 + log(3))*x^2
+ 4*x*log(3)^2)*log(x))/((x^2 + 8*x + 16)*log(x + 1)^2*log(x)^2 - 2*(x^2*(log(3) + 1) + 4*x*(2*log(3) + 1) +
16*log(3))*log(x + 1)*log(x)^2 + ((log(3)^2 + 2*log(3) + 1)*x^2 + 8*(log(3)^2 + log(3))*x + 16*log(3)^2)*log(x
)^2)

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mupad [B]  time = 1.64, size = 366, normalized size = 9.15 $$\begin{array}{c}\frac{\frac{6x{\ln \left(x^2\right)}^2}{{(x+4)}^2}-\frac{3x\ln \left(x^2\right)}{x+4}+15}{{\ln \left(x^2\right)}^2}-\frac{\frac{3x}{x+4}-\frac{6x\ln \left(x^2\right)}{{(x+4)}^2}+\frac{3x{\ln \left(x^2\right)}^2(x-4)}{{(x+4)}^3}}{\ln \left(x^2\right)}-\frac{\frac{84x}{5}+\frac{48}{5}}{x^2+8x+16}-\frac{\ln \left(x^2\right)(12x-3x^2)}{x^3+12x^2+48x+64}+\frac{6(-x^6{\ln \left(x^2\right)}^2+5x^6\ln \left(x^2\right)-5x^5{\ln \left(x^2\right)}^2+45x^5\ln \left(x^2\right)-16x^4{\ln \left(x^2\right)}^2+180x^4\ln \left(x^2\right)-12x^3{\ln \left(x^2\right)}^2+380x^3\ln \left(x^2\right)+240x^2\ln \left(x^2\right))}{5{\ln \left(x^2\right)}^2(x-\ln (\frac{x}{3}+\frac{1}{3})(x+4)){(x+4)}^2(x^3+5x^2+16x+12)}+\frac{3(x^7{\ln \left(x^2\right)}^2+5x^6{\ln \left(x^2\right)}^2+16x^5{\ln \left(x^2\right)}^2+12x^4{\ln \left(x^2\right)}^2)}{5{\ln \left(x^2\right)}^2{(x+4)}^2({\ln (\frac{x}{3}+\frac{1}{3})}^2{(x+4)}^2+x^2-2x\ln (\frac{x}{3}+\frac{1}{3})(x+4))(x^3+5x^2+16x+12)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(x/3 + 1/3)^2*(14400*x + 21600*x^2 + 8100*x^3 + 900*x^4) - log(x/3 + 1/3)*(3600*x^2 + 4500*x^3 + 900*
x^4) - log(x/3 + 1/3)^3*(33600*x + 18000*x^2 + 3900*x^3 + 300*x^4 + 19200) + log(x^2)^3*(log(x/3 + 1/3)^3*(24*
x^2 + 24*x^3) - 6*x^4*log(x/3 + 1/3)) + log(x^2)*(log(x/3 + 1/3)^3*(960*x + 1440*x^2 + 540*x^3 + 60*x^4) - log
(x/3 + 1/3)^2*(480*x^2 + 600*x^3 + 120*x^4) + log(x/3 + 1/3)*(60*x^3 + 60*x^4)) - log(x^2)^2*(log(x/3 + 1/3)^3
*(480*x + 600*x^2 + 120*x^3) - log(x/3 + 1/3)^2*(120*x^2 + 120*x^3) - log(x/3 + 1/3)*(120*x^3 + 30*x^4) + 30*x
^4) + 300*x^3 + 300*x^4)/(log(x^2)^3*(log(x/3 + 1/3)^2*(240*x^2 + 360*x^3 + 135*x^4 + 15*x^5) - log(x/3 + 1/3)
^3*(320*x + 560*x^2 + 300*x^3 + 65*x^4 + 5*x^5) - log(x/3 + 1/3)*(60*x^3 + 75*x^4 + 15*x^5) + 5*x^4 + 5*x^5)),
x)

[Out]

((6*x*log(x^2)^2)/(x + 4)^2 - (3*x*log(x^2))/(x + 4) + 15)/log(x^2)^2 - ((3*x)/(x + 4) - (6*x*log(x^2))/(x + 4
)^2 + (3*x*log(x^2)^2*(x - 4))/(x + 4)^3)/log(x^2) - ((84*x)/5 + 48/5)/(8*x + x^2 + 16) - (log(x^2)*(12*x - 3*
x^2))/(48*x + 12*x^2 + x^3 + 64) + (6*(240*x^2*log(x^2) + 380*x^3*log(x^2) + 180*x^4*log(x^2) + 45*x^5*log(x^2
) + 5*x^6*log(x^2) - 12*x^3*log(x^2)^2 - 16*x^4*log(x^2)^2 - 5*x^5*log(x^2)^2 - x^6*log(x^2)^2))/(5*log(x^2)^2
*(x - log(x/3 + 1/3)*(x + 4))*(x + 4)^2*(16*x + 5*x^2 + x^3 + 12)) + (3*(12*x^4*log(x^2)^2 + 16*x^5*log(x^2)^2
+ 5*x^6*log(x^2)^2 + x^7*log(x^2)^2))/(5*log(x^2)^2*(x + 4)^2*(log(x/3 + 1/3)^2*(x + 4)^2 + x^2 - 2*x*log(x/3
+ 1/3)*(x + 4))*(16*x + 5*x^2 + x^3 + 12))

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sympy [B]  time = 1.19, size = 240, normalized size = 6.00 $$\begin{array}{c}\frac{24(-x-2)}{5x^2+40x+80}+\frac{-3x^4\log \left(x^2\right)+30x^4+120x^3+(6x^4\log \left(x^2\right)-30x^4+24x^3\log \left(x^2\right)-240x^3-480x^2)\log (\frac{x}{3}+\frac{1}{3})}{5x^4\log \left(x^2\right)+40x^3\log \left(x^2\right)+80x^2\log \left(x^2\right)+(-10x^4\log \left(x^2\right)-120x^3\log \left(x^2\right)-480x^2\log \left(x^2\right)-640x\log \left(x^2\right))\log (\frac{x}{3}+\frac{1}{3})+(5x^4\log \left(x^2\right)+80x^3\log \left(x^2\right)+480x^2\log \left(x^2\right)+1280x\log \left(x^2\right)+1280\log \left(x^2\right))\log {(\frac{x}{3}+\frac{1}{3})}^2}+\frac{-6x\log \left(x^2\right)+15x+60}{(x+4)\log {\left(x^2\right)}^2}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((24*x**3+24*x**2)*ln(1/3*x+1/3)**3-6*x**4*ln(1/3*x+1/3))*ln(x**2)**3+((-120*x**3-600*x**2-480*x)*l
n(1/3*x+1/3)**3+(120*x**3+120*x**2)*ln(1/3*x+1/3)**2+(30*x**4+120*x**3)*ln(1/3*x+1/3)-30*x**4)*ln(x**2)**2+((6
0*x**4+540*x**3+1440*x**2+960*x)*ln(1/3*x+1/3)**3+(-120*x**4-600*x**3-480*x**2)*ln(1/3*x+1/3)**2+(60*x**4+60*x
**3)*ln(1/3*x+1/3))*ln(x**2)+(-300*x**4-3900*x**3-18000*x**2-33600*x-19200)*ln(1/3*x+1/3)**3+(900*x**4+8100*x*
*3+21600*x**2+14400*x)*ln(1/3*x+1/3)**2+(-900*x**4-4500*x**3-3600*x**2)*ln(1/3*x+1/3)+300*x**4+300*x**3)/((5*x
**5+65*x**4+300*x**3+560*x**2+320*x)*ln(1/3*x+1/3)**3+(-15*x**5-135*x**4-360*x**3-240*x**2)*ln(1/3*x+1/3)**2+(
15*x**5+75*x**4+60*x**3)*ln(1/3*x+1/3)-5*x**5-5*x**4)/ln(x**2)**3,x)

[Out]

24*(-x - 2)/(5*x**2 + 40*x + 80) + (-3*x**4*log(x**2) + 30*x**4 + 120*x**3 + (6*x**4*log(x**2) - 30*x**4 + 24*
x**3*log(x**2) - 240*x**3 - 480*x**2)*log(x/3 + 1/3))/(5*x**4*log(x**2) + 40*x**3*log(x**2) + 80*x**2*log(x**2
) + (-10*x**4*log(x**2) - 120*x**3*log(x**2) - 480*x**2*log(x**2) - 640*x*log(x**2))*log(x/3 + 1/3) + (5*x**4*
log(x**2) + 80*x**3*log(x**2) + 480*x**2*log(x**2) + 1280*x*log(x**2) + 1280*log(x**2))*log(x/3 + 1/3)**2) + (
-6*x*log(x**2) + 15*x + 60)/((x + 4)*log(x**2)**2)

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