Integrand size = 11, antiderivative size = 186 \[ \int \frac {x^{12}}{(a+b x)^{10}} \, dx=\frac {55 a^2 x}{b^{12}}-\frac {5 a x^2}{b^{11}}+\frac {x^3}{3 b^{10}}-\frac {a^{12}}{9 b^{13} (a+b x)^9}+\frac {3 a^{11}}{2 b^{13} (a+b x)^8}-\frac {66 a^{10}}{7 b^{13} (a+b x)^7}+\frac {110 a^9}{3 b^{13} (a+b x)^6}-\frac {99 a^8}{b^{13} (a+b x)^5}+\frac {198 a^7}{b^{13} (a+b x)^4}-\frac {308 a^6}{b^{13} (a+b x)^3}+\frac {396 a^5}{b^{13} (a+b x)^2}-\frac {495 a^4}{b^{13} (a+b x)}-\frac {220 a^3 \log (a+b x)}{b^{13}} \] Output:
55*a^2*x/b^12-5*a*x^2/b^11+1/3*x^3/b^10-1/9*a^12/b^13/(b*x+a)^9+3/2*a^11/b ^13/(b*x+a)^8-66/7*a^10/b^13/(b*x+a)^7+110/3*a^9/b^13/(b*x+a)^6-99*a^8/b^1 3/(b*x+a)^5+198*a^7/b^13/(b*x+a)^4-308*a^6/b^13/(b*x+a)^3+396*a^5/b^13/(b* x+a)^2-495*a^4/b^13/(b*x+a)-220*a^3*ln(b*x+a)/b^13
Time = 0.02 (sec) , antiderivative size = 161, normalized size of antiderivative = 0.87 \[ \int \frac {x^{12}}{(a+b x)^{10}} \, dx=-\frac {35201 a^{12}+289089 a^{11} b x+1031616 a^{10} b^2 x^2+2074464 a^9 b^3 x^3+2529576 a^8 b^4 x^4+1831032 a^7 b^5 x^5+638568 a^6 b^6 x^6-58968 a^5 b^7 x^7-139482 a^4 b^8 x^8-43218 a^3 b^9 x^9-2772 a^2 b^{10} x^{10}+252 a b^{11} x^{11}-42 b^{12} x^{12}+27720 a^3 (a+b x)^9 \log (a+b x)}{126 b^{13} (a+b x)^9} \] Input:
Integrate[x^12/(a + b*x)^10,x]
Output:
-1/126*(35201*a^12 + 289089*a^11*b*x + 1031616*a^10*b^2*x^2 + 2074464*a^9* b^3*x^3 + 2529576*a^8*b^4*x^4 + 1831032*a^7*b^5*x^5 + 638568*a^6*b^6*x^6 - 58968*a^5*b^7*x^7 - 139482*a^4*b^8*x^8 - 43218*a^3*b^9*x^9 - 2772*a^2*b^1 0*x^10 + 252*a*b^11*x^11 - 42*b^12*x^12 + 27720*a^3*(a + b*x)^9*Log[a + b* x])/(b^13*(a + b*x)^9)
Time = 0.33 (sec) , antiderivative size = 186, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {49, 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.
| \(\displaystyle \int \frac {x^{12}}{(a+b x)^{10}} \, dx\) |
| \(\Big \downarrow \) 49 |
| \(\displaystyle \int \left (\frac {a^{12}}{b^{12} (a+b x)^{10}}-\frac {12 a^{11}}{b^{12} (a+b x)^9}+\frac {66 a^{10}}{b^{12} (a+b x)^8}-\frac {220 a^9}{b^{12} (a+b x)^7}+\frac {495 a^8}{b^{12} (a+b x)^6}-\frac {792 a^7}{b^{12} (a+b x)^5}+\frac {924 a^6}{b^{12} (a+b x)^4}-\frac {792 a^5}{b^{12} (a+b x)^3}+\frac {495 a^4}{b^{12} (a+b x)^2}-\frac {220 a^3}{b^{12} (a+b x)}+\frac {55 a^2}{b^{12}}-\frac {10 a x}{b^{11}}+\frac {x^2}{b^{10}}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\frac {a^{12}}{9 b^{13} (a+b x)^9}+\frac {3 a^{11}}{2 b^{13} (a+b x)^8}-\frac {66 a^{10}}{7 b^{13} (a+b x)^7}+\frac {110 a^9}{3 b^{13} (a+b x)^6}-\frac {99 a^8}{b^{13} (a+b x)^5}+\frac {198 a^7}{b^{13} (a+b x)^4}-\frac {308 a^6}{b^{13} (a+b x)^3}+\frac {396 a^5}{b^{13} (a+b x)^2}-\frac {495 a^4}{b^{13} (a+b x)}-\frac {220 a^3 \log (a+b x)}{b^{13}}+\frac {55 a^2 x}{b^{12}}-\frac {5 a x^2}{b^{11}}+\frac {x^3}{3 b^{10}}\) |
Input:
Int[x^12/(a + b*x)^10,x]
Output:
(55*a^2*x)/b^12 - (5*a*x^2)/b^11 + x^3/(3*b^10) - a^12/(9*b^13*(a + b*x)^9 ) + (3*a^11)/(2*b^13*(a + b*x)^8) - (66*a^10)/(7*b^13*(a + b*x)^7) + (110* a^9)/(3*b^13*(a + b*x)^6) - (99*a^8)/(b^13*(a + b*x)^5) + (198*a^7)/(b^13* (a + b*x)^4) - (308*a^6)/(b^13*(a + b*x)^3) + (396*a^5)/(b^13*(a + b*x)^2) - (495*a^4)/(b^13*(a + b*x)) - (220*a^3*Log[a + b*x])/b^13
Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int [ExpandIntegrand[(a + b*x)^m*(c + d*x)^n, x], x] /; FreeQ[{a, b, c, d}, x] && IGtQ[m, 0] && IGtQ[m + n + 2, 0]
Time = 0.12 (sec) , antiderivative size = 143, normalized size of antiderivative = 0.77
| method | result | size |
| risch | \(\frac {x^{3}}{3 b^{10}}-\frac {5 a \,x^{2}}{b^{11}}+\frac {55 a^{2} x}{b^{12}}+\frac {-495 a^{4} b^{7} x^{8}-3564 a^{5} b^{6} x^{7}-11396 a^{6} b^{5} x^{6}-21054 a^{7} b^{4} x^{5}-24519 b^{3} a^{8} x^{4}-\frac {55198 b^{2} a^{9} x^{3}}{3}-\frac {60742 a^{10} b \,x^{2}}{7}-\frac {32891 a^{11} x}{14}-\frac {35201 a^{12}}{126 b}}{b^{12} \left (b x +a \right )^{9}}-\frac {220 a^{3} \ln \left (b x +a \right )}{b^{13}}\) | \(143\) |
| norman | \(\frac {\frac {x^{12}}{3 b}-\frac {2 a \,x^{11}}{b^{2}}+\frac {22 a^{2} x^{10}}{b^{3}}-\frac {78419 a^{12}}{126 b^{13}}-\frac {1980 a^{4} x^{8}}{b^{5}}-\frac {11880 a^{5} x^{7}}{b^{6}}-\frac {33880 a^{6} x^{6}}{b^{7}}-\frac {57750 a^{7} x^{5}}{b^{8}}-\frac {63294 a^{8} x^{4}}{b^{9}}-\frac {45276 a^{9} x^{3}}{b^{10}}-\frac {143748 a^{10} x^{2}}{7 b^{11}}-\frac {75339 a^{11} x}{14 b^{12}}}{\left (b x +a \right )^{9}}-\frac {220 a^{3} \ln \left (b x +a \right )}{b^{13}}\) | \(147\) |
| default | \(\frac {\frac {1}{3} b^{2} x^{3}-5 a b \,x^{2}+55 a^{2} x}{b^{12}}-\frac {a^{12}}{9 b^{13} \left (b x +a \right )^{9}}-\frac {99 a^{8}}{b^{13} \left (b x +a \right )^{5}}+\frac {198 a^{7}}{b^{13} \left (b x +a \right )^{4}}+\frac {3 a^{11}}{2 b^{13} \left (b x +a \right )^{8}}+\frac {396 a^{5}}{b^{13} \left (b x +a \right )^{2}}-\frac {495 a^{4}}{b^{13} \left (b x +a \right )}-\frac {220 a^{3} \ln \left (b x +a \right )}{b^{13}}-\frac {308 a^{6}}{b^{13} \left (b x +a \right )^{3}}-\frac {66 a^{10}}{7 b^{13} \left (b x +a \right )^{7}}+\frac {110 a^{9}}{3 b^{13} \left (b x +a \right )^{6}}\) | \(177\) |
| parallelrisch | \(-\frac {4268880 a^{6} x^{6} b^{6}+7276500 a^{7} x^{5} b^{5}+7975044 a^{8} x^{4} b^{4}+5704776 a^{9} x^{3} b^{3}+2587464 a^{10} x^{2} b^{2}+678051 a^{11} x b +249480 a^{4} x^{8} b^{8}+1496880 a^{5} x^{7} b^{7}-42 b^{12} x^{12}+78419 a^{12}-2772 a^{2} x^{10} b^{10}+252 a \,x^{11} b^{11}+27720 \ln \left (b x +a \right ) a^{12}+27720 \ln \left (b x +a \right ) x^{9} a^{3} b^{9}+249480 \ln \left (b x +a \right ) x^{8} a^{4} b^{8}+997920 \ln \left (b x +a \right ) x^{7} a^{5} b^{7}+2328480 \ln \left (b x +a \right ) x^{6} a^{6} b^{6}+3492720 \ln \left (b x +a \right ) x^{5} a^{7} b^{5}+3492720 \ln \left (b x +a \right ) x^{4} a^{8} b^{4}+2328480 \ln \left (b x +a \right ) x^{3} a^{9} b^{3}+997920 \ln \left (b x +a \right ) x^{2} a^{10} b^{2}+249480 \ln \left (b x +a \right ) x \,a^{11} b}{126 b^{13} \left (b x +a \right )^{9}}\) | \(291\) |
Input:
int(x^12/(b*x+a)^10,x,method=_RETURNVERBOSE)
Output:
1/3*x^3/b^10-5*a*x^2/b^11+55*a^2*x/b^12+(-495*a^4*b^7*x^8-3564*a^5*b^6*x^7 -11396*a^6*b^5*x^6-21054*a^7*b^4*x^5-24519*b^3*a^8*x^4-55198/3*b^2*a^9*x^3 -60742/7*a^10*b*x^2-32891/14*a^11*x-35201/126*a^12/b)/b^12/(b*x+a)^9-220*a ^3*ln(b*x+a)/b^13
Time = 0.08 (sec) , antiderivative size = 338, normalized size of antiderivative = 1.82 \[ \int \frac {x^{12}}{(a+b x)^{10}} \, dx=\frac {42 \, b^{12} x^{12} - 252 \, a b^{11} x^{11} + 2772 \, a^{2} b^{10} x^{10} + 43218 \, a^{3} b^{9} x^{9} + 139482 \, a^{4} b^{8} x^{8} + 58968 \, a^{5} b^{7} x^{7} - 638568 \, a^{6} b^{6} x^{6} - 1831032 \, a^{7} b^{5} x^{5} - 2529576 \, a^{8} b^{4} x^{4} - 2074464 \, a^{9} b^{3} x^{3} - 1031616 \, a^{10} b^{2} x^{2} - 289089 \, a^{11} b x - 35201 \, a^{12} - 27720 \, {\left (a^{3} b^{9} x^{9} + 9 \, a^{4} b^{8} x^{8} + 36 \, a^{5} b^{7} x^{7} + 84 \, a^{6} b^{6} x^{6} + 126 \, a^{7} b^{5} x^{5} + 126 \, a^{8} b^{4} x^{4} + 84 \, a^{9} b^{3} x^{3} + 36 \, a^{10} b^{2} x^{2} + 9 \, a^{11} b x + a^{12}\right )} \log \left (b x + a\right )}{126 \, {\left (b^{22} x^{9} + 9 \, a b^{21} x^{8} + 36 \, a^{2} b^{20} x^{7} + 84 \, a^{3} b^{19} x^{6} + 126 \, a^{4} b^{18} x^{5} + 126 \, a^{5} b^{17} x^{4} + 84 \, a^{6} b^{16} x^{3} + 36 \, a^{7} b^{15} x^{2} + 9 \, a^{8} b^{14} x + a^{9} b^{13}\right )}} \] Input:
integrate(x^12/(b*x+a)^10,x, algorithm="fricas")
Output:
1/126*(42*b^12*x^12 - 252*a*b^11*x^11 + 2772*a^2*b^10*x^10 + 43218*a^3*b^9 *x^9 + 139482*a^4*b^8*x^8 + 58968*a^5*b^7*x^7 - 638568*a^6*b^6*x^6 - 18310 32*a^7*b^5*x^5 - 2529576*a^8*b^4*x^4 - 2074464*a^9*b^3*x^3 - 1031616*a^10* b^2*x^2 - 289089*a^11*b*x - 35201*a^12 - 27720*(a^3*b^9*x^9 + 9*a^4*b^8*x^ 8 + 36*a^5*b^7*x^7 + 84*a^6*b^6*x^6 + 126*a^7*b^5*x^5 + 126*a^8*b^4*x^4 + 84*a^9*b^3*x^3 + 36*a^10*b^2*x^2 + 9*a^11*b*x + a^12)*log(b*x + a))/(b^22* x^9 + 9*a*b^21*x^8 + 36*a^2*b^20*x^7 + 84*a^3*b^19*x^6 + 126*a^4*b^18*x^5 + 126*a^5*b^17*x^4 + 84*a^6*b^16*x^3 + 36*a^7*b^15*x^2 + 9*a^8*b^14*x + a^ 9*b^13)
Time = 0.62 (sec) , antiderivative size = 250, normalized size of antiderivative = 1.34 \[ \int \frac {x^{12}}{(a+b x)^{10}} \, dx=- \frac {220 a^{3} \log {\left (a + b x \right )}}{b^{13}} + \frac {55 a^{2} x}{b^{12}} - \frac {5 a x^{2}}{b^{11}} + \frac {- 35201 a^{12} - 296019 a^{11} b x - 1093356 a^{10} b^{2} x^{2} - 2318316 a^{9} b^{3} x^{3} - 3089394 a^{8} b^{4} x^{4} - 2652804 a^{7} b^{5} x^{5} - 1435896 a^{6} b^{6} x^{6} - 449064 a^{5} b^{7} x^{7} - 62370 a^{4} b^{8} x^{8}}{126 a^{9} b^{13} + 1134 a^{8} b^{14} x + 4536 a^{7} b^{15} x^{2} + 10584 a^{6} b^{16} x^{3} + 15876 a^{5} b^{17} x^{4} + 15876 a^{4} b^{18} x^{5} + 10584 a^{3} b^{19} x^{6} + 4536 a^{2} b^{20} x^{7} + 1134 a b^{21} x^{8} + 126 b^{22} x^{9}} + \frac {x^{3}}{3 b^{10}} \] Input:
integrate(x**12/(b*x+a)**10,x)
Output:
-220*a**3*log(a + b*x)/b**13 + 55*a**2*x/b**12 - 5*a*x**2/b**11 + (-35201* a**12 - 296019*a**11*b*x - 1093356*a**10*b**2*x**2 - 2318316*a**9*b**3*x** 3 - 3089394*a**8*b**4*x**4 - 2652804*a**7*b**5*x**5 - 1435896*a**6*b**6*x* *6 - 449064*a**5*b**7*x**7 - 62370*a**4*b**8*x**8)/(126*a**9*b**13 + 1134* a**8*b**14*x + 4536*a**7*b**15*x**2 + 10584*a**6*b**16*x**3 + 15876*a**5*b **17*x**4 + 15876*a**4*b**18*x**5 + 10584*a**3*b**19*x**6 + 4536*a**2*b**2 0*x**7 + 1134*a*b**21*x**8 + 126*b**22*x**9) + x**3/(3*b**10)
Time = 0.04 (sec) , antiderivative size = 234, normalized size of antiderivative = 1.26 \[ \int \frac {x^{12}}{(a+b x)^{10}} \, dx=-\frac {62370 \, a^{4} b^{8} x^{8} + 449064 \, a^{5} b^{7} x^{7} + 1435896 \, a^{6} b^{6} x^{6} + 2652804 \, a^{7} b^{5} x^{5} + 3089394 \, a^{8} b^{4} x^{4} + 2318316 \, a^{9} b^{3} x^{3} + 1093356 \, a^{10} b^{2} x^{2} + 296019 \, a^{11} b x + 35201 \, a^{12}}{126 \, {\left (b^{22} x^{9} + 9 \, a b^{21} x^{8} + 36 \, a^{2} b^{20} x^{7} + 84 \, a^{3} b^{19} x^{6} + 126 \, a^{4} b^{18} x^{5} + 126 \, a^{5} b^{17} x^{4} + 84 \, a^{6} b^{16} x^{3} + 36 \, a^{7} b^{15} x^{2} + 9 \, a^{8} b^{14} x + a^{9} b^{13}\right )}} - \frac {220 \, a^{3} \log \left (b x + a\right )}{b^{13}} + \frac {b^{2} x^{3} - 15 \, a b x^{2} + 165 \, a^{2} x}{3 \, b^{12}} \] Input:
integrate(x^12/(b*x+a)^10,x, algorithm="maxima")
Output:
-1/126*(62370*a^4*b^8*x^8 + 449064*a^5*b^7*x^7 + 1435896*a^6*b^6*x^6 + 265 2804*a^7*b^5*x^5 + 3089394*a^8*b^4*x^4 + 2318316*a^9*b^3*x^3 + 1093356*a^1 0*b^2*x^2 + 296019*a^11*b*x + 35201*a^12)/(b^22*x^9 + 9*a*b^21*x^8 + 36*a^ 2*b^20*x^7 + 84*a^3*b^19*x^6 + 126*a^4*b^18*x^5 + 126*a^5*b^17*x^4 + 84*a^ 6*b^16*x^3 + 36*a^7*b^15*x^2 + 9*a^8*b^14*x + a^9*b^13) - 220*a^3*log(b*x + a)/b^13 + 1/3*(b^2*x^3 - 15*a*b*x^2 + 165*a^2*x)/b^12
Time = 0.12 (sec) , antiderivative size = 149, normalized size of antiderivative = 0.80 \[ \int \frac {x^{12}}{(a+b x)^{10}} \, dx=-\frac {220 \, a^{3} \log \left ({\left | b x + a \right |}\right )}{b^{13}} - \frac {62370 \, a^{4} b^{8} x^{8} + 449064 \, a^{5} b^{7} x^{7} + 1435896 \, a^{6} b^{6} x^{6} + 2652804 \, a^{7} b^{5} x^{5} + 3089394 \, a^{8} b^{4} x^{4} + 2318316 \, a^{9} b^{3} x^{3} + 1093356 \, a^{10} b^{2} x^{2} + 296019 \, a^{11} b x + 35201 \, a^{12}}{126 \, {\left (b x + a\right )}^{9} b^{13}} + \frac {b^{20} x^{3} - 15 \, a b^{19} x^{2} + 165 \, a^{2} b^{18} x}{3 \, b^{30}} \] Input:
integrate(x^12/(b*x+a)^10,x, algorithm="giac")
Output:
-220*a^3*log(abs(b*x + a))/b^13 - 1/126*(62370*a^4*b^8*x^8 + 449064*a^5*b^ 7*x^7 + 1435896*a^6*b^6*x^6 + 2652804*a^7*b^5*x^5 + 3089394*a^8*b^4*x^4 + 2318316*a^9*b^3*x^3 + 1093356*a^10*b^2*x^2 + 296019*a^11*b*x + 35201*a^12) /((b*x + a)^9*b^13) + 1/3*(b^20*x^3 - 15*a*b^19*x^2 + 165*a^2*b^18*x)/b^30
Time = 0.62 (sec) , antiderivative size = 151, normalized size of antiderivative = 0.81 \[ \int \frac {x^{12}}{(a+b x)^{10}} \, dx=-\frac {6\,a\,{\left (a+b\,x\right )}^2-\frac {{\left (a+b\,x\right )}^3}{3}+\frac {495\,a^4}{a+b\,x}-\frac {396\,a^5}{{\left (a+b\,x\right )}^2}+\frac {308\,a^6}{{\left (a+b\,x\right )}^3}-\frac {198\,a^7}{{\left (a+b\,x\right )}^4}+\frac {99\,a^8}{{\left (a+b\,x\right )}^5}-\frac {110\,a^9}{3\,{\left (a+b\,x\right )}^6}+\frac {66\,a^{10}}{7\,{\left (a+b\,x\right )}^7}-\frac {3\,a^{11}}{2\,{\left (a+b\,x\right )}^8}+\frac {a^{12}}{9\,{\left (a+b\,x\right )}^9}+220\,a^3\,\ln \left (a+b\,x\right )-66\,a^2\,b\,x}{b^{13}} \] Input:
int(x^12/(a + b*x)^10,x)
Output:
-(6*a*(a + b*x)^2 - (a + b*x)^3/3 + (495*a^4)/(a + b*x) - (396*a^5)/(a + b *x)^2 + (308*a^6)/(a + b*x)^3 - (198*a^7)/(a + b*x)^4 + (99*a^8)/(a + b*x) ^5 - (110*a^9)/(3*(a + b*x)^6) + (66*a^10)/(7*(a + b*x)^7) - (3*a^11)/(2*( a + b*x)^8) + a^12/(9*(a + b*x)^9) + 220*a^3*log(a + b*x) - 66*a^2*b*x)/b^ 13
Time = 0.16 (sec) , antiderivative size = 378, normalized size of antiderivative = 2.03 \[ \int \frac {x^{12}}{(a+b x)^{10}} \, dx=\frac {-27720 \,\mathrm {log}\left (b x +a \right ) a^{12}-249480 \,\mathrm {log}\left (b x +a \right ) a^{11} b x -997920 \,\mathrm {log}\left (b x +a \right ) a^{10} b^{2} x^{2}-2328480 \,\mathrm {log}\left (b x +a \right ) a^{9} b^{3} x^{3}-3492720 \,\mathrm {log}\left (b x +a \right ) a^{8} b^{4} x^{4}-3492720 \,\mathrm {log}\left (b x +a \right ) a^{7} b^{5} x^{5}-2328480 \,\mathrm {log}\left (b x +a \right ) a^{6} b^{6} x^{6}-997920 \,\mathrm {log}\left (b x +a \right ) a^{5} b^{7} x^{7}-249480 \,\mathrm {log}\left (b x +a \right ) a^{4} b^{8} x^{8}-27720 \,\mathrm {log}\left (b x +a \right ) a^{3} b^{9} x^{9}-50699 a^{12}-428571 a^{11} b x -1589544 a^{10} b^{2} x^{2}-3376296 a^{9} b^{3} x^{3}-4482324 a^{8} b^{4} x^{4}-3783780 a^{7} b^{5} x^{5}-1940400 a^{6} b^{6} x^{6}-498960 a^{5} b^{7} x^{7}+27720 a^{3} b^{9} x^{9}+2772 a^{2} b^{10} x^{10}-252 a \,b^{11} x^{11}+42 b^{12} x^{12}}{126 b^{13} \left (b^{9} x^{9}+9 a \,b^{8} x^{8}+36 a^{2} b^{7} x^{7}+84 a^{3} b^{6} x^{6}+126 a^{4} b^{5} x^{5}+126 a^{5} b^{4} x^{4}+84 a^{6} b^{3} x^{3}+36 a^{7} b^{2} x^{2}+9 a^{8} b x +a^{9}\right )} \] Input:
int(x^12/(b*x+a)^10,x)
Output:
( - 27720*log(a + b*x)*a**12 - 249480*log(a + b*x)*a**11*b*x - 997920*log( a + b*x)*a**10*b**2*x**2 - 2328480*log(a + b*x)*a**9*b**3*x**3 - 3492720*l og(a + b*x)*a**8*b**4*x**4 - 3492720*log(a + b*x)*a**7*b**5*x**5 - 2328480 *log(a + b*x)*a**6*b**6*x**6 - 997920*log(a + b*x)*a**5*b**7*x**7 - 249480 *log(a + b*x)*a**4*b**8*x**8 - 27720*log(a + b*x)*a**3*b**9*x**9 - 50699*a **12 - 428571*a**11*b*x - 1589544*a**10*b**2*x**2 - 3376296*a**9*b**3*x**3 - 4482324*a**8*b**4*x**4 - 3783780*a**7*b**5*x**5 - 1940400*a**6*b**6*x** 6 - 498960*a**5*b**7*x**7 + 27720*a**3*b**9*x**9 + 2772*a**2*b**10*x**10 - 252*a*b**11*x**11 + 42*b**12*x**12)/(126*b**13*(a**9 + 9*a**8*b*x + 36*a* *7*b**2*x**2 + 84*a**6*b**3*x**3 + 126*a**5*b**4*x**4 + 126*a**4*b**5*x**5 + 84*a**3*b**6*x**6 + 36*a**2*b**7*x**7 + 9*a*b**8*x**8 + b**9*x**9))