∫ x3+(x+8x2−2x3) log(3)+(−4+15x−8x2+x3) log2(3)+(x log(3)−x log2(3)) log(x)_________________________________________________________ x3+(8x2−2x3) log(3)+(16x−8x2+x3) log2(3) dx

3.38.32 \(\int \frac {x^3+(x+8 x^2-2 x^3) \log (3)+(-4+15 x-8 x^2+x^3) \log ^2(3)+(x \log (3)-x \log ^2(3)) \log (x)}{x^3+(8 x^2-2 x^3) \log (3)+(16 x-8 x^2+x^3) \log ^2(3)} \, dx\)

Optimal. Leaf size=22 \[ -6+x-\frac {2+\log (x)}{4-x+\frac {x}{\log (3)}} \]

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Rubi [B] time = 0.92, antiderivative size = 136, normalized size of antiderivative = 6.18, number of steps used = 11, number of rules used = 6, integrand size = 90, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {6688, 6742, 43, 44, 2314, 31} \begin {gather*} x-\frac {16 \log ^2(3)}{(1-\log (3)) (x (1-\log (3))+\log (81))}+\frac {x (1-\log (3)) \log (x)}{4 (x (1-\log (3))+\log (81))}-\frac {\log (x)}{4}+\frac {8 \log (3) \log (81)}{(1-\log (3)) (x (1-\log (3))+\log (81))}-\frac {\log (3) (1+15 \log (3))}{(1-\log (3)) (x (1-\log (3))+\log (81))}-\frac {\log (3)}{x (1-\log (3))+\log (81)} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Int[(x^3 + (x + 8*x^2 - 2*x^3)*Log[3] + (-4 + 15*x - 8*x^2 + x^3)*Log[3]^2 + (x*Log[3] - x*Log[3]^2)*Log[x])/(

x^3 + (8*x^2 - 2*x^3)*Log[3] + (16*x - 8*x^2 + x^3)*Log[3]^2),x]

[Out]

x - Log[3]/(x*(1 - Log[3]) + Log[81]) - (16*Log[3]^2)/((1 - Log[3])*(x*(1 - Log[3]) + Log[81])) - (Log[3]*(1 +

15*Log[3]))/((1 - Log[3])*(x*(1 - Log[3]) + Log[81])) + (8*Log[3]*Log[81])/((1 - Log[3])*(x*(1 - Log[3]) + Lo

g[81])) - Log[x]/4 + (x*(1 - Log[3])*Log[x])/(4*(x*(1 - Log[3]) + Log[81]))

Rule 31

Int[((a_) + (b_.)*(x_))^(-1), x_Symbol] :> Simp[Log[RemoveContent[a + b*x, x]]/b, x] /; FreeQ[{a, b}, x]

Rule 43

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d

*x)^n, x], x] /; FreeQ[{a, b, c, d, n}, x] && NeQ[b*c - a*d, 0] && IGtQ[m, 0] && ( !IntegerQ[n] || (EqQ[c, 0]

&& LeQ[7*m + 4*n + 4, 0]) || LtQ[9*m + 5*(n + 1), 0] || GtQ[m + n + 2, 0])

Rule 44

Int[((a_) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d*

x)^n, x], x] /; FreeQ[{a, b, c, d}, x] && NeQ[b*c - a*d, 0] && ILtQ[m, 0] && IntegerQ[n] && !(IGtQ[n, 0] && L

tQ[m + n + 2, 0])

Rule 2314

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*((d_) + (e_.)*(x_)^(r_.))^(q_), x_Symbol] :> Simp[(x*(d + e*x^r)^(q

+ 1)*(a + b*Log[c*x^n]))/d, x] - Dist[(b*n)/d, Int[(d + e*x^r)^(q + 1), x], x] /; FreeQ[{a, b, c, d, e, n, q,

r}, x] && EqQ[r*(q + 1) + 1, 0]

Rule 6688

Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; SimplerIntegrandQ[v, u, x]]

Rule 6742

Int[u_, x_Symbol] :> With[{v = ExpandIntegrand[u, x]}, Int[v, x] /; SumQ[v]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {x^3 (-1+\log (3))^2-8 x^2 (-1+\log (3)) \log (3)-4 \log ^2(3)+x \log (3) (1+15 \log (3))-x (-1+\log (3)) \log (3) \log (x)}{x (x (-1+\log (3))-4 \log (3))^2} \, dx\\ &=\int \left (\frac {x^2 (1-\log (3))^2}{(x (1-\log (3))+4 \log (3))^2}+\frac {8 x (1-\log (3)) \log (3)}{(x (1-\log (3))+4 \log (3))^2}-\frac {4 \log ^2(3)}{x (x (1-\log (3))+4 \log (3))^2}+\frac {\log (3) (1+15 \log (3))}{(x (1-\log (3))+4 \log (3))^2}+\frac {(1-\log (3)) \log (3) \log (x)}{(x (1-\log (3))+4 \log (3))^2}\right ) \, dx\\ &=-\frac {\log (3) (1+15 \log (3))}{(1-\log (3)) (x (1-\log (3))+\log (81))}+(1-\log (3))^2 \int \frac {x^2}{(x (1-\log (3))+4 \log (3))^2} \, dx+((1-\log (3)) \log (3)) \int \frac {\log (x)}{(x (1-\log (3))+4 \log (3))^2} \, dx+(8 (1-\log (3)) \log (3)) \int \frac {x}{(x (1-\log (3))+4 \log (3))^2} \, dx-\left (4 \log ^2(3)\right ) \int \frac {1}{x (x (1-\log (3))+4 \log (3))^2} \, dx\\ &=-\frac {\log (3) (1+15 \log (3))}{(1-\log (3)) (x (1-\log (3))+\log (81))}+\frac {x (1-\log (3)) \log (x)}{4 (x (1-\log (3))+\log (81))}+(1-\log (3))^2 \int \left (\frac {1}{(-1+\log (3))^2}+\frac {16 \log ^2(3)}{(-1+\log (3))^2 (x (1-\log (3))+4 \log (3))^2}-\frac {8 \log (3)}{(-1+\log (3))^2 (x (1-\log (3))+4 \log (3))}\right ) \, dx+\frac {1}{4} (-1+\log (3)) \int \frac {1}{x (1-\log (3))+4 \log (3)} \, dx+(8 (1-\log (3)) \log (3)) \int \left (\frac {1}{(1-\log (3)) (x (1-\log (3))+4 \log (3))}+\frac {\log (81)}{(-1+\log (3)) (x (1-\log (3))+4 \log (3))^2}\right ) \, dx-\left (4 \log ^2(3)\right ) \int \left (\frac {1}{16 x \log ^2(3)}+\frac {-1+\log (3)}{4 \log (3) (x (1-\log (3))+4 \log (3))^2}+\frac {-1+\log (3)}{16 \log ^2(3) (x (1-\log (3))+4 \log (3))}\right ) \, dx\\ &=x-\frac {\log (3)}{x (1-\log (3))+\log (81)}-\frac {16 \log ^2(3)}{(1-\log (3)) (x (1-\log (3))+\log (81))}-\frac {\log (3) (1+15 \log (3))}{(1-\log (3)) (x (1-\log (3))+\log (81))}+\frac {8 \log (3) \log (81)}{(1-\log (3)) (x (1-\log (3))+\log (81))}-\frac {\log (x)}{4}+\frac {x (1-\log (3)) \log (x)}{4 (x (1-\log (3))+\log (81))}\\ \end {aligned} \end {gather*}

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Mathematica [A] time = 0.16, size = 35, normalized size = 1.59 \begin {gather*} \frac {x^2 (-1+\log (3))-4 x \log (3)+\log (9)+\log (3) \log (x)}{x (-1+\log (3))-4 \log (3)} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[(x^3 + (x + 8*x^2 - 2*x^3)*Log[3] + (-4 + 15*x - 8*x^2 + x^3)*Log[3]^2 + (x*Log[3] - x*Log[3]^2)*Log

[x])/(x^3 + (8*x^2 - 2*x^3)*Log[3] + (16*x - 8*x^2 + x^3)*Log[3]^2),x]

[Out]

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

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fricas [A] time = 0.70, size = 36, normalized size = 1.64 \begin {gather*} -\frac {x^{2} - {\left (x^{2} - 4 \, x + 2\right )} \log \relax (3) - \log \relax (3) \log \relax (x)}{{\left (x - 4\right )} \log \relax (3) - x} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x*log(3)^2+x*log(3))*log(x)+(x^3-8*x^2+15*x-4)*log(3)^2+(-2*x^3+8*x^2+x)*log(3)+x^3)/((x^3-8*x^2+

16*x)*log(3)^2+(-2*x^3+8*x^2)*log(3)+x^3),x, algorithm="fricas")

[Out]

-(x^2 - (x^2 - 4*x + 2)*log(3) - log(3)*log(x))/((x - 4)*log(3) - x)

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giac [A] time = 0.17, size = 39, normalized size = 1.77 \begin {gather*} x + \frac {\log \relax (3) \log \relax (x)}{x \log \relax (3) - x - 4 \, \log \relax (3)} + \frac {2 \, \log \relax (3)}{x \log \relax (3) - x - 4 \, \log \relax (3)} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x*log(3)^2+x*log(3))*log(x)+(x^3-8*x^2+15*x-4)*log(3)^2+(-2*x^3+8*x^2+x)*log(3)+x^3)/((x^3-8*x^2+

16*x)*log(3)^2+(-2*x^3+8*x^2)*log(3)+x^3),x, algorithm="giac")

[Out]

x + log(3)*log(x)/(x*log(3) - x - 4*log(3)) + 2*log(3)/(x*log(3) - x - 4*log(3))

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maple [A] time = 0.17, size = 38, normalized size = 1.73


method	result	size

norman	\(\frac {\ln \relax (3) \ln \relax (x )+\left (\ln \relax (3)-1\right ) x^{2}+\left (-\frac {7 \ln \relax (3)}{2}-\frac {1}{2}\right ) x}{x \ln \relax (3)-4 \ln \relax (3)-x}\)	\(38\)
risch	\(\frac {\ln \relax (3) \ln \relax (x )}{x \ln \relax (3)-4 \ln \relax (3)-x}+\frac {x^{2} \ln \relax (3)-4 x \ln \relax (3)-x^{2}+2 \ln \relax (3)}{x \ln \relax (3)-4 \ln \relax (3)-x}\)	\(57\)
default	\(x -\frac {\ln \relax (x )}{4}+\frac {\ln \left (x \ln \relax (3)-4 \ln \relax (3)-x \right ) \ln \relax (3)}{4 \ln \relax (3)-4}-\frac {\ln \left (x \ln \relax (3)-4 \ln \relax (3)-x \right )}{4 \left (\ln \relax (3)-1\right )}+\frac {2 \ln \relax (3)}{x \ln \relax (3)-4 \ln \relax (3)-x}-\frac {\ln \relax (3) \ln \left (\left (\ln \relax (3)-1\right ) x -4 \ln \relax (3)\right )}{4 \left (\ln \relax (3)-1\right )}+\frac {x \ln \relax (3) \ln \relax (x )}{4 x \ln \relax (3)-16 \ln \relax (3)-4 x}+\frac {\ln \left (\left (\ln \relax (3)-1\right ) x -4 \ln \relax (3)\right )}{4 \ln \relax (3)-4}-\frac {\ln \relax (x ) x}{4 \left (x \ln \relax (3)-4 \ln \relax (3)-x \right )}\)	\(151\)

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(((-x*ln(3)^2+x*ln(3))*ln(x)+(x^3-8*x^2+15*x-4)*ln(3)^2+(-2*x^3+8*x^2+x)*ln(3)+x^3)/((x^3-8*x^2+16*x)*ln(3)

^2+(-2*x^3+8*x^2)*ln(3)+x^3),x,method=_RETURNVERBOSE)

[Out]

(ln(3)*ln(x)+(ln(3)-1)*x^2+(-7/2*ln(3)-1/2)*x)/(x*ln(3)-4*ln(3)-x)

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maxima [B] time = 0.38, size = 737, normalized size = 33.50 result too large to display

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x*log(3)^2+x*log(3))*log(x)+(x^3-8*x^2+15*x-4)*log(3)^2+(-2*x^3+8*x^2+x)*log(3)+x^3)/((x^3-8*x^2+

16*x)*log(3)^2+(-2*x^3+8*x^2)*log(3)+x^3),x, algorithm="maxima")

[Out]

(16*log(3)^2/(4*log(3)^4 - 12*log(3)^3 - (log(3)^4 - 4*log(3)^3 + 6*log(3)^2 - 4*log(3) + 1)*x + 12*log(3)^2 -

4*log(3)) + 8*log(3)*log(x*(log(3) - 1) - 4*log(3))/(log(3)^3 - 3*log(3)^2 + 3*log(3) - 1) + x/(log(3)^2 - 2*

log(3) + 1))*log(3)^2 - 8*(4*log(3)/(4*log(3)^3 - (log(3)^3 - 3*log(3)^2 + 3*log(3) - 1)*x - 8*log(3)^2 + 4*lo

g(3)) + log(x*(log(3) - 1) - 4*log(3))/(log(3)^2 - 2*log(3) + 1))*log(3)^2 - 1/4*(log(x*(log(3) - 1) - 4*log(3

))/(log(3)^2 - log(3)) - log(x)/(log(3)^2 - log(3)))*log(3)^2 + 1/4*(4/((log(3)^2 - log(3))*x - 4*log(3)^2) +

log(x*(log(3) - 1) - 4*log(3))/log(3)^2 - log(x)/log(3)^2)*log(3)^2 - 2*(16*log(3)^2/(4*log(3)^4 - 12*log(3)^3

- (log(3)^4 - 4*log(3)^3 + 6*log(3)^2 - 4*log(3) + 1)*x + 12*log(3)^2 - 4*log(3)) + 8*log(3)*log(x*(log(3) -

1) - 4*log(3))/(log(3)^3 - 3*log(3)^2 + 3*log(3) - 1) + x/(log(3)^2 - 2*log(3) + 1))*log(3) + 8*(4*log(3)/(4*l

og(3)^3 - (log(3)^3 - 3*log(3)^2 + 3*log(3) - 1)*x - 8*log(3)^2 + 4*log(3)) + log(x*(log(3) - 1) - 4*log(3))/(

log(3)^2 - 2*log(3) + 1))*log(3) + 1/4*(log(x*(log(3) - 1) - 4*log(3))/(log(3)^2 - log(3)) - log(x)/(log(3)^2

- log(3)))*log(3) + log(3)^2*log(x)/((log(3)^2 - 2*log(3) + 1)*x - 4*log(3)^2 + 4*log(3)) + 16*log(3)^2/(4*log

(3)^4 - 12*log(3)^3 - (log(3)^4 - 4*log(3)^3 + 6*log(3)^2 - 4*log(3) + 1)*x + 12*log(3)^2 - 4*log(3)) - 15*log

(3)^2/((log(3)^2 - 2*log(3) + 1)*x - 4*log(3)^2 + 4*log(3)) + 8*log(3)*log(x*(log(3) - 1) - 4*log(3))/(log(3)^

3 - 3*log(3)^2 + 3*log(3) - 1) - log(3)*log(x)/((log(3)^2 - 2*log(3) + 1)*x - 4*log(3)^2 + 4*log(3)) + x/(log(

3)^2 - 2*log(3) + 1) - log(3)/((log(3)^2 - 2*log(3) + 1)*x - 4*log(3)^2 + 4*log(3))

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mupad [B] time = 12.82, size = 7411, normalized size = 336.86 result too large to display

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((log(3)*(x + 8*x^2 - 2*x^3) + log(3)^2*(15*x - 8*x^2 + x^3 - 4) + log(x)*(x*log(3) - x*log(3)^2) + x^3)/(l

og(3)^2*(16*x - 8*x^2 + x^3) + log(3)*(8*x^2 - 2*x^3) + x^3),x)

[Out]

log((((log(3)^2*(log(9) - 2*log(3))^(1/2))/2 - (13*log(3)^3*(log(9) - 2*log(3))^(1/2))/2 + (3*log(3)^4*(log(9)

- 2*log(3))^(1/2))/8 - (log(3)^5*(log(9) - 2*log(3))^(1/2))/4 - log(9)^2*((log(3)*(log(9) - 2*log(3))^(1/2))/

8 - (log(9) - 2*log(3))^(1/2)/8) + (7*log(3)*(log(9) - 2*log(3))^(1/2))/4 - 8*log(3)^3 + 8*log(3)^4 + log(9)*(

(7*log(3)^2*(log(9) - 2*log(3))^(1/2))/2 + (3*log(3)^3*(log(9) - 2*log(3))^(1/2))/8 - (13*log(3)*(log(9) - 2*l

og(3))^(1/2))/8 + 4*log(3)^2 - 4*log(3)^3 - (log(9) - 2*log(3))^(1/2)/4) + (log(9) - 2*log(3))^(1/2)/8)/(2*log

(3) - log(9) - 4*log(3)*log(9) + 2*log(3)*log(9)^2 - 2*log(3)^2*log(9) - 4*log(3)^3*log(9) - log(3)^4*log(9) +

4*log(3)^3 + 2*log(3)^5 + 2*log(9)^2 - log(9)^3 + 2*log(3)^2*log(9)^2) + 1/8)*((4*(104*log(3)^5*log(9) - 44*l

og(3)^4*log(9) - 16*log(3)^3*log(9) + 20*log(3)^6*log(9) + 8*log(3)^3 + 52*log(3)^4 + 152*log(3)^5 - 472*log(3

)^6 + 144*log(3)^7 - 12*log(3)^8 + 8*log(3)^3*log(9)^2 - 8*log(3)^4*log(9)^2))/(log(3)^2 - log(9) + 1) - (((lo

g(3)^2*(log(9) - 2*log(3))^(1/2))/2 - (13*log(3)^3*(log(9) - 2*log(3))^(1/2))/2 + (3*log(3)^4*(log(9) - 2*log(

3))^(1/2))/8 - (log(3)^5*(log(9) - 2*log(3))^(1/2))/4 - log(9)^2*((log(3)*(log(9) - 2*log(3))^(1/2))/8 - (log(

9) - 2*log(3))^(1/2)/8) + (7*log(3)*(log(9) - 2*log(3))^(1/2))/4 - 8*log(3)^3 + 8*log(3)^4 + log(9)*((7*log(3)

^2*(log(9) - 2*log(3))^(1/2))/2 + (3*log(3)^3*(log(9) - 2*log(3))^(1/2))/8 - (13*log(3)*(log(9) - 2*log(3))^(1

/2))/8 + 4*log(3)^2 - 4*log(3)^3 - (log(9) - 2*log(3))^(1/2)/4) + (log(9) - 2*log(3))^(1/2)/8)/(2*log(3) - log

(9) - 4*log(3)*log(9) + 2*log(3)*log(9)^2 - 2*log(3)^2*log(9) - 4*log(3)^3*log(9) - log(3)^4*log(9) + 4*log(3)

^3 + 2*log(3)^5 + 2*log(9)^2 - log(9)^3 + 2*log(3)^2*log(9)^2) + 1/8)*((4*(64*log(3)^3*log(9) - 64*log(3)^4*lo

g(9) + 64*log(3)^5*log(9) - 64*log(3)^6*log(9) - 32*log(3)^3 + 32*log(3)^4 - 64*log(3)^5 + 64*log(3)^6 - 32*lo

g(3)^7 + 32*log(3)^8 - 32*log(3)^3*log(9)^2 + 32*log(3)^4*log(9)^2))/(log(3)^2 - log(9) + 1) - (x*(768*log(3)^

3*log(9) + 1536*log(3)^5*log(9) + 768*log(3)^7*log(9) + 32*log(3)^2 - 256*log(3)^3 + 128*log(3)^4 - 768*log(3)

^5 + 192*log(3)^6 - 768*log(3)^7 + 128*log(3)^8 - 256*log(3)^9 + 32*log(3)^10 - 192*log(3)^2*log(9)^2 + 256*lo

g(3)^2*log(9)^3 - 768*log(3)^3*log(9)^2 - 96*log(3)^2*log(9)^4 + 256*log(3)^3*log(9)^3 - 384*log(3)^4*log(9)^2

+ 256*log(3)^4*log(9)^3 - 768*log(3)^5*log(9)^2 - 192*log(3)^6*log(9)^2))/(2*log(3)^2 - 2*log(3)^2*log(9) - 2

*log(9) + log(3)^4 + log(9)^2 + 1)) + (x*(832*log(3)^4*log(9) - 240*log(3)^3*log(9) - 48*log(3)^2*log(9) + 108

8*log(3)^5*log(9) - 1232*log(3)^6*log(9) - 720*log(3)^7*log(9) - 64*log(3)^8*log(9) + 12*log(3)^2 + 120*log(3)

^3 + 72*log(3)^4 - 1960*log(3)^5 + 2176*log(3)^6 - 2232*log(3)^7 + 2136*log(3)^8 - 152*log(3)^9 + 20*log(3)^10

+ 72*log(3)^2*log(9)^2 - 48*log(3)^2*log(9)^3 + 120*log(3)^3*log(9)^2 + 12*log(3)^2*log(9)^4 - 856*log(3)^4*l

og(9)^2 - 48*log(3)^4*log(9)^3 + 872*log(3)^5*log(9)^2 + 80*log(3)^6*log(9)^2))/(2*log(3)^2 - 2*log(3)^2*log(9

) - 2*log(9) + log(3)^4 + log(9)^2 + 1)) + (4*(30*log(3)^5*log(9) - 15*log(3)^4*log(9) + log(3)^6*log(9) + 15*

log(3)^4 + 34*log(3)^5 - 114*log(3)^6 + 34*log(3)^7 - log(3)^8))/(log(3)^2 - log(9) + 1) - (x*(836*log(3)^5*lo

g(9) - 161*log(3)^4*log(9) - 806*log(3)^6*log(9) - 124*log(3)^7*log(9) - log(3)^8*log(9) + 193*log(3)^4 + 92*l

og(3)^5 - 1785*log(3)^6 + 1912*log(3)^7 + 71*log(3)^8 + 28*log(3)^9 + log(3)^10 - 32*log(3)^4*log(9)^2 + 32*lo

g(3)^5*log(9)^2))/(2*log(3)^2 - 2*log(3)^2*log(9) - 2*log(9) + log(3)^4 + log(9)^2 + 1))*(((log(3)^2*(log(9) -

2*log(3))^(1/2))/2 - (13*log(3)^3*(log(9) - 2*log(3))^(1/2))/2 + (3*log(3)^4*(log(9) - 2*log(3))^(1/2))/8 - (

log(3)^5*(log(9) - 2*log(3))^(1/2))/4 - log(9)^2*((log(3)*(log(9) - 2*log(3))^(1/2))/8 - (log(9) - 2*log(3))^(

1/2)/8) + (7*log(3)*(log(9) - 2*log(3))^(1/2))/4 - 8*log(3)^3 + 8*log(3)^4 + log(9)*((7*log(3)^2*(log(9) - 2*l

og(3))^(1/2))/2 + (3*log(3)^3*(log(9) - 2*log(3))^(1/2))/8 - (13*log(3)*(log(9) - 2*log(3))^(1/2))/8 + 4*log(3

)^2 - 4*log(3)^3 - (log(9) - 2*log(3))^(1/2)/4) + (log(9) - 2*log(3))^(1/2)/8)/(2*log(3) - log(9) - 4*log(3)*l

og(9) + 2*log(3)*log(9)^2 - 2*log(3)^2*log(9) - 4*log(3)^3*log(9) - log(3)^4*log(9) + 4*log(3)^3 + 2*log(3)^5

+ 2*log(9)^2 - log(9)^3 + 2*log(3)^2*log(9)^2) + 1/8) - log((4*(30*log(3)^5*log(9) - 15*log(3)^4*log(9) + log(

3)^6*log(9) + 15*log(3)^4 + 34*log(3)^5 - 114*log(3)^6 + 34*log(3)^7 - log(3)^8))/(log(3)^2 - log(9) + 1) - (1

04*log(3)^5*log(9) - 44*log(3)^4*log(9) - 16*log(3)^3*log(9) + 20*log(3)^6*log(9) + 8*log(3)^3 + 52*log(3)^4 +

152*log(3)^5 - 472*log(3)^6 + 144*log(3)^7 - 12*log(3)^8 + 8*log(3)^3*log(9)^2 - 8*log(3)^4*log(9)^2)/(log(3)

^2 - log(9) + 1) - (64*log(3)^3*log(9) - 64*log(3)^4*log(9) + 64*log(3)^5*log(9) - 64*log(3)^6*log(9) - 32*log

(3)^3 + 32*log(3)^4 - 64*log(3)^5 + 64*log(3)^6 - 32*log(3)^7 + 32*log(3)^8 - 32*log(3)^3*log(9)^2 + 32*log(3)

^4*log(9)^2)/(4*(log(3)^2 - log(9) + 1)) + (x*(768*log(3)^3*log(9) + 1536*log(3)^5*log(9) + 768*log(3)^7*log(9

) + 32*log(3)^2 - 256*log(3)^3 + 128*log(3)^4 - 768*log(3)^5 + 192*log(3)^6 - 768*log(3)^7 + 128*log(3)^8 - 25

6*log(3)^9 + 32*log(3)^10 - 192*log(3)^2*log(9)^2 + 256*log(3)^2*log(9)^3 - 768*log(3)^3*log(9)^2 - 96*log(3)^

2*log(9)^4 + 256*log(3)^3*log(9)^3 - 384*log(3)^4*log(9)^2 + 256*log(3)^4*log(9)^3 - 768*log(3)^5*log(9)^2 - 1

92*log(3)^6*log(9)^2))/(16*(2*log(3)^2 - 2*log(3)^2*log(9) - 2*log(9) + log(3)^4 + log(9)^2 + 1)) - (x*(832*lo

g(3)^4*log(9) - 240*log(3)^3*log(9) - 48*log(3)^2*log(9) + 1088*log(3)^5*log(9) - 1232*log(3)^6*log(9) - 720*l

og(3)^7*log(9) - 64*log(3)^8*log(9) + 12*log(3)^2 + 120*log(3)^3 + 72*log(3)^4 - 1960*log(3)^5 + 2176*log(3)^6

- 2232*log(3)^7 + 2136*log(3)^8 - 152*log(3)^9 + 20*log(3)^10 + 72*log(3)^2*log(9)^2 - 48*log(3)^2*log(9)^3 +

120*log(3)^3*log(9)^2 + 12*log(3)^2*log(9)^4 - 856*log(3)^4*log(9)^2 - 48*log(3)^4*log(9)^3 + 872*log(3)^5*lo

g(9)^2 + 80*log(3)^6*log(9)^2))/(4*(2*log(3)^2 - 2*log(3)^2*log(9) - 2*log(9) + log(3)^4 + log(9)^2 + 1)) - (x

*(836*log(3)^5*log(9) - 161*log(3)^4*log(9) - 806*log(3)^6*log(9) - 124*log(3)^7*log(9) - log(3)^8*log(9) + 19

3*log(3)^4 + 92*log(3)^5 - 1785*log(3)^6 + 1912*log(3)^7 + 71*log(3)^8 + 28*log(3)^9 + log(3)^10 - 32*log(3)^4

*log(9)^2 + 32*log(3)^5*log(9)^2))/(2*log(3)^2 - 2*log(3)^2*log(9) - 2*log(9) + log(3)^4 + log(9)^2 + 1))/4 -

log(x*log(3) - 4*log(3) - x)/4 - log((4*(30*log(3)^5*log(9) - 15*log(3)^4*log(9) + log(3)^6*log(9) + 15*log(3)

^4 + 34*log(3)^5 - 114*log(3)^6 + 34*log(3)^7 - log(3)^8))/(log(3)^2 - log(9) + 1) - (((log(3)^2*(log(9) - 2*l

og(3))^(1/2))/2 - (13*log(3)^3*(log(9) - 2*log(3))^(1/2))/2 + (3*log(3)^4*(log(9) - 2*log(3))^(1/2))/8 - (log(

3)^5*(log(9) - 2*log(3))^(1/2))/4 - log(9)^2*((log(3)*(log(9) - 2*log(3))^(1/2))/8 - (log(9) - 2*log(3))^(1/2)

/8) + (7*log(3)*(log(9) - 2*log(3))^(1/2))/4 + 8*log(3)^3 - 8*log(3)^4 + log(9)*((7*log(3)^2*(log(9) - 2*log(3

))^(1/2))/2 + (3*log(3)^3*(log(9) - 2*log(3))^(1/2))/8 - (13*log(3)*(log(9) - 2*log(3))^(1/2))/8 - 4*log(3)^2

+ 4*log(3)^3 - (log(9) - 2*log(3))^(1/2)/4) + (log(9) - 2*log(3))^(1/2)/8)/(2*log(3) - log(9) - 4*log(3)*log(9

) + 2*log(3)*log(9)^2 - 2*log(3)^2*log(9) - 4*log(3)^3*log(9) - log(3)^4*log(9) + 4*log(3)^3 + 2*log(3)^5 + 2*

log(9)^2 - log(9)^3 + 2*log(3)^2*log(9)^2) - 1/8)*((4*(104*log(3)^5*log(9) - 44*log(3)^4*log(9) - 16*log(3)^3*

log(9) + 20*log(3)^6*log(9) + 8*log(3)^3 + 52*log(3)^4 + 152*log(3)^5 - 472*log(3)^6 + 144*log(3)^7 - 12*log(3

)^8 + 8*log(3)^3*log(9)^2 - 8*log(3)^4*log(9)^2))/(log(3)^2 - log(9) + 1) + (((log(3)^2*(log(9) - 2*log(3))^(1

/2))/2 - (13*log(3)^3*(log(9) - 2*log(3))^(1/2))/2 + (3*log(3)^4*(log(9) - 2*log(3))^(1/2))/8 - (log(3)^5*(log

(9) - 2*log(3))^(1/2))/4 - log(9)^2*((log(3)*(log(9) - 2*log(3))^(1/2))/8 - (log(9) - 2*log(3))^(1/2)/8) + (7*

log(3)*(log(9) - 2*log(3))^(1/2))/4 + 8*log(3)^3 - 8*log(3)^4 + log(9)*((7*log(3)^2*(log(9) - 2*log(3))^(1/2))

/2 + (3*log(3)^3*(log(9) - 2*log(3))^(1/2))/8 - (13*log(3)*(log(9) - 2*log(3))^(1/2))/8 - 4*log(3)^2 + 4*log(3

)^3 - (log(9) - 2*log(3))^(1/2)/4) + (log(9) - 2*log(3))^(1/2)/8)/(2*log(3) - log(9) - 4*log(3)*log(9) + 2*log

(3)*log(9)^2 - 2*log(3)^2*log(9) - 4*log(3)^3*log(9) - log(3)^4*log(9) + 4*log(3)^3 + 2*log(3)^5 + 2*log(9)^2

- log(9)^3 + 2*log(3)^2*log(9)^2) - 1/8)*((4*(64*log(3)^3*log(9) - 64*log(3)^4*log(9) + 64*log(3)^5*log(9) - 6

4*log(3)^6*log(9) - 32*log(3)^3 + 32*log(3)^4 - 64*log(3)^5 + 64*log(3)^6 - 32*log(3)^7 + 32*log(3)^8 - 32*log

(3)^3*log(9)^2 + 32*log(3)^4*log(9)^2))/(log(3)^2 - log(9) + 1) - (x*(768*log(3)^3*log(9) + 1536*log(3)^5*log(

9) + 768*log(3)^7*log(9) + 32*log(3)^2 - 256*log(3)^3 + 128*log(3)^4 - 768*log(3)^5 + 192*log(3)^6 - 768*log(3

)^7 + 128*log(3)^8 - 256*log(3)^9 + 32*log(3)^10 - 192*log(3)^2*log(9)^2 + 256*log(3)^2*log(9)^3 - 768*log(3)^

3*log(9)^2 - 96*log(3)^2*log(9)^4 + 256*log(3)^3*log(9)^3 - 384*log(3)^4*log(9)^2 + 256*log(3)^4*log(9)^3 - 76

8*log(3)^5*log(9)^2 - 192*log(3)^6*log(9)^2))/(2*log(3)^2 - 2*log(3)^2*log(9) - 2*log(9) + log(3)^4 + log(9)^2

+ 1)) + (x*(832*log(3)^4*log(9) - 240*log(3)^3*log(9) - 48*log(3)^2*log(9) + 1088*log(3)^5*log(9) - 1232*log(

3)^6*log(9) - 720*log(3)^7*log(9) - 64*log(3)^8*log(9) + 12*log(3)^2 + 120*log(3)^3 + 72*log(3)^4 - 1960*log(3

)^5 + 2176*log(3)^6 - 2232*log(3)^7 + 2136*log(3)^8 - 152*log(3)^9 + 20*log(3)^10 + 72*log(3)^2*log(9)^2 - 48*

log(3)^2*log(9)^3 + 120*log(3)^3*log(9)^2 + 12*log(3)^2*log(9)^4 - 856*log(3)^4*log(9)^2 - 48*log(3)^4*log(9)^

3 + 872*log(3)^5*log(9)^2 + 80*log(3)^6*log(9)^2))/(2*log(3)^2 - 2*log(3)^2*log(9) - 2*log(9) + log(3)^4 + log

(9)^2 + 1)) - (x*(836*log(3)^5*log(9) - 161*log(3)^4*log(9) - 806*log(3)^6*log(9) - 124*log(3)^7*log(9) - log(

3)^8*log(9) + 193*log(3)^4 + 92*log(3)^5 - 1785*log(3)^6 + 1912*log(3)^7 + 71*log(3)^8 + 28*log(3)^9 + log(3)^

10 - 32*log(3)^4*log(9)^2 + 32*log(3)^5*log(9)^2))/(2*log(3)^2 - 2*log(3)^2*log(9) - 2*log(9) + log(3)^4 + log

(9)^2 + 1))*(((log(3)^2*(log(9) - 2*log(3))^(1/2))/2 - (13*log(3)^3*(log(9) - 2*log(3))^(1/2))/2 + (3*log(3)^4

*(log(9) - 2*log(3))^(1/2))/8 - (log(3)^5*(log(9) - 2*log(3))^(1/2))/4 - log(9)^2*((log(3)*(log(9) - 2*log(3))

^(1/2))/8 - (log(9) - 2*log(3))^(1/2)/8) + (7*log(3)*(log(9) - 2*log(3))^(1/2))/4 + 8*log(3)^3 - 8*log(3)^4 +

log(9)*((7*log(3)^2*(log(9) - 2*log(3))^(1/2))/2 + (3*log(3)^3*(log(9) - 2*log(3))^(1/2))/8 - (13*log(3)*(log(

9) - 2*log(3))^(1/2))/8 - 4*log(3)^2 + 4*log(3)^3 - (log(9) - 2*log(3))^(1/2)/4) + (log(9) - 2*log(3))^(1/2)/8

)/(2*log(3) - log(9) - 4*log(3)*log(9) + 2*log(3)*log(9)^2 - 2*log(3)^2*log(9) - 4*log(3)^3*log(9) - log(3)^4*

log(9) + 4*log(3)^3 + 2*log(3)^5 + 2*log(9)^2 - log(9)^3 + 2*log(3)^2*log(9)^2) - 1/8) + x/(log(3)^2 - log(9)

+ 1) - (log((((8*log(3) - 8*log(3)*log(9) + 8*log(3)^2*log(9) - 8*log(3)^2 + 8*log(3)^3 - 8*log(3)^4)/(log(3)^

2 - log(9) + 1) + (2*x*(2*log(3)^2 - 2*log(3)^2*log(9) - 2*log(9) + log(3)^4 + log(9)^2 + 1))/(log(3)^2 - log(

9) + 1))*(((512*log(3)*log(9) - 512*log(3)*log(9)^2 + 1024*log(3)^2*log(9) - 1024*log(3)^4*log(9) - 512*log(3)

^5*log(9) - 1024*log(3)^2 + 1024*log(3)^6 + 512*log(3)^3*log(9)^2)^2/(4*(128*log(3) - 64*log(9) - 384*log(3)*l

og(9) + 384*log(3)*log(9)^2 - 192*log(3)^2*log(9) - 128*log(3)*log(9)^3 - 768*log(3)^3*log(9) - 192*log(3)^4*l

og(9) - 384*log(3)^5*log(9) - 64*log(3)^6*log(9) + 384*log(3)^3 + 384*log(3)^5 + 128*log(3)^7 + 192*log(9)^2 -

192*log(9)^3 + 64*log(9)^4 + 384*log(3)^2*log(9)^2 - 192*log(3)^2*log(9)^3 + 384*log(3)^3*log(9)^2 + 192*log(

3)^4*log(9)^2)^2) - (64*log(3)*log(9) - 3*log(9) - 64*log(3) - 198*log(3)^2*log(9) - 64*log(3)^3*log(9) - 1091

*log(3)^4*log(9) + 1155*log(3)^2 - 2048*log(3)^3 + 1155*log(3)^4 + 2112*log(3)^5 + log(3)^6 + 3*log(9)^2 - log

(9)^3 + 67*log(3)^2*log(9)^2 + 1)/(128*log(3) - 64*log(9) - 384*log(3)*log(9) + 384*log(3)*log(9)^2 - 192*log(

3)^2*log(9) - 128*log(3)*log(9)^3 - 768*log(3)^3*log(9) - 192*log(3)^4*log(9) - 384*log(3)^5*log(9) - 64*log(3

)^6*log(9) + 384*log(3)^3 + 384*log(3)^5 + 128*log(3)^7 + 192*log(9)^2 - 192*log(9)^3 + 64*log(9)^4 + 384*log(

3)^2*log(9)^2 - 192*log(3)^2*log(9)^3 + 384*log(3)^3*log(9)^2 + 192*log(3)^4*log(9)^2))^(1/2) + (512*log(3)*lo

g(9) - 512*log(3)*log(9)^2 + 1024*log(3)^2*log(9) - 1024*log(3)^4*log(9) - 512*log(3)^5*log(9) - 1024*log(3)^2

+ 1024*log(3)^6 + 512*log(3)^3*log(9)^2)/(2*(128*log(3) - 64*log(9) - 384*log(3)*log(9) + 384*log(3)*log(9)^2

- 192*log(3)^2*log(9) - 128*log(3)*log(9)^3 - 768*log(3)^3*log(9) - 192*log(3)^4*log(9) - 384*log(3)^5*log(9)

- 64*log(3)^6*log(9) + 384*log(3)^3 + 384*log(3)^5 + 128*log(3)^7 + 192*log(9)^2 - 192*log(9)^3 + 64*log(9)^4

+ 384*log(3)^2*log(9)^2 - 192*log(3)^2*log(9)^3 + 384*log(3)^3*log(9)^2 + 192*log(3)^4*log(9)^2))) + (log(3)

- log(3)*log(9) + 33*log(3)^3)/(log(3)^2 - log(9) + 1) + (2*x*(4*log(3) - 4*log(3)^3))/(log(3)^2 - log(9) + 1)

)*((log(3) - log(3)*log(9) + 33*log(3)^3)/(log(3)^2 - log(9) + 1) - ((8*log(3) - 8*log(3)*log(9) + 8*log(3)^2*

log(9) - 8*log(3)^2 + 8*log(3)^3 - 8*log(3)^4)/(log(3)^2 - log(9) + 1) + (2*x*(2*log(3)^2 - 2*log(3)^2*log(9)

- 2*log(9) + log(3)^4 + log(9)^2 + 1))/(log(3)^2 - log(9) + 1))*(((512*log(3)*log(9) - 512*log(3)*log(9)^2 + 1

024*log(3)^2*log(9) - 1024*log(3)^4*log(9) - 512*log(3)^5*log(9) - 1024*log(3)^2 + 1024*log(3)^6 + 512*log(3)^

3*log(9)^2)^2/(4*(128*log(3) - 64*log(9) - 384*log(3)*log(9) + 384*log(3)*log(9)^2 - 192*log(3)^2*log(9) - 128

*log(3)*log(9)^3 - 768*log(3)^3*log(9) - 192*log(3)^4*log(9) - 384*log(3)^5*log(9) - 64*log(3)^6*log(9) + 384*

log(3)^3 + 384*log(3)^5 + 128*log(3)^7 + 192*log(9)^2 - 192*log(9)^3 + 64*log(9)^4 + 384*log(3)^2*log(9)^2 - 1

92*log(3)^2*log(9)^3 + 384*log(3)^3*log(9)^2 + 192*log(3)^4*log(9)^2)^2) - (64*log(3)*log(9) - 3*log(9) - 64*l

og(3) - 198*log(3)^2*log(9) - 64*log(3)^3*log(9) - 1091*log(3)^4*log(9) + 1155*log(3)^2 - 2048*log(3)^3 + 1155

*log(3)^4 + 2112*log(3)^5 + log(3)^6 + 3*log(9)^2 - log(9)^3 + 67*log(3)^2*log(9)^2 + 1)/(128*log(3) - 64*log(

9) - 384*log(3)*log(9) + 384*log(3)*log(9)^2 - 192*log(3)^2*log(9) - 128*log(3)*log(9)^3 - 768*log(3)^3*log(9)

- 192*log(3)^4*log(9) - 384*log(3)^5*log(9) - 64*log(3)^6*log(9) + 384*log(3)^3 + 384*log(3)^5 + 128*log(3)^7

+ 192*log(9)^2 - 192*log(9)^3 + 64*log(9)^4 + 384*log(3)^2*log(9)^2 - 192*log(3)^2*log(9)^3 + 384*log(3)^3*lo

g(9)^2 + 192*log(3)^4*log(9)^2))^(1/2) - (512*log(3)*log(9) - 512*log(3)*log(9)^2 + 1024*log(3)^2*log(9) - 102

4*log(3)^4*log(9) - 512*log(3)^5*log(9) - 1024*log(3)^2 + 1024*log(3)^6 + 512*log(3)^3*log(9)^2)/(2*(128*log(3

) - 64*log(9) - 384*log(3)*log(9) + 384*log(3)*log(9)^2 - 192*log(3)^2*log(9) - 128*log(3)*log(9)^3 - 768*log(

3)^3*log(9) - 192*log(3)^4*log(9) - 384*log(3)^5*log(9) - 64*log(3)^6*log(9) + 384*log(3)^3 + 384*log(3)^5 + 1

28*log(3)^7 + 192*log(9)^2 - 192*log(9)^3 + 64*log(9)^4 + 384*log(3)^2*log(9)^2 - 192*log(3)^2*log(9)^3 + 384*

log(3)^3*log(9)^2 + 192*log(3)^4*log(9)^2))) + (2*x*(4*log(3) - 4*log(3)^3))/(log(3)^2 - log(9) + 1)))*(512*lo

g(3)*log(9) - 512*log(3)*log(9)^2 + 1024*log(3)^2*log(9) - 1024*log(3)^4*log(9) - 512*log(3)^5*log(9) - 1024*l

og(3)^2 + 1024*log(3)^6 + 512*log(3)^3*log(9)^2))/(2*(128*log(3) - 64*log(9) - 384*log(3)*log(9) + 384*log(3)*

log(9)^2 - 192*log(3)^2*log(9) - 128*log(3)*log(9)^3 - 768*log(3)^3*log(9) - 192*log(3)^4*log(9) - 384*log(3)^

5*log(9) - 64*log(3)^6*log(9) + 384*log(3)^3 + 384*log(3)^5 + 128*log(3)^7 + 192*log(9)^2 - 192*log(9)^3 + 64*

log(9)^4 + 384*log(3)^2*log(9)^2 - 192*log(3)^2*log(9)^3 + 384*log(3)^3*log(9)^2 + 192*log(3)^4*log(9)^2)) + (

log(((((8*log(3)*log(9) - 8*log(3)^2*log(9) - 16*log(3)^2 + 16*log(3)^3)^2/(4*(2*log(3) - log(9) - 4*log(3)*lo

g(9) + 2*log(3)*log(9)^2 - 2*log(3)^2*log(9) - 4*log(3)^3*log(9) - log(3)^4*log(9) + 4*log(3)^3 + 2*log(3)^5 +

2*log(9)^2 - log(9)^3 + 2*log(3)^2*log(9)^2)^2) - (4*log(3)^2)/(2*log(3) - log(9) - 4*log(3)*log(9) + 2*log(3

)*log(9)^2 - 2*log(3)^2*log(9) - 4*log(3)^3*log(9) - log(3)^4*log(9) + 4*log(3)^3 + 2*log(3)^5 + 2*log(9)^2 -

log(9)^3 + 2*log(3)^2*log(9)^2))^(1/2) + (8*log(3)*log(9) - 8*log(3)^2*log(9) - 16*log(3)^2 + 16*log(3)^3)/(2*

(2*log(3) - log(9) - 4*log(3)*log(9) + 2*log(3)*log(9)^2 - 2*log(3)^2*log(9) - 4*log(3)^3*log(9) - log(3)^4*lo

g(9) + 4*log(3)^3 + 2*log(3)^5 + 2*log(9)^2 - log(9)^3 + 2*log(3)^2*log(9)^2)))*((8*(log(3) - log(3)*log(9) +

log(3)^2*log(9) - log(3)^2 + log(3)^3 - log(3)^4))/(log(3)^2 - log(9) + 1) + (2*x*(2*log(3)^2 - 2*log(3)^2*log

(9) - 2*log(9) + log(3)^4 + log(9)^2 + 1))/(log(3)^2 - log(9) + 1)) + (16*log(3)^2)/(log(3)^2 - log(9) + 1) +

(2*x*(4*log(3) - 4*log(3)^2))/(log(3)^2 - log(9) + 1))*((16*log(3)^2)/(log(3)^2 - log(9) + 1) - (((8*log(3)*lo

g(9) - 8*log(3)^2*log(9) - 16*log(3)^2 + 16*log(3)^3)^2/(4*(2*log(3) - log(9) - 4*log(3)*log(9) + 2*log(3)*log

(9)^2 - 2*log(3)^2*log(9) - 4*log(3)^3*log(9) - log(3)^4*log(9) + 4*log(3)^3 + 2*log(3)^5 + 2*log(9)^2 - log(9

)^3 + 2*log(3)^2*log(9)^2)^2) - (4*log(3)^2)/(2*log(3) - log(9) - 4*log(3)*log(9) + 2*log(3)*log(9)^2 - 2*log(

3)^2*log(9) - 4*log(3)^3*log(9) - log(3)^4*log(9) + 4*log(3)^3 + 2*log(3)^5 + 2*log(9)^2 - log(9)^3 + 2*log(3)

^2*log(9)^2))^(1/2) - (8*log(3)*log(9) - 8*log(3)^2*log(9) - 16*log(3)^2 + 16*log(3)^3)/(2*(2*log(3) - log(9)

- 4*log(3)*log(9) + 2*log(3)*log(9)^2 - 2*log(3)^2*log(9) - 4*log(3)^3*log(9) - log(3)^4*log(9) + 4*log(3)^3 +

2*log(3)^5 + 2*log(9)^2 - log(9)^3 + 2*log(3)^2*log(9)^2)))*((8*(log(3) - log(3)*log(9) + log(3)^2*log(9) - l

og(3)^2 + log(3)^3 - log(3)^4))/(log(3)^2 - log(9) + 1) + (2*x*(2*log(3)^2 - 2*log(3)^2*log(9) - 2*log(9) + lo

g(3)^4 + log(9)^2 + 1))/(log(3)^2 - log(9) + 1)) + (2*x*(4*log(3) - 4*log(3)^2))/(log(3)^2 - log(9) + 1)))*(8*

log(3)*log(9) - 8*log(3)^2*log(9) - 16*log(3)^2 + 16*log(3)^3))/(2*(2*log(3) - log(9) - 4*log(3)*log(9) + 2*lo

g(3)*log(9)^2 - 2*log(3)^2*log(9) - 4*log(3)^3*log(9) - log(3)^4*log(9) + 4*log(3)^3 + 2*log(3)^5 + 2*log(9)^2

- log(9)^3 + 2*log(3)^2*log(9)^2)) - (2*x*log(3))/(log(3)^2 - log(9) + 1) + (x*log(3)^2)/(log(3)^2 - log(9) +

1) + (atan((x + 4*log(3) - x*log(9) + x*log(3)^2 - 4*log(3)^2)/(4*log(3)*(2*log(3) - log(9))^(1/2)))*(66*log(

3)^2 - 2*log(9) - 34*log(3)^2*log(9) - 32*log(3) + 32*log(3)^3 + log(3)^4 + log(9)^2 + 1))/(4*(2*log(3) - log(

9))^(1/2)*(log(3)^2 - log(9) + 1)^2) - (x^2*log(x)*(log(3) - 1))/(4*(4*x*log(3) - x^2*log(3) + x^2)) + (4*log(

3)*atan((x + 4*log(3) - x*log(9) + x*log(3)^2 - 4*log(3)^2)/(4*log(3)*(2*log(3) - log(9))^(1/2)))*(log(9) - 4*

log(3) + log(3)^2 + 1))/((2*log(3) - log(9))^(1/2)*(2*log(3)^2 - 2*log(3)^2*log(9) - 2*log(9) + log(3)^4 + log

(9)^2 + 1))

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sympy [B] time = 0.45, size = 36, normalized size = 1.64 \begin {gather*} x + \frac {\log {\relax (3 )} \log {\relax (x )}}{- x + x \log {\relax (3 )} - 4 \log {\relax (3 )}} + \frac {2 \log {\relax (3 )}}{x \left (-1 + \log {\relax (3 )}\right ) - 4 \log {\relax (3 )}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x*ln(3)**2+x*ln(3))*ln(x)+(x**3-8*x**2+15*x-4)*ln(3)**2+(-2*x**3+8*x**2+x)*ln(3)+x**3)/((x**3-8*x

**2+16*x)*ln(3)**2+(-2*x**3+8*x**2)*ln(3)+x**3),x)

[Out]

x + log(3)*log(x)/(-x + x*log(3) - 4*log(3)) + 2*log(3)/(x*(-1 + log(3)) - 4*log(3))

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