3.69.84 $\int \frac{200x+120x^2-22x^3-12x^4+2x^5+(-60x^2+22x^3+18x^4-4x^5)\log (x)+(-400x-360x^2+88x^3+60x^4-12x^5){\log }^2(x)+(-200x-180x^2+44x^3+30x^4-6x^5){\log }^3(x)}{3{\log }^3(x)}dx$

Optimal. Leaf size=28 $$3(1-\frac{1}{9}(-5+x{)}^2(2+x{)}^2{(x+\frac{x}{\log (x)})}^2)$$

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Rubi [B]  time = 1.94, antiderivative size = 122, normalized size of antiderivative = 4.36, number of steps used = 54, number of rules used = 8, integrand size = 114, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.070, Rules used = {12, 6688, 6742, 1590, 2356, 2306, 2309, 2178} $$\begin{array}{c}-\frac{x^6}{3{\log }^2(x)}-\frac{2x^6}{3\log (x)}+\frac{2x^5}{{\log }^2(x)}+\frac{4x^5}{\log (x)}+\frac{11x^4}{3{\log }^2(x)}+\frac{22x^4}{3\log (x)}-\frac{20x^3}{{\log }^2(x)}-\frac{40x^3}{\log (x)}-\frac{1}{3}(5-x{)}^2(x+2{)}^2{x}^2-\frac{100x^2}{3{\log }^2(x)}-\frac{200x^2}{3\log (x)}\end{array}$$

Antiderivative was successfully verified.

[In]

Int[(200*x + 120*x^2 - 22*x^3 - 12*x^4 + 2*x^5 + (-60*x^2 + 22*x^3 + 18*x^4 - 4*x^5)*Log[x] + (-400*x - 360*x^
2 + 88*x^3 + 60*x^4 - 12*x^5)*Log[x]^2 + (-200*x - 180*x^2 + 44*x^3 + 30*x^4 - 6*x^5)*Log[x]^3)/(3*Log[x]^3),x
]

[Out]

-1/3*((5 - x)^2*x^2*(2 + x)^2) - (100*x^2)/(3*Log[x]^2) - (20*x^3)/Log[x]^2 + (11*x^4)/(3*Log[x]^2) + (2*x^5)/
Log[x]^2 - x^6/(3*Log[x]^2) - (200*x^2)/(3*Log[x]) - (40*x^3)/Log[x] + (22*x^4)/(3*Log[x]) + (4*x^5)/Log[x] -
(2*x^6)/(3*Log[x])

Rule 12

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

Rule 1590

Int[(Pp_)*(Qq_)^(m_.)*(Rr_)^(n_.), x_Symbol] :> With[{p = Expon[Pp, x], q = Expon[Qq, x], r = Expon[Rr, x]}, S
imp[(Coeff[Pp, x, p]*x^(p - q - r + 1)*Qq^(m + 1)*Rr^(n + 1))/((p + m*q + n*r + 1)*Coeff[Qq, x, q]*Coeff[Rr, x
, r]), x] /; NeQ[p + m*q + n*r + 1, 0] && EqQ[(p + m*q + n*r + 1)*Coeff[Qq, x, q]*Coeff[Rr, x, r]*Pp, Coeff[Pp
, x, p]*x^(p - q - r)*((p - q - r + 1)*Qq*Rr + (m + 1)*x*Rr*D[Qq, x] + (n + 1)*x*Qq*D[Rr, x])]] /; FreeQ[{m, n
}, x] && PolyQ[Pp, x] && PolyQ[Qq, x] && PolyQ[Rr, x] && NeQ[m, -1] && NeQ[n, -1]

Rule 2178

Int[(F_)^((g_.)*((e_.) + (f_.)*(x_)))/((c_.) + (d_.)*(x_)), x_Symbol] :> Simp[(F^(g*(e - (c*f)/d))*ExpIntegral
Ei[(f*g*(c + d*x)*Log[F])/d])/d, x] /; FreeQ[{F, c, d, e, f, g}, x] &&  !$UseGamma === True

Rule 2306

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_)*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[((d*x)^(m + 1)*(a + b*Log
[c*x^n])^(p + 1))/(b*d*n*(p + 1)), x] - Dist[(m + 1)/(b*n*(p + 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] && LtQ[p, -1]

Rule 2309

Int[((a_.) + Log[(c_.)*(x_)]*(b_.))^(p_)*(x_)^(m_.), x_Symbol] :> Dist[1/c^(m + 1), Subst[Int[E^((m + 1)*x)*(a
+ b*x)^p, x], x, Log[c*x]], x] /; FreeQ[{a, b, c, p}, x] && IntegerQ[m]

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 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{array}{c}\begin{array}{rl}\text{integral}& =\frac{1}{3}\int \frac{200x+120x^2-22x^3-12x^4+2x^5+(-60x^2+22x^3+18x^4-4x^5)\log (x)+(-400x-360x^2+88x^3+60x^4-12x^5){\log }^2(x)+(-200x-180x^2+44x^3+30x^4-6x^5){\log }^3(x)}{{\log }^3(x)}dx\\ & =\frac{1}{3}\int \frac{2x(10+3x-x^2)(1+\log (x))(10+3x-x^2+(-10-6x+3x^2)\log (x)+(-10-6x+3x^2){\log }^2(x))}{{\log }^3(x)}dx\\ & =\frac{2}{3}\int \frac{x(10+3x-x^2)(1+\log (x))(10+3x-x^2+(-10-6x+3x^2)\log (x)+(-10-6x+3x^2){\log }^2(x))}{{\log }^3(x)}dx\\ & =\frac{2}{3}\int (-((-5+x)x(2+x)(-10-6x+3x^2))+\frac{x{(-10-3x+x^2)}^2}{{\log }^3(x)}-\frac{x^2(30-11x-9x^2+2x^3)}{{\log }^2(x)}-\frac{2(-5+x)x(2+x)(-10-6x+3x^2)}{\log (x)})dx\\ & =-(\frac{2}{3}\int (-5+x)x(2+x)(-10-6x+3x^2)dx)+\frac{2}{3}\int \frac{x{(-10-3x+x^2)}^2}{{\log }^3(x)}dx-\frac{2}{3}\int \frac{x^2(30-11x-9x^2+2x^3)}{{\log }^2(x)}dx-\frac{4}{3}\int \frac{(-5+x)x(2+x)(-10-6x+3x^2)}{\log (x)}dx\\ & =-\frac{1}{3}(5-x{)}^2{x}^2(2+x{)}^2+\frac{2}{3}\int (\frac{100x}{{\log }^3(x)}+\frac{60x^2}{{\log }^3(x)}-\frac{11x^3}{{\log }^3(x)}-\frac{6x^4}{{\log }^3(x)}+\frac{x^5}{{\log }^3(x)})dx-\frac{2}{3}\int (\frac{30x^2}{{\log }^2(x)}-\frac{11x^3}{{\log }^2(x)}-\frac{9x^4}{{\log }^2(x)}+\frac{2x^5}{{\log }^2(x)})dx-\frac{4}{3}\int (\frac{100x}{\log (x)}+\frac{90x^2}{\log (x)}-\frac{22x^3}{\log (x)}-\frac{15x^4}{\log (x)}+\frac{3x^5}{\log (x)})dx\\ & =-\frac{1}{3}(5-x{)}^2{x}^2(2+x{)}^2+\frac{2}{3}\int \frac{x^5}{{\log }^3(x)}dx-\frac{4}{3}\int \frac{x^5}{{\log }^2(x)}dx-4\int \frac{x^4}{{\log }^3(x)}dx-4\int \frac{x^5}{\log (x)}dx+6\int \frac{x^4}{{\log }^2(x)}dx-\frac{22}{3}\int \frac{x^3}{{\log }^3(x)}dx+\frac{22}{3}\int \frac{x^3}{{\log }^2(x)}dx-20\int \frac{x^2}{{\log }^2(x)}dx+20\int \frac{x^4}{\log (x)}dx+\frac{88}{3}\int \frac{x^3}{\log (x)}dx+40\int \frac{x^2}{{\log }^3(x)}dx+\frac{200}{3}\int \frac{x}{{\log }^3(x)}dx-120\int \frac{x^2}{\log (x)}dx-\frac{400}{3}\int \frac{x}{\log (x)}dx\\ & =-\frac{1}{3}(5-x{)}^2{x}^2(2+x{)}^2-\frac{100x^2}{3{\log }^2(x)}-\frac{20x^3}{{\log }^2(x)}+\frac{11x^4}{3{\log }^2(x)}+\frac{2x^5}{{\log }^2(x)}-\frac{x^6}{3{\log }^2(x)}+\frac{20x^3}{\log (x)}-\frac{22x^4}{3\log (x)}-\frac{6x^5}{\log (x)}+\frac{4x^6}{3\log (x)}+2\int \frac{x^5}{{\log }^2(x)}dx-4\mathrm{Subst}(\int \frac{e^{6x}}{x}dx,x,\log (x))-8\int \frac{x^5}{\log (x)}dx-10\int \frac{x^4}{{\log }^2(x)}dx-\frac{44}{3}\int \frac{x^3}{{\log }^2(x)}dx+20\mathrm{Subst}(\int \frac{e^{5x}}{x}dx,x,\log (x))+\frac{88}{3}\int \frac{x^3}{\log (x)}dx+\frac{88}{3}\mathrm{Subst}(\int \frac{e^{4x}}{x}dx,x,\log (x))+30\int \frac{x^4}{\log (x)}dx+60\int \frac{x^2}{{\log }^2(x)}dx-60\int \frac{x^2}{\log (x)}dx+\frac{200}{3}\int \frac{x}{{\log }^2(x)}dx-120\mathrm{Subst}(\int \frac{e^{3x}}{x}dx,x,\log (x))-\frac{400}{3}\mathrm{Subst}(\int \frac{e^{2x}}{x}dx,x,\log (x))\\ & =-\frac{1}{3}(5-x{)}^2{x}^2(2+x{)}^2-\frac{400}{3}\text{Ei}(2\log (x))-120\text{Ei}(3\log (x))+\frac{88}{3}\text{Ei}(4\log (x))+20\text{Ei}(5\log (x))-4\text{Ei}(6\log (x))-\frac{100x^2}{3{\log }^2(x)}-\frac{20x^3}{{\log }^2(x)}+\frac{11x^4}{3{\log }^2(x)}+\frac{2x^5}{{\log }^2(x)}-\frac{x^6}{3{\log }^2(x)}-\frac{200x^2}{3\log (x)}-\frac{40x^3}{\log (x)}+\frac{22x^4}{3\log (x)}+\frac{4x^5}{\log (x)}-\frac{2x^6}{3\log (x)}-8\mathrm{Subst}(\int \frac{e^{6x}}{x}dx,x,\log (x))+12\int \frac{x^5}{\log (x)}dx+\frac{88}{3}\mathrm{Subst}(\int \frac{e^{4x}}{x}dx,x,\log (x))+30\mathrm{Subst}(\int \frac{e^{5x}}{x}dx,x,\log (x))-50\int \frac{x^4}{\log (x)}dx-\frac{176}{3}\int \frac{x^3}{\log (x)}dx-60\mathrm{Subst}(\int \frac{e^{3x}}{x}dx,x,\log (x))+\frac{400}{3}\int \frac{x}{\log (x)}dx+180\int \frac{x^2}{\log (x)}dx\\ & =-\frac{1}{3}(5-x{)}^2{x}^2(2+x{)}^2-\frac{400}{3}\text{Ei}(2\log (x))-180\text{Ei}(3\log (x))+\frac{176}{3}\text{Ei}(4\log (x))+50\text{Ei}(5\log (x))-12\text{Ei}(6\log (x))-\frac{100x^2}{3{\log }^2(x)}-\frac{20x^3}{{\log }^2(x)}+\frac{11x^4}{3{\log }^2(x)}+\frac{2x^5}{{\log }^2(x)}-\frac{x^6}{3{\log }^2(x)}-\frac{200x^2}{3\log (x)}-\frac{40x^3}{\log (x)}+\frac{22x^4}{3\log (x)}+\frac{4x^5}{\log (x)}-\frac{2x^6}{3\log (x)}+12\mathrm{Subst}(\int \frac{e^{6x}}{x}dx,x,\log (x))-50\mathrm{Subst}(\int \frac{e^{5x}}{x}dx,x,\log (x))-\frac{176}{3}\mathrm{Subst}(\int \frac{e^{4x}}{x}dx,x,\log (x))+\frac{400}{3}\mathrm{Subst}(\int \frac{e^{2x}}{x}dx,x,\log (x))+180\mathrm{Subst}(\int \frac{e^{3x}}{x}dx,x,\log (x))\\ & =-\frac{1}{3}(5-x{)}^2{x}^2(2+x{)}^2-\frac{100x^2}{3{\log }^2(x)}-\frac{20x^3}{{\log }^2(x)}+\frac{11x^4}{3{\log }^2(x)}+\frac{2x^5}{{\log }^2(x)}-\frac{x^6}{3{\log }^2(x)}-\frac{200x^2}{3\log (x)}-\frac{40x^3}{\log (x)}+\frac{22x^4}{3\log (x)}+\frac{4x^5}{\log (x)}-\frac{2x^6}{3\log (x)}\end{array}\end{array}$$

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Mathematica [A]  time = 0.22, size = 27, normalized size = 0.96 $$\begin{array}{c}-\frac{x^2{(-10-3x+x^2)}^2(1+\log (x){)}^2}{3{\log }^2(x)}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(200*x + 120*x^2 - 22*x^3 - 12*x^4 + 2*x^5 + (-60*x^2 + 22*x^3 + 18*x^4 - 4*x^5)*Log[x] + (-400*x -
360*x^2 + 88*x^3 + 60*x^4 - 12*x^5)*Log[x]^2 + (-200*x - 180*x^2 + 44*x^3 + 30*x^4 - 6*x^5)*Log[x]^3)/(3*Log[x
]^3),x]

[Out]

-1/3*(x^2*(-10 - 3*x + x^2)^2*(1 + Log[x])^2)/Log[x]^2

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fricas [B]  time = 1.00, size = 87, normalized size = 3.11 $$\begin{array}{c}-\frac{x^6-6x^5-11x^4+60x^3+(x^6-6x^5-11x^4+60x^3+100x^2)\log (x{)}^2+100x^2+2(x^6-6x^5-11x^4+60x^3+100x^2)\log (x)}{3\log (x{)}^2}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*((-6*x^5+30*x^4+44*x^3-180*x^2-200*x)*log(x)^3+(-12*x^5+60*x^4+88*x^3-360*x^2-400*x)*log(x)^2+(-
4*x^5+18*x^4+22*x^3-60*x^2)*log(x)+2*x^5-12*x^4-22*x^3+120*x^2+200*x)/log(x)^3,x, algorithm="fricas")

[Out]

-1/3*(x^6 - 6*x^5 - 11*x^4 + 60*x^3 + (x^6 - 6*x^5 - 11*x^4 + 60*x^3 + 100*x^2)*log(x)^2 + 100*x^2 + 2*(x^6 -
6*x^5 - 11*x^4 + 60*x^3 + 100*x^2)*log(x))/log(x)^2

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giac [B]  time = 0.17, size = 116, normalized size = 4.14 $$\begin{array}{c}-\frac{1}{3}{x}^6+2x^5-\frac{2x^6}{3\log (x)}+\frac{11}{3}{x}^4-\frac{x^6}{3\log (x{)}^2}+\frac{4x^5}{\log (x)}-20x^3+\frac{2x^5}{\log (x{)}^2}+\frac{22x^4}{3\log (x)}-\frac{100}{3}{x}^2+\frac{11x^4}{3\log (x{)}^2}-\frac{40x^3}{\log (x)}-\frac{20x^3}{\log (x{)}^2}-\frac{200x^2}{3\log (x)}-\frac{100x^2}{3\log (x{)}^2}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*((-6*x^5+30*x^4+44*x^3-180*x^2-200*x)*log(x)^3+(-12*x^5+60*x^4+88*x^3-360*x^2-400*x)*log(x)^2+(-
4*x^5+18*x^4+22*x^3-60*x^2)*log(x)+2*x^5-12*x^4-22*x^3+120*x^2+200*x)/log(x)^3,x, algorithm="giac")

[Out]

-1/3*x^6 + 2*x^5 - 2/3*x^6/log(x) + 11/3*x^4 - 1/3*x^6/log(x)^2 + 4*x^5/log(x) - 20*x^3 + 2*x^5/log(x)^2 + 22/
3*x^4/log(x) - 100/3*x^2 + 11/3*x^4/log(x)^2 - 40*x^3/log(x) - 20*x^3/log(x)^2 - 200/3*x^2/log(x) - 100/3*x^2/
log(x)^2

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maple [B]  time = 0.03, size = 84, normalized size = 3.00

method	result	size
risch	$-\frac{x^6}{3}+2x^5+\frac{11x^4}{3}-20x^3-\frac{100x^2}{3}-\frac{x^2(2x^4\ln (x)+x^4-12x^3\ln (x)-6x^3-22x^2\ln (x)-11x^2+120x\ln (x)+60x+200\ln (x)+100)}{3\ln (x{)}^2}$	$84$
norman	$\frac{-\frac{100x^2}{3}-20x^3+\frac{11x^4}{3}+2x^5-\frac{x^6}{3}-\frac{200x^2\ln (x)}{3}-\frac{100x^2\ln (x{)}^2}{3}-40x^3\ln (x)-20x^3\ln (x{)}^2+\frac{22x^4\ln (x)}{3}+\frac{11x^4\ln (x{)}^2}{3}+4x^5\ln (x)+2x^5\ln (x{)}^2-\frac{2x^6\ln (x)}{3}-\frac{x^6\ln (x{)}^2}{3}}{\ln (x{)}^2}$	$112$
default	$-\frac{200x^2}{3\ln (x)}-\frac{x^6}{3}+2x^5+\frac{11x^4}{3}-20x^3-\frac{100x^2}{3}-\frac{100x^2}{3\ln (x{)}^2}+\frac{22x^4}{3\ln (x)}-\frac{40x^3}{\ln (x)}+\frac{11x^4}{3\ln (x{)}^2}-\frac{20x^3}{\ln (x{)}^2}+\frac{4x^5}{\ln (x)}+\frac{2x^5}{\ln (x{)}^2}-\frac{2x^6}{3\ln (x)}-\frac{x^6}{3\ln (x{)}^2}$	$117$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/3*((-6*x^5+30*x^4+44*x^3-180*x^2-200*x)*ln(x)^3+(-12*x^5+60*x^4+88*x^3-360*x^2-400*x)*ln(x)^2+(-4*x^5+18
*x^4+22*x^3-60*x^2)*ln(x)+2*x^5-12*x^4-22*x^3+120*x^2+200*x)/ln(x)^3,x,method=_RETURNVERBOSE)

[Out]

-1/3*x^6+2*x^5+11/3*x^4-20*x^3-100/3*x^2-1/3*x^2*(2*x^4*ln(x)+x^4-12*x^3*ln(x)-6*x^3-22*x^2*ln(x)-11*x^2+120*x
*ln(x)+60*x+200*ln(x)+100)/ln(x)^2

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maxima [C]  time = 0.43, size = 133, normalized size = 4.75 $$\begin{array}{c}-\frac{1}{3}{x}^6+2x^5+\frac{11}{3}{x}^4-20x^3-\frac{100}{3}{x}^2-4\mathrm{E}\mathrm{i}(6\log (x))+20\mathrm{E}\mathrm{i}(5\log (x))+\frac{88}{3}\mathrm{E}\mathrm{i}(4\log (x))-120\mathrm{E}\mathrm{i}(3\log (x))-\frac{400}{3}\mathrm{E}\mathrm{i}(2\log (x))-60\mathrm{\Gamma }(-1,-3\log (x))+\frac{88}{3}\mathrm{\Gamma }(-1,-4\log (x))+30\mathrm{\Gamma }(-1,-5\log (x))-8\mathrm{\Gamma }(-1,-6\log (x))-\frac{800}{3}\mathrm{\Gamma }(-2,-2\log (x))-360\mathrm{\Gamma }(-2,-3\log (x))+\frac{352}{3}\mathrm{\Gamma }(-2,-4\log (x))+100\mathrm{\Gamma }(-2,-5\log (x))-24\mathrm{\Gamma }(-2,-6\log (x))\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*((-6*x^5+30*x^4+44*x^3-180*x^2-200*x)*log(x)^3+(-12*x^5+60*x^4+88*x^3-360*x^2-400*x)*log(x)^2+(-
4*x^5+18*x^4+22*x^3-60*x^2)*log(x)+2*x^5-12*x^4-22*x^3+120*x^2+200*x)/log(x)^3,x, algorithm="maxima")

[Out]

-1/3*x^6 + 2*x^5 + 11/3*x^4 - 20*x^3 - 100/3*x^2 - 4*Ei(6*log(x)) + 20*Ei(5*log(x)) + 88/3*Ei(4*log(x)) - 120*
Ei(3*log(x)) - 400/3*Ei(2*log(x)) - 60*gamma(-1, -3*log(x)) + 88/3*gamma(-1, -4*log(x)) + 30*gamma(-1, -5*log(
x)) - 8*gamma(-1, -6*log(x)) - 800/3*gamma(-2, -2*log(x)) - 360*gamma(-2, -3*log(x)) + 352/3*gamma(-2, -4*log(
x)) + 100*gamma(-2, -5*log(x)) - 24*gamma(-2, -6*log(x))

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mupad [B]  time = 4.21, size = 27, normalized size = 0.96 $$\begin{array}{c}-\frac{x^2{(\ln (x)+1)}^2{(-x^2+3x+10)}^2}{3{\ln (x)}^2}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-((log(x)*(60*x^2 - 22*x^3 - 18*x^4 + 4*x^5))/3 - (200*x)/3 + (log(x)^3*(200*x + 180*x^2 - 44*x^3 - 30*x^4
+ 6*x^5))/3 + (log(x)^2*(400*x + 360*x^2 - 88*x^3 - 60*x^4 + 12*x^5))/3 - 40*x^2 + (22*x^3)/3 + 4*x^4 - (2*x^
5)/3)/log(x)^3,x)

[Out]

-(x^2*(log(x) + 1)^2*(3*x - x^2 + 10)^2)/(3*log(x)^2)

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sympy [B]  time = 0.19, size = 87, normalized size = 3.11 $$\begin{array}{c}-\frac{x^6}{3}+2x^5+\frac{11x^4}{3}-20x^3-\frac{100x^2}{3}+\frac{-x^6+6x^5+11x^4-60x^3-100x^2+(-2x^6+12x^5+22x^4-120x^3-200x^2)\log (x)}{3\log {(x)}^2}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*((-6*x**5+30*x**4+44*x**3-180*x**2-200*x)*ln(x)**3+(-12*x**5+60*x**4+88*x**3-360*x**2-400*x)*ln(
x)**2+(-4*x**5+18*x**4+22*x**3-60*x**2)*ln(x)+2*x**5-12*x**4-22*x**3+120*x**2+200*x)/ln(x)**3,x)

[Out]

-x**6/3 + 2*x**5 + 11*x**4/3 - 20*x**3 - 100*x**2/3 + (-x**6 + 6*x**5 + 11*x**4 - 60*x**3 - 100*x**2 + (-2*x**
6 + 12*x**5 + 22*x**4 - 120*x**3 - 200*x**2)*log(x))/(3*log(x)**2)

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