\(\int \frac {(4 x^6+8 x^3 \log (4)) \log (\frac {121 x^4-110 x^5+25 x^6+(110 x^2-50 x^3) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+(4 x^2-2 x^3) \log (4)+\log ^2(4)})+(44 x^5-42 x^6+10 x^7+(42 x^3-20 x^4) \log (4)+10 x \log ^2(4)) \log ^2(\frac {121 x^4-110 x^5+25 x^6+(110 x^2-50 x^3) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+(4 x^2-2 x^3) \log (4)+\log ^2(4)})}{22 x^4-21 x^5+5 x^6+(21 x^2-10 x^3) \log (4)+5 \log ^2(4)} \, dx\) [2806]

Optimal result

Integrand size = 238, antiderivative size = 29 \[ \int \frac {\left (4 x^6+8 x^3 \log (4)\right ) \log \left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )+\left (44 x^5-42 x^6+10 x^7+\left (42 x^3-20 x^4\right ) \log (4)+10 x \log ^2(4)\right ) \log ^2\left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )}{22 x^4-21 x^5+5 x^6+\left (21 x^2-10 x^3\right ) \log (4)+5 \log ^2(4)} \, dx=x^2 \log ^2\left (\left (-5+\frac {x}{-2 x+x^2-\frac {\log (4)}{x}}\right )^2\right ) \]

[Out]

ln((-5+x/(x^2-2*x-2*ln(2)/x))^2)^2*x^2

Rubi [A] (verified)

Time = 145.85 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.38, number of steps used = 61, number of rules used = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.080, Rules used = {6820, 6874, 2125, 2106, 2104, 814, 648, 632, 210, 642, 2605, 12, 2608, 2603, 1642, 2092, 2090, 719, 31} \[ \int \frac {\left (4 x^6+8 x^3 \log (4)\right ) \log \left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )+\left (44 x^5-42 x^6+10 x^7+\left (42 x^3-20 x^4\right ) \log (4)+10 x \log ^2(4)\right ) \log ^2\left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )}{22 x^4-21 x^5+5 x^6+\left (21 x^2-10 x^3\right ) \log (4)+5 \log ^2(4)} \, dx=x^2 \log ^2\left (\frac {\left (-5 x^3+11 x^2+5 \log (4)\right )^2}{\left (-x^3+2 x^2+\log (4)\right )^2}\right ) \]

[In]

Int[((4*x^6 + 8*x^3*Log[4])*Log[(121*x^4 - 110*x^5 + 25*x^6 + (110*x^2 - 50*x^3)*Log[4] + 25*Log[4]^2)/(4*x^4
- 4*x^5 + x^6 + (4*x^2 - 2*x^3)*Log[4] + Log[4]^2)] + (44*x^5 - 42*x^6 + 10*x^7 + (42*x^3 - 20*x^4)*Log[4] + 1
0*x*Log[4]^2)*Log[(121*x^4 - 110*x^5 + 25*x^6 + (110*x^2 - 50*x^3)*Log[4] + 25*Log[4]^2)/(4*x^4 - 4*x^5 + x^6
+ (4*x^2 - 2*x^3)*Log[4] + Log[4]^2)]^2)/(22*x^4 - 21*x^5 + 5*x^6 + (21*x^2 - 10*x^3)*Log[4] + 5*Log[4]^2),x]

[Out]

x^2*Log[(11*x^2 - 5*x^3 + 5*Log[4])^2/(2*x^2 - x^3 + Log[4])^2]^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 210

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

Rule 632

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 642

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

Rule 648

Int[((d_.) + (e_.)*(x_))/((a_) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> Dist[(2*c*d - b*e)/(2*c), Int[1/(a +
b*x + c*x^2), x], x] + Dist[e/(2*c), Int[(b + 2*c*x)/(a + b*x + c*x^2), 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 719

Int[1/(((d_.) + (e_.)*(x_))*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)), x_Symbol] :> Dist[e^2/(c*d^2 - b*d*e + a*e^2
), Int[1/(d + e*x), x], x] + Dist[1/(c*d^2 - b*d*e + a*e^2), Int[(c*d - b*e - c*e*x)/(a + b*x + c*x^2), 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]

Rule 814

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 1642

Int[(Pq_)*((d_.) + (e_.)*(x_))^(m_.)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> Int[ExpandIntegra
nd[(d + e*x)^m*Pq*(a + b*x + c*x^2)^p, x], x] /; FreeQ[{a, b, c, d, e, m}, x] && PolyQ[Pq, x] && IGtQ[p, -2]

Rule 2090

Int[((a_.) + (b_.)*(x_) + (d_.)*(x_)^3)^(p_), x_Symbol] :> With[{r = Rt[-9*a*d^2 + Sqrt[3]*d*Sqrt[4*b^3*d + 27
*a^2*d^2], 3]}, Dist[1/d^(2*p), Int[Simp[18^(1/3)*b*(d/(3*r)) - r/18^(1/3) + d*x, x]^p*Simp[b*(d/3) + 12^(1/3)
*b^2*(d^2/(3*r^2)) + r^2/(3*12^(1/3)) - d*(2^(1/3)*b*(d/(3^(1/3)*r)) - r/18^(1/3))*x + d^2*x^2, x]^p, x], x]]
/; FreeQ[{a, b, d}, x] && NeQ[4*b^3 + 27*a^2*d, 0] && IntegerQ[p]

Rule 2092

Int[(P3_)^(p_), x_Symbol] :> With[{a = Coeff[P3, x, 0], b = Coeff[P3, x, 1], c = Coeff[P3, x, 2], d = Coeff[P3
, x, 3]}, Subst[Int[Simp[(2*c^3 - 9*b*c*d + 27*a*d^2)/(27*d^2) - (c^2 - 3*b*d)*(x/(3*d)) + d*x^3, x]^p, x], x,
x + c/(3*d)] /; NeQ[c, 0]] /; FreeQ[p, x] && PolyQ[P3, x, 3]

Rule 2104

Int[((e_.) + (f_.)*(x_))^(m_.)*((a_) + (b_.)*(x_) + (d_.)*(x_)^3)^(p_), x_Symbol] :> With[{r = Rt[-9*a*d^2 + S
qrt[3]*d*Sqrt[4*b^3*d + 27*a^2*d^2], 3]}, Dist[1/d^(2*p), Int[(e + f*x)^m*Simp[18^(1/3)*b*(d/(3*r)) - r/18^(1/
3) + d*x, x]^p*Simp[b*(d/3) + 12^(1/3)*b^2*(d^2/(3*r^2)) + r^2/(3*12^(1/3)) - d*(2^(1/3)*b*(d/(3^(1/3)*r)) - r
/18^(1/3))*x + d^2*x^2, x]^p, x], x]] /; FreeQ[{a, b, d, e, f, m}, x] && NeQ[4*b^3 + 27*a^2*d, 0] && ILtQ[p, 0
]

Rule 2106

Int[(P3_)^(p_.)*((e_.) + (f_.)*(x_))^(m_.), x_Symbol] :> With[{a = Coeff[P3, x, 0], b = Coeff[P3, x, 1], c = C
oeff[P3, x, 2], d = Coeff[P3, x, 3]}, Subst[Int[((3*d*e - c*f)/(3*d) + f*x)^m*Simp[(2*c^3 - 9*b*c*d + 27*a*d^2
)/(27*d^2) - (c^2 - 3*b*d)*(x/(3*d)) + d*x^3, x]^p, x], x, x + c/(3*d)] /; NeQ[c, 0]] /; FreeQ[{e, f, m, p}, x
] && PolyQ[P3, x, 3]

Rule 2125

Int[(Pm_)/(Qn_), x_Symbol] :> With[{m = Expon[Pm, x], n = Expon[Qn, x]}, Simp[Coeff[Pm, x, m]*(Log[Qn]/(n*Coef
f[Qn, x, n])), x] + Dist[1/(n*Coeff[Qn, x, n]), Int[ExpandToSum[n*Coeff[Qn, x, n]*Pm - Coeff[Pm, x, m]*D[Qn, x
], x]/Qn, x], x] /; EqQ[m, n - 1]] /; PolyQ[Pm, x] && PolyQ[Qn, x]

Rule 2603

Int[((a_.) + Log[(c_.)*(RFx_)^(p_.)]*(b_.))^(n_.), x_Symbol] :> Simp[x*(a + b*Log[c*RFx^p])^n, x] - Dist[b*n*p
, Int[SimplifyIntegrand[x*(a + b*Log[c*RFx^p])^(n - 1)*(D[RFx, x]/RFx), x], x], x] /; FreeQ[{a, b, c, p}, x] &
& RationalFunctionQ[RFx, x] && IGtQ[n, 0]

Rule 2605

Int[((a_.) + Log[(c_.)*(RFx_)^(p_.)]*(b_.))^(n_.)*((d_.) + (e_.)*(x_))^(m_.), x_Symbol] :> Simp[(d + e*x)^(m +
1)*((a + b*Log[c*RFx^p])^n/(e*(m + 1))), x] - Dist[b*n*(p/(e*(m + 1))), Int[SimplifyIntegrand[(d + e*x)^(m +
1)*(a + b*Log[c*RFx^p])^(n - 1)*(D[RFx, x]/RFx), x], x], x] /; FreeQ[{a, b, c, d, e, m, p}, x] && RationalFunc
tionQ[RFx, x] && IGtQ[n, 0] && (EqQ[n, 1] || IntegerQ[m]) && NeQ[m, -1]

Rule 2608

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

Rule 6820

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

Rule 6874

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

Rubi steps \begin{align*} \text {integral}& = \int \frac {\log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right ) \left (4 x^6+8 x^3 \log (4)+2 \left (22 x^5-21 x^6+5 x^7+21 x^3 \log (4)-10 x^4 \log (4)+5 x \log ^2(4)\right ) \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )\right )}{22 x^4-21 x^5+5 x^6+21 x^2 \log (4)-10 x^3 \log (4)+5 \log ^2(4)} \, dx \\ & = \int \left (\frac {4 x^3 \left (x^3+\log (16)\right ) \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{\left (-11 x^2+5 x^3-5 \log (4)\right ) \left (-2 x^2+x^3-\log (4)\right )}+2 x \log ^2\left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )\right ) \, dx \\ & = 2 \int x \log ^2\left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right ) \, dx+4 \int \frac {x^3 \left (x^3+\log (16)\right ) \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{\left (-11 x^2+5 x^3-5 \log (4)\right ) \left (-2 x^2+x^3-\log (4)\right )} \, dx \\ & = x^2 \log ^2\left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )-2 \int \frac {2 x^3 \left (x^3+\log (16)\right ) \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{\left (2 x^2-x^3+\log (4)\right ) \left (11 x^2-5 x^3+5 \log (4)\right )} \, dx+4 \int \left (\frac {1}{5} \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )+\frac {\left (-4 x^2-\log (16)-x \log (64)\right ) \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{-2 x^2+x^3-\log (4)}+\frac {\left (121 x^2+55 \log (4)+25 x \log (64)\right ) \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{5 \left (-11 x^2+5 x^3-5 \log (4)\right )}\right ) \, dx \\ & = x^2 \log ^2\left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )+\frac {4}{5} \int \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right ) \, dx+\frac {4}{5} \int \frac {\left (121 x^2+55 \log (4)+25 x \log (64)\right ) \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{-11 x^2+5 x^3-5 \log (4)} \, dx-4 \int \frac {x^3 \left (x^3+\log (16)\right ) \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{\left (2 x^2-x^3+\log (4)\right ) \left (11 x^2-5 x^3+5 \log (4)\right )} \, dx+4 \int \frac {\left (-4 x^2-\log (16)-x \log (64)\right ) \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{-2 x^2+x^3-\log (4)} \, dx \\ & = \frac {4}{5} x \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )+x^2 \log ^2\left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )-\frac {4}{5} \int \frac {2 x^2 \left (x^3+\log (16)\right )}{\left (2 x^2-x^3+\log (4)\right ) \left (11 x^2-5 x^3+5 \log (4)\right )} \, dx+\frac {4}{5} \int \left (\frac {121 x^2 \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{-11 x^2+5 x^3-5 \log (4)}+\frac {55 \log (4) \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{-11 x^2+5 x^3-5 \log (4)}+\frac {25 x \log (64) \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{-11 x^2+5 x^3-5 \log (4)}\right ) \, dx+4 \int \left (-\frac {4 x^2 \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{-2 x^2+x^3-\log (4)}-\frac {\log (16) \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{-2 x^2+x^3-\log (4)}-\frac {x \log (64) \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{-2 x^2+x^3-\log (4)}\right ) \, dx-4 \int \left (\frac {1}{5} \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )+\frac {\left (-4 x^2-\log (16)-x \log (64)\right ) \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{-2 x^2+x^3-\log (4)}+\frac {\left (121 x^2+55 \log (4)+25 x \log (64)\right ) \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{5 \left (-11 x^2+5 x^3-5 \log (4)\right )}\right ) \, dx \\ & = \frac {4}{5} x \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )+x^2 \log ^2\left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )-\frac {4}{5} \int \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right ) \, dx-\frac {4}{5} \int \frac {\left (121 x^2+55 \log (4)+25 x \log (64)\right ) \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{-11 x^2+5 x^3-5 \log (4)} \, dx-\frac {8}{5} \int \frac {x^2 \left (x^3+\log (16)\right )}{\left (2 x^2-x^3+\log (4)\right ) \left (11 x^2-5 x^3+5 \log (4)\right )} \, dx-4 \int \frac {\left (-4 x^2-\log (16)-x \log (64)\right ) \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{-2 x^2+x^3-\log (4)} \, dx-16 \int \frac {x^2 \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{-2 x^2+x^3-\log (4)} \, dx+\frac {484}{5} \int \frac {x^2 \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{-11 x^2+5 x^3-5 \log (4)} \, dx+(44 \log (4)) \int \frac {\log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{-11 x^2+5 x^3-5 \log (4)} \, dx-(4 \log (16)) \int \frac {\log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{-2 x^2+x^3-\log (4)} \, dx-(4 \log (64)) \int \frac {x \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{-2 x^2+x^3-\log (4)} \, dx+(20 \log (64)) \int \frac {x \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{-11 x^2+5 x^3-5 \log (4)} \, dx \\ & = x^2 \log ^2\left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )+\frac {4}{5} \int \frac {2 x^2 \left (x^3+\log (16)\right )}{\left (2 x^2-x^3+\log (4)\right ) \left (11 x^2-5 x^3+5 \log (4)\right )} \, dx-\frac {4}{5} \int \left (\frac {121 x^2 \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{-11 x^2+5 x^3-5 \log (4)}+\frac {55 \log (4) \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{-11 x^2+5 x^3-5 \log (4)}+\frac {25 x \log (64) \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{-11 x^2+5 x^3-5 \log (4)}\right ) \, dx-\frac {8}{5} \int \left (\frac {-2 x^2-\log (64)}{-2 x^2+x^3-\log (4)}+\frac {11 x^2+5 \log (64)}{-11 x^2+5 x^3-5 \log (4)}\right ) \, dx-4 \int \left (-\frac {4 x^2 \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{-2 x^2+x^3-\log (4)}-\frac {\log (16) \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{-2 x^2+x^3-\log (4)}-\frac {x \log (64) \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{-2 x^2+x^3-\log (4)}\right ) \, dx-16 \int \frac {x^2 \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{-2 x^2+x^3-\log (4)} \, dx+\frac {484}{5} \int \frac {x^2 \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{-11 x^2+5 x^3-5 \log (4)} \, dx+(44 \log (4)) \int \frac {\log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{-11 x^2+5 x^3-5 \log (4)} \, dx-(4 \log (16)) \int \frac {\log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{-2 x^2+x^3-\log (4)} \, dx-(4 \log (64)) \int \frac {x \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{-2 x^2+x^3-\log (4)} \, dx+(20 \log (64)) \int \frac {x \log \left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )}{-11 x^2+5 x^3-5 \log (4)} \, dx \\ & = x^2 \log ^2\left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )+\frac {8}{5} \int \frac {x^2 \left (x^3+\log (16)\right )}{\left (2 x^2-x^3+\log (4)\right ) \left (11 x^2-5 x^3+5 \log (4)\right )} \, dx-\frac {8}{5} \int \frac {-2 x^2-\log (64)}{-2 x^2+x^3-\log (4)} \, dx-\frac {8}{5} \int \frac {11 x^2+5 \log (64)}{-11 x^2+5 x^3-5 \log (4)} \, dx \\ & = -\frac {88}{75} \log \left (-11 x^2+5 x^3-5 \log (4)\right )+\frac {16}{15} \log \left (-2 x^2+x^3-\log (4)\right )+x^2 \log ^2\left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )-\frac {8}{75} \int \frac {242 x+75 \log (64)}{-11 x^2+5 x^3-5 \log (4)} \, dx-\frac {8}{15} \int \frac {-8 x-3 \log (64)}{-2 x^2+x^3-\log (4)} \, dx+\frac {8}{5} \int \left (\frac {-2 x^2-\log (64)}{-2 x^2+x^3-\log (4)}+\frac {11 x^2+5 \log (64)}{-11 x^2+5 x^3-5 \log (4)}\right ) \, dx \\ & = -\frac {88}{75} \log \left (-11 x^2+5 x^3-5 \log (4)\right )+\frac {16}{15} \log \left (-2 x^2+x^3-\log (4)\right )+x^2 \log ^2\left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )-\frac {8}{75} \text {Subst}\left (\int \frac {242 x+\frac {1}{15} (2662+1125 \log (64))}{-\frac {121 x}{15}+5 x^3+\frac {1}{675} (-2662-3375 \log (4))} \, dx,x,-\frac {11}{15}+x\right )-\frac {8}{15} \text {Subst}\left (\int \frac {-8 x+\frac {1}{3} (-16-9 \log (64))}{-\frac {4 x}{3}+x^3+\frac {1}{27} (-16-27 \log (4))} \, dx,x,-\frac {2}{3}+x\right )+\frac {8}{5} \int \frac {-2 x^2-\log (64)}{-2 x^2+x^3-\log (4)} \, dx+\frac {8}{5} \int \frac {11 x^2+5 \log (64)}{-11 x^2+5 x^3-5 \log (4)} \, dx \\ & = x^2 \log ^2\left (\frac {\left (11 x^2-5 x^3+5 \log (4)\right )^2}{\left (2 x^2-x^3+\log (4)\right )^2}\right )+\frac {8}{75} \int \frac {242 x+75 \log (64)}{-11 x^2+5 x^3-5 \log (4)} \, dx+\frac {8}{15} \int \frac {-8 x-3 \log (64)}{-2 x^2+x^3-\log (4)} \, dx-\frac {8}{15} \text {Subst}\left (\int \frac {-8 x+\frac {1}{3} (-16-9 \log (64))}{\left (x^2+\frac {1}{3} x \left (4 \sqrt [3]{\frac {2}{16+27 \log (4)+3 \sqrt {3 \log (4) (32+27 \log (4))}}}+\sqrt [3]{\frac {1}{2} \left (16+27 \log (4)+3 \sqrt {3 \log (4) (32+27 \log (4))}\right )}\right )+\frac {1}{18} \left (-8+32 \left (\frac {2}{16+27 \log (4)+3 \sqrt {3 \log (4) (32+27 \log (4))}}\right )^{2/3}+\sqrt [3]{2} \left (16+27 \log (4)+3 \sqrt {3 \log (4) (32+27 \log (4))}\right )^{2/3}\right )\right ) \left (x-\frac {\frac {8}{\sqrt [3]{16+27 \log (4)+3 \sqrt {3 \log (4) (32+27 \log (4))}}}+\sqrt [3]{2 \left (16+27 \log (4)+3 \sqrt {3 \log (4) (32+27 \log (4))}\right )}}{3\ 2^{2/3}}\right )} \, dx,x,-\frac {2}{3}+x\right )-\frac {8}{3} \text {Subst}\left (\int \frac {242 x+\frac {1}{15} (2662+1125 \log (64))}{\left (25 x^2+\frac {5}{3} x \left (121 \sqrt [3]{\frac {2}{2662+3375 \log (4)+15 \sqrt {15 \log (4) (5324+3375 \log (4))}}}+\sqrt [3]{\frac {1}{2} \left (2662+3375 \log (4)+15 \sqrt {15 \log (4) (5324+3375 \log (4))}\right )}\right )+\frac {1}{18} \left (-242+29282 \left (\frac {2}{2662+3375 \log (4)+15 \sqrt {15 \log (4) (5324+3375 \log (4))}}\right )^{2/3}+\sqrt [3]{2} \left (2662+3375 \log (4)+15 \sqrt {15 \log (4) (5324+3375 \log (4))}\right )^{2/3}\right )\right ) \left (5 x-\frac {\frac {242}{\sqrt [3]{2662+3375 \log (4)+15 \sqrt {15 \log (4) (5324+3375 \log (4))}}}+\sqrt [3]{2 \left (2662+3375 \log (4)+15 \sqrt {15 \log (4) (5324+3375 \log (4))}\right )}}{3\ 2^{2/3}}\right )} \, dx,x,-\frac {11}{15}+x\right ) \\ & = \text {Too large to display} \\ \end{align*}

Mathematica [C] (warning: unable to verify)

Result contains higher order function than in optimal. Order 9 vs. order 3 in optimal.

Time = 15.12 (sec) , antiderivative size = 57407, normalized size of antiderivative = 1979.55 \[ \int \frac {\left (4 x^6+8 x^3 \log (4)\right ) \log \left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )+\left (44 x^5-42 x^6+10 x^7+\left (42 x^3-20 x^4\right ) \log (4)+10 x \log ^2(4)\right ) \log ^2\left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )}{22 x^4-21 x^5+5 x^6+\left (21 x^2-10 x^3\right ) \log (4)+5 \log ^2(4)} \, dx=\text {Result too large to show} \]

[In]

Integrate[((4*x^6 + 8*x^3*Log[4])*Log[(121*x^4 - 110*x^5 + 25*x^6 + (110*x^2 - 50*x^3)*Log[4] + 25*Log[4]^2)/(
4*x^4 - 4*x^5 + x^6 + (4*x^2 - 2*x^3)*Log[4] + Log[4]^2)] + (44*x^5 - 42*x^6 + 10*x^7 + (42*x^3 - 20*x^4)*Log[
4] + 10*x*Log[4]^2)*Log[(121*x^4 - 110*x^5 + 25*x^6 + (110*x^2 - 50*x^3)*Log[4] + 25*Log[4]^2)/(4*x^4 - 4*x^5
+ x^6 + (4*x^2 - 2*x^3)*Log[4] + Log[4]^2)]^2)/(22*x^4 - 21*x^5 + 5*x^6 + (21*x^2 - 10*x^3)*Log[4] + 5*Log[4]^
2),x]

[Out]

Result too large to show

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(81\) vs. \(2(29)=58\).

Time = 1.28 (sec) , antiderivative size = 82, normalized size of antiderivative = 2.83

method	result	size
parallelrisch	\(x^{2} \ln \left (\frac {100 \ln \left (2\right )^{2}+2 \left (-50 x^{3}+110 x^{2}\right ) \ln \left (2\right )+25 x^{6}-110 x^{5}+121 x^{4}}{x^{6}-4 x^{5}-4 x^{3} \ln \left (2\right )+4 x^{4}+8 x^{2} \ln \left (2\right )+4 \ln \left (2\right )^{2}}\right )^{2}\)	\(82\)
norman	\(x^{2} \ln \left (\frac {100 \ln \left (2\right )^{2}+2 \left (-50 x^{3}+110 x^{2}\right ) \ln \left (2\right )+25 x^{6}-110 x^{5}+121 x^{4}}{4 \ln \left (2\right )^{2}+2 \left (-2 x^{3}+4 x^{2}\right ) \ln \left (2\right )+x^{6}-4 x^{5}+4 x^{4}}\right )^{2}\)	\(83\)
risch	\(x^{2} \ln \left (\frac {100 \ln \left (2\right )^{2}+2 \left (-50 x^{3}+110 x^{2}\right ) \ln \left (2\right )+25 x^{6}-110 x^{5}+121 x^{4}}{4 \ln \left (2\right )^{2}+2 \left (-2 x^{3}+4 x^{2}\right ) \ln \left (2\right )+x^{6}-4 x^{5}+4 x^{4}}\right )^{2}\)	\(83\)

[In]

int(((40*x*ln(2)^2+2*(-20*x^4+42*x^3)*ln(2)+10*x^7-42*x^6+44*x^5)*ln((100*ln(2)^2+2*(-50*x^3+110*x^2)*ln(2)+25
*x^6-110*x^5+121*x^4)/(4*ln(2)^2+2*(-2*x^3+4*x^2)*ln(2)+x^6-4*x^5+4*x^4))^2+(16*x^3*ln(2)+4*x^6)*ln((100*ln(2)
^2+2*(-50*x^3+110*x^2)*ln(2)+25*x^6-110*x^5+121*x^4)/(4*ln(2)^2+2*(-2*x^3+4*x^2)*ln(2)+x^6-4*x^5+4*x^4)))/(20*
ln(2)^2+2*(-10*x^3+21*x^2)*ln(2)+5*x^6-21*x^5+22*x^4),x,method=_RETURNVERBOSE)

[Out]

x^2*ln((100*ln(2)^2+2*(-50*x^3+110*x^2)*ln(2)+25*x^6-110*x^5+121*x^4)/(x^6-4*x^5-4*x^3*ln(2)+4*x^4+8*x^2*ln(2)
+4*ln(2)^2))^2

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 80 vs. \(2 (29) = 58\).

Time = 0.27 (sec) , antiderivative size = 80, normalized size of antiderivative = 2.76 \[ \int \frac {\left (4 x^6+8 x^3 \log (4)\right ) \log \left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )+\left (44 x^5-42 x^6+10 x^7+\left (42 x^3-20 x^4\right ) \log (4)+10 x \log ^2(4)\right ) \log ^2\left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )}{22 x^4-21 x^5+5 x^6+\left (21 x^2-10 x^3\right ) \log (4)+5 \log ^2(4)} \, dx=x^{2} \log \left (\frac {25 \, x^{6} - 110 \, x^{5} + 121 \, x^{4} - 20 \, {\left (5 \, x^{3} - 11 \, x^{2}\right )} \log \left (2\right ) + 100 \, \log \left (2\right )^{2}}{x^{6} - 4 \, x^{5} + 4 \, x^{4} - 4 \, {\left (x^{3} - 2 \, x^{2}\right )} \log \left (2\right ) + 4 \, \log \left (2\right )^{2}}\right )^{2} \]

[In]

integrate(((40*x*log(2)^2+2*(-20*x^4+42*x^3)*log(2)+10*x^7-42*x^6+44*x^5)*log((100*log(2)^2+2*(-50*x^3+110*x^2
)*log(2)+25*x^6-110*x^5+121*x^4)/(4*log(2)^2+2*(-2*x^3+4*x^2)*log(2)+x^6-4*x^5+4*x^4))^2+(16*x^3*log(2)+4*x^6)
*log((100*log(2)^2+2*(-50*x^3+110*x^2)*log(2)+25*x^6-110*x^5+121*x^4)/(4*log(2)^2+2*(-2*x^3+4*x^2)*log(2)+x^6-
4*x^5+4*x^4)))/(20*log(2)^2+2*(-10*x^3+21*x^2)*log(2)+5*x^6-21*x^5+22*x^4),x, algorithm="fricas")

[Out]

x^2*log((25*x^6 - 110*x^5 + 121*x^4 - 20*(5*x^3 - 11*x^2)*log(2) + 100*log(2)^2)/(x^6 - 4*x^5 + 4*x^4 - 4*(x^3
- 2*x^2)*log(2) + 4*log(2)^2))^2

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 75 vs. \(2 (24) = 48\).

Time = 0.20 (sec) , antiderivative size = 75, normalized size of antiderivative = 2.59 \[ \int \frac {\left (4 x^6+8 x^3 \log (4)\right ) \log \left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )+\left (44 x^5-42 x^6+10 x^7+\left (42 x^3-20 x^4\right ) \log (4)+10 x \log ^2(4)\right ) \log ^2\left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )}{22 x^4-21 x^5+5 x^6+\left (21 x^2-10 x^3\right ) \log (4)+5 \log ^2(4)} \, dx=x^{2} \log {\left (\frac {25 x^{6} - 110 x^{5} + 121 x^{4} + \left (- 100 x^{3} + 220 x^{2}\right ) \log {\left (2 \right )} + 100 \log {\left (2 \right )}^{2}}{x^{6} - 4 x^{5} + 4 x^{4} + \left (- 4 x^{3} + 8 x^{2}\right ) \log {\left (2 \right )} + 4 \log {\left (2 \right )}^{2}} \right )}^{2} \]

[In]

integrate(((40*x*ln(2)**2+2*(-20*x**4+42*x**3)*ln(2)+10*x**7-42*x**6+44*x**5)*ln((100*ln(2)**2+2*(-50*x**3+110
*x**2)*ln(2)+25*x**6-110*x**5+121*x**4)/(4*ln(2)**2+2*(-2*x**3+4*x**2)*ln(2)+x**6-4*x**5+4*x**4))**2+(16*x**3*
ln(2)+4*x**6)*ln((100*ln(2)**2+2*(-50*x**3+110*x**2)*ln(2)+25*x**6-110*x**5+121*x**4)/(4*ln(2)**2+2*(-2*x**3+4
*x**2)*ln(2)+x**6-4*x**5+4*x**4)))/(20*ln(2)**2+2*(-10*x**3+21*x**2)*ln(2)+5*x**6-21*x**5+22*x**4),x)

[Out]

x**2*log((25*x**6 - 110*x**5 + 121*x**4 + (-100*x**3 + 220*x**2)*log(2) + 100*log(2)**2)/(x**6 - 4*x**5 + 4*x*
*4 + (-4*x**3 + 8*x**2)*log(2) + 4*log(2)**2))**2

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 80 vs. \(2 (29) = 58\).

Time = 0.33 (sec) , antiderivative size = 80, normalized size of antiderivative = 2.76 \[ \int \frac {\left (4 x^6+8 x^3 \log (4)\right ) \log \left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )+\left (44 x^5-42 x^6+10 x^7+\left (42 x^3-20 x^4\right ) \log (4)+10 x \log ^2(4)\right ) \log ^2\left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )}{22 x^4-21 x^5+5 x^6+\left (21 x^2-10 x^3\right ) \log (4)+5 \log ^2(4)} \, dx=4 \, x^{2} \log \left (5 \, x^{3} - 11 \, x^{2} - 10 \, \log \left (2\right )\right )^{2} - 8 \, x^{2} \log \left (5 \, x^{3} - 11 \, x^{2} - 10 \, \log \left (2\right )\right ) \log \left (x^{3} - 2 \, x^{2} - 2 \, \log \left (2\right )\right ) + 4 \, x^{2} \log \left (x^{3} - 2 \, x^{2} - 2 \, \log \left (2\right )\right )^{2} \]

[In]

integrate(((40*x*log(2)^2+2*(-20*x^4+42*x^3)*log(2)+10*x^7-42*x^6+44*x^5)*log((100*log(2)^2+2*(-50*x^3+110*x^2
)*log(2)+25*x^6-110*x^5+121*x^4)/(4*log(2)^2+2*(-2*x^3+4*x^2)*log(2)+x^6-4*x^5+4*x^4))^2+(16*x^3*log(2)+4*x^6)
*log((100*log(2)^2+2*(-50*x^3+110*x^2)*log(2)+25*x^6-110*x^5+121*x^4)/(4*log(2)^2+2*(-2*x^3+4*x^2)*log(2)+x^6-
4*x^5+4*x^4)))/(20*log(2)^2+2*(-10*x^3+21*x^2)*log(2)+5*x^6-21*x^5+22*x^4),x, algorithm="maxima")

[Out]

4*x^2*log(5*x^3 - 11*x^2 - 10*log(2))^2 - 8*x^2*log(5*x^3 - 11*x^2 - 10*log(2))*log(x^3 - 2*x^2 - 2*log(2)) +
4*x^2*log(x^3 - 2*x^2 - 2*log(2))^2

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 162 vs. \(2 (29) = 58\).

Time = 3.86 (sec) , antiderivative size = 162, normalized size of antiderivative = 5.59 \[ \int \frac {\left (4 x^6+8 x^3 \log (4)\right ) \log \left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )+\left (44 x^5-42 x^6+10 x^7+\left (42 x^3-20 x^4\right ) \log (4)+10 x \log ^2(4)\right ) \log ^2\left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )}{22 x^4-21 x^5+5 x^6+\left (21 x^2-10 x^3\right ) \log (4)+5 \log ^2(4)} \, dx=x^{2} \log \left (25 \, x^{6} - 110 \, x^{5} + 121 \, x^{4} - 100 \, x^{3} \log \left (2\right ) + 220 \, x^{2} \log \left (2\right ) + 100 \, \log \left (2\right )^{2}\right )^{2} - 2 \, x^{2} \log \left (25 \, x^{6} - 110 \, x^{5} + 121 \, x^{4} - 100 \, x^{3} \log \left (2\right ) + 220 \, x^{2} \log \left (2\right ) + 100 \, \log \left (2\right )^{2}\right ) \log \left (x^{6} - 4 \, x^{5} + 4 \, x^{4} - 4 \, x^{3} \log \left (2\right ) + 8 \, x^{2} \log \left (2\right ) + 4 \, \log \left (2\right )^{2}\right ) + x^{2} \log \left (x^{6} - 4 \, x^{5} + 4 \, x^{4} - 4 \, x^{3} \log \left (2\right ) + 8 \, x^{2} \log \left (2\right ) + 4 \, \log \left (2\right )^{2}\right )^{2} \]

[In]

integrate(((40*x*log(2)^2+2*(-20*x^4+42*x^3)*log(2)+10*x^7-42*x^6+44*x^5)*log((100*log(2)^2+2*(-50*x^3+110*x^2
)*log(2)+25*x^6-110*x^5+121*x^4)/(4*log(2)^2+2*(-2*x^3+4*x^2)*log(2)+x^6-4*x^5+4*x^4))^2+(16*x^3*log(2)+4*x^6)
*log((100*log(2)^2+2*(-50*x^3+110*x^2)*log(2)+25*x^6-110*x^5+121*x^4)/(4*log(2)^2+2*(-2*x^3+4*x^2)*log(2)+x^6-
4*x^5+4*x^4)))/(20*log(2)^2+2*(-10*x^3+21*x^2)*log(2)+5*x^6-21*x^5+22*x^4),x, algorithm="giac")

[Out]

x^2*log(25*x^6 - 110*x^5 + 121*x^4 - 100*x^3*log(2) + 220*x^2*log(2) + 100*log(2)^2)^2 - 2*x^2*log(25*x^6 - 11
0*x^5 + 121*x^4 - 100*x^3*log(2) + 220*x^2*log(2) + 100*log(2)^2)*log(x^6 - 4*x^5 + 4*x^4 - 4*x^3*log(2) + 8*x
^2*log(2) + 4*log(2)^2) + x^2*log(x^6 - 4*x^5 + 4*x^4 - 4*x^3*log(2) + 8*x^2*log(2) + 4*log(2)^2)^2

Mupad [F(-1)]

Timed out. \[ \int \frac {\left (4 x^6+8 x^3 \log (4)\right ) \log \left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )+\left (44 x^5-42 x^6+10 x^7+\left (42 x^3-20 x^4\right ) \log (4)+10 x \log ^2(4)\right ) \log ^2\left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )}{22 x^4-21 x^5+5 x^6+\left (21 x^2-10 x^3\right ) \log (4)+5 \log ^2(4)} \, dx=\int \frac {\left (2\,\ln \left (2\right )\,\left (42\,x^3-20\,x^4\right )+40\,x\,{\ln \left (2\right )}^2+44\,x^5-42\,x^6+10\,x^7\right )\,{\ln \left (\frac {2\,\ln \left (2\right )\,\left (110\,x^2-50\,x^3\right )+100\,{\ln \left (2\right )}^2+121\,x^4-110\,x^5+25\,x^6}{2\,\ln \left (2\right )\,\left (4\,x^2-2\,x^3\right )+4\,{\ln \left (2\right )}^2+4\,x^4-4\,x^5+x^6}\right )}^2+\left (4\,x^6+16\,\ln \left (2\right )\,x^3\right )\,\ln \left (\frac {2\,\ln \left (2\right )\,\left (110\,x^2-50\,x^3\right )+100\,{\ln \left (2\right )}^2+121\,x^4-110\,x^5+25\,x^6}{2\,\ln \left (2\right )\,\left (4\,x^2-2\,x^3\right )+4\,{\ln \left (2\right )}^2+4\,x^4-4\,x^5+x^6}\right )}{2\,\ln \left (2\right )\,\left (21\,x^2-10\,x^3\right )+20\,{\ln \left (2\right )}^2+22\,x^4-21\,x^5+5\,x^6} \,d x \]

[In]

int((log((2*log(2)*(110*x^2 - 50*x^3) + 100*log(2)^2 + 121*x^4 - 110*x^5 + 25*x^6)/(2*log(2)*(4*x^2 - 2*x^3) +
4*log(2)^2 + 4*x^4 - 4*x^5 + x^6))^2*(2*log(2)*(42*x^3 - 20*x^4) + 40*x*log(2)^2 + 44*x^5 - 42*x^6 + 10*x^7)
+ log((2*log(2)*(110*x^2 - 50*x^3) + 100*log(2)^2 + 121*x^4 - 110*x^5 + 25*x^6)/(2*log(2)*(4*x^2 - 2*x^3) + 4*
log(2)^2 + 4*x^4 - 4*x^5 + x^6))*(16*x^3*log(2) + 4*x^6))/(2*log(2)*(21*x^2 - 10*x^3) + 20*log(2)^2 + 22*x^4 -
21*x^5 + 5*x^6),x)

[Out]

int((log((2*log(2)*(110*x^2 - 50*x^3) + 100*log(2)^2 + 121*x^4 - 110*x^5 + 25*x^6)/(2*log(2)*(4*x^2 - 2*x^3) +
4*log(2)^2 + 4*x^4 - 4*x^5 + x^6))^2*(2*log(2)*(42*x^3 - 20*x^4) + 40*x*log(2)^2 + 44*x^5 - 42*x^6 + 10*x^7)
+ log((2*log(2)*(110*x^2 - 50*x^3) + 100*log(2)^2 + 121*x^4 - 110*x^5 + 25*x^6)/(2*log(2)*(4*x^2 - 2*x^3) + 4*
log(2)^2 + 4*x^4 - 4*x^5 + x^6))*(16*x^3*log(2) + 4*x^6))/(2*log(2)*(21*x^2 - 10*x^3) + 20*log(2)^2 + 22*x^4 -
21*x^5 + 5*x^6), x)