3.50.28 \(\int \frac {-512-2304 x-2224 x^2+420 x^3+1044 x^4+52 x^5-180 x^6-12 x^7+12 x^8+(-1024-2048 x-288 x^2+1000 x^3+232 x^4-192 x^5-32 x^6+16 x^7) \log (x)+(-256-192 x+144 x^2+92 x^3-36 x^4-12 x^5+4 x^6) \log ^2(x)}{-64-48 x+36 x^2+23 x^3-9 x^4-3 x^5+x^6} \, dx\)

Optimal. Leaf size=25 \[ x \left (-4+4 \left (1+x+\frac {x}{4+x-x^2}+\log (x)\right )^2\right ) \]

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Rubi [B]  time = 1.69, antiderivative size = 771, normalized size of antiderivative = 30.84, number of steps used = 85, number of rules used = 24, integrand size = 144, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {6688, 12, 6742, 614, 618, 206, 638, 738, 728, 722, 818, 773, 632, 31, 800, 2357, 2295, 2304, 2314, 2316, 2315, 2317, 2391, 2296} \begin {gather*} \frac {654 x^4}{289}+\frac {4960 x^3}{289}+\frac {26 (41 x+260) x^2}{289 \left (-x^2+x+4\right )}+\frac {14 x^2}{289}+\frac {11898 (x+8) x}{289 \left (-x^2+x+4\right )}+\frac {1112 (x+8) x}{17 \left (-x^2+x+4\right )^2}+\frac {2224 (12-7 x)}{289 \left (-x^2+x+4\right )}-\frac {4992 (1-2 x)}{289 \left (-x^2+x+4\right )}-\frac {256 (1-2 x)}{17 \left (-x^2+x+4\right )^2}+\frac {1152 (x+8)}{17 \left (-x^2+x+4\right )^2}+8 x^2 \log (x)-\frac {6 (x+8) x^7}{17 \left (-x^2+x+4\right )^2}+\frac {6 (x+8) x^6}{17 \left (-x^2+x+4\right )^2}+\frac {24 (23 x+116) x^5}{289 \left (-x^2+x+4\right )}+\frac {90 (x+8) x^5}{17 \left (-x^2+x+4\right )^2}-\frac {18 (25 x+132) x^4}{289 \left (-x^2+x+4\right )}-\frac {26 (x+8) x^4}{17 \left (-x^2+x+4\right )^2}-\frac {180 (29 x+164) x^3}{289 \left (-x^2+x+4\right )}+\frac {210 (1-2 x) x^3}{17 \left (-x^2+x+4\right )^2}-\frac {522 (x+8) x^3}{17 \left (-x^2+x+4\right )^2}-\frac {27504 x}{289}+4 x \log ^2(x)+\frac {128 x \log (x)}{17 \left (1-\sqrt {17}\right ) \left (-2 x-\sqrt {17}+1\right )}+\frac {144 x \log (x)}{17 \left (-2 x-\sqrt {17}+1\right )}+\frac {128 x \log (x)}{17 \left (1+\sqrt {17}\right ) \left (-2 x+\sqrt {17}+1\right )}+\frac {144 x \log (x)}{17 \left (-2 x+\sqrt {17}+1\right )}+8 x \log (x)+\frac {64 \log \left (-2 x-\sqrt {17}+1\right )}{17 \left (1-\sqrt {17}\right )}+\frac {26 \left (4913-521 \sqrt {17}\right ) \log \left (-2 x-\sqrt {17}+1\right )}{4913}-\frac {270 \left (4913-1801 \sqrt {17}\right ) \log \left (-2 x-\sqrt {17}+1\right )}{4913}-\frac {36 \left (14739-2843 \sqrt {17}\right ) \log \left (-2 x-\sqrt {17}+1\right )}{4913}+\frac {12 \left (142477-39429 \sqrt {17}\right ) \log \left (-2 x-\sqrt {17}+1\right )}{4913}+\frac {72}{17} \log \left (-2 x-\sqrt {17}+1\right )+\frac {12 \left (142477+39429 \sqrt {17}\right ) \log \left (-2 x+\sqrt {17}+1\right )}{4913}-\frac {36 \left (14739+2843 \sqrt {17}\right ) \log \left (-2 x+\sqrt {17}+1\right )}{4913}-\frac {270 \left (4913+1801 \sqrt {17}\right ) \log \left (-2 x+\sqrt {17}+1\right )}{4913}+\frac {26 \left (4913+521 \sqrt {17}\right ) \log \left (-2 x+\sqrt {17}+1\right )}{4913}+\frac {64 \log \left (-2 x+\sqrt {17}+1\right )}{17 \left (1+\sqrt {17}\right )}+\frac {72}{17} \log \left (-2 x+\sqrt {17}+1\right )+\frac {201536 \tanh ^{-1}\left (\frac {1-2 x}{\sqrt {17}}\right )}{289 \sqrt {17}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-512 - 2304*x - 2224*x^2 + 420*x^3 + 1044*x^4 + 52*x^5 - 180*x^6 - 12*x^7 + 12*x^8 + (-1024 - 2048*x - 28
8*x^2 + 1000*x^3 + 232*x^4 - 192*x^5 - 32*x^6 + 16*x^7)*Log[x] + (-256 - 192*x + 144*x^2 + 92*x^3 - 36*x^4 - 1
2*x^5 + 4*x^6)*Log[x]^2)/(-64 - 48*x + 36*x^2 + 23*x^3 - 9*x^4 - 3*x^5 + x^6),x]

[Out]

(-27504*x)/289 + (14*x^2)/289 + (4960*x^3)/289 + (654*x^4)/289 - (256*(1 - 2*x))/(17*(4 + x - x^2)^2) + (210*(
1 - 2*x)*x^3)/(17*(4 + x - x^2)^2) + (1152*(8 + x))/(17*(4 + x - x^2)^2) + (1112*x*(8 + x))/(17*(4 + x - x^2)^
2) - (522*x^3*(8 + x))/(17*(4 + x - x^2)^2) - (26*x^4*(8 + x))/(17*(4 + x - x^2)^2) + (90*x^5*(8 + x))/(17*(4
+ x - x^2)^2) + (6*x^6*(8 + x))/(17*(4 + x - x^2)^2) - (6*x^7*(8 + x))/(17*(4 + x - x^2)^2) + (2224*(12 - 7*x)
)/(289*(4 + x - x^2)) - (4992*(1 - 2*x))/(289*(4 + x - x^2)) + (11898*x*(8 + x))/(289*(4 + x - x^2)) + (24*x^5
*(116 + 23*x))/(289*(4 + x - x^2)) - (18*x^4*(132 + 25*x))/(289*(4 + x - x^2)) - (180*x^3*(164 + 29*x))/(289*(
4 + x - x^2)) + (26*x^2*(260 + 41*x))/(289*(4 + x - x^2)) + (201536*ArcTanh[(1 - 2*x)/Sqrt[17]])/(289*Sqrt[17]
) + (72*Log[1 - Sqrt[17] - 2*x])/17 + (12*(142477 - 39429*Sqrt[17])*Log[1 - Sqrt[17] - 2*x])/4913 - (36*(14739
- 2843*Sqrt[17])*Log[1 - Sqrt[17] - 2*x])/4913 - (270*(4913 - 1801*Sqrt[17])*Log[1 - Sqrt[17] - 2*x])/4913 +
(26*(4913 - 521*Sqrt[17])*Log[1 - Sqrt[17] - 2*x])/4913 + (64*Log[1 - Sqrt[17] - 2*x])/(17*(1 - Sqrt[17])) + (
72*Log[1 + Sqrt[17] - 2*x])/17 + (64*Log[1 + Sqrt[17] - 2*x])/(17*(1 + Sqrt[17])) + (26*(4913 + 521*Sqrt[17])*
Log[1 + Sqrt[17] - 2*x])/4913 - (270*(4913 + 1801*Sqrt[17])*Log[1 + Sqrt[17] - 2*x])/4913 - (36*(14739 + 2843*
Sqrt[17])*Log[1 + Sqrt[17] - 2*x])/4913 + (12*(142477 + 39429*Sqrt[17])*Log[1 + Sqrt[17] - 2*x])/4913 + 8*x*Lo
g[x] + (144*x*Log[x])/(17*(1 - Sqrt[17] - 2*x)) + (128*x*Log[x])/(17*(1 - Sqrt[17])*(1 - Sqrt[17] - 2*x)) + (1
44*x*Log[x])/(17*(1 + Sqrt[17] - 2*x)) + (128*x*Log[x])/(17*(1 + Sqrt[17])*(1 + Sqrt[17] - 2*x)) + 8*x^2*Log[x
] + 4*x*Log[x]^2

Rule 12

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

Rule 31

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

Rule 206

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(1*ArcTanh[(Rt[-b, 2]*x)/Rt[a, 2]])/(Rt[a, 2]*Rt[-b, 2]), x]
/; FreeQ[{a, b}, x] && NegQ[a/b] && (GtQ[a, 0] || LtQ[b, 0])

Rule 614

Int[((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Simp[((b + 2*c*x)*(a + b*x + c*x^2)^(p + 1))/((p +
1)*(b^2 - 4*a*c)), x] - Dist[(2*c*(2*p + 3))/((p + 1)*(b^2 - 4*a*c)), Int[(a + b*x + c*x^2)^(p + 1), x], x] /;
FreeQ[{a, b, c}, x] && NeQ[b^2 - 4*a*c, 0] && LtQ[p, -1] && NeQ[p, -3/2] && IntegerQ[4*p]

Rule 618

Int[((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(-1), x_Symbol] :> Dist[-2, Subst[Int[1/Simp[b^2 - 4*a*c - x^2, x], x]
, x, b + 2*c*x], x] /; FreeQ[{a, b, c}, x] && NeQ[b^2 - 4*a*c, 0]

Rule 632

Int[((d_.) + (e_.)*(x_))/((a_) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> With[{q = Rt[b^2 - 4*a*c, 2]}, Dist[
(c*d - e*(b/2 - q/2))/q, Int[1/(b/2 - q/2 + c*x), x], x] - Dist[(c*d - e*(b/2 + q/2))/q, Int[1/(b/2 + q/2 + c*
x), x], x]] /; FreeQ[{a, b, c, d, e}, x] && NeQ[2*c*d - b*e, 0] && NeQ[b^2 - 4*a*c, 0] && NiceSqrtQ[b^2 - 4*a*
c]

Rule 638

Int[((d_.) + (e_.)*(x_))*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Simp[((b*d - 2*a*e + (2*c*d -
b*e)*x)*(a + b*x + c*x^2)^(p + 1))/((p + 1)*(b^2 - 4*a*c)), x] - Dist[((2*p + 3)*(2*c*d - b*e))/((p + 1)*(b^2
- 4*a*c)), Int[(a + b*x + c*x^2)^(p + 1), x], x] /; FreeQ[{a, b, c, d, e}, x] && NeQ[2*c*d - b*e, 0] && NeQ[b^
2 - 4*a*c, 0] && LtQ[p, -1] && NeQ[p, -3/2]

Rule 722

Int[((d_.) + (e_.)*(x_))^(m_)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Simp[((d + e*x)^(m - 1)*(
d*b - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(p + 1))/((p + 1)*(b^2 - 4*a*c)), x] - Dist[(2*(2*p + 3)*(c*d
^2 - b*d*e + a*e^2))/((p + 1)*(b^2 - 4*a*c)), Int[(d + e*x)^(m - 2)*(a + b*x + c*x^2)^(p + 1), x], x] /; FreeQ
[{a, b, c, d, e}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - b*d*e + a*e^2, 0] && NeQ[2*c*d - b*e, 0] && EqQ[m +
2*p + 2, 0] && LtQ[p, -1]

Rule 728

Int[((d_.) + (e_.)*(x_))^(m_)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Simp[((d + e*x)^m*(b + 2*
c*x)*(a + b*x + c*x^2)^(p + 1))/((p + 1)*(b^2 - 4*a*c)), x] + Dist[(m*(2*c*d - b*e))/((p + 1)*(b^2 - 4*a*c)),
Int[(d + e*x)^(m - 1)*(a + b*x + c*x^2)^(p + 1), x], x] /; FreeQ[{a, b, c, d, e, m, p}, x] && NeQ[b^2 - 4*a*c,
0] && NeQ[c*d^2 - b*d*e + a*e^2, 0] && NeQ[2*c*d - b*e, 0] && EqQ[m + 2*p + 3, 0] && LtQ[p, -1]

Rule 738

Int[((d_.) + (e_.)*(x_))^(m_)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Simp[((d + e*x)^(m - 1)*(
d*b - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(p + 1))/((p + 1)*(b^2 - 4*a*c)), x] + Dist[1/((p + 1)*(b^2 -
4*a*c)), Int[(d + e*x)^(m - 2)*Simp[e*(2*a*e*(m - 1) + b*d*(2*p - m + 4)) - 2*c*d^2*(2*p + 3) + e*(b*e - 2*d*
c)*(m + 2*p + 2)*x, x]*(a + b*x + c*x^2)^(p + 1), x], x] /; FreeQ[{a, b, c, d, e}, x] && NeQ[b^2 - 4*a*c, 0] &
& NeQ[c*d^2 - b*d*e + a*e^2, 0] && NeQ[2*c*d - b*e, 0] && LtQ[p, -1] && GtQ[m, 1] && IntQuadraticQ[a, b, c, d,
e, m, p, x]

Rule 773

Int[(((d_.) + (e_.)*(x_))*((f_) + (g_.)*(x_)))/((a_.) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> Simp[(e*g*x)/
c, x] + Dist[1/c, Int[(c*d*f - a*e*g + (c*e*f + c*d*g - b*e*g)*x)/(a + b*x + c*x^2), x], x] /; FreeQ[{a, b, c,
d, e, f, g}, x] && NeQ[b^2 - 4*a*c, 0]

Rule 800

Int[(((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_)))/((a_.) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> Int[Exp
andIntegrand[((d + e*x)^m*(f + g*x))/(a + b*x + c*x^2), x], x] /; FreeQ[{a, b, c, d, e, f, g}, x] && NeQ[b^2 -
4*a*c, 0] && NeQ[c*d^2 - b*d*e + a*e^2, 0] && IntegerQ[m]

Rule 818

Int[((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_))*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> -Si
mp[((d + e*x)^(m - 1)*(a + b*x + c*x^2)^(p + 1)*(2*a*c*(e*f + d*g) - b*(c*d*f + a*e*g) - (2*c^2*d*f + b^2*e*g
- c*(b*e*f + b*d*g + 2*a*e*g))*x))/(c*(p + 1)*(b^2 - 4*a*c)), x] - Dist[1/(c*(p + 1)*(b^2 - 4*a*c)), Int[(d +
e*x)^(m - 2)*(a + b*x + c*x^2)^(p + 1)*Simp[2*c^2*d^2*f*(2*p + 3) + b*e*g*(a*e*(m - 1) + b*d*(p + 2)) - c*(2*a
*e*(e*f*(m - 1) + d*g*m) + b*d*(d*g*(2*p + 3) - e*f*(m - 2*p - 4))) + e*(b^2*e*g*(m + p + 1) + 2*c^2*d*f*(m +
2*p + 2) - c*(2*a*e*g*m + b*(e*f + d*g)*(m + 2*p + 2)))*x, x], x], x] /; FreeQ[{a, b, c, d, e, f, g}, x] && Ne
Q[b^2 - 4*a*c, 0] && NeQ[c*d^2 - b*d*e + a*e^2, 0] && LtQ[p, -1] && GtQ[m, 1] && ((EqQ[m, 2] && EqQ[p, -3] &&
RationalQ[a, b, c, d, e, f, g]) ||  !ILtQ[m + 2*p + 3, 0])

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 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 2315

Int[Log[(c_.)*(x_)]/((d_) + (e_.)*(x_)), x_Symbol] :> -Simp[PolyLog[2, 1 - c*x]/e, x] /; FreeQ[{c, d, e}, x] &
& EqQ[e + c*d, 0]

Rule 2316

Int[((a_.) + Log[(c_.)*(x_)]*(b_.))/((d_) + (e_.)*(x_)), x_Symbol] :> Simp[((a + b*Log[-((c*d)/e)])*Log[d + e*
x])/e, x] + Dist[b, Int[Log[-((e*x)/d)]/(d + e*x), x], x] /; FreeQ[{a, b, c, d, e}, x] && GtQ[-((c*d)/e), 0]

Rule 2317

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

Rule 2357

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*(RFx_), x_Symbol] :> With[{u = ExpandIntegrand[(a + b*Log[c*x^
n])^p, RFx, x]}, Int[u, x] /; SumQ[u]] /; FreeQ[{a, b, c, n}, x] && RationalFunctionQ[RFx, x] && IGtQ[p, 0]

Rule 2391

Int[Log[(c_.)*((d_) + (e_.)*(x_)^(n_.))]/(x_), x_Symbol] :> -Simp[PolyLog[2, -(c*e*x^n)]/n, x] /; FreeQ[{c, d,
e, n}, x] && EqQ[c*d, 1]

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 {4 \left (128+576 x+556 x^2-105 x^3-261 x^4-13 x^5+45 x^6+3 x^7-3 x^8-\left (-256-512 x-72 x^2+250 x^3+58 x^4-48 x^5-8 x^6+4 x^7\right ) \log (x)-\left (-4-x+x^2\right )^3 \log ^2(x)\right )}{\left (4+x-x^2\right )^3} \, dx\\ &=4 \int \frac {128+576 x+556 x^2-105 x^3-261 x^4-13 x^5+45 x^6+3 x^7-3 x^8-\left (-256-512 x-72 x^2+250 x^3+58 x^4-48 x^5-8 x^6+4 x^7\right ) \log (x)-\left (-4-x+x^2\right )^3 \log ^2(x)}{\left (4+x-x^2\right )^3} \, dx\\ &=4 \int \left (-\frac {128}{\left (-4-x+x^2\right )^3}-\frac {576 x}{\left (-4-x+x^2\right )^3}-\frac {556 x^2}{\left (-4-x+x^2\right )^3}+\frac {105 x^3}{\left (-4-x+x^2\right )^3}+\frac {261 x^4}{\left (-4-x+x^2\right )^3}+\frac {13 x^5}{\left (-4-x+x^2\right )^3}-\frac {45 x^6}{\left (-4-x+x^2\right )^3}-\frac {3 x^7}{\left (-4-x+x^2\right )^3}+\frac {3 x^8}{\left (-4-x+x^2\right )^3}+\frac {2 \left (32+56 x+3 x^2-18 x^3-2 x^4+2 x^5\right ) \log (x)}{\left (-4-x+x^2\right )^2}+\log ^2(x)\right ) \, dx\\ &=4 \int \log ^2(x) \, dx+8 \int \frac {\left (32+56 x+3 x^2-18 x^3-2 x^4+2 x^5\right ) \log (x)}{\left (-4-x+x^2\right )^2} \, dx-12 \int \frac {x^7}{\left (-4-x+x^2\right )^3} \, dx+12 \int \frac {x^8}{\left (-4-x+x^2\right )^3} \, dx+52 \int \frac {x^5}{\left (-4-x+x^2\right )^3} \, dx-180 \int \frac {x^6}{\left (-4-x+x^2\right )^3} \, dx+420 \int \frac {x^3}{\left (-4-x+x^2\right )^3} \, dx-512 \int \frac {1}{\left (-4-x+x^2\right )^3} \, dx+1044 \int \frac {x^4}{\left (-4-x+x^2\right )^3} \, dx-2224 \int \frac {x^2}{\left (-4-x+x^2\right )^3} \, dx-2304 \int \frac {x}{\left (-4-x+x^2\right )^3} \, dx\\ &=-\frac {256 (1-2 x)}{17 \left (4+x-x^2\right )^2}+\frac {210 (1-2 x) x^3}{17 \left (4+x-x^2\right )^2}+\frac {1152 (8+x)}{17 \left (4+x-x^2\right )^2}+\frac {1112 x (8+x)}{17 \left (4+x-x^2\right )^2}-\frac {522 x^3 (8+x)}{17 \left (4+x-x^2\right )^2}-\frac {26 x^4 (8+x)}{17 \left (4+x-x^2\right )^2}+\frac {90 x^5 (8+x)}{17 \left (4+x-x^2\right )^2}+\frac {6 x^6 (8+x)}{17 \left (4+x-x^2\right )^2}-\frac {6 x^7 (8+x)}{17 \left (4+x-x^2\right )^2}+4 x \log ^2(x)+\frac {6}{17} \int \frac {(-48-3 x) x^5}{\left (-4-x+x^2\right )^2} \, dx-\frac {6}{17} \int \frac {(-56-4 x) x^6}{\left (-4-x+x^2\right )^2} \, dx-\frac {26}{17} \int \frac {(-32-x) x^3}{\left (-4-x+x^2\right )^2} \, dx+\frac {90}{17} \int \frac {(-40-2 x) x^4}{\left (-4-x+x^2\right )^2} \, dx-8 \int \log (x) \, dx+8 \int \left (2 \log (x)+2 x \log (x)+\frac {(4+9 x) \log (x)}{\left (-4-x+x^2\right )^2}+\frac {\log (x)}{-4-x+x^2}\right ) \, dx-\frac {630}{17} \int \frac {x^2}{\left (-4-x+x^2\right )^2} \, dx+\frac {1112}{17} \int \frac {-8+2 x}{\left (-4-x+x^2\right )^2} \, dx+\frac {1536}{17} \int \frac {1}{\left (-4-x+x^2\right )^2} \, dx+\frac {3456}{17} \int \frac {1}{\left (-4-x+x^2\right )^2} \, dx+\frac {12528}{17} \int \frac {x^2}{\left (-4-x+x^2\right )^2} \, dx\\ &=8 x-\frac {256 (1-2 x)}{17 \left (4+x-x^2\right )^2}+\frac {210 (1-2 x) x^3}{17 \left (4+x-x^2\right )^2}+\frac {1152 (8+x)}{17 \left (4+x-x^2\right )^2}+\frac {1112 x (8+x)}{17 \left (4+x-x^2\right )^2}-\frac {522 x^3 (8+x)}{17 \left (4+x-x^2\right )^2}-\frac {26 x^4 (8+x)}{17 \left (4+x-x^2\right )^2}+\frac {90 x^5 (8+x)}{17 \left (4+x-x^2\right )^2}+\frac {6 x^6 (8+x)}{17 \left (4+x-x^2\right )^2}-\frac {6 x^7 (8+x)}{17 \left (4+x-x^2\right )^2}+\frac {2224 (12-7 x)}{289 \left (4+x-x^2\right )}-\frac {4992 (1-2 x)}{289 \left (4+x-x^2\right )}+\frac {11898 x (8+x)}{289 \left (4+x-x^2\right )}+\frac {24 x^5 (116+23 x)}{289 \left (4+x-x^2\right )}-\frac {18 x^4 (132+25 x)}{289 \left (4+x-x^2\right )}-\frac {180 x^3 (164+29 x)}{289 \left (4+x-x^2\right )}+\frac {26 x^2 (260+41 x)}{289 \left (4+x-x^2\right )}-8 x \log (x)+4 x \log ^2(x)+\frac {6}{289} \int \frac {(-1584-276 x) x^3}{-4-x+x^2} \, dx-\frac {6}{289} \int \frac {(-2320-436 x) x^4}{-4-x+x^2} \, dx-\frac {26}{289} \int \frac {(-520-58 x) x}{-4-x+x^2} \, dx+\frac {90}{289} \int \frac {(-984-150 x) x^2}{-4-x+x^2} \, dx+8 \int \frac {(4+9 x) \log (x)}{\left (-4-x+x^2\right )^2} \, dx+8 \int \frac {\log (x)}{-4-x+x^2} \, dx-\frac {3072}{289} \int \frac {1}{-4-x+x^2} \, dx+16 \int \log (x) \, dx+16 \int x \log (x) \, dx-\frac {5040}{289} \int \frac {1}{-4-x+x^2} \, dx-\frac {6912}{289} \int \frac {1}{-4-x+x^2} \, dx+\frac {15568}{289} \int \frac {1}{-4-x+x^2} \, dx+\frac {100224}{289} \int \frac {1}{-4-x+x^2} \, dx\\ &=-\frac {804 x}{289}-4 x^2-\frac {256 (1-2 x)}{17 \left (4+x-x^2\right )^2}+\frac {210 (1-2 x) x^3}{17 \left (4+x-x^2\right )^2}+\frac {1152 (8+x)}{17 \left (4+x-x^2\right )^2}+\frac {1112 x (8+x)}{17 \left (4+x-x^2\right )^2}-\frac {522 x^3 (8+x)}{17 \left (4+x-x^2\right )^2}-\frac {26 x^4 (8+x)}{17 \left (4+x-x^2\right )^2}+\frac {90 x^5 (8+x)}{17 \left (4+x-x^2\right )^2}+\frac {6 x^6 (8+x)}{17 \left (4+x-x^2\right )^2}-\frac {6 x^7 (8+x)}{17 \left (4+x-x^2\right )^2}+\frac {2224 (12-7 x)}{289 \left (4+x-x^2\right )}-\frac {4992 (1-2 x)}{289 \left (4+x-x^2\right )}+\frac {11898 x (8+x)}{289 \left (4+x-x^2\right )}+\frac {24 x^5 (116+23 x)}{289 \left (4+x-x^2\right )}-\frac {18 x^4 (132+25 x)}{289 \left (4+x-x^2\right )}-\frac {180 x^3 (164+29 x)}{289 \left (4+x-x^2\right )}+\frac {26 x^2 (260+41 x)}{289 \left (4+x-x^2\right )}+8 x \log (x)+8 x^2 \log (x)+4 x \log ^2(x)+\frac {6}{289} \int \left (-2964-1860 x-276 x^2-\frac {12 (988+867 x)}{-4-x+x^2}\right ) \, dx-\frac {6}{289} \int \left (-15524-4500 x-2756 x^2-436 x^3-\frac {4 (15524+8381 x)}{-4-x+x^2}\right ) \, dx-\frac {26}{289} \int \frac {-232-578 x}{-4-x+x^2} \, dx+\frac {90}{289} \int \left (-1134-150 x-\frac {6 (756+289 x)}{-4-x+x^2}\right ) \, dx+8 \int \left (-\frac {2 \log (x)}{\sqrt {17} \left (1+\sqrt {17}-2 x\right )}-\frac {2 \log (x)}{\sqrt {17} \left (-1+\sqrt {17}+2 x\right )}\right ) \, dx+8 \int \left (\frac {4 \log (x)}{\left (-4-x+x^2\right )^2}+\frac {9 x \log (x)}{\left (-4-x+x^2\right )^2}\right ) \, dx+\frac {6144}{289} \operatorname {Subst}\left (\int \frac {1}{17-x^2} \, dx,x,-1+2 x\right )+\frac {10080}{289} \operatorname {Subst}\left (\int \frac {1}{17-x^2} \, dx,x,-1+2 x\right )+\frac {13824}{289} \operatorname {Subst}\left (\int \frac {1}{17-x^2} \, dx,x,-1+2 x\right )-\frac {31136}{289} \operatorname {Subst}\left (\int \frac {1}{17-x^2} \, dx,x,-1+2 x\right )-\frac {200448}{289} \operatorname {Subst}\left (\int \frac {1}{17-x^2} \, dx,x,-1+2 x\right )\\ &=-\frac {27504 x}{289}+\frac {14 x^2}{289}+\frac {4960 x^3}{289}+\frac {654 x^4}{289}-\frac {256 (1-2 x)}{17 \left (4+x-x^2\right )^2}+\frac {210 (1-2 x) x^3}{17 \left (4+x-x^2\right )^2}+\frac {1152 (8+x)}{17 \left (4+x-x^2\right )^2}+\frac {1112 x (8+x)}{17 \left (4+x-x^2\right )^2}-\frac {522 x^3 (8+x)}{17 \left (4+x-x^2\right )^2}-\frac {26 x^4 (8+x)}{17 \left (4+x-x^2\right )^2}+\frac {90 x^5 (8+x)}{17 \left (4+x-x^2\right )^2}+\frac {6 x^6 (8+x)}{17 \left (4+x-x^2\right )^2}-\frac {6 x^7 (8+x)}{17 \left (4+x-x^2\right )^2}+\frac {2224 (12-7 x)}{289 \left (4+x-x^2\right )}-\frac {4992 (1-2 x)}{289 \left (4+x-x^2\right )}+\frac {11898 x (8+x)}{289 \left (4+x-x^2\right )}+\frac {24 x^5 (116+23 x)}{289 \left (4+x-x^2\right )}-\frac {18 x^4 (132+25 x)}{289 \left (4+x-x^2\right )}-\frac {180 x^3 (164+29 x)}{289 \left (4+x-x^2\right )}+\frac {26 x^2 (260+41 x)}{289 \left (4+x-x^2\right )}+\frac {201536 \tanh ^{-1}\left (\frac {1-2 x}{\sqrt {17}}\right )}{289 \sqrt {17}}+8 x \log (x)+8 x^2 \log (x)+4 x \log ^2(x)+\frac {24}{289} \int \frac {15524+8381 x}{-4-x+x^2} \, dx-\frac {72}{289} \int \frac {988+867 x}{-4-x+x^2} \, dx-\frac {540}{289} \int \frac {756+289 x}{-4-x+x^2} \, dx+32 \int \frac {\log (x)}{\left (-4-x+x^2\right )^2} \, dx+72 \int \frac {x \log (x)}{\left (-4-x+x^2\right )^2} \, dx-\frac {16 \int \frac {\log (x)}{1+\sqrt {17}-2 x} \, dx}{\sqrt {17}}-\frac {16 \int \frac {\log (x)}{-1+\sqrt {17}+2 x} \, dx}{\sqrt {17}}+\frac {\left (26 \left (4913-521 \sqrt {17}\right )\right ) \int \frac {1}{-\frac {1}{2}+\frac {\sqrt {17}}{2}+x} \, dx}{4913}+\frac {\left (26 \left (4913+521 \sqrt {17}\right )\right ) \int \frac {1}{-\frac {1}{2}-\frac {\sqrt {17}}{2}+x} \, dx}{4913}\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.06, size = 83, normalized size = 3.32 \begin {gather*} 4 \left (-2 x+2 x^2+x^3+\frac {4+5 x}{\left (-4-x+x^2\right )^2}+\frac {-15-11 x}{-4-x+x^2}-2 \log (x)+\frac {2 \left (-4-5 x-5 x^2+x^4\right ) \log (x)}{-4-x+x^2}+x \log ^2(x)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-512 - 2304*x - 2224*x^2 + 420*x^3 + 1044*x^4 + 52*x^5 - 180*x^6 - 12*x^7 + 12*x^8 + (-1024 - 2048*
x - 288*x^2 + 1000*x^3 + 232*x^4 - 192*x^5 - 32*x^6 + 16*x^7)*Log[x] + (-256 - 192*x + 144*x^2 + 92*x^3 - 36*x
^4 - 12*x^5 + 4*x^6)*Log[x]^2)/(-64 - 48*x + 36*x^2 + 23*x^3 - 9*x^4 - 3*x^5 + x^6),x]

[Out]

4*(-2*x + 2*x^2 + x^3 + (4 + 5*x)/(-4 - x + x^2)^2 + (-15 - 11*x)/(-4 - x + x^2) - 2*Log[x] + (2*(-4 - 5*x - 5
*x^2 + x^4)*Log[x])/(-4 - x + x^2) + x*Log[x]^2)

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fricas [B]  time = 1.14, size = 108, normalized size = 4.32 \begin {gather*} \frac {4 \, {\left (x^{7} - 13 \, x^{5} - 2 \, x^{4} + 35 \, x^{3} + {\left (x^{5} - 2 \, x^{4} - 7 \, x^{3} + 8 \, x^{2} + 16 \, x\right )} \log \relax (x)^{2} + 12 \, x^{2} + 2 \, {\left (x^{6} - x^{5} - 10 \, x^{4} + 2 \, x^{3} + 28 \, x^{2} + 16 \, x\right )} \log \relax (x) + 32 \, x + 64\right )}}{x^{4} - 2 \, x^{3} - 7 \, x^{2} + 8 \, x + 16} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^6-12*x^5-36*x^4+92*x^3+144*x^2-192*x-256)*log(x)^2+(16*x^7-32*x^6-192*x^5+232*x^4+1000*x^3-288
*x^2-2048*x-1024)*log(x)+12*x^8-12*x^7-180*x^6+52*x^5+1044*x^4+420*x^3-2224*x^2-2304*x-512)/(x^6-3*x^5-9*x^4+2
3*x^3+36*x^2-48*x-64),x, algorithm="fricas")

[Out]

4*(x^7 - 13*x^5 - 2*x^4 + 35*x^3 + (x^5 - 2*x^4 - 7*x^3 + 8*x^2 + 16*x)*log(x)^2 + 12*x^2 + 2*(x^6 - x^5 - 10*
x^4 + 2*x^3 + 28*x^2 + 16*x)*log(x) + 32*x + 64)/(x^4 - 2*x^3 - 7*x^2 + 8*x + 16)

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giac [B]  time = 0.23, size = 86, normalized size = 3.44 \begin {gather*} 4 \, x^{3} + 4 \, x \log \relax (x)^{2} + 8 \, x^{2} + 8 \, {\left (x^{2} + x - \frac {x + 4}{x^{2} - x - 4}\right )} \log \relax (x) - 8 \, x - \frac {4 \, {\left (11 \, x^{3} + 4 \, x^{2} - 64 \, x - 64\right )}}{x^{4} - 2 \, x^{3} - 7 \, x^{2} + 8 \, x + 16} - 8 \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^6-12*x^5-36*x^4+92*x^3+144*x^2-192*x-256)*log(x)^2+(16*x^7-32*x^6-192*x^5+232*x^4+1000*x^3-288
*x^2-2048*x-1024)*log(x)+12*x^8-12*x^7-180*x^6+52*x^5+1044*x^4+420*x^3-2224*x^2-2304*x-512)/(x^6-3*x^5-9*x^4+2
3*x^3+36*x^2-48*x-64),x, algorithm="giac")

[Out]

4*x^3 + 4*x*log(x)^2 + 8*x^2 + 8*(x^2 + x - (x + 4)/(x^2 - x - 4))*log(x) - 8*x - 4*(11*x^3 + 4*x^2 - 64*x - 6
4)/(x^4 - 2*x^3 - 7*x^2 + 8*x + 16) - 8*log(x)

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maple [B]  time = 0.07, size = 108, normalized size = 4.32

method	result	size
risch	\(4 x \ln \relax (x )^{2}+\frac {8 \left (x^{4}-5 x^{2}-5 x -4\right ) \ln \relax (x )}{x^{2}-x -4}-\frac {4 \left (-x^{7}+2 x^{4} \ln \relax (x )+13 x^{5}-4 x^{3} \ln \relax (x )+2 x^{4}-14 x^{2} \ln \relax (x )-35 x^{3}+16 x \ln \relax (x )-12 x^{2}+32 \ln \relax (x )-32 x -64\right )}{\left (x^{2}-x -4\right )^{2}}\)	\(108\)
default	\(4 x \ln \relax (x )^{2}+8 x \ln \relax (x )-8 x +4 x^{3}+8 x^{2}-\frac {4 \left (11 x^{3}+4 x^{2}-64 x -64\right )}{\left (x^{2}-x -4\right )^{2}}+8 x^{2} \ln \relax (x )-\frac {8 \ln \relax (x ) \left (\sqrt {17}\, \ln \left (\frac {1+\sqrt {17}-2 x}{1+\sqrt {17}}\right ) x^{2}-\sqrt {17}\, \ln \left (\frac {-1+\sqrt {17}+2 x}{-1+\sqrt {17}}\right ) x^{2}-\sqrt {17}\, \ln \left (\frac {1+\sqrt {17}-2 x}{1+\sqrt {17}}\right ) x +\sqrt {17}\, \ln \left (\frac {-1+\sqrt {17}+2 x}{-1+\sqrt {17}}\right ) x -4 \sqrt {17}\, \ln \left (\frac {1+\sqrt {17}-2 x}{1+\sqrt {17}}\right )+4 \sqrt {17}\, \ln \left (\frac {-1+\sqrt {17}+2 x}{-1+\sqrt {17}}\right )+17 x^{2}\right )}{17 \left (x^{2}-x -4\right )}+\frac {8 \sqrt {17}\, \ln \relax (x ) \ln \left (\frac {1+\sqrt {17}-2 x}{1+\sqrt {17}}\right )}{17}-\frac {8 \sqrt {17}\, \ln \relax (x ) \ln \left (\frac {-1+\sqrt {17}+2 x}{-1+\sqrt {17}}\right )}{17}\)	\(267\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((4*x^6-12*x^5-36*x^4+92*x^3+144*x^2-192*x-256)*ln(x)^2+(16*x^7-32*x^6-192*x^5+232*x^4+1000*x^3-288*x^2-20
48*x-1024)*ln(x)+12*x^8-12*x^7-180*x^6+52*x^5+1044*x^4+420*x^3-2224*x^2-2304*x-512)/(x^6-3*x^5-9*x^4+23*x^3+36
*x^2-48*x-64),x,method=_RETURNVERBOSE)

[Out]

4*x*ln(x)^2+8*(x^4-5*x^2-5*x-4)/(x^2-x-4)*ln(x)-4*(-x^7+2*x^4*ln(x)+13*x^5-4*x^3*ln(x)+2*x^4-14*x^2*ln(x)-35*x
^3+16*x*ln(x)-12*x^2+32*ln(x)-32*x-64)/(x^2-x-4)^2

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maxima [B]  time = 0.50, size = 405, normalized size = 16.20 \begin {gather*} 4 \, x^{3} + 12 \, x^{2} - \frac {6 \, {\left (37898 \, x^{3} + 23495 \, x^{2} - 180872 \, x - 197904\right )}}{289 \, {\left (x^{4} - 2 \, x^{3} - 7 \, x^{2} + 8 \, x + 16\right )}} + \frac {6 \, {\left (11264 \, x^{3} + 12293 \, x^{2} - 56696 \, x - 74032\right )}}{289 \, {\left (x^{4} - 2 \, x^{3} - 7 \, x^{2} + 8 \, x + 16\right )}} + \frac {90 \, {\left (4134 \, x^{3} + 1891 \, x^{2} - 17512 \, x - 17232\right )}}{289 \, {\left (x^{4} - 2 \, x^{3} - 7 \, x^{2} + 8 \, x + 16\right )}} - \frac {26 \, {\left (924 \, x^{3} + 1793 \, x^{2} - 4696 \, x - 7536\right )}}{289 \, {\left (x^{4} - 2 \, x^{3} - 7 \, x^{2} + 8 \, x + 16\right )}} - \frac {522 \, {\left (386 \, x^{3} - x^{2} - 1096 \, x - 656\right )}}{289 \, {\left (x^{4} - 2 \, x^{3} - 7 \, x^{2} + 8 \, x + 16\right )}} - \frac {210 \, {\left (24 \, x^{3} + 253 \, x^{2} - 152 \, x - 496\right )}}{289 \, {\left (x^{4} - 2 \, x^{3} - 7 \, x^{2} + 8 \, x + 16\right )}} + \frac {1112 \, {\left (14 \, x^{3} - 21 \, x^{2} + 104 \, x + 96\right )}}{289 \, {\left (x^{4} - 2 \, x^{3} - 7 \, x^{2} + 8 \, x + 16\right )}} - \frac {256 \, {\left (12 \, x^{3} - 18 \, x^{2} - 76 \, x + 41\right )}}{289 \, {\left (x^{4} - 2 \, x^{3} - 7 \, x^{2} + 8 \, x + 16\right )}} - \frac {1152 \, {\left (6 \, x^{3} - 9 \, x^{2} - 38 \, x - 124\right )}}{289 \, {\left (x^{4} - 2 \, x^{3} - 7 \, x^{2} + 8 \, x + 16\right )}} - \frac {4 \, {\left (x^{4} + x^{3} - {\left (x^{3} - x^{2} - 4 \, x\right )} \log \relax (x)^{2} - 6 \, x^{2} - 2 \, {\left (x^{4} - 6 \, x^{2} - 4 \, x\right )} \log \relax (x) - 8 \, x\right )}}{x^{2} - x - 4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^6-12*x^5-36*x^4+92*x^3+144*x^2-192*x-256)*log(x)^2+(16*x^7-32*x^6-192*x^5+232*x^4+1000*x^3-288
*x^2-2048*x-1024)*log(x)+12*x^8-12*x^7-180*x^6+52*x^5+1044*x^4+420*x^3-2224*x^2-2304*x-512)/(x^6-3*x^5-9*x^4+2
3*x^3+36*x^2-48*x-64),x, algorithm="maxima")

[Out]

4*x^3 + 12*x^2 - 6/289*(37898*x^3 + 23495*x^2 - 180872*x - 197904)/(x^4 - 2*x^3 - 7*x^2 + 8*x + 16) + 6/289*(1
1264*x^3 + 12293*x^2 - 56696*x - 74032)/(x^4 - 2*x^3 - 7*x^2 + 8*x + 16) + 90/289*(4134*x^3 + 1891*x^2 - 17512
*x - 17232)/(x^4 - 2*x^3 - 7*x^2 + 8*x + 16) - 26/289*(924*x^3 + 1793*x^2 - 4696*x - 7536)/(x^4 - 2*x^3 - 7*x^
2 + 8*x + 16) - 522/289*(386*x^3 - x^2 - 1096*x - 656)/(x^4 - 2*x^3 - 7*x^2 + 8*x + 16) - 210/289*(24*x^3 + 25
3*x^2 - 152*x - 496)/(x^4 - 2*x^3 - 7*x^2 + 8*x + 16) + 1112/289*(14*x^3 - 21*x^2 + 104*x + 96)/(x^4 - 2*x^3 -
7*x^2 + 8*x + 16) - 256/289*(12*x^3 - 18*x^2 - 76*x + 41)/(x^4 - 2*x^3 - 7*x^2 + 8*x + 16) - 1152/289*(6*x^3
- 9*x^2 - 38*x - 124)/(x^4 - 2*x^3 - 7*x^2 + 8*x + 16) - 4*(x^4 + x^3 - (x^3 - x^2 - 4*x)*log(x)^2 - 6*x^2 - 2
*(x^4 - 6*x^2 - 4*x)*log(x) - 8*x)/(x^2 - x - 4)

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mupad [B]  time = 4.55, size = 89, normalized size = 3.56 \begin {gather*} 4\,x\,{\ln \relax (x)}^2-8\,\ln \relax (x)-8\,x+8\,x^2+4\,x^3+\frac {-44\,x^3-16\,x^2+256\,x+256}{x^4-2\,x^3-7\,x^2+8\,x+16}+\frac {\ln \relax (x)\,\left (-8\,x^4+40\,x^2+40\,x+32\right )}{-x^2+x+4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2304*x + log(x)*(2048*x + 288*x^2 - 1000*x^3 - 232*x^4 + 192*x^5 + 32*x^6 - 16*x^7 + 1024) + 2224*x^2 - 4
20*x^3 - 1044*x^4 - 52*x^5 + 180*x^6 + 12*x^7 - 12*x^8 + log(x)^2*(192*x - 144*x^2 - 92*x^3 + 36*x^4 + 12*x^5
- 4*x^6 + 256) + 512)/(48*x - 36*x^2 - 23*x^3 + 9*x^4 + 3*x^5 - x^6 + 64),x)

[Out]

4*x*log(x)^2 - 8*log(x) - 8*x + 8*x^2 + 4*x^3 + (256*x - 16*x^2 - 44*x^3 + 256)/(8*x - 7*x^2 - 2*x^3 + x^4 + 1
6) + (log(x)*(40*x + 40*x^2 - 8*x^4 + 32))/(x - x^2 + 4)

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sympy [B]  time = 0.39, size = 85, normalized size = 3.40 \begin {gather*} 4 x^{3} + 8 x^{2} + 4 x \log {\relax (x )}^{2} - 8 x + \frac {- 44 x^{3} - 16 x^{2} + 256 x + 256}{x^{4} - 2 x^{3} - 7 x^{2} + 8 x + 16} - 8 \log {\relax (x )} + \frac {\left (8 x^{4} - 40 x^{2} - 40 x - 32\right ) \log {\relax (x )}}{x^{2} - x - 4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x**6-12*x**5-36*x**4+92*x**3+144*x**2-192*x-256)*ln(x)**2+(16*x**7-32*x**6-192*x**5+232*x**4+100
0*x**3-288*x**2-2048*x-1024)*ln(x)+12*x**8-12*x**7-180*x**6+52*x**5+1044*x**4+420*x**3-2224*x**2-2304*x-512)/(
x**6-3*x**5-9*x**4+23*x**3+36*x**2-48*x-64),x)

[Out]

4*x**3 + 8*x**2 + 4*x*log(x)**2 - 8*x + (-44*x**3 - 16*x**2 + 256*x + 256)/(x**4 - 2*x**3 - 7*x**2 + 8*x + 16)
- 8*log(x) + (8*x**4 - 40*x**2 - 40*x - 32)*log(x)/(x**2 - x - 4)

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