Integrand size = 98, antiderivative size = 21 \[ \int \frac {7938+17406 x-36774 x^2+22422 x^3-6186 x^4+906 x^5-82 x^6+2 x^7+\left (-486-1188 x+1926 x^2-960 x^3+222 x^4-28 x^5+2 x^6\right ) \log (x)}{-243 x+405 x^2-270 x^3+90 x^4-15 x^5+x^6} \, dx=\left (-3 \left (3-\frac {2}{3-x}\right )^2+x+\log (x)\right )^2 \] Output:
(x+ln(x)-3*(3-2/(3-x))^2)^2
Leaf count is larger than twice the leaf count of optimal. \(66\) vs. \(2(21)=42\).
Time = 0.07 (sec) , antiderivative size = 66, normalized size of antiderivative = 3.14 \[ \int \frac {7938+17406 x-36774 x^2+22422 x^3-6186 x^4+906 x^5-82 x^6+2 x^7+\left (-486-1188 x+1926 x^2-960 x^3+222 x^4-28 x^5+2 x^6\right ) \log (x)}{-243 x+405 x^2-270 x^3+90 x^4-15 x^5+x^6} \, dx=\frac {-31608+31266 x-7551 x^2-1320 x^3+702 x^4-66 x^5+x^6+2 (-3+x)^2 \left (-147+135 x-33 x^2+x^3\right ) \log (x)+(-3+x)^4 \log ^2(x)}{(-3+x)^4} \] Input:
Integrate[(7938 + 17406*x - 36774*x^2 + 22422*x^3 - 6186*x^4 + 906*x^5 - 8 2*x^6 + 2*x^7 + (-486 - 1188*x + 1926*x^2 - 960*x^3 + 222*x^4 - 28*x^5 + 2 *x^6)*Log[x])/(-243*x + 405*x^2 - 270*x^3 + 90*x^4 - 15*x^5 + x^6),x]
Output:
(-31608 + 31266*x - 7551*x^2 - 1320*x^3 + 702*x^4 - 66*x^5 + x^6 + 2*(-3 + x)^2*(-147 + 135*x - 33*x^2 + x^3)*Log[x] + (-3 + x)^4*Log[x]^2)/(-3 + x) ^4
Leaf count is larger than twice the leaf count of optimal. \(89\) vs. \(2(21)=42\).
Time = 1.50 (sec) , antiderivative size = 89, normalized size of antiderivative = 4.24, number of steps used = 7, number of rules used = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {2026, 2007, 7292, 27, 25, 7293, 2009}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {2 x^7-82 x^6+906 x^5-6186 x^4+22422 x^3-36774 x^2+\left (2 x^6-28 x^5+222 x^4-960 x^3+1926 x^2-1188 x-486\right ) \log (x)+17406 x+7938}{x^6-15 x^5+90 x^4-270 x^3+405 x^2-243 x} \, dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {2 x^7-82 x^6+906 x^5-6186 x^4+22422 x^3-36774 x^2+\left (2 x^6-28 x^5+222 x^4-960 x^3+1926 x^2-1188 x-486\right ) \log (x)+17406 x+7938}{x \left (x^5-15 x^4+90 x^3-270 x^2+405 x-243\right )}dx\) |
| \(\Big \downarrow \) 2007 |
| \(\displaystyle \int \frac {2 x^7-82 x^6+906 x^5-6186 x^4+22422 x^3-36774 x^2+\left (2 x^6-28 x^5+222 x^4-960 x^3+1926 x^2-1188 x-486\right ) \log (x)+17406 x+7938}{(x-3)^5 x}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {2 \left (-x^4+8 x^3-54 x^2+84 x+27\right ) \left (x^3-33 x^2+x^2 \log (x)+135 x-6 x \log (x)+9 \log (x)-147\right )}{(3-x)^5 x}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int -\frac {\left (-x^4+8 x^3-54 x^2+84 x+27\right ) \left (-x^3-\log (x) x^2+33 x^2+6 \log (x) x-135 x-9 \log (x)+147\right )}{(3-x)^5 x}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -2 \int \frac {\left (-x^4+8 x^3-54 x^2+84 x+27\right ) \left (-x^3-\log (x) x^2+33 x^2+6 \log (x) x-135 x-9 \log (x)+147\right )}{(3-x)^5 x}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (-\frac {\left (x^4-8 x^3+54 x^2-84 x-27\right ) x^2}{(x-3)^5}+\frac {33 \left (x^4-8 x^3+54 x^2-84 x-27\right ) x}{(x-3)^5}-\frac {135 \left (x^4-8 x^3+54 x^2-84 x-27\right )}{(x-3)^5}+\frac {147 \left (x^4-8 x^3+54 x^2-84 x-27\right )}{(x-3)^5 x}-\frac {\left (x^4-8 x^3+54 x^2-84 x-27\right ) \log (x)}{(x-3)^3 x}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -2 \left (-\frac {x^2}{2}+27 x+\frac {852}{3-x}-\frac {936}{(3-x)^2}+\frac {432}{(3-x)^3}-\frac {72}{(3-x)^4}-\frac {\log ^2(x)}{2}-\frac {12 x \log (x)}{3-x}-x \log (x)+\frac {12 \log (x)}{(3-x)^2}+15 \log (x)\right )\) |
Input:
Int[(7938 + 17406*x - 36774*x^2 + 22422*x^3 - 6186*x^4 + 906*x^5 - 82*x^6 + 2*x^7 + (-486 - 1188*x + 1926*x^2 - 960*x^3 + 222*x^4 - 28*x^5 + 2*x^6)* Log[x])/(-243*x + 405*x^2 - 270*x^3 + 90*x^4 - 15*x^5 + x^6),x]
Output:
-2*(-72/(3 - x)^4 + 432/(3 - x)^3 - 936/(3 - x)^2 + 852/(3 - x) + 27*x - x ^2/2 + 15*Log[x] + (12*Log[x])/(3 - x)^2 - x*Log[x] - (12*x*Log[x])/(3 - x ) - Log[x]^2/2)
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{a = Rt[Coeff[Px, x, 0], Expon[Px, x]], b = Rt[Coeff[Px, x, Expon[Px, x]], Expon[Px, x]]}, Int[u*(a + b*x)^(Ex pon[Px, x]*p), x] /; EqQ[Px, (a + b*x)^Expon[Px, x]]] /; IntegerQ[p] && Pol yQ[Px, x] && GtQ[Expon[Px, x], 1] && NeQ[Coeff[Px, x, 0], 0]
Int[(Fx_.)*(Px_)^(p_.), x_Symbol] :> With[{r = Expon[Px, x, Min]}, Int[x^(p *r)*ExpandToSum[Px/x^r, x]^p*Fx, x] /; IGtQ[r, 0]] /; PolyQ[Px, x] && Integ erQ[p] && !MonomialQ[Px, x] && (ILtQ[p, 0] || !PolyQ[u, x])
Leaf count of result is larger than twice the leaf count of optimal. \(71\) vs. \(2(21)=42\).
Time = 1.35 (sec) , antiderivative size = 72, normalized size of antiderivative = 3.43
| method | result | size |
| default | \(x^{2}-54 x -\frac {98 \ln \left (x \right )}{3}+\frac {144}{\left (-3+x \right )^{4}}+\frac {864}{\left (-3+x \right )^{3}}+\frac {1872}{\left (-3+x \right )^{2}}+\frac {1704}{-3+x}+2 x \ln \left (x \right )+\ln \left (x \right )^{2}+\frac {8 \ln \left (x \right ) x \left (-6+x \right )}{3 \left (-3+x \right )^{2}}-\frac {24 \ln \left (x \right ) x}{-3+x}\) | \(72\) |
| parts | \(x^{2}-54 x -\frac {98 \ln \left (x \right )}{3}+\frac {144}{\left (-3+x \right )^{4}}+\frac {864}{\left (-3+x \right )^{3}}+\frac {1872}{\left (-3+x \right )^{2}}+\frac {1704}{-3+x}+2 x \ln \left (x \right )+\ln \left (x \right )^{2}+\frac {8 \ln \left (x \right ) x \left (-6+x \right )}{3 \left (-3+x \right )^{2}}-\frac {24 \ln \left (x \right ) x}{-3+x}\) | \(72\) |
| risch | \(\ln \left (x \right )^{2}+\frac {2 \left (x^{3}-6 x^{2}-27 x +96\right ) \ln \left (x \right )}{x^{2}-6 x +9}-\frac {-x^{6}+54 x^{4} \ln \left (x \right )+66 x^{5}-648 x^{3} \ln \left (x \right )-702 x^{4}+2916 x^{2} \ln \left (x \right )+1320 x^{3}-5832 x \ln \left (x \right )+7551 x^{2}+4374 \ln \left (x \right )-31266 x +31608}{\left (x^{2}-6 x +9\right )^{2}}\) | \(105\) |
| norman | \(\frac {x^{6}+x^{4} \ln \left (x \right )^{2}-45459 x^{2}-2646 \ln \left (x \right )+7104 x^{3}+107082 x -2508 x^{2} \ln \left (x \right )-78 x^{4} \ln \left (x \right )+684 x^{3} \ln \left (x \right )+4194 x \ln \left (x \right )-66 x^{5}+81 \ln \left (x \right )^{2}-108 x \ln \left (x \right )^{2}+54 x^{2} \ln \left (x \right )^{2}-12 x^{3} \ln \left (x \right )^{2}+2 x^{5} \ln \left (x \right )-88470}{\left (-3+x \right )^{4}}\) | \(106\) |
| parallelrisch | \(\frac {x^{6}+x^{4} \ln \left (x \right )^{2}-45459 x^{2}-2646 \ln \left (x \right )+7104 x^{3}+107082 x -2508 x^{2} \ln \left (x \right )-78 x^{4} \ln \left (x \right )+684 x^{3} \ln \left (x \right )+4194 x \ln \left (x \right )-66 x^{5}+81 \ln \left (x \right )^{2}-108 x \ln \left (x \right )^{2}+54 x^{2} \ln \left (x \right )^{2}-12 x^{3} \ln \left (x \right )^{2}+2 x^{5} \ln \left (x \right )-88470}{x^{4}-12 x^{3}+54 x^{2}-108 x +81}\) | \(121\) |
Input:
int(((2*x^6-28*x^5+222*x^4-960*x^3+1926*x^2-1188*x-486)*ln(x)+2*x^7-82*x^6 +906*x^5-6186*x^4+22422*x^3-36774*x^2+17406*x+7938)/(x^6-15*x^5+90*x^4-270 *x^3+405*x^2-243*x),x,method=_RETURNVERBOSE)
Output:
x^2-54*x-98/3*ln(x)+144/(-3+x)^4+864/(-3+x)^3+1872/(-3+x)^2+1704/(-3+x)+2* x*ln(x)+ln(x)^2+8/3*ln(x)*x*(-6+x)/(-3+x)^2-24*ln(x)*x/(-3+x)
Leaf count of result is larger than twice the leaf count of optimal. 99 vs. \(2 (23) = 46\).
Time = 0.09 (sec) , antiderivative size = 99, normalized size of antiderivative = 4.71 \[ \int \frac {7938+17406 x-36774 x^2+22422 x^3-6186 x^4+906 x^5-82 x^6+2 x^7+\left (-486-1188 x+1926 x^2-960 x^3+222 x^4-28 x^5+2 x^6\right ) \log (x)}{-243 x+405 x^2-270 x^3+90 x^4-15 x^5+x^6} \, dx=\frac {x^{6} - 66 \, x^{5} + 702 \, x^{4} - 1320 \, x^{3} + {\left (x^{4} - 12 \, x^{3} + 54 \, x^{2} - 108 \, x + 81\right )} \log \left (x\right )^{2} - 7551 \, x^{2} + 2 \, {\left (x^{5} - 39 \, x^{4} + 342 \, x^{3} - 1254 \, x^{2} + 2097 \, x - 1323\right )} \log \left (x\right ) + 31266 \, x - 31608}{x^{4} - 12 \, x^{3} + 54 \, x^{2} - 108 \, x + 81} \] Input:
integrate(((2*x^6-28*x^5+222*x^4-960*x^3+1926*x^2-1188*x-486)*log(x)+2*x^7 -82*x^6+906*x^5-6186*x^4+22422*x^3-36774*x^2+17406*x+7938)/(x^6-15*x^5+90* x^4-270*x^3+405*x^2-243*x),x, algorithm="fricas")
Output:
(x^6 - 66*x^5 + 702*x^4 - 1320*x^3 + (x^4 - 12*x^3 + 54*x^2 - 108*x + 81)* log(x)^2 - 7551*x^2 + 2*(x^5 - 39*x^4 + 342*x^3 - 1254*x^2 + 2097*x - 1323 )*log(x) + 31266*x - 31608)/(x^4 - 12*x^3 + 54*x^2 - 108*x + 81)
Leaf count of result is larger than twice the leaf count of optimal. 76 vs. \(2 (15) = 30\).
Time = 0.15 (sec) , antiderivative size = 76, normalized size of antiderivative = 3.62 \[ \int \frac {7938+17406 x-36774 x^2+22422 x^3-6186 x^4+906 x^5-82 x^6+2 x^7+\left (-486-1188 x+1926 x^2-960 x^3+222 x^4-28 x^5+2 x^6\right ) \log (x)}{-243 x+405 x^2-270 x^3+90 x^4-15 x^5+x^6} \, dx=x^{2} - 54 x + \frac {1704 x^{3} - 13464 x^{2} + 35640 x - 31608}{x^{4} - 12 x^{3} + 54 x^{2} - 108 x + 81} + \log {\left (x \right )}^{2} - 54 \log {\left (x \right )} + \frac {\left (2 x^{3} - 12 x^{2} - 54 x + 192\right ) \log {\left (x \right )}}{x^{2} - 6 x + 9} \] Input:
integrate(((2*x**6-28*x**5+222*x**4-960*x**3+1926*x**2-1188*x-486)*ln(x)+2 *x**7-82*x**6+906*x**5-6186*x**4+22422*x**3-36774*x**2+17406*x+7938)/(x**6 -15*x**5+90*x**4-270*x**3+405*x**2-243*x),x)
Output:
x**2 - 54*x + (1704*x**3 - 13464*x**2 + 35640*x - 31608)/(x**4 - 12*x**3 + 54*x**2 - 108*x + 81) + log(x)**2 - 54*log(x) + (2*x**3 - 12*x**2 - 54*x + 192)*log(x)/(x**2 - 6*x + 9)
Leaf count of result is larger than twice the leaf count of optimal. 336 vs. \(2 (23) = 46\).
Time = 0.08 (sec) , antiderivative size = 336, normalized size of antiderivative = 16.00 \[ \int \frac {7938+17406 x-36774 x^2+22422 x^3-6186 x^4+906 x^5-82 x^6+2 x^7+\left (-486-1188 x+1926 x^2-960 x^3+222 x^4-28 x^5+2 x^6\right ) \log (x)}{-243 x+405 x^2-270 x^3+90 x^4-15 x^5+x^6} \, dx=x^{2} - 52 \, x - \frac {27 \, {\left (80 \, x^{3} - 630 \, x^{2} + 1692 \, x - 1539\right )}}{2 \, {\left (x^{4} - 12 \, x^{3} + 54 \, x^{2} - 108 \, x + 81\right )}} + \frac {369 \, {\left (40 \, x^{3} - 300 \, x^{2} + 780 \, x - 693\right )}}{2 \, {\left (x^{4} - 12 \, x^{3} + 54 \, x^{2} - 108 \, x + 81\right )}} - \frac {1359 \, {\left (16 \, x^{3} - 108 \, x^{2} + 264 \, x - 225\right )}}{2 \, {\left (x^{4} - 12 \, x^{3} + 54 \, x^{2} - 108 \, x + 81\right )}} + \frac {3093 \, {\left (4 \, x^{3} - 18 \, x^{2} + 36 \, x - 27\right )}}{2 \, {\left (x^{4} - 12 \, x^{3} + 54 \, x^{2} - 108 \, x + 81\right )}} + \frac {49 \, {\left (4 \, x^{3} - 42 \, x^{2} + 156 \, x - 225\right )}}{2 \, {\left (x^{4} - 12 \, x^{3} + 54 \, x^{2} - 108 \, x + 81\right )}} - \frac {11211 \, {\left (2 \, x^{2} - 4 \, x + 3\right )}}{2 \, {\left (x^{4} - 12 \, x^{3} + 54 \, x^{2} - 108 \, x + 81\right )}} - \frac {6 \, x^{3} - 3 \, {\left (x^{2} - 6 \, x + 9\right )} \log \left (x\right )^{2} - 36 \, x^{2} - 2 \, {\left (3 \, x^{3} - 50 \, x^{2} + 111 \, x\right )} \log \left (x\right ) + 78 \, x - 72}{3 \, {\left (x^{2} - 6 \, x + 9\right )}} + \frac {6129 \, {\left (4 \, x - 3\right )}}{2 \, {\left (x^{4} - 12 \, x^{3} + 54 \, x^{2} - 108 \, x + 81\right )}} - \frac {8703}{2 \, {\left (x^{4} - 12 \, x^{3} + 54 \, x^{2} - 108 \, x + 81\right )}} - \frac {98}{3} \, \log \left (x\right ) \] Input:
integrate(((2*x^6-28*x^5+222*x^4-960*x^3+1926*x^2-1188*x-486)*log(x)+2*x^7 -82*x^6+906*x^5-6186*x^4+22422*x^3-36774*x^2+17406*x+7938)/(x^6-15*x^5+90* x^4-270*x^3+405*x^2-243*x),x, algorithm="maxima")
Output:
x^2 - 52*x - 27/2*(80*x^3 - 630*x^2 + 1692*x - 1539)/(x^4 - 12*x^3 + 54*x^ 2 - 108*x + 81) + 369/2*(40*x^3 - 300*x^2 + 780*x - 693)/(x^4 - 12*x^3 + 5 4*x^2 - 108*x + 81) - 1359/2*(16*x^3 - 108*x^2 + 264*x - 225)/(x^4 - 12*x^ 3 + 54*x^2 - 108*x + 81) + 3093/2*(4*x^3 - 18*x^2 + 36*x - 27)/(x^4 - 12*x ^3 + 54*x^2 - 108*x + 81) + 49/2*(4*x^3 - 42*x^2 + 156*x - 225)/(x^4 - 12* x^3 + 54*x^2 - 108*x + 81) - 11211/2*(2*x^2 - 4*x + 3)/(x^4 - 12*x^3 + 54* x^2 - 108*x + 81) - 1/3*(6*x^3 - 3*(x^2 - 6*x + 9)*log(x)^2 - 36*x^2 - 2*( 3*x^3 - 50*x^2 + 111*x)*log(x) + 78*x - 72)/(x^2 - 6*x + 9) + 6129/2*(4*x - 3)/(x^4 - 12*x^3 + 54*x^2 - 108*x + 81) - 8703/2/(x^4 - 12*x^3 + 54*x^2 - 108*x + 81) - 98/3*log(x)
\[ \int \frac {7938+17406 x-36774 x^2+22422 x^3-6186 x^4+906 x^5-82 x^6+2 x^7+\left (-486-1188 x+1926 x^2-960 x^3+222 x^4-28 x^5+2 x^6\right ) \log (x)}{-243 x+405 x^2-270 x^3+90 x^4-15 x^5+x^6} \, dx=\int { \frac {2 \, {\left (x^{7} - 41 \, x^{6} + 453 \, x^{5} - 3093 \, x^{4} + 11211 \, x^{3} - 18387 \, x^{2} + {\left (x^{6} - 14 \, x^{5} + 111 \, x^{4} - 480 \, x^{3} + 963 \, x^{2} - 594 \, x - 243\right )} \log \left (x\right ) + 8703 \, x + 3969\right )}}{x^{6} - 15 \, x^{5} + 90 \, x^{4} - 270 \, x^{3} + 405 \, x^{2} - 243 \, x} \,d x } \] Input:
integrate(((2*x^6-28*x^5+222*x^4-960*x^3+1926*x^2-1188*x-486)*log(x)+2*x^7 -82*x^6+906*x^5-6186*x^4+22422*x^3-36774*x^2+17406*x+7938)/(x^6-15*x^5+90* x^4-270*x^3+405*x^2-243*x),x, algorithm="giac")
Output:
integrate(2*(x^7 - 41*x^6 + 453*x^5 - 3093*x^4 + 11211*x^3 - 18387*x^2 + ( x^6 - 14*x^5 + 111*x^4 - 480*x^3 + 963*x^2 - 594*x - 243)*log(x) + 8703*x + 3969)/(x^6 - 15*x^5 + 90*x^4 - 270*x^3 + 405*x^2 - 243*x), x)
Time = 4.10 (sec) , antiderivative size = 62, normalized size of antiderivative = 2.95 \[ \int \frac {7938+17406 x-36774 x^2+22422 x^3-6186 x^4+906 x^5-82 x^6+2 x^7+\left (-486-1188 x+1926 x^2-960 x^3+222 x^4-28 x^5+2 x^6\right ) \log (x)}{-243 x+405 x^2-270 x^3+90 x^4-15 x^5+x^6} \, dx={\ln \left (x\right )}^2-54\,\ln \left (x\right )-\frac {x\,\left (1800\,\ln \left (x\right )-35640\right )-1728\,\ln \left (x\right )+x^3\,\left (72\,\ln \left (x\right )-1704\right )-x^2\,\left (624\,\ln \left (x\right )-13464\right )+31608}{{\left (x-3\right )}^4}+x\,\left (2\,\ln \left (x\right )-54\right )+x^2 \] Input:
int(-(17406*x - log(x)*(1188*x - 1926*x^2 + 960*x^3 - 222*x^4 + 28*x^5 - 2 *x^6 + 486) - 36774*x^2 + 22422*x^3 - 6186*x^4 + 906*x^5 - 82*x^6 + 2*x^7 + 7938)/(243*x - 405*x^2 + 270*x^3 - 90*x^4 + 15*x^5 - x^6),x)
Output:
log(x)^2 - 54*log(x) - (x*(1800*log(x) - 35640) - 1728*log(x) + x^3*(72*lo g(x) - 1704) - x^2*(624*log(x) - 13464) + 31608)/(x - 3)^4 + x*(2*log(x) - 54) + x^2
Time = 0.16 (sec) , antiderivative size = 130, normalized size of antiderivative = 6.19 \[ \int \frac {7938+17406 x-36774 x^2+22422 x^3-6186 x^4+906 x^5-82 x^6+2 x^7+\left (-486-1188 x+1926 x^2-960 x^3+222 x^4-28 x^5+2 x^6\right ) \log (x)}{-243 x+405 x^2-270 x^3+90 x^4-15 x^5+x^6} \, dx=\frac {3 \mathrm {log}\left (x \right )^{2} x^{4}-36 \mathrm {log}\left (x \right )^{2} x^{3}+162 \mathrm {log}\left (x \right )^{2} x^{2}-324 \mathrm {log}\left (x \right )^{2} x +243 \mathrm {log}\left (x \right )^{2}+6 \,\mathrm {log}\left (x \right ) x^{5}-234 \,\mathrm {log}\left (x \right ) x^{4}+2052 \,\mathrm {log}\left (x \right ) x^{3}-7524 \,\mathrm {log}\left (x \right ) x^{2}+12582 \,\mathrm {log}\left (x \right ) x -7938 \,\mathrm {log}\left (x \right )+3 x^{6}-198 x^{5}+1792 x^{4}-192 x^{3}-39609 x^{2}+127710 x -120258}{3 x^{4}-36 x^{3}+162 x^{2}-324 x +243} \] Input:
int(((2*x^6-28*x^5+222*x^4-960*x^3+1926*x^2-1188*x-486)*log(x)+2*x^7-82*x^ 6+906*x^5-6186*x^4+22422*x^3-36774*x^2+17406*x+7938)/(x^6-15*x^5+90*x^4-27 0*x^3+405*x^2-243*x),x)
Output:
(3*log(x)**2*x**4 - 36*log(x)**2*x**3 + 162*log(x)**2*x**2 - 324*log(x)**2 *x + 243*log(x)**2 + 6*log(x)*x**5 - 234*log(x)*x**4 + 2052*log(x)*x**3 - 7524*log(x)*x**2 + 12582*log(x)*x - 7938*log(x) + 3*x**6 - 198*x**5 + 1792 *x**4 - 192*x**3 - 39609*x**2 + 127710*x - 120258)/(3*(x**4 - 12*x**3 + 54 *x**2 - 108*x + 81))