Integrand size = 172, antiderivative size = 24 \[ \int \frac {1144 x^3+168 x^4-48 x^5-39754 x^6-29862 x^7-5292 x^8+504 x^9+144 x^{10}+\left (168 x-24 x^2-2288 x^3-18186 x^4-7794 x^5+216 x^7\right ) \log (x)+\left (-336 x-2574 x^2-378 x^3+108 x^4\right ) \log ^2(x)+(-126+18 x) \log ^3(x)}{3087 x^6+2646 x^7+756 x^8+72 x^9+\left (1323 x^4+756 x^5+108 x^6\right ) \log (x)+\left (189 x^2+54 x^3\right ) \log ^2(x)+9 \log ^3(x)} \, dx=\left (7-x-\frac {4}{3 \left (7+2 x+\frac {\log (x)}{x^2}\right )}\right )^2 \] Output:
(7-4/(6*x+3*ln(x)/x^2+21)-x)^2
Leaf count is larger than twice the leaf count of optimal. \(49\) vs. \(2(24)=48\).
Time = 0.05 (sec) , antiderivative size = 49, normalized size of antiderivative = 2.04 \[ \int \frac {1144 x^3+168 x^4-48 x^5-39754 x^6-29862 x^7-5292 x^8+504 x^9+144 x^{10}+\left (168 x-24 x^2-2288 x^3-18186 x^4-7794 x^5+216 x^7\right ) \log (x)+\left (-336 x-2574 x^2-378 x^3+108 x^4\right ) \log ^2(x)+(-126+18 x) \log ^3(x)}{3087 x^6+2646 x^7+756 x^8+72 x^9+\left (1323 x^4+756 x^5+108 x^6\right ) \log (x)+\left (189 x^2+54 x^3\right ) \log ^2(x)+9 \log ^3(x)} \, dx=\frac {1}{9} x \left (-126+9 x+\frac {16 x^3}{\left (x^2 (7+2 x)+\log (x)\right )^2}+\frac {24 (-7+x) x}{x^2 (7+2 x)+\log (x)}\right ) \] Input:
Integrate[(1144*x^3 + 168*x^4 - 48*x^5 - 39754*x^6 - 29862*x^7 - 5292*x^8 + 504*x^9 + 144*x^10 + (168*x - 24*x^2 - 2288*x^3 - 18186*x^4 - 7794*x^5 + 216*x^7)*Log[x] + (-336*x - 2574*x^2 - 378*x^3 + 108*x^4)*Log[x]^2 + (-12 6 + 18*x)*Log[x]^3)/(3087*x^6 + 2646*x^7 + 756*x^8 + 72*x^9 + (1323*x^4 + 756*x^5 + 108*x^6)*Log[x] + (189*x^2 + 54*x^3)*Log[x]^2 + 9*Log[x]^3),x]
Output:
(x*(-126 + 9*x + (16*x^3)/(x^2*(7 + 2*x) + Log[x])^2 + (24*(-7 + x)*x)/(x^ 2*(7 + 2*x) + Log[x])))/9
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.
| \(\displaystyle \int \frac {144 x^{10}+504 x^9-5292 x^8-29862 x^7-39754 x^6-48 x^5+168 x^4+1144 x^3+\left (108 x^4-378 x^3-2574 x^2-336 x\right ) \log ^2(x)+\left (216 x^7-7794 x^5-18186 x^4-2288 x^3-24 x^2+168 x\right ) \log (x)+(18 x-126) \log ^3(x)}{72 x^9+756 x^8+2646 x^7+3087 x^6+\left (54 x^3+189 x^2\right ) \log ^2(x)+\left (108 x^6+756 x^5+1323 x^4\right ) \log (x)+9 \log ^3(x)} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {144 x^{10}+504 x^9-5292 x^8-29862 x^7-39754 x^6-48 x^5+168 x^4+1144 x^3+\left (108 x^4-378 x^3-2574 x^2-336 x\right ) \log ^2(x)+\left (216 x^7-7794 x^5-18186 x^4-2288 x^3-24 x^2+168 x\right ) \log (x)+(18 x-126) \log ^3(x)}{9 \left (2 x^3+7 x^2+\log (x)\right )^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{9} \int \frac {2 \left (72 x^{10}+252 x^9-2646 x^8-14931 x^7-19877 x^6-24 x^5+84 x^4+572 x^3-9 (7-x) \log ^3(x)-3 \left (-18 x^4+63 x^3+429 x^2+56 x\right ) \log ^2(x)+\left (108 x^7-3897 x^5-9093 x^4-1144 x^3-12 x^2+84 x\right ) \log (x)\right )}{\left (2 x^3+7 x^2+\log (x)\right )^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2}{9} \int \frac {72 x^{10}+252 x^9-2646 x^8-14931 x^7-19877 x^6-24 x^5+84 x^4+572 x^3-9 (7-x) \log ^3(x)-3 \left (-18 x^4+63 x^3+429 x^2+56 x\right ) \log ^2(x)+\left (108 x^7-3897 x^5-9093 x^4-1144 x^3-12 x^2+84 x\right ) \log (x)}{\left (2 x^3+7 x^2+\log (x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {2}{9} \int \left (\frac {16 \left (-6 x^3-14 x^2-1\right ) x^3}{\left (2 x^3+7 x^2+\log (x)\right )^3}+\frac {12 (3 x-14) x}{2 x^3+7 x^2+\log (x)}-\frac {4 \left (18 x^4-84 x^3-302 x^2+3 x-21\right ) x}{\left (2 x^3+7 x^2+\log (x)\right )^2}+9 (x-7)\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {2}{9} \left (-16 \int \frac {x^3}{\left (2 x^3+7 x^2+\log (x)\right )^3}dx+84 \int \frac {x}{\left (2 x^3+7 x^2+\log (x)\right )^2}dx-12 \int \frac {x^2}{\left (2 x^3+7 x^2+\log (x)\right )^2}dx+1208 \int \frac {x^3}{\left (2 x^3+7 x^2+\log (x)\right )^2}dx-168 \int \frac {x}{2 x^3+7 x^2+\log (x)}dx+36 \int \frac {x^2}{2 x^3+7 x^2+\log (x)}dx-96 \int \frac {x^6}{\left (2 x^3+7 x^2+\log (x)\right )^3}dx-224 \int \frac {x^5}{\left (2 x^3+7 x^2+\log (x)\right )^3}dx-72 \int \frac {x^5}{\left (2 x^3+7 x^2+\log (x)\right )^2}dx+336 \int \frac {x^4}{\left (2 x^3+7 x^2+\log (x)\right )^2}dx+\frac {9}{2} (7-x)^2\right )\) |
Input:
Int[(1144*x^3 + 168*x^4 - 48*x^5 - 39754*x^6 - 29862*x^7 - 5292*x^8 + 504* x^9 + 144*x^10 + (168*x - 24*x^2 - 2288*x^3 - 18186*x^4 - 7794*x^5 + 216*x ^7)*Log[x] + (-336*x - 2574*x^2 - 378*x^3 + 108*x^4)*Log[x]^2 + (-126 + 18 *x)*Log[x]^3)/(3087*x^6 + 2646*x^7 + 756*x^8 + 72*x^9 + (1323*x^4 + 756*x^ 5 + 108*x^6)*Log[x] + (189*x^2 + 54*x^3)*Log[x]^2 + 9*Log[x]^3),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(52\) vs. \(2(23)=46\).
Time = 10.12 (sec) , antiderivative size = 53, normalized size of antiderivative = 2.21
| method | result | size |
| risch | \(x^{2}-14 x +\frac {8 \left (6 x^{4}-21 x^{3}-145 x^{2}+3 x \ln \left (x \right )-21 \ln \left (x \right )\right ) x^{2}}{9 \left (2 x^{3}+7 x^{2}+\ln \left (x \right )\right )^{2}}\) | \(53\) |
| default | \(x^{2}-14 x -\frac {4 \left (126 x^{5}+6 x^{3} \ln \left (x \right )+437 x^{4}+84 x^{2} \ln \left (x \right )+3 \ln \left (x \right )^{2}\right )}{9 \left (2 x^{3}+7 x^{2}+\ln \left (x \right )\right )^{2}}\) | \(56\) |
| parallelrisch | \(\frac {36 x^{5} \ln \left (x \right )-1740 x^{3} \ln \left (x \right )-378 x^{4} \ln \left (x \right )-126 x \ln \left (x \right )^{2}-168 x^{2} \ln \left (x \right )+36 x^{8}+9 x^{2} \ln \left (x \right )^{2}-3039 x^{6}-252 x^{7}-1160 x^{4}-6342 x^{5}}{36 x^{6}+252 x^{5}+441 x^{4}+36 x^{3} \ln \left (x \right )+126 x^{2} \ln \left (x \right )+9 \ln \left (x \right )^{2}}\) | \(109\) |
Input:
int(((18*x-126)*ln(x)^3+(108*x^4-378*x^3-2574*x^2-336*x)*ln(x)^2+(216*x^7- 7794*x^5-18186*x^4-2288*x^3-24*x^2+168*x)*ln(x)+144*x^10+504*x^9-5292*x^8- 29862*x^7-39754*x^6-48*x^5+168*x^4+1144*x^3)/(9*ln(x)^3+(54*x^3+189*x^2)*l n(x)^2+(108*x^6+756*x^5+1323*x^4)*ln(x)+72*x^9+756*x^8+2646*x^7+3087*x^6), x,method=_RETURNVERBOSE)
Output:
x^2-14*x+8/9*(6*x^4-21*x^3-145*x^2+3*x*ln(x)-21*ln(x))*x^2/(2*x^3+7*x^2+ln (x))^2
Leaf count of result is larger than twice the leaf count of optimal. 103 vs. \(2 (24) = 48\).
Time = 0.08 (sec) , antiderivative size = 103, normalized size of antiderivative = 4.29 \[ \int \frac {1144 x^3+168 x^4-48 x^5-39754 x^6-29862 x^7-5292 x^8+504 x^9+144 x^{10}+\left (168 x-24 x^2-2288 x^3-18186 x^4-7794 x^5+216 x^7\right ) \log (x)+\left (-336 x-2574 x^2-378 x^3+108 x^4\right ) \log ^2(x)+(-126+18 x) \log ^3(x)}{3087 x^6+2646 x^7+756 x^8+72 x^9+\left (1323 x^4+756 x^5+108 x^6\right ) \log (x)+\left (189 x^2+54 x^3\right ) \log ^2(x)+9 \log ^3(x)} \, dx=\frac {36 \, x^{8} - 252 \, x^{7} - 3039 \, x^{6} - 6342 \, x^{5} - 1160 \, x^{4} + 9 \, {\left (x^{2} - 14 \, x\right )} \log \left (x\right )^{2} + 6 \, {\left (6 \, x^{5} - 63 \, x^{4} - 290 \, x^{3} - 28 \, x^{2}\right )} \log \left (x\right )}{9 \, {\left (4 \, x^{6} + 28 \, x^{5} + 49 \, x^{4} + 2 \, {\left (2 \, x^{3} + 7 \, x^{2}\right )} \log \left (x\right ) + \log \left (x\right )^{2}\right )}} \] Input:
integrate(((18*x-126)*log(x)^3+(108*x^4-378*x^3-2574*x^2-336*x)*log(x)^2+( 216*x^7-7794*x^5-18186*x^4-2288*x^3-24*x^2+168*x)*log(x)+144*x^10+504*x^9- 5292*x^8-29862*x^7-39754*x^6-48*x^5+168*x^4+1144*x^3)/(9*log(x)^3+(54*x^3+ 189*x^2)*log(x)^2+(108*x^6+756*x^5+1323*x^4)*log(x)+72*x^9+756*x^8+2646*x^ 7+3087*x^6),x, algorithm="fricas")
Output:
1/9*(36*x^8 - 252*x^7 - 3039*x^6 - 6342*x^5 - 1160*x^4 + 9*(x^2 - 14*x)*lo g(x)^2 + 6*(6*x^5 - 63*x^4 - 290*x^3 - 28*x^2)*log(x))/(4*x^6 + 28*x^5 + 4 9*x^4 + 2*(2*x^3 + 7*x^2)*log(x) + log(x)^2)
Leaf count of result is larger than twice the leaf count of optimal. 70 vs. \(2 (19) = 38\).
Time = 0.11 (sec) , antiderivative size = 70, normalized size of antiderivative = 2.92 \[ \int \frac {1144 x^3+168 x^4-48 x^5-39754 x^6-29862 x^7-5292 x^8+504 x^9+144 x^{10}+\left (168 x-24 x^2-2288 x^3-18186 x^4-7794 x^5+216 x^7\right ) \log (x)+\left (-336 x-2574 x^2-378 x^3+108 x^4\right ) \log ^2(x)+(-126+18 x) \log ^3(x)}{3087 x^6+2646 x^7+756 x^8+72 x^9+\left (1323 x^4+756 x^5+108 x^6\right ) \log (x)+\left (189 x^2+54 x^3\right ) \log ^2(x)+9 \log ^3(x)} \, dx=x^{2} - 14 x + \frac {48 x^{6} - 168 x^{5} - 1160 x^{4} + \left (24 x^{3} - 168 x^{2}\right ) \log {\left (x \right )}}{36 x^{6} + 252 x^{5} + 441 x^{4} + \left (36 x^{3} + 126 x^{2}\right ) \log {\left (x \right )} + 9 \log {\left (x \right )}^{2}} \] Input:
integrate(((18*x-126)*ln(x)**3+(108*x**4-378*x**3-2574*x**2-336*x)*ln(x)** 2+(216*x**7-7794*x**5-18186*x**4-2288*x**3-24*x**2+168*x)*ln(x)+144*x**10+ 504*x**9-5292*x**8-29862*x**7-39754*x**6-48*x**5+168*x**4+1144*x**3)/(9*ln (x)**3+(54*x**3+189*x**2)*ln(x)**2+(108*x**6+756*x**5+1323*x**4)*ln(x)+72* x**9+756*x**8+2646*x**7+3087*x**6),x)
Output:
x**2 - 14*x + (48*x**6 - 168*x**5 - 1160*x**4 + (24*x**3 - 168*x**2)*log(x ))/(36*x**6 + 252*x**5 + 441*x**4 + (36*x**3 + 126*x**2)*log(x) + 9*log(x) **2)
Leaf count of result is larger than twice the leaf count of optimal. 103 vs. \(2 (24) = 48\).
Time = 0.08 (sec) , antiderivative size = 103, normalized size of antiderivative = 4.29 \[ \int \frac {1144 x^3+168 x^4-48 x^5-39754 x^6-29862 x^7-5292 x^8+504 x^9+144 x^{10}+\left (168 x-24 x^2-2288 x^3-18186 x^4-7794 x^5+216 x^7\right ) \log (x)+\left (-336 x-2574 x^2-378 x^3+108 x^4\right ) \log ^2(x)+(-126+18 x) \log ^3(x)}{3087 x^6+2646 x^7+756 x^8+72 x^9+\left (1323 x^4+756 x^5+108 x^6\right ) \log (x)+\left (189 x^2+54 x^3\right ) \log ^2(x)+9 \log ^3(x)} \, dx=\frac {36 \, x^{8} - 252 \, x^{7} - 3039 \, x^{6} - 6342 \, x^{5} - 1160 \, x^{4} + 9 \, {\left (x^{2} - 14 \, x\right )} \log \left (x\right )^{2} + 6 \, {\left (6 \, x^{5} - 63 \, x^{4} - 290 \, x^{3} - 28 \, x^{2}\right )} \log \left (x\right )}{9 \, {\left (4 \, x^{6} + 28 \, x^{5} + 49 \, x^{4} + 2 \, {\left (2 \, x^{3} + 7 \, x^{2}\right )} \log \left (x\right ) + \log \left (x\right )^{2}\right )}} \] Input:
integrate(((18*x-126)*log(x)^3+(108*x^4-378*x^3-2574*x^2-336*x)*log(x)^2+( 216*x^7-7794*x^5-18186*x^4-2288*x^3-24*x^2+168*x)*log(x)+144*x^10+504*x^9- 5292*x^8-29862*x^7-39754*x^6-48*x^5+168*x^4+1144*x^3)/(9*log(x)^3+(54*x^3+ 189*x^2)*log(x)^2+(108*x^6+756*x^5+1323*x^4)*log(x)+72*x^9+756*x^8+2646*x^ 7+3087*x^6),x, algorithm="maxima")
Output:
1/9*(36*x^8 - 252*x^7 - 3039*x^6 - 6342*x^5 - 1160*x^4 + 9*(x^2 - 14*x)*lo g(x)^2 + 6*(6*x^5 - 63*x^4 - 290*x^3 - 28*x^2)*log(x))/(4*x^6 + 28*x^5 + 4 9*x^4 + 2*(2*x^3 + 7*x^2)*log(x) + log(x)^2)
Leaf count of result is larger than twice the leaf count of optimal. 75 vs. \(2 (24) = 48\).
Time = 0.14 (sec) , antiderivative size = 75, normalized size of antiderivative = 3.12 \[ \int \frac {1144 x^3+168 x^4-48 x^5-39754 x^6-29862 x^7-5292 x^8+504 x^9+144 x^{10}+\left (168 x-24 x^2-2288 x^3-18186 x^4-7794 x^5+216 x^7\right ) \log (x)+\left (-336 x-2574 x^2-378 x^3+108 x^4\right ) \log ^2(x)+(-126+18 x) \log ^3(x)}{3087 x^6+2646 x^7+756 x^8+72 x^9+\left (1323 x^4+756 x^5+108 x^6\right ) \log (x)+\left (189 x^2+54 x^3\right ) \log ^2(x)+9 \log ^3(x)} \, dx=x^{2} - 14 \, x + \frac {8 \, {\left (6 \, x^{6} - 21 \, x^{5} - 145 \, x^{4} + 3 \, x^{3} \log \left (x\right ) - 21 \, x^{2} \log \left (x\right )\right )}}{9 \, {\left (4 \, x^{6} + 28 \, x^{5} + 49 \, x^{4} + 4 \, x^{3} \log \left (x\right ) + 14 \, x^{2} \log \left (x\right ) + \log \left (x\right )^{2}\right )}} \] Input:
integrate(((18*x-126)*log(x)^3+(108*x^4-378*x^3-2574*x^2-336*x)*log(x)^2+( 216*x^7-7794*x^5-18186*x^4-2288*x^3-24*x^2+168*x)*log(x)+144*x^10+504*x^9- 5292*x^8-29862*x^7-39754*x^6-48*x^5+168*x^4+1144*x^3)/(9*log(x)^3+(54*x^3+ 189*x^2)*log(x)^2+(108*x^6+756*x^5+1323*x^4)*log(x)+72*x^9+756*x^8+2646*x^ 7+3087*x^6),x, algorithm="giac")
Output:
x^2 - 14*x + 8/9*(6*x^6 - 21*x^5 - 145*x^4 + 3*x^3*log(x) - 21*x^2*log(x)) /(4*x^6 + 28*x^5 + 49*x^4 + 4*x^3*log(x) + 14*x^2*log(x) + log(x)^2)
Timed out. \[ \int \frac {1144 x^3+168 x^4-48 x^5-39754 x^6-29862 x^7-5292 x^8+504 x^9+144 x^{10}+\left (168 x-24 x^2-2288 x^3-18186 x^4-7794 x^5+216 x^7\right ) \log (x)+\left (-336 x-2574 x^2-378 x^3+108 x^4\right ) \log ^2(x)+(-126+18 x) \log ^3(x)}{3087 x^6+2646 x^7+756 x^8+72 x^9+\left (1323 x^4+756 x^5+108 x^6\right ) \log (x)+\left (189 x^2+54 x^3\right ) \log ^2(x)+9 \log ^3(x)} \, dx=\int -\frac {{\ln \left (x\right )}^2\,\left (-108\,x^4+378\,x^3+2574\,x^2+336\,x\right )+\ln \left (x\right )\,\left (-216\,x^7+7794\,x^5+18186\,x^4+2288\,x^3+24\,x^2-168\,x\right )-1144\,x^3-168\,x^4+48\,x^5+39754\,x^6+29862\,x^7+5292\,x^8-504\,x^9-144\,x^{10}-{\ln \left (x\right )}^3\,\left (18\,x-126\right )}{9\,{\ln \left (x\right )}^3+\ln \left (x\right )\,\left (108\,x^6+756\,x^5+1323\,x^4\right )+{\ln \left (x\right )}^2\,\left (54\,x^3+189\,x^2\right )+3087\,x^6+2646\,x^7+756\,x^8+72\,x^9} \,d x \] Input:
int(-(log(x)^2*(336*x + 2574*x^2 + 378*x^3 - 108*x^4) + log(x)*(24*x^2 - 1 68*x + 2288*x^3 + 18186*x^4 + 7794*x^5 - 216*x^7) - 1144*x^3 - 168*x^4 + 4 8*x^5 + 39754*x^6 + 29862*x^7 + 5292*x^8 - 504*x^9 - 144*x^10 - log(x)^3*( 18*x - 126))/(9*log(x)^3 + log(x)*(1323*x^4 + 756*x^5 + 108*x^6) + log(x)^ 2*(189*x^2 + 54*x^3) + 3087*x^6 + 2646*x^7 + 756*x^8 + 72*x^9),x)
Output:
int(-(log(x)^2*(336*x + 2574*x^2 + 378*x^3 - 108*x^4) + log(x)*(24*x^2 - 1 68*x + 2288*x^3 + 18186*x^4 + 7794*x^5 - 216*x^7) - 1144*x^3 - 168*x^4 + 4 8*x^5 + 39754*x^6 + 29862*x^7 + 5292*x^8 - 504*x^9 - 144*x^10 - log(x)^3*( 18*x - 126))/(9*log(x)^3 + log(x)*(1323*x^4 + 756*x^5 + 108*x^6) + log(x)^ 2*(189*x^2 + 54*x^3) + 3087*x^6 + 2646*x^7 + 756*x^8 + 72*x^9), x)
Time = 0.15 (sec) , antiderivative size = 110, normalized size of antiderivative = 4.58 \[ \int \frac {1144 x^3+168 x^4-48 x^5-39754 x^6-29862 x^7-5292 x^8+504 x^9+144 x^{10}+\left (168 x-24 x^2-2288 x^3-18186 x^4-7794 x^5+216 x^7\right ) \log (x)+\left (-336 x-2574 x^2-378 x^3+108 x^4\right ) \log ^2(x)+(-126+18 x) \log ^3(x)}{3087 x^6+2646 x^7+756 x^8+72 x^9+\left (1323 x^4+756 x^5+108 x^6\right ) \log (x)+\left (189 x^2+54 x^3\right ) \log ^2(x)+9 \log ^3(x)} \, dx=\frac {441 \mathrm {log}\left (x \right )^{2} x^{2}-6174 \mathrm {log}\left (x \right )^{2} x +1160 \mathrm {log}\left (x \right )^{2}+1764 \,\mathrm {log}\left (x \right ) x^{5}-18522 \,\mathrm {log}\left (x \right ) x^{4}-80620 \,\mathrm {log}\left (x \right ) x^{3}+8008 \,\mathrm {log}\left (x \right ) x^{2}+1764 x^{8}-12348 x^{7}-144271 x^{6}-278278 x^{5}}{441 \mathrm {log}\left (x \right )^{2}+1764 \,\mathrm {log}\left (x \right ) x^{3}+6174 \,\mathrm {log}\left (x \right ) x^{2}+1764 x^{6}+12348 x^{5}+21609 x^{4}} \] Input:
int(((18*x-126)*log(x)^3+(108*x^4-378*x^3-2574*x^2-336*x)*log(x)^2+(216*x^ 7-7794*x^5-18186*x^4-2288*x^3-24*x^2+168*x)*log(x)+144*x^10+504*x^9-5292*x ^8-29862*x^7-39754*x^6-48*x^5+168*x^4+1144*x^3)/(9*log(x)^3+(54*x^3+189*x^ 2)*log(x)^2+(108*x^6+756*x^5+1323*x^4)*log(x)+72*x^9+756*x^8+2646*x^7+3087 *x^6),x)
Output:
(441*log(x)**2*x**2 - 6174*log(x)**2*x + 1160*log(x)**2 + 1764*log(x)*x**5 - 18522*log(x)*x**4 - 80620*log(x)*x**3 + 8008*log(x)*x**2 + 1764*x**8 - 12348*x**7 - 144271*x**6 - 278278*x**5)/(441*(log(x)**2 + 4*log(x)*x**3 + 14*log(x)*x**2 + 4*x**6 + 28*x**5 + 49*x**4))