Integrand size = 17, antiderivative size = 143 \[ \int x^m (1+x) \left (1+2 x+x^2\right )^5 \, dx=\frac {x^{1+m}}{1+m}+\frac {11 x^{2+m}}{2+m}+\frac {55 x^{3+m}}{3+m}+\frac {165 x^{4+m}}{4+m}+\frac {330 x^{5+m}}{5+m}+\frac {462 x^{6+m}}{6+m}+\frac {462 x^{7+m}}{7+m}+\frac {330 x^{8+m}}{8+m}+\frac {165 x^{9+m}}{9+m}+\frac {55 x^{10+m}}{10+m}+\frac {11 x^{11+m}}{11+m}+\frac {x^{12+m}}{12+m} \] Output:
x^(1+m)/(1+m)+11*x^(2+m)/(2+m)+55*x^(3+m)/(3+m)+165*x^(4+m)/(4+m)+330*x^(5 +m)/(5+m)+462*x^(6+m)/(6+m)+462*x^(7+m)/(7+m)+330*x^(8+m)/(8+m)+165*x^(9+m )/(9+m)+55*x^(10+m)/(10+m)+11*x^(11+m)/(11+m)+x^(12+m)/(12+m)
Time = 0.10 (sec) , antiderivative size = 119, normalized size of antiderivative = 0.83 \[ \int x^m (1+x) \left (1+2 x+x^2\right )^5 \, dx=x^{1+m} \left (\frac {1}{1+m}+\frac {11 x}{2+m}+\frac {55 x^2}{3+m}+\frac {165 x^3}{4+m}+\frac {330 x^4}{5+m}+\frac {462 x^5}{6+m}+\frac {462 x^6}{7+m}+\frac {330 x^7}{8+m}+\frac {165 x^8}{9+m}+\frac {55 x^9}{10+m}+\frac {11 x^{10}}{11+m}+\frac {x^{11}}{12+m}\right ) \] Input:
Integrate[x^m*(1 + x)*(1 + 2*x + x^2)^5,x]
Output:
x^(1 + m)*((1 + m)^(-1) + (11*x)/(2 + m) + (55*x^2)/(3 + m) + (165*x^3)/(4 + m) + (330*x^4)/(5 + m) + (462*x^5)/(6 + m) + (462*x^6)/(7 + m) + (330*x ^7)/(8 + m) + (165*x^8)/(9 + m) + (55*x^9)/(10 + m) + (11*x^10)/(11 + m) + x^11/(12 + m))
Time = 0.47 (sec) , antiderivative size = 143, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.176, Rules used = {1184, 53, 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.
| \(\displaystyle \int (x+1) \left (x^2+2 x+1\right )^5 x^m \, dx\) |
| \(\Big \downarrow \) 1184 |
| \(\displaystyle \int (x+1)^{11} x^mdx\) |
| \(\Big \downarrow \) 53 |
| \(\displaystyle \int \left (11 x^{m+1}+55 x^{m+2}+165 x^{m+3}+330 x^{m+4}+462 x^{m+5}+462 x^{m+6}+330 x^{m+7}+165 x^{m+8}+55 x^{m+9}+11 x^{m+10}+x^{m+11}+x^m\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {x^{m+1}}{m+1}+\frac {11 x^{m+2}}{m+2}+\frac {55 x^{m+3}}{m+3}+\frac {165 x^{m+4}}{m+4}+\frac {330 x^{m+5}}{m+5}+\frac {462 x^{m+6}}{m+6}+\frac {462 x^{m+7}}{m+7}+\frac {330 x^{m+8}}{m+8}+\frac {165 x^{m+9}}{m+9}+\frac {55 x^{m+10}}{m+10}+\frac {11 x^{m+11}}{m+11}+\frac {x^{m+12}}{m+12}\) |
Input:
Int[x^m*(1 + x)*(1 + 2*x + x^2)^5,x]
Output:
x^(1 + m)/(1 + m) + (11*x^(2 + m))/(2 + m) + (55*x^(3 + m))/(3 + m) + (165 *x^(4 + m))/(4 + m) + (330*x^(5 + m))/(5 + m) + (462*x^(6 + m))/(6 + m) + (462*x^(7 + m))/(7 + m) + (330*x^(8 + m))/(8 + m) + (165*x^(9 + m))/(9 + m ) + (55*x^(10 + m))/(10 + m) + (11*x^(11 + m))/(11 + m) + x^(12 + m)/(12 + m)
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, n}, x] && IGtQ[m, 0] && ( !IntegerQ[n] || (EqQ[c, 0] && LeQ[7*m + 4*n + 4, 0]) || LtQ[9*m + 5*(n + 1), 0] || GtQ[m + n + 2, 0])
Int[((d_.) + (e_.)*(x_))^(m_.)*((f_.) + (g_.)*(x_))^(n_.)*((a_) + (b_.)*(x_ ) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> Simp[1/c^p Int[(d + e*x)^m*(f + g*x )^n*(b/2 + c*x)^(2*p), x], x] /; FreeQ[{a, b, c, d, e, f, g, m, n}, x] && E qQ[b^2 - 4*a*c, 0] && IntegerQ[p]
Leaf count of result is larger than twice the leaf count of optimal. \(1094\) vs. \(2(143)=286\).
Time = 0.92 (sec) , antiderivative size = 1095, normalized size of antiderivative = 7.66
| method | result | size |
| risch | \(\text {Expression too large to display}\) | \(1095\) |
| gosper | \(\text {Expression too large to display}\) | \(1096\) |
| orering | \(\text {Expression too large to display}\) | \(1110\) |
| parallelrisch | \(\text {Expression too large to display}\) | \(1561\) |
Input:
int(x^m*(x+1)*(x^2+2*x+1)^5,x,method=_RETURNVERBOSE)
Output:
x^m*(m^11*x^11+11*m^11*x^10+66*m^10*x^11+55*m^11*x^9+737*m^10*x^10+1925*m^ 9*x^11+165*m^11*x^8+3740*m^10*x^9+21780*m^9*x^10+32670*m^8*x^11+330*m^11*x ^7+11385*m^10*x^8+112035*m^9*x^9+373890*m^8*x^10+357423*m^7*x^11+462*m^11* x^6+23100*m^10*x^7+345840*m^9*x^8+1947000*m^8*x^9+4131303*m^7*x^10+2637558 *m^6*x^11+462*m^11*x^5+32802*m^10*x^6+711810*m^9*x^7+6089490*m^8*x^8+21750 465*m^7*x^9+30748641*m^6*x^10+13339535*m^5*x^11+330*m^11*x^4+33264*m^10*x^ 5+1025640*m^9*x^6+12709620*m^8*x^7+68855985*m^7*x^8+163460220*m^6*x^9+1566 57490*m^5*x^10+45995730*m^4*x^11+165*m^11*x^3+24090*m^10*x^4+1055670*m^9*x ^5+18586260*m^8*x^6+145645830*m^7*x^7+523190745*m^6*x^8+839860505*m^5*x^9+ 543539260*m^4*x^10+105258076*m^3*x^11+55*m^11*x^2+12210*m^10*x^3+776160*m^ 9*x^4+19431720*m^8*x^5+216148086*m^7*x^6+1120622580*m^6*x^7+2714671410*m^5 *x^8+2935253200*m^4*x^9+1250343336*m^3*x^10+150917976*m^2*x^11+11*m^11*x+4 125*m^10*x^2+399465*m^9*x^3+14523300*m^8*x^4+229661586*m^7*x^5+1687068306* m^6*x^6+5881795590*m^5*x^7+9569532060*m^4*x^8+6793843980*m^3*x^9+180038707 2*m^2*x^10+120543840*m*x^11+m^11+836*m^10*x+137060*m^9*x^2+7604190*m^8*x^3 +174706290*m^7*x^4+1822135392*m^6*x^5+8976008580*m^5*x^6+20948784780*m^4*x ^7+22313339400*m^3*x^8+9832379040*m^2*x^9+1442897280*m*x^10+39916800*x^11+ 77*m^10+28215*m^9*x+2656170*m^8*x^2+93244635*m^7*x^3+1412257770*m^6*x^4+98 52674370*m^5*x^5+32372349240*m^4*x^6+49287977640*m^3*x^7+32492401920*m^2*x ^8+7911984960*m*x^9+479001600*x^10+2640*m^9+557040*m^8*x+33251955*m^7*x...
Leaf count of result is larger than twice the leaf count of optimal. 757 vs. \(2 (143) = 286\).
Time = 0.09 (sec) , antiderivative size = 757, normalized size of antiderivative = 5.29 \[ \int x^m (1+x) \left (1+2 x+x^2\right )^5 \, dx=\text {Too large to display} \] Input:
integrate(x^m*(1+x)*(x^2+2*x+1)^5,x, algorithm="fricas")
Output:
((m^11 + 66*m^10 + 1925*m^9 + 32670*m^8 + 357423*m^7 + 2637558*m^6 + 13339 535*m^5 + 45995730*m^4 + 105258076*m^3 + 150917976*m^2 + 120543840*m + 399 16800)*x^12 + 11*(m^11 + 67*m^10 + 1980*m^9 + 33990*m^8 + 375573*m^7 + 279 5331*m^6 + 14241590*m^5 + 49412660*m^4 + 113667576*m^3 + 163671552*m^2 + 1 31172480*m + 43545600)*x^11 + 55*(m^11 + 68*m^10 + 2037*m^9 + 35400*m^8 + 395463*m^7 + 2972004*m^6 + 15270191*m^5 + 53368240*m^4 + 123524436*m^3 + 1 78770528*m^2 + 143854272*m + 47900160)*x^10 + 165*(m^11 + 69*m^10 + 2096*m ^9 + 36906*m^8 + 417309*m^7 + 3170853*m^6 + 16452554*m^5 + 57997164*m^4 + 135232360*m^3 + 196923648*m^2 + 159246720*m + 53222400)*x^9 + 330*(m^11 + 70*m^10 + 2157*m^9 + 38514*m^8 + 441351*m^7 + 3395826*m^6 + 17823623*m^5 + 63481166*m^4 + 149357508*m^3 + 219154824*m^2 + 178320960*m + 59875200)*x^ 8 + 462*(m^11 + 71*m^10 + 2220*m^9 + 40230*m^8 + 467853*m^7 + 3651663*m^6 + 19428590*m^5 + 70070020*m^4 + 166716696*m^3 + 246998016*m^2 + 202573440* m + 68428800)*x^7 + 462*(m^11 + 72*m^10 + 2285*m^9 + 42060*m^8 + 497103*m^ 7 + 3944016*m^6 + 21326135*m^5 + 78113340*m^4 + 188526796*m^3 + 282854112* m^2 + 234434880*m + 79833600)*x^6 + 330*(m^11 + 73*m^10 + 2352*m^9 + 44010 *m^8 + 529413*m^7 + 4279569*m^6 + 23592386*m^5 + 88108220*m^4 + 216665736* m^3 + 330686208*m^2 + 278128512*m + 95800320)*x^5 + 165*(m^11 + 74*m^10 + 2421*m^9 + 46086*m^8 + 565119*m^7 + 4666158*m^6 + 26325599*m^5 + 100767754 *m^4 + 254135820*m^3 + 397471608*m^2 + 341673120*m + 119750400)*x^4 + 5...
Leaf count of result is larger than twice the leaf count of optimal. 11008 vs. \(2 (117) = 234\).
Time = 1.04 (sec) , antiderivative size = 11008, normalized size of antiderivative = 76.98 \[ \int x^m (1+x) \left (1+2 x+x^2\right )^5 \, dx=\text {Too large to display} \] Input:
integrate(x**m*(1+x)*(x**2+2*x+1)**5,x)
Output:
Piecewise((log(x) - 11/x - 55/(2*x**2) - 55/x**3 - 165/(2*x**4) - 462/(5*x **5) - 77/x**6 - 330/(7*x**7) - 165/(8*x**8) - 55/(9*x**9) - 11/(10*x**10) - 1/(11*x**11), Eq(m, -12)), (x + 11*log(x) - 55/x - 165/(2*x**2) - 110/x **3 - 231/(2*x**4) - 462/(5*x**5) - 55/x**6 - 165/(7*x**7) - 55/(8*x**8) - 11/(9*x**9) - 1/(10*x**10), Eq(m, -11)), (x**2/2 + 11*x + 55*log(x) - 165 /x - 165/x**2 - 154/x**3 - 231/(2*x**4) - 66/x**5 - 55/(2*x**6) - 55/(7*x* *7) - 11/(8*x**8) - 1/(9*x**9), Eq(m, -10)), (x**3/3 + 11*x**2/2 + 55*x + 165*log(x) - 330/x - 231/x**2 - 154/x**3 - 165/(2*x**4) - 33/x**5 - 55/(6* x**6) - 11/(7*x**7) - 1/(8*x**8), Eq(m, -9)), (x**4/4 + 11*x**3/3 + 55*x** 2/2 + 165*x + 330*log(x) - 462/x - 231/x**2 - 110/x**3 - 165/(4*x**4) - 11 /x**5 - 11/(6*x**6) - 1/(7*x**7), Eq(m, -8)), (x**5/5 + 11*x**4/4 + 55*x** 3/3 + 165*x**2/2 + 330*x + 462*log(x) - 462/x - 165/x**2 - 55/x**3 - 55/(4 *x**4) - 11/(5*x**5) - 1/(6*x**6), Eq(m, -7)), (x**6/6 + 11*x**5/5 + 55*x* *4/4 + 55*x**3 + 165*x**2 + 462*x + 462*log(x) - 330/x - 165/(2*x**2) - 55 /(3*x**3) - 11/(4*x**4) - 1/(5*x**5), Eq(m, -6)), (x**7/7 + 11*x**6/6 + 11 *x**5 + 165*x**4/4 + 110*x**3 + 231*x**2 + 462*x + 330*log(x) - 165/x - 55 /(2*x**2) - 11/(3*x**3) - 1/(4*x**4), Eq(m, -5)), (x**8/8 + 11*x**7/7 + 55 *x**6/6 + 33*x**5 + 165*x**4/2 + 154*x**3 + 231*x**2 + 330*x + 165*log(x) - 55/x - 11/(2*x**2) - 1/(3*x**3), Eq(m, -4)), (x**9/9 + 11*x**8/8 + 55*x* *7/7 + 55*x**6/2 + 66*x**5 + 231*x**4/2 + 154*x**3 + 165*x**2 + 165*x +...
Time = 0.03 (sec) , antiderivative size = 143, normalized size of antiderivative = 1.00 \[ \int x^m (1+x) \left (1+2 x+x^2\right )^5 \, dx=\frac {x^{m + 12}}{m + 12} + \frac {11 \, x^{m + 11}}{m + 11} + \frac {55 \, x^{m + 10}}{m + 10} + \frac {165 \, x^{m + 9}}{m + 9} + \frac {330 \, x^{m + 8}}{m + 8} + \frac {462 \, x^{m + 7}}{m + 7} + \frac {462 \, x^{m + 6}}{m + 6} + \frac {330 \, x^{m + 5}}{m + 5} + \frac {165 \, x^{m + 4}}{m + 4} + \frac {55 \, x^{m + 3}}{m + 3} + \frac {11 \, x^{m + 2}}{m + 2} + \frac {x^{m + 1}}{m + 1} \] Input:
integrate(x^m*(1+x)*(x^2+2*x+1)^5,x, algorithm="maxima")
Output:
x^(m + 12)/(m + 12) + 11*x^(m + 11)/(m + 11) + 55*x^(m + 10)/(m + 10) + 16 5*x^(m + 9)/(m + 9) + 330*x^(m + 8)/(m + 8) + 462*x^(m + 7)/(m + 7) + 462* x^(m + 6)/(m + 6) + 330*x^(m + 5)/(m + 5) + 165*x^(m + 4)/(m + 4) + 55*x^( m + 3)/(m + 3) + 11*x^(m + 2)/(m + 2) + x^(m + 1)/(m + 1)
Leaf count of result is larger than twice the leaf count of optimal. 1560 vs. \(2 (143) = 286\).
Time = 0.27 (sec) , antiderivative size = 1560, normalized size of antiderivative = 10.91 \[ \int x^m (1+x) \left (1+2 x+x^2\right )^5 \, dx=\text {Too large to display} \] Input:
integrate(x^m*(1+x)*(x^2+2*x+1)^5,x, algorithm="giac")
Output:
(m^11*x^12*x^m + 11*m^11*x^11*x^m + 66*m^10*x^12*x^m + 55*m^11*x^10*x^m + 737*m^10*x^11*x^m + 1925*m^9*x^12*x^m + 165*m^11*x^9*x^m + 3740*m^10*x^10* x^m + 21780*m^9*x^11*x^m + 32670*m^8*x^12*x^m + 330*m^11*x^8*x^m + 11385*m ^10*x^9*x^m + 112035*m^9*x^10*x^m + 373890*m^8*x^11*x^m + 357423*m^7*x^12* x^m + 462*m^11*x^7*x^m + 23100*m^10*x^8*x^m + 345840*m^9*x^9*x^m + 1947000 *m^8*x^10*x^m + 4131303*m^7*x^11*x^m + 2637558*m^6*x^12*x^m + 462*m^11*x^6 *x^m + 32802*m^10*x^7*x^m + 711810*m^9*x^8*x^m + 6089490*m^8*x^9*x^m + 217 50465*m^7*x^10*x^m + 30748641*m^6*x^11*x^m + 13339535*m^5*x^12*x^m + 330*m ^11*x^5*x^m + 33264*m^10*x^6*x^m + 1025640*m^9*x^7*x^m + 12709620*m^8*x^8* x^m + 68855985*m^7*x^9*x^m + 163460220*m^6*x^10*x^m + 156657490*m^5*x^11*x ^m + 45995730*m^4*x^12*x^m + 165*m^11*x^4*x^m + 24090*m^10*x^5*x^m + 10556 70*m^9*x^6*x^m + 18586260*m^8*x^7*x^m + 145645830*m^7*x^8*x^m + 523190745* m^6*x^9*x^m + 839860505*m^5*x^10*x^m + 543539260*m^4*x^11*x^m + 105258076* m^3*x^12*x^m + 55*m^11*x^3*x^m + 12210*m^10*x^4*x^m + 776160*m^9*x^5*x^m + 19431720*m^8*x^6*x^m + 216148086*m^7*x^7*x^m + 1120622580*m^6*x^8*x^m + 2 714671410*m^5*x^9*x^m + 2935253200*m^4*x^10*x^m + 1250343336*m^3*x^11*x^m + 150917976*m^2*x^12*x^m + 11*m^11*x^2*x^m + 4125*m^10*x^3*x^m + 399465*m^ 9*x^4*x^m + 14523300*m^8*x^5*x^m + 229661586*m^7*x^6*x^m + 1687068306*m^6* x^7*x^m + 5881795590*m^5*x^8*x^m + 9569532060*m^4*x^9*x^m + 6793843980*m^3 *x^10*x^m + 1800387072*m^2*x^11*x^m + 120543840*m*x^12*x^m + m^11*x*x^m...
Time = 11.70 (sec) , antiderivative size = 1459, normalized size of antiderivative = 10.20 \[ \int x^m (1+x) \left (1+2 x+x^2\right )^5 \, dx=\text {Too large to display} \] Input:
int(x^m*(x + 1)*(2*x + x^2 + 1)^5,x)
Output:
(x^m*x^8*(58845916800*m + 72321091920*m^2 + 49287977640*m^3 + 20948784780* m^4 + 5881795590*m^5 + 1120622580*m^6 + 145645830*m^7 + 12709620*m^8 + 711 810*m^9 + 23100*m^10 + 330*m^11 + 19758816000))/(1486442880*m + 1931559552 *m^2 + 1414014888*m^3 + 657206836*m^4 + 206070150*m^5 + 44990231*m^6 + 692 6634*m^7 + 749463*m^8 + 55770*m^9 + 2717*m^10 + 78*m^11 + m^12 + 479001600 ) + (x^m*x^10*(7911984960*m + 9832379040*m^2 + 6793843980*m^3 + 2935253200 *m^4 + 839860505*m^5 + 163460220*m^6 + 21750465*m^7 + 1947000*m^8 + 112035 *m^9 + 3740*m^10 + 55*m^11 + 2634508800))/(1486442880*m + 1931559552*m^2 + 1414014888*m^3 + 657206836*m^4 + 206070150*m^5 + 44990231*m^6 + 6926634*m ^7 + 749463*m^8 + 55770*m^9 + 2717*m^10 + 78*m^11 + m^12 + 479001600) + (x ^m*x^2*(6858181440*m + 7194486816*m^2 + 4179838476*m^3 + 1524718360*m^4 + 371026645*m^5 + 61932948*m^6 + 7130013*m^7 + 557040*m^8 + 28215*m^9 + 836* m^10 + 11*m^11 + 2634508800))/(1486442880*m + 1931559552*m^2 + 1414014888* m^3 + 657206836*m^4 + 206070150*m^5 + 44990231*m^6 + 6926634*m^7 + 749463* m^8 + 55770*m^9 + 2717*m^10 + 78*m^11 + m^12 + 479001600) + (x^m*x^11*(144 2897280*m + 1800387072*m^2 + 1250343336*m^3 + 543539260*m^4 + 156657490*m^ 5 + 30748641*m^6 + 4131303*m^7 + 373890*m^8 + 21780*m^9 + 737*m^10 + 11*m^ 11 + 479001600))/(1486442880*m + 1931559552*m^2 + 1414014888*m^3 + 6572068 36*m^4 + 206070150*m^5 + 44990231*m^6 + 6926634*m^7 + 749463*m^8 + 55770*m ^9 + 2717*m^10 + 78*m^11 + m^12 + 479001600) + (x^m*x^6*(108308914560*m...
Time = 0.26 (sec) , antiderivative size = 1094, normalized size of antiderivative = 7.65 \[ \int x^m (1+x) \left (1+2 x+x^2\right )^5 \, dx =\text {Too large to display} \] Input:
int(x^m*(1+x)*(x^2+2*x+1)^5,x)
Output:
(x**m*x*(m**11*x**11 + 11*m**11*x**10 + 55*m**11*x**9 + 165*m**11*x**8 + 3 30*m**11*x**7 + 462*m**11*x**6 + 462*m**11*x**5 + 330*m**11*x**4 + 165*m** 11*x**3 + 55*m**11*x**2 + 11*m**11*x + m**11 + 66*m**10*x**11 + 737*m**10* x**10 + 3740*m**10*x**9 + 11385*m**10*x**8 + 23100*m**10*x**7 + 32802*m**1 0*x**6 + 33264*m**10*x**5 + 24090*m**10*x**4 + 12210*m**10*x**3 + 4125*m** 10*x**2 + 836*m**10*x + 77*m**10 + 1925*m**9*x**11 + 21780*m**9*x**10 + 11 2035*m**9*x**9 + 345840*m**9*x**8 + 711810*m**9*x**7 + 1025640*m**9*x**6 + 1055670*m**9*x**5 + 776160*m**9*x**4 + 399465*m**9*x**3 + 137060*m**9*x** 2 + 28215*m**9*x + 2640*m**9 + 32670*m**8*x**11 + 373890*m**8*x**10 + 1947 000*m**8*x**9 + 6089490*m**8*x**8 + 12709620*m**8*x**7 + 18586260*m**8*x** 6 + 19431720*m**8*x**5 + 14523300*m**8*x**4 + 7604190*m**8*x**3 + 2656170* m**8*x**2 + 557040*m**8*x + 53130*m**8 + 357423*m**7*x**11 + 4131303*m**7* x**10 + 21750465*m**7*x**9 + 68855985*m**7*x**8 + 145645830*m**7*x**7 + 21 6148086*m**7*x**6 + 229661586*m**7*x**5 + 174706290*m**7*x**4 + 93244635*m **7*x**3 + 33251955*m**7*x**2 + 7130013*m**7*x + 696333*m**7 + 2637558*m** 6*x**11 + 30748641*m**6*x**10 + 163460220*m**6*x**9 + 523190745*m**6*x**8 + 1120622580*m**6*x**7 + 1687068306*m**6*x**6 + 1822135392*m**6*x**5 + 141 2257770*m**6*x**4 + 769916070*m**6*x**3 + 281209005*m**6*x**2 + 61932948*m **6*x + 6230301*m**6 + 13339535*m**5*x**11 + 156657490*m**5*x**10 + 839860 505*m**5*x**9 + 2714671410*m**5*x**8 + 5881795590*m**5*x**7 + 897600858...