3.89.63 \(\int (2 x^2-4 x \log (2)+2 \log ^2(2)+(3 x^2-4 x \log (2)+\log ^2(2)) \log (\frac {x^2}{\log ^4(3)})+(-12 x+12 \log (2)) \log (x^3) \log (\frac {x^2}{\log ^4(3)})+12 \log ^3(x^3) \log (\frac {x^2}{\log ^4(3)})+\log ^4(x^3) (2+\log (\frac {x^2}{\log ^4(3)}))+\log ^2(x^3) (-4 x+4 \log (2)+(-4 x+2 \log (2)) \log (\frac {x^2}{\log ^4(3)}))) \, dx\)

Optimal. Leaf size=25 \[ x \left (-x+\log (2)+\log ^2\left (x^3\right )\right )^2 \log \left (\frac {x^2}{\log ^4(3)}\right ) \]

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Rubi [B]  time = 0.62, antiderivative size = 368, normalized size of antiderivative = 14.72, number of steps used = 55, number of rules used = 13, integrand size = 132, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.098, Rules used = {2356, 2304, 2295, 2313, 2557, 12, 2296, 2361, 6742, 2330, 2305, 2366, 14} \begin {gather*} -2 x \log ^4\left (x^3\right )+24 x \log ^3\left (x^3\right )-216 x \log ^2\left (x^3\right )+1296 x \log \left (x^3\right )+24 x \log (2) \log \left (x^3\right )-9 x^2 \log \left (\frac {x^2}{\log ^4(3)}\right )-1944 x \log \left (\frac {x^2}{\log ^4(3)}\right )+9 \left (x^2-2 x \log (4)\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-2 x^2 \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )+36 x \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )+1944 x \left (\log \left (\frac {x^2}{\log ^4(3)}\right )+2\right )+x \log ^2(2) \log \left (\frac {x^2}{\log ^4(3)}\right )+x \left (\log \left (\frac {x^2}{\log ^4(3)}\right )+2\right ) \log ^4\left (x^3\right )+648 x \log \left (\frac {x^2}{\log ^4(3)}\right ) \log \left (x^3\right )-648 x \left (\log \left (\frac {x^2}{\log ^4(3)}\right )+2\right ) \log \left (x^3\right )+x^3 \log \left (\frac {x^2}{\log ^4(3)}\right )+12 x \log \left (\frac {x^2}{\log ^4(3)}\right ) \log ^3\left (x^3\right )-12 x \left (\log \left (\frac {x^2}{\log ^4(3)}\right )+2\right ) \log ^3\left (x^3\right )-2 x^2 \log \left (\frac {x^2}{\log ^4(3)}\right ) \log ^2\left (x^3\right )-108 x \log \left (\frac {x^2}{\log ^4(3)}\right ) \log ^2\left (x^3\right )+2 x \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right ) \log ^2\left (x^3\right )+108 x \left (\log \left (\frac {x^2}{\log ^4(3)}\right )+2\right ) \log ^2\left (x^3\right )-6 x^2 \log \left (x^3\right )+6 \left (x^2-2 x \log (4)\right ) \log \left (x^3\right )-3888 x+72 x \log (4)-144 x \log (2) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[2*x^2 - 4*x*Log[2] + 2*Log[2]^2 + (3*x^2 - 4*x*Log[2] + Log[2]^2)*Log[x^2/Log[3]^4] + (-12*x + 12*Log[2])*
Log[x^3]*Log[x^2/Log[3]^4] + 12*Log[x^3]^3*Log[x^2/Log[3]^4] + Log[x^3]^4*(2 + Log[x^2/Log[3]^4]) + Log[x^3]^2
*(-4*x + 4*Log[2] + (-4*x + 2*Log[2])*Log[x^2/Log[3]^4]),x]

[Out]

-3888*x - 144*x*Log[2] + 72*x*Log[4] + 1296*x*Log[x^3] - 6*x^2*Log[x^3] + 24*x*Log[2]*Log[x^3] + 6*(x^2 - 2*x*
Log[4])*Log[x^3] - 216*x*Log[x^3]^2 + 24*x*Log[x^3]^3 - 2*x*Log[x^3]^4 - 1944*x*Log[x^2/Log[3]^4] - 9*x^2*Log[
x^2/Log[3]^4] + x^3*Log[x^2/Log[3]^4] + 36*x*Log[2]*Log[x^2/Log[3]^4] - 2*x^2*Log[2]*Log[x^2/Log[3]^4] + x*Log
[2]^2*Log[x^2/Log[3]^4] + 9*(x^2 - 2*x*Log[4])*Log[x^2/Log[3]^4] + 648*x*Log[x^3]*Log[x^2/Log[3]^4] - 108*x*Lo
g[x^3]^2*Log[x^2/Log[3]^4] - 2*x^2*Log[x^3]^2*Log[x^2/Log[3]^4] + 2*x*Log[2]*Log[x^3]^2*Log[x^2/Log[3]^4] + 12
*x*Log[x^3]^3*Log[x^2/Log[3]^4] + 1944*x*(2 + Log[x^2/Log[3]^4]) - 648*x*Log[x^3]*(2 + Log[x^2/Log[3]^4]) + 10
8*x*Log[x^3]^2*(2 + Log[x^2/Log[3]^4]) - 12*x*Log[x^3]^3*(2 + Log[x^2/Log[3]^4]) + x*Log[x^3]^4*(2 + Log[x^2/L
og[3]^4])

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 14

Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x], x] /; FreeQ[{c, m}, x] && SumQ[u]
&&  !LinearQ[u, x] &&  !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]

Rule 2295

Int[Log[(c_.)*(x_)^(n_.)], x_Symbol] :> Simp[x*Log[c*x^n], x] - Simp[n*x, x] /; FreeQ[{c, n}, x]

Rule 2296

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.), x_Symbol] :> Simp[x*(a + b*Log[c*x^n])^p, x] - Dist[b*n*p, In
t[(a + b*Log[c*x^n])^(p - 1), x], x] /; FreeQ[{a, b, c, n}, x] && GtQ[p, 0] && IntegerQ[2*p]

Rule 2304

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[((d*x)^(m + 1)*(a + b*Log[c*x^
n]))/(d*(m + 1)), x] - Simp[(b*n*(d*x)^(m + 1))/(d*(m + 1)^2), x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[m, -1
]

Rule 2305

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[((d*x)^(m + 1)*(a + b*Lo
g[c*x^n])^p)/(d*(m + 1)), x] - Dist[(b*n*p)/(m + 1), Int[(d*x)^m*(a + b*Log[c*x^n])^(p - 1), x], x] /; FreeQ[{
a, b, c, d, m, n}, x] && NeQ[m, -1] && GtQ[p, 0]

Rule 2313

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*((d_) + (e_.)*(x_)^(r_.))^(q_.), x_Symbol] :> With[{u = IntHide[(d +
e*x^r)^q, x]}, Simp[u*(a + b*Log[c*x^n]), x] - Dist[b*n, Int[SimplifyIntegrand[u/x, x], x], x]] /; FreeQ[{a,
b, c, d, e, n, r}, x] && IGtQ[q, 0]

Rule 2330

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*((d_) + (e_.)*(x_)^(r_.))^(q_.), x_Symbol] :> With[{u = Expand
Integrand[(a + b*Log[c*x^n])^p, (d + e*x^r)^q, x]}, Int[u, x] /; SumQ[u]] /; FreeQ[{a, b, c, d, e, n, p, q, r}
, x] && IntegerQ[q] && (GtQ[q, 0] || (IGtQ[p, 0] && IntegerQ[r]))

Rule 2356

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*(Polyx_), x_Symbol] :> Int[ExpandIntegrand[Polyx*(a + b*Log[c*
x^n])^p, x], x] /; FreeQ[{a, b, c, n, p}, x] && PolynomialQ[Polyx, x]

Rule 2361

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*((d_.) + Log[(f_.)*(x_)^(r_.)]*(e_.)), x_Symbol] :> With[{u =
IntHide[(a + b*Log[c*x^n])^p, x]}, Dist[d + e*Log[f*x^r], u, x] - Dist[e*r, Int[SimplifyIntegrand[u/x, x], x],
x]] /; FreeQ[{a, b, c, d, e, f, n, p, r}, x]

Rule 2366

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*((d_.) + Log[(f_.)*(x_)^(r_.)]*(e_.))*((g_.)*(x_))^(m_.), x_Sy
mbol] :> With[{u = IntHide[(g*x)^m*(a + b*Log[c*x^n])^p, x]}, Dist[d + e*Log[f*x^r], u, x] - Dist[e*r, Int[Sim
plifyIntegrand[u/x, x], x], x]] /; FreeQ[{a, b, c, d, e, f, g, m, n, p, r}, x] &&  !(EqQ[p, 1] && EqQ[a, 0] &&
NeQ[d, 0])

Rule 2557

Int[Log[v_]*Log[w_]*(u_), x_Symbol] :> With[{z = IntHide[u, x]}, Dist[Log[v]*Log[w], z, x] + (-Int[SimplifyInt
egrand[(z*Log[w]*D[v, x])/v, x], x] - Int[SimplifyIntegrand[(z*Log[v]*D[w, x])/w, x], x]) /; InverseFunctionFr
eeQ[z, x]] /; InverseFunctionFreeQ[v, x] && InverseFunctionFreeQ[w, 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} &=\frac {2 x^3}{3}-2 x^2 \log (2)+2 x \log ^2(2)+12 \int \log ^3\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right ) \, dx+\int \left (3 x^2-4 x \log (2)+\log ^2(2)\right ) \log \left (\frac {x^2}{\log ^4(3)}\right ) \, dx+\int (-12 x+12 \log (2)) \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right ) \, dx+\int \log ^4\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right ) \, dx+\int \log ^2\left (x^3\right ) \left (-4 x+4 \log (2)+(-4 x+2 \log (2)) \log \left (\frac {x^2}{\log ^4(3)}\right )\right ) \, dx\\ &=\frac {2 x^3}{3}-2 x^2 \log (2)+2 x \log ^2(2)-1944 x \log \left (\frac {x^2}{\log ^4(3)}\right )+648 x \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-6 x^2 \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 x \log (2) \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-108 x \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 x \log ^3\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+1944 x \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-648 x \log \left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+108 x \log ^2\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-12 x \log ^3\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+x \log ^4\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-2 \int \left (1944-648 \log \left (x^3\right )+108 \log ^2\left (x^3\right )-12 \log ^3\left (x^3\right )+\log ^4\left (x^3\right )\right ) \, dx-24 \int \left (-162+54 \log \left (x^3\right )-9 \log ^2\left (x^3\right )+\log ^3\left (x^3\right )\right ) \, dx-\int 12 (-x+\log (4)) \log \left (x^3\right ) \, dx-\int 18 (-x+\log (4)) \log \left (\frac {x^2}{\log ^4(3)}\right ) \, dx+\int \left (3 x^2 \log \left (\frac {x^2}{\log ^4(3)}\right )-4 x \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )+\log ^2(2) \log \left (\frac {x^2}{\log ^4(3)}\right )\right ) \, dx+\int \left (-4 (x-\log (2)) \log ^2\left (x^3\right )-2 (2 x-\log (2)) \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )\right ) \, dx\\ &=\frac {2 x^3}{3}-2 x^2 \log (2)+2 x \log ^2(2)-1944 x \log \left (\frac {x^2}{\log ^4(3)}\right )+648 x \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-6 x^2 \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 x \log (2) \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-108 x \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 x \log ^3\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+1944 x \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-648 x \log \left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+108 x \log ^2\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-12 x \log ^3\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+x \log ^4\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-2 \int \log ^4\left (x^3\right ) \, dx-2 \int (2 x-\log (2)) \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right ) \, dx+3 \int x^2 \log \left (\frac {x^2}{\log ^4(3)}\right ) \, dx-4 \int (x-\log (2)) \log ^2\left (x^3\right ) \, dx-12 \int (-x+\log (4)) \log \left (x^3\right ) \, dx-18 \int (-x+\log (4)) \log \left (\frac {x^2}{\log ^4(3)}\right ) \, dx-(4 \log (2)) \int x \log \left (\frac {x^2}{\log ^4(3)}\right ) \, dx+\log ^2(2) \int \log \left (\frac {x^2}{\log ^4(3)}\right ) \, dx\\ &=6 \left (x^2-2 x \log (4)\right ) \log \left (x^3\right )-2 x \log ^4\left (x^3\right )-1944 x \log \left (\frac {x^2}{\log ^4(3)}\right )+x^3 \log \left (\frac {x^2}{\log ^4(3)}\right )-2 x^2 \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )+x \log ^2(2) \log \left (\frac {x^2}{\log ^4(3)}\right )+9 \left (x^2-2 x \log (4)\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+648 x \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-6 x^2 \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 x \log (2) \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-108 x \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 x \log ^3\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+1944 x \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-648 x \log \left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+108 x \log ^2\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-12 x \log ^3\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+x \log ^4\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-2 \int \left (2 x \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-\log (2) \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )\right ) \, dx-4 \int \left (x \log ^2\left (x^3\right )-\log (2) \log ^2\left (x^3\right )\right ) \, dx+24 \int \log ^3\left (x^3\right ) \, dx+2 \left (36 \int \left (-\frac {x}{2}+\log (4)\right ) \, dx\right )\\ &=2 \left (-9 x^2+36 x \log (4)\right )+6 \left (x^2-2 x \log (4)\right ) \log \left (x^3\right )+24 x \log ^3\left (x^3\right )-2 x \log ^4\left (x^3\right )-1944 x \log \left (\frac {x^2}{\log ^4(3)}\right )+x^3 \log \left (\frac {x^2}{\log ^4(3)}\right )-2 x^2 \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )+x \log ^2(2) \log \left (\frac {x^2}{\log ^4(3)}\right )+9 \left (x^2-2 x \log (4)\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+648 x \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-6 x^2 \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 x \log (2) \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-108 x \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 x \log ^3\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+1944 x \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-648 x \log \left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+108 x \log ^2\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-12 x \log ^3\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+x \log ^4\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-4 \int x \log ^2\left (x^3\right ) \, dx-4 \int x \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right ) \, dx-216 \int \log ^2\left (x^3\right ) \, dx+(2 \log (2)) \int \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right ) \, dx+(4 \log (2)) \int \log ^2\left (x^3\right ) \, dx\\ &=2 \left (-9 x^2+36 x \log (4)\right )+6 \left (x^2-2 x \log (4)\right ) \log \left (x^3\right )-216 x \log ^2\left (x^3\right )-2 x^2 \log ^2\left (x^3\right )+4 x \log (2) \log ^2\left (x^3\right )+24 x \log ^3\left (x^3\right )-2 x \log ^4\left (x^3\right )-1944 x \log \left (\frac {x^2}{\log ^4(3)}\right )-9 x^2 \log \left (\frac {x^2}{\log ^4(3)}\right )+x^3 \log \left (\frac {x^2}{\log ^4(3)}\right )+36 x \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )-2 x^2 \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )+x \log ^2(2) \log \left (\frac {x^2}{\log ^4(3)}\right )+9 \left (x^2-2 x \log (4)\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+648 x \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-108 x \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-2 x^2 \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+2 x \log (2) \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 x \log ^3\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+1944 x \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-648 x \log \left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+108 x \log ^2\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-12 x \log ^3\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+x \log ^4\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+8 \int \frac {1}{4} x \left (9-6 \log \left (x^3\right )+2 \log ^2\left (x^3\right )\right ) \, dx+12 \int x \log \left (x^3\right ) \, dx+1296 \int \log \left (x^3\right ) \, dx-(4 \log (2)) \int \left (18-6 \log \left (x^3\right )+\log ^2\left (x^3\right )\right ) \, dx-(24 \log (2)) \int \log \left (x^3\right ) \, dx\\ &=-3888 x-9 x^2+2 \left (-9 x^2+36 x \log (4)\right )+1296 x \log \left (x^3\right )+6 x^2 \log \left (x^3\right )-24 x \log (2) \log \left (x^3\right )+6 \left (x^2-2 x \log (4)\right ) \log \left (x^3\right )-216 x \log ^2\left (x^3\right )-2 x^2 \log ^2\left (x^3\right )+4 x \log (2) \log ^2\left (x^3\right )+24 x \log ^3\left (x^3\right )-2 x \log ^4\left (x^3\right )-1944 x \log \left (\frac {x^2}{\log ^4(3)}\right )-9 x^2 \log \left (\frac {x^2}{\log ^4(3)}\right )+x^3 \log \left (\frac {x^2}{\log ^4(3)}\right )+36 x \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )-2 x^2 \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )+x \log ^2(2) \log \left (\frac {x^2}{\log ^4(3)}\right )+9 \left (x^2-2 x \log (4)\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+648 x \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-108 x \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-2 x^2 \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+2 x \log (2) \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 x \log ^3\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+1944 x \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-648 x \log \left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+108 x \log ^2\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-12 x \log ^3\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+x \log ^4\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+2 \int x \left (9-6 \log \left (x^3\right )+2 \log ^2\left (x^3\right )\right ) \, dx-(4 \log (2)) \int \log ^2\left (x^3\right ) \, dx+(24 \log (2)) \int \log \left (x^3\right ) \, dx\\ &=-3888 x-9 x^2-72 x \log (2)+2 \left (-9 x^2+36 x \log (4)\right )+1296 x \log \left (x^3\right )+6 x^2 \log \left (x^3\right )+6 \left (x^2-2 x \log (4)\right ) \log \left (x^3\right )-216 x \log ^2\left (x^3\right )-2 x^2 \log ^2\left (x^3\right )+24 x \log ^3\left (x^3\right )-2 x \log ^4\left (x^3\right )-1944 x \log \left (\frac {x^2}{\log ^4(3)}\right )-9 x^2 \log \left (\frac {x^2}{\log ^4(3)}\right )+x^3 \log \left (\frac {x^2}{\log ^4(3)}\right )+36 x \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )-2 x^2 \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )+x \log ^2(2) \log \left (\frac {x^2}{\log ^4(3)}\right )+9 \left (x^2-2 x \log (4)\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+648 x \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-108 x \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-2 x^2 \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+2 x \log (2) \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 x \log ^3\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+1944 x \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-648 x \log \left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+108 x \log ^2\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-12 x \log ^3\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+x \log ^4\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+2 \int \left (9 x-6 x \log \left (x^3\right )+2 x \log ^2\left (x^3\right )\right ) \, dx+(24 \log (2)) \int \log \left (x^3\right ) \, dx\\ &=-3888 x-144 x \log (2)+2 \left (-9 x^2+36 x \log (4)\right )+1296 x \log \left (x^3\right )+6 x^2 \log \left (x^3\right )+24 x \log (2) \log \left (x^3\right )+6 \left (x^2-2 x \log (4)\right ) \log \left (x^3\right )-216 x \log ^2\left (x^3\right )-2 x^2 \log ^2\left (x^3\right )+24 x \log ^3\left (x^3\right )-2 x \log ^4\left (x^3\right )-1944 x \log \left (\frac {x^2}{\log ^4(3)}\right )-9 x^2 \log \left (\frac {x^2}{\log ^4(3)}\right )+x^3 \log \left (\frac {x^2}{\log ^4(3)}\right )+36 x \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )-2 x^2 \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )+x \log ^2(2) \log \left (\frac {x^2}{\log ^4(3)}\right )+9 \left (x^2-2 x \log (4)\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+648 x \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-108 x \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-2 x^2 \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+2 x \log (2) \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 x \log ^3\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+1944 x \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-648 x \log \left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+108 x \log ^2\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-12 x \log ^3\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+x \log ^4\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+4 \int x \log ^2\left (x^3\right ) \, dx-12 \int x \log \left (x^3\right ) \, dx\\ &=-3888 x+9 x^2-144 x \log (2)+2 \left (-9 x^2+36 x \log (4)\right )+1296 x \log \left (x^3\right )+24 x \log (2) \log \left (x^3\right )+6 \left (x^2-2 x \log (4)\right ) \log \left (x^3\right )-216 x \log ^2\left (x^3\right )+24 x \log ^3\left (x^3\right )-2 x \log ^4\left (x^3\right )-1944 x \log \left (\frac {x^2}{\log ^4(3)}\right )-9 x^2 \log \left (\frac {x^2}{\log ^4(3)}\right )+x^3 \log \left (\frac {x^2}{\log ^4(3)}\right )+36 x \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )-2 x^2 \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )+x \log ^2(2) \log \left (\frac {x^2}{\log ^4(3)}\right )+9 \left (x^2-2 x \log (4)\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+648 x \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-108 x \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-2 x^2 \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+2 x \log (2) \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 x \log ^3\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+1944 x \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-648 x \log \left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+108 x \log ^2\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-12 x \log ^3\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+x \log ^4\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-12 \int x \log \left (x^3\right ) \, dx\\ &=-3888 x+18 x^2-144 x \log (2)+2 \left (-9 x^2+36 x \log (4)\right )+1296 x \log \left (x^3\right )-6 x^2 \log \left (x^3\right )+24 x \log (2) \log \left (x^3\right )+6 \left (x^2-2 x \log (4)\right ) \log \left (x^3\right )-216 x \log ^2\left (x^3\right )+24 x \log ^3\left (x^3\right )-2 x \log ^4\left (x^3\right )-1944 x \log \left (\frac {x^2}{\log ^4(3)}\right )-9 x^2 \log \left (\frac {x^2}{\log ^4(3)}\right )+x^3 \log \left (\frac {x^2}{\log ^4(3)}\right )+36 x \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )-2 x^2 \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )+x \log ^2(2) \log \left (\frac {x^2}{\log ^4(3)}\right )+9 \left (x^2-2 x \log (4)\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+648 x \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-108 x \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-2 x^2 \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+2 x \log (2) \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 x \log ^3\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+1944 x \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-648 x \log \left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+108 x \log ^2\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-12 x \log ^3\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+x \log ^4\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.25, size = 112, normalized size = 4.48 \begin {gather*} \frac {1}{2} x \left (-4 \log ^2(2)+\log ^2(4)+\log \left (x^2\right ) \left (2 x^2+2 \log ^2(2)-x \log (16)+(-4 x+\log (16)) \log ^2\left (x^3\right )+2 \log ^4\left (x^3\right )\right )-8 x^2 \log (\log (3))-8 \log ^2(2) \log (\log (3))+x \log (65536) \log (\log (3))+(16 x-\log (65536)) \log ^2\left (x^3\right ) \log (\log (3))-8 \log ^4\left (x^3\right ) \log (\log (3))\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[2*x^2 - 4*x*Log[2] + 2*Log[2]^2 + (3*x^2 - 4*x*Log[2] + Log[2]^2)*Log[x^2/Log[3]^4] + (-12*x + 12*Lo
g[2])*Log[x^3]*Log[x^2/Log[3]^4] + 12*Log[x^3]^3*Log[x^2/Log[3]^4] + Log[x^3]^4*(2 + Log[x^2/Log[3]^4]) + Log[
x^3]^2*(-4*x + 4*Log[2] + (-4*x + 2*Log[2])*Log[x^2/Log[3]^4]),x]

[Out]

(x*(-4*Log[2]^2 + Log[4]^2 + Log[x^2]*(2*x^2 + 2*Log[2]^2 - x*Log[16] + (-4*x + Log[16])*Log[x^3]^2 + 2*Log[x^
3]^4) - 8*x^2*Log[Log[3]] - 8*Log[2]^2*Log[Log[3]] + x*Log[65536]*Log[Log[3]] + (16*x - Log[65536])*Log[x^3]^2
*Log[Log[3]] - 8*Log[x^3]^4*Log[Log[3]]))/2

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fricas [B]  time = 0.60, size = 192, normalized size = 7.68 \begin {gather*} \frac {1}{16} \, x \log \left (\log \relax (3)^{12}\right )^{4} \log \left (\frac {x^{2}}{\log \relax (3)^{4}}\right ) + \frac {3}{4} \, x \log \left (\log \relax (3)^{12}\right )^{3} \log \left (\frac {x^{2}}{\log \relax (3)^{4}}\right )^{2} + \frac {81}{16} \, x \log \left (\frac {x^{2}}{\log \relax (3)^{4}}\right )^{5} - \frac {9}{2} \, {\left (x^{2} - x \log \relax (2)\right )} \log \left (\frac {x^{2}}{\log \relax (3)^{4}}\right )^{3} + \frac {1}{8} \, {\left (27 \, x \log \left (\frac {x^{2}}{\log \relax (3)^{4}}\right )^{3} - 4 \, {\left (x^{2} - x \log \relax (2)\right )} \log \left (\frac {x^{2}}{\log \relax (3)^{4}}\right )\right )} \log \left (\log \relax (3)^{12}\right )^{2} + \frac {3}{4} \, {\left (9 \, x \log \left (\frac {x^{2}}{\log \relax (3)^{4}}\right )^{4} - 4 \, {\left (x^{2} - x \log \relax (2)\right )} \log \left (\frac {x^{2}}{\log \relax (3)^{4}}\right )^{2}\right )} \log \left (\log \relax (3)^{12}\right ) + {\left (x^{3} - 2 \, x^{2} \log \relax (2) + x \log \relax (2)^{2}\right )} \log \left (\frac {x^{2}}{\log \relax (3)^{4}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((log(x^2/log(3)^4)+2)*log(x^3)^4+12*log(x^2/log(3)^4)*log(x^3)^3+((2*log(2)-4*x)*log(x^2/log(3)^4)+4
*log(2)-4*x)*log(x^3)^2+(12*log(2)-12*x)*log(x^2/log(3)^4)*log(x^3)+(log(2)^2-4*x*log(2)+3*x^2)*log(x^2/log(3)
^4)+2*log(2)^2-4*x*log(2)+2*x^2,x, algorithm="fricas")

[Out]

1/16*x*log(log(3)^12)^4*log(x^2/log(3)^4) + 3/4*x*log(log(3)^12)^3*log(x^2/log(3)^4)^2 + 81/16*x*log(x^2/log(3
)^4)^5 - 9/2*(x^2 - x*log(2))*log(x^2/log(3)^4)^3 + 1/8*(27*x*log(x^2/log(3)^4)^3 - 4*(x^2 - x*log(2))*log(x^2
/log(3)^4))*log(log(3)^12)^2 + 3/4*(9*x*log(x^2/log(3)^4)^4 - 4*(x^2 - x*log(2))*log(x^2/log(3)^4)^2)*log(log(
3)^12) + (x^3 - 2*x^2*log(2) + x*log(2)^2)*log(x^2/log(3)^4)

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giac [B]  time = 0.25, size = 114, normalized size = 4.56 \begin {gather*} -324 \, x {\left (\log \left (\log \relax (3)\right ) + 2\right )} \log \relax (x)^{4} + 162 \, x \log \relax (x)^{5} + 648 \, x \log \relax (x)^{4} - 36 \, {\left (x^{2} - x \log \relax (2)\right )} \log \relax (x)^{3} + 36 \, {\left (x^{2} {\left (2 \, \log \left (\log \relax (3)\right ) + 1\right )} - 2 \, {\left (\log \relax (2) \log \left (\log \relax (3)\right ) + \log \relax (2)\right )} x\right )} \log \relax (x)^{2} - 36 \, {\left (x^{2} - 2 \, x \log \relax (2)\right )} \log \relax (x)^{2} + {\left (x^{3} - 2 \, x^{2} \log \relax (2) + x \log \relax (2)^{2}\right )} \log \left (\frac {x^{2}}{\log \relax (3)^{4}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((log(x^2/log(3)^4)+2)*log(x^3)^4+12*log(x^2/log(3)^4)*log(x^3)^3+((2*log(2)-4*x)*log(x^2/log(3)^4)+4
*log(2)-4*x)*log(x^3)^2+(12*log(2)-12*x)*log(x^2/log(3)^4)*log(x^3)+(log(2)^2-4*x*log(2)+3*x^2)*log(x^2/log(3)
^4)+2*log(2)^2-4*x*log(2)+2*x^2,x, algorithm="giac")

[Out]

-324*x*(log(log(3)) + 2)*log(x)^4 + 162*x*log(x)^5 + 648*x*log(x)^4 - 36*(x^2 - x*log(2))*log(x)^3 + 36*(x^2*(
2*log(log(3)) + 1) - 2*(log(2)*log(log(3)) + log(2))*x)*log(x)^2 - 36*(x^2 - 2*x*log(2))*log(x)^2 + (x^3 - 2*x
^2*log(2) + x*log(2)^2)*log(x^2/log(3)^4)

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maple [B]  time = 1.57, size = 141, normalized size = 5.64

method	result	size
default	\(x^{3} \ln \left (x^{2}\right )-8 x \ln \relax (2) \ln \left (\ln \relax (3)\right ) \ln \left (x^{3}\right )^{2}+2 x \ln \relax (2) \ln \left (x^{2}\right ) \ln \left (x^{3}\right )^{2}-4 x^{3} \ln \left (\ln \relax (3)\right )+\ln \relax (2)^{2} \ln \left (x^{2}\right ) x -4 \ln \relax (2)^{2} \ln \left (\ln \relax (3)\right ) x -2 \ln \relax (2) x^{2} \ln \left (x^{2}\right )+8 x^{2} \ln \relax (2) \ln \left (\ln \relax (3)\right )+\ln \left (x^{3}\right )^{4} \ln \left (x^{2}\right ) x -4 \ln \left (\ln \relax (3)\right ) x \ln \left (x^{3}\right )^{4}-2 x^{2} \ln \left (x^{2}\right ) \ln \left (x^{3}\right )^{2}+8 x^{2} \ln \left (\ln \relax (3)\right ) \ln \left (x^{3}\right )^{2}\)	\(141\)
risch	\(\text {Expression too large to display}\)	\(16204\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((ln(x^2/ln(3)^4)+2)*ln(x^3)^4+12*ln(x^2/ln(3)^4)*ln(x^3)^3+((2*ln(2)-4*x)*ln(x^2/ln(3)^4)+4*ln(2)-4*x)*ln(
x^3)^2+(12*ln(2)-12*x)*ln(x^2/ln(3)^4)*ln(x^3)+(ln(2)^2-4*x*ln(2)+3*x^2)*ln(x^2/ln(3)^4)+2*ln(2)^2-4*x*ln(2)+2
*x^2,x,method=_RETURNVERBOSE)

[Out]

x^3*ln(x^2)-8*x*ln(2)*ln(ln(3))*ln(x^3)^2+2*x*ln(2)*ln(x^2)*ln(x^3)^2-4*x^3*ln(ln(3))+ln(2)^2*ln(x^2)*x-4*ln(2
)^2*ln(ln(3))*x-2*ln(2)*x^2*ln(x^2)+8*x^2*ln(2)*ln(ln(3))+ln(x^3)^4*ln(x^2)*x-4*ln(ln(3))*x*ln(x^3)^4-2*x^2*ln
(x^2)*ln(x^3)^2+8*x^2*ln(ln(3))*ln(x^3)^2

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maxima [B]  time = 0.48, size = 71, normalized size = 2.84 \begin {gather*} x \log \left (x^{3}\right )^{4} \log \left (\frac {x^{2}}{\log \relax (3)^{4}}\right ) - 2 \, {\left (x^{2} - x \log \relax (2)\right )} \log \left (x^{3}\right )^{2} \log \left (\frac {x^{2}}{\log \relax (3)^{4}}\right ) + {\left (x^{3} - 2 \, x^{2} \log \relax (2) + x \log \relax (2)^{2}\right )} \log \left (\frac {x^{2}}{\log \relax (3)^{4}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((log(x^2/log(3)^4)+2)*log(x^3)^4+12*log(x^2/log(3)^4)*log(x^3)^3+((2*log(2)-4*x)*log(x^2/log(3)^4)+4
*log(2)-4*x)*log(x^3)^2+(12*log(2)-12*x)*log(x^2/log(3)^4)*log(x^3)+(log(2)^2-4*x*log(2)+3*x^2)*log(x^2/log(3)
^4)+2*log(2)^2-4*x*log(2)+2*x^2,x, algorithm="maxima")

[Out]

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

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int 12\,{\ln \left (x^3\right )}^3\,\ln \left (\frac {x^2}{{\ln \relax (3)}^4}\right )-4\,x\,\ln \relax (2)+\ln \left (\frac {x^2}{{\ln \relax (3)}^4}\right )\,\left (3\,x^2-4\,\ln \relax (2)\,x+{\ln \relax (2)}^2\right )+2\,{\ln \relax (2)}^2+{\ln \left (x^3\right )}^4\,\left (\ln \left (\frac {x^2}{{\ln \relax (3)}^4}\right )+2\right )-{\ln \left (x^3\right )}^2\,\left (4\,x-4\,\ln \relax (2)+\ln \left (\frac {x^2}{{\ln \relax (3)}^4}\right )\,\left (4\,x-2\,\ln \relax (2)\right )\right )+2\,x^2-\ln \left (x^3\right )\,\ln \left (\frac {x^2}{{\ln \relax (3)}^4}\right )\,\left (12\,x-12\,\ln \relax (2)\right ) \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(12*log(x^3)^3*log(x^2/log(3)^4) - 4*x*log(2) + log(x^2/log(3)^4)*(log(2)^2 - 4*x*log(2) + 3*x^2) + 2*log(2
)^2 + log(x^3)^4*(log(x^2/log(3)^4) + 2) - log(x^3)^2*(4*x - 4*log(2) + log(x^2/log(3)^4)*(4*x - 2*log(2))) +
2*x^2 - log(x^3)*log(x^2/log(3)^4)*(12*x - 12*log(2)),x)

[Out]

int(12*log(x^3)^3*log(x^2/log(3)^4) - 4*x*log(2) + log(x^2/log(3)^4)*(log(2)^2 - 4*x*log(2) + 3*x^2) + 2*log(2
)^2 + log(x^3)^4*(log(x^2/log(3)^4) + 2) - log(x^3)^2*(4*x - 4*log(2) + log(x^2/log(3)^4)*(4*x - 2*log(2))) +
2*x^2 - log(x^3)*log(x^2/log(3)^4)*(12*x - 12*log(2)), x)

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sympy [B]  time = 0.42, size = 146, normalized size = 5.84 \begin {gather*} - 4 x^{3} \log {\left (\log {\relax (3 )} \right )} + 8 x^{2} \log {\relax (2 )} \log {\left (\log {\relax (3 )} \right )} + \frac {2 x \log {\left (x^{3} \right )}^{5}}{3} - 4 x \log {\left (x^{3} \right )}^{4} \log {\left (\log {\relax (3 )} \right )} - 4 x \log {\relax (2 )}^{2} \log {\left (\log {\relax (3 )} \right )} + \left (- \frac {4 x^{2}}{3} + \frac {4 x \log {\relax (2 )}}{3}\right ) \log {\left (x^{3} \right )}^{3} + \left (8 x^{2} \log {\left (\log {\relax (3 )} \right )} - 8 x \log {\relax (2 )} \log {\left (\log {\relax (3 )} \right )}\right ) \log {\left (x^{3} \right )}^{2} + \left (\frac {2 x^{3}}{3} - \frac {4 x^{2} \log {\relax (2 )}}{3} + \frac {2 x \log {\relax (2 )}^{2}}{3}\right ) \log {\left (x^{3} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((ln(x**2/ln(3)**4)+2)*ln(x**3)**4+12*ln(x**2/ln(3)**4)*ln(x**3)**3+((2*ln(2)-4*x)*ln(x**2/ln(3)**4)+
4*ln(2)-4*x)*ln(x**3)**2+(12*ln(2)-12*x)*ln(x**2/ln(3)**4)*ln(x**3)+(ln(2)**2-4*x*ln(2)+3*x**2)*ln(x**2/ln(3)*
*4)+2*ln(2)**2-4*x*ln(2)+2*x**2,x)

[Out]

-4*x**3*log(log(3)) + 8*x**2*log(2)*log(log(3)) + 2*x*log(x**3)**5/3 - 4*x*log(x**3)**4*log(log(3)) - 4*x*log(
2)**2*log(log(3)) + (-4*x**2/3 + 4*x*log(2)/3)*log(x**3)**3 + (8*x**2*log(log(3)) - 8*x*log(2)*log(log(3)))*lo
g(x**3)**2 + (2*x**3/3 - 4*x**2*log(2)/3 + 2*x*log(2)**2/3)*log(x**3)

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