3.7.99 \(\int x^m (a+b x)^{10} \, dx\)
Optimal. Leaf size=187 \[ \frac {a^{10} x^{m+1}}{m+1}+\frac {10 a^9 b x^{m+2}}{m+2}+\frac {45 a^8 b^2 x^{m+3}}{m+3}+\frac {120 a^7 b^3 x^{m+4}}{m+4}+\frac {210 a^6 b^4 x^{m+5}}{m+5}+\frac {252 a^5 b^5 x^{m+6}}{m+6}+\frac {210 a^4 b^6 x^{m+7}}{m+7}+\frac {120 a^3 b^7 x^{m+8}}{m+8}+\frac {45 a^2 b^8 x^{m+9}}{m+9}+\frac {10 a b^9 x^{m+10}}{m+10}+\frac {b^{10} x^{m+11}}{m+11} \]
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Rubi [A] time = 0.08, antiderivative size = 187, normalized size of antiderivative = 1.00,
number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used =
{43} \begin {gather*} \frac {45 a^8 b^2 x^{m+3}}{m+3}+\frac {120 a^7 b^3 x^{m+4}}{m+4}+\frac {210 a^6 b^4 x^{m+5}}{m+5}+\frac {252 a^5 b^5 x^{m+6}}{m+6}+\frac {210 a^4 b^6 x^{m+7}}{m+7}+\frac {120 a^3 b^7 x^{m+8}}{m+8}+\frac {45 a^2 b^8 x^{m+9}}{m+9}+\frac {10 a^9 b x^{m+2}}{m+2}+\frac {a^{10} x^{m+1}}{m+1}+\frac {10 a b^9 x^{m+10}}{m+10}+\frac {b^{10} x^{m+11}}{m+11} \end {gather*}
Antiderivative was successfully verified.
[In]
Int[x^m*(a + b*x)^10,x]
[Out]
(a^10*x^(1 + m))/(1 + m) + (10*a^9*b*x^(2 + m))/(2 + m) + (45*a^8*b^2*x^(3 + m))/(3 + m) + (120*a^7*b^3*x^(4 +
m))/(4 + m) + (210*a^6*b^4*x^(5 + m))/(5 + m) + (252*a^5*b^5*x^(6 + m))/(6 + m) + (210*a^4*b^6*x^(7 + m))/(7
+ m) + (120*a^3*b^7*x^(8 + m))/(8 + m) + (45*a^2*b^8*x^(9 + m))/(9 + m) + (10*a*b^9*x^(10 + m))/(10 + m) + (b^
10*x^(11 + m))/(11 + m)
Rule 43
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] && NeQ[b*c - a*d, 0] && 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])
Rubi steps
\begin {align*} \int x^m (a+b x)^{10} \, dx &=\int \left (a^{10} x^m+10 a^9 b x^{1+m}+45 a^8 b^2 x^{2+m}+120 a^7 b^3 x^{3+m}+210 a^6 b^4 x^{4+m}+252 a^5 b^5 x^{5+m}+210 a^4 b^6 x^{6+m}+120 a^3 b^7 x^{7+m}+45 a^2 b^8 x^{8+m}+10 a b^9 x^{9+m}+b^{10} x^{10+m}\right ) \, dx\\ &=\frac {a^{10} x^{1+m}}{1+m}+\frac {10 a^9 b x^{2+m}}{2+m}+\frac {45 a^8 b^2 x^{3+m}}{3+m}+\frac {120 a^7 b^3 x^{4+m}}{4+m}+\frac {210 a^6 b^4 x^{5+m}}{5+m}+\frac {252 a^5 b^5 x^{6+m}}{6+m}+\frac {210 a^4 b^6 x^{7+m}}{7+m}+\frac {120 a^3 b^7 x^{8+m}}{8+m}+\frac {45 a^2 b^8 x^{9+m}}{9+m}+\frac {10 a b^9 x^{10+m}}{10+m}+\frac {b^{10} x^{11+m}}{11+m}\\ \end {align*}
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Mathematica [A] time = 0.11, size = 166, normalized size = 0.89 \begin {gather*} x^{m+1} \left (\frac {a^{10}}{m+1}+\frac {10 a^9 b x}{m+2}+\frac {45 a^8 b^2 x^2}{m+3}+\frac {120 a^7 b^3 x^3}{m+4}+\frac {210 a^6 b^4 x^4}{m+5}+\frac {252 a^5 b^5 x^5}{m+6}+\frac {210 a^4 b^6 x^6}{m+7}+\frac {120 a^3 b^7 x^7}{m+8}+\frac {45 a^2 b^8 x^8}{m+9}+\frac {10 a b^9 x^9}{m+10}+\frac {b^{10} x^{10}}{m+11}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[x^m*(a + b*x)^10,x]
[Out]
x^(1 + m)*(a^10/(1 + m) + (10*a^9*b*x)/(2 + m) + (45*a^8*b^2*x^2)/(3 + m) + (120*a^7*b^3*x^3)/(4 + m) + (210*a
^6*b^4*x^4)/(5 + m) + (252*a^5*b^5*x^5)/(6 + m) + (210*a^4*b^6*x^6)/(7 + m) + (120*a^3*b^7*x^7)/(8 + m) + (45*
a^2*b^8*x^8)/(9 + m) + (10*a*b^9*x^9)/(10 + m) + (b^10*x^10)/(11 + m))
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IntegrateAlgebraic [F] time = 0.18, size = 0, normalized size = 0.00 \begin {gather*} \int x^m (a+b x)^{10} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
IntegrateAlgebraic[x^m*(a + b*x)^10,x]
[Out]
Defer[IntegrateAlgebraic][x^m*(a + b*x)^10, x]
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fricas [B] time = 1.17, size = 1277, normalized size = 6.83
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(x^m*(b*x+a)^10,x, algorithm="fricas")
[Out]
((b^10*m^10 + 55*b^10*m^9 + 1320*b^10*m^8 + 18150*b^10*m^7 + 157773*b^10*m^6 + 902055*b^10*m^5 + 3416930*b^10*
m^4 + 8409500*b^10*m^3 + 12753576*b^10*m^2 + 10628640*b^10*m + 3628800*b^10)*x^11 + 10*(a*b^9*m^10 + 56*a*b^9*
m^9 + 1365*a*b^9*m^8 + 19020*a*b^9*m^7 + 167223*a*b^9*m^6 + 965328*a*b^9*m^5 + 3686255*a*b^9*m^4 + 9133180*a*b
^9*m^3 + 13926276*a*b^9*m^2 + 11655216*a*b^9*m + 3991680*a*b^9)*x^10 + 45*(a^2*b^8*m^10 + 57*a^2*b^8*m^9 + 141
2*a^2*b^8*m^8 + 19962*a^2*b^8*m^7 + 177765*a^2*b^8*m^6 + 1037673*a^2*b^8*m^5 + 4000478*a^2*b^8*m^4 + 9991428*a
^2*b^8*m^3 + 15335224*a^2*b^8*m^2 + 12900960*a^2*b^8*m + 4435200*a^2*b^8)*x^9 + 120*(a^3*b^7*m^10 + 58*a^3*b^7
*m^9 + 1461*a^3*b^7*m^8 + 20982*a^3*b^7*m^7 + 189567*a^3*b^7*m^6 + 1121022*a^3*b^7*m^5 + 4371359*a^3*b^7*m^4 +
11024858*a^3*b^7*m^3 + 17059212*a^3*b^7*m^2 + 14444280*a^3*b^7*m + 4989600*a^3*b^7)*x^8 + 210*(a^4*b^6*m^10 +
59*a^4*b^6*m^9 + 1512*a^4*b^6*m^8 + 22086*a^4*b^6*m^7 + 202821*a^4*b^6*m^6 + 1217811*a^4*b^6*m^5 + 4814858*a^
4*b^6*m^4 + 12291724*a^4*b^6*m^3 + 19216008*a^4*b^6*m^2 + 16405920*a^4*b^6*m + 5702400*a^4*b^6)*x^7 + 252*(a^5
*b^5*m^10 + 60*a^5*b^5*m^9 + 1565*a^5*b^5*m^8 + 23280*a^5*b^5*m^7 + 217743*a^5*b^5*m^6 + 1331100*a^5*b^5*m^5 +
5352935*a^5*b^5*m^4 + 13878120*a^5*b^5*m^3 + 21989356*a^5*b^5*m^2 + 18981840*a^5*b^5*m + 6652800*a^5*b^5)*x^6
+ 210*(a^6*b^4*m^10 + 61*a^6*b^4*m^9 + 1620*a^6*b^4*m^8 + 24570*a^6*b^4*m^7 + 234573*a^6*b^4*m^6 + 1464693*a^
6*b^4*m^5 + 6016070*a^6*b^4*m^4 + 15915380*a^6*b^4*m^3 + 25681176*a^6*b^4*m^2 + 22512096*a^6*b^4*m + 7983360*a
^6*b^4)*x^5 + 120*(a^7*b^3*m^10 + 62*a^7*b^3*m^9 + 1677*a^7*b^3*m^8 + 25962*a^7*b^3*m^7 + 253575*a^7*b^3*m^6 +
1623258*a^7*b^3*m^5 + 6846503*a^7*b^3*m^4 + 18609718*a^7*b^3*m^3 + 30819204*a^7*b^3*m^2 + 27641160*a^7*b^3*m
+ 9979200*a^7*b^3)*x^4 + 45*(a^8*b^2*m^10 + 63*a^8*b^2*m^9 + 1736*a^8*b^2*m^8 + 27462*a^8*b^2*m^7 + 275037*a^8
*b^2*m^6 + 1812447*a^8*b^2*m^5 + 7902194*a^8*b^2*m^4 + 22289148*a^8*b^2*m^3 + 38390632*a^8*b^2*m^2 + 35746080*
a^8*b^2*m + 13305600*a^8*b^2)*x^3 + 10*(a^9*b*m^10 + 64*a^9*b*m^9 + 1797*a^9*b*m^8 + 29076*a^9*b*m^7 + 299271*
a^9*b*m^6 + 2039016*a^9*b*m^5 + 9261503*a^9*b*m^4 + 27472724*a^9*b*m^3 + 50312628*a^9*b*m^2 + 50292720*a^9*b*m
+ 19958400*a^9*b)*x^2 + (a^10*m^10 + 65*a^10*m^9 + 1860*a^10*m^8 + 30810*a^10*m^7 + 326613*a^10*m^6 + 2310945
*a^10*m^5 + 11028590*a^10*m^4 + 34967140*a^10*m^3 + 70290936*a^10*m^2 + 80627040*a^10*m + 39916800*a^10)*x)*x^
m/(m^11 + 66*m^10 + 1925*m^9 + 32670*m^8 + 357423*m^7 + 2637558*m^6 + 13339535*m^5 + 45995730*m^4 + 105258076*
m^3 + 150917976*m^2 + 120543840*m + 39916800)
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giac [B] time = 1.20, size = 1925, normalized size = 10.29
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(x^m*(b*x+a)^10,x, algorithm="giac")
[Out]
(b^10*m^10*x^11*x^m + 10*a*b^9*m^10*x^10*x^m + 55*b^10*m^9*x^11*x^m + 45*a^2*b^8*m^10*x^9*x^m + 560*a*b^9*m^9*
x^10*x^m + 1320*b^10*m^8*x^11*x^m + 120*a^3*b^7*m^10*x^8*x^m + 2565*a^2*b^8*m^9*x^9*x^m + 13650*a*b^9*m^8*x^10
*x^m + 18150*b^10*m^7*x^11*x^m + 210*a^4*b^6*m^10*x^7*x^m + 6960*a^3*b^7*m^9*x^8*x^m + 63540*a^2*b^8*m^8*x^9*x
^m + 190200*a*b^9*m^7*x^10*x^m + 157773*b^10*m^6*x^11*x^m + 252*a^5*b^5*m^10*x^6*x^m + 12390*a^4*b^6*m^9*x^7*x
^m + 175320*a^3*b^7*m^8*x^8*x^m + 898290*a^2*b^8*m^7*x^9*x^m + 1672230*a*b^9*m^6*x^10*x^m + 902055*b^10*m^5*x^
11*x^m + 210*a^6*b^4*m^10*x^5*x^m + 15120*a^5*b^5*m^9*x^6*x^m + 317520*a^4*b^6*m^8*x^7*x^m + 2517840*a^3*b^7*m
^7*x^8*x^m + 7999425*a^2*b^8*m^6*x^9*x^m + 9653280*a*b^9*m^5*x^10*x^m + 3416930*b^10*m^4*x^11*x^m + 120*a^7*b^
3*m^10*x^4*x^m + 12810*a^6*b^4*m^9*x^5*x^m + 394380*a^5*b^5*m^8*x^6*x^m + 4638060*a^4*b^6*m^7*x^7*x^m + 227480
40*a^3*b^7*m^6*x^8*x^m + 46695285*a^2*b^8*m^5*x^9*x^m + 36862550*a*b^9*m^4*x^10*x^m + 8409500*b^10*m^3*x^11*x^
m + 45*a^8*b^2*m^10*x^3*x^m + 7440*a^7*b^3*m^9*x^4*x^m + 340200*a^6*b^4*m^8*x^5*x^m + 5866560*a^5*b^5*m^7*x^6*
x^m + 42592410*a^4*b^6*m^6*x^7*x^m + 134522640*a^3*b^7*m^5*x^8*x^m + 180021510*a^2*b^8*m^4*x^9*x^m + 91331800*
a*b^9*m^3*x^10*x^m + 12753576*b^10*m^2*x^11*x^m + 10*a^9*b*m^10*x^2*x^m + 2835*a^8*b^2*m^9*x^3*x^m + 201240*a^
7*b^3*m^8*x^4*x^m + 5159700*a^6*b^4*m^7*x^5*x^m + 54871236*a^5*b^5*m^6*x^6*x^m + 255740310*a^4*b^6*m^5*x^7*x^m
+ 524563080*a^3*b^7*m^4*x^8*x^m + 449614260*a^2*b^8*m^3*x^9*x^m + 139262760*a*b^9*m^2*x^10*x^m + 10628640*b^1
0*m*x^11*x^m + a^10*m^10*x*x^m + 640*a^9*b*m^9*x^2*x^m + 78120*a^8*b^2*m^8*x^3*x^m + 3115440*a^7*b^3*m^7*x^4*x
^m + 49260330*a^6*b^4*m^6*x^5*x^m + 335437200*a^5*b^5*m^5*x^6*x^m + 1011120180*a^4*b^6*m^4*x^7*x^m + 132298296
0*a^3*b^7*m^3*x^8*x^m + 690085080*a^2*b^8*m^2*x^9*x^m + 116552160*a*b^9*m*x^10*x^m + 3628800*b^10*x^11*x^m + 6
5*a^10*m^9*x*x^m + 17970*a^9*b*m^8*x^2*x^m + 1235790*a^8*b^2*m^7*x^3*x^m + 30429000*a^7*b^3*m^6*x^4*x^m + 3075
85530*a^6*b^4*m^5*x^5*x^m + 1348939620*a^5*b^5*m^4*x^6*x^m + 2581262040*a^4*b^6*m^3*x^7*x^m + 2047105440*a^3*b
^7*m^2*x^8*x^m + 580543200*a^2*b^8*m*x^9*x^m + 39916800*a*b^9*x^10*x^m + 1860*a^10*m^8*x*x^m + 290760*a^9*b*m^
7*x^2*x^m + 12376665*a^8*b^2*m^6*x^3*x^m + 194790960*a^7*b^3*m^5*x^4*x^m + 1263374700*a^6*b^4*m^4*x^5*x^m + 34
97286240*a^5*b^5*m^3*x^6*x^m + 4035361680*a^4*b^6*m^2*x^7*x^m + 1733313600*a^3*b^7*m*x^8*x^m + 199584000*a^2*b
^8*x^9*x^m + 30810*a^10*m^7*x*x^m + 2992710*a^9*b*m^6*x^2*x^m + 81560115*a^8*b^2*m^5*x^3*x^m + 821580360*a^7*b
^3*m^4*x^4*x^m + 3342229800*a^6*b^4*m^3*x^5*x^m + 5541317712*a^5*b^5*m^2*x^6*x^m + 3445243200*a^4*b^6*m*x^7*x^
m + 598752000*a^3*b^7*x^8*x^m + 326613*a^10*m^6*x*x^m + 20390160*a^9*b*m^5*x^2*x^m + 355598730*a^8*b^2*m^4*x^3
*x^m + 2233166160*a^7*b^3*m^3*x^4*x^m + 5393046960*a^6*b^4*m^2*x^5*x^m + 4783423680*a^5*b^5*m*x^6*x^m + 119750
4000*a^4*b^6*x^7*x^m + 2310945*a^10*m^5*x*x^m + 92615030*a^9*b*m^4*x^2*x^m + 1003011660*a^8*b^2*m^3*x^3*x^m +
3698304480*a^7*b^3*m^2*x^4*x^m + 4727540160*a^6*b^4*m*x^5*x^m + 1676505600*a^5*b^5*x^6*x^m + 11028590*a^10*m^4
*x*x^m + 274727240*a^9*b*m^3*x^2*x^m + 1727578440*a^8*b^2*m^2*x^3*x^m + 3316939200*a^7*b^3*m*x^4*x^m + 1676505
600*a^6*b^4*x^5*x^m + 34967140*a^10*m^3*x*x^m + 503126280*a^9*b*m^2*x^2*x^m + 1608573600*a^8*b^2*m*x^3*x^m + 1
197504000*a^7*b^3*x^4*x^m + 70290936*a^10*m^2*x*x^m + 502927200*a^9*b*m*x^2*x^m + 598752000*a^8*b^2*x^3*x^m +
80627040*a^10*m*x*x^m + 199584000*a^9*b*x^2*x^m + 39916800*a^10*x*x^m)/(m^11 + 66*m^10 + 1925*m^9 + 32670*m^8
+ 357423*m^7 + 2637558*m^6 + 13339535*m^5 + 45995730*m^4 + 105258076*m^3 + 150917976*m^2 + 120543840*m + 39916
800)
________________________________________________________________________________________
maple [B] time = 0.01, size = 1535, normalized size = 8.21
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(x^m*(b*x+a)^10,x)
[Out]
x^(m+1)*(b^10*m^10*x^10+10*a*b^9*m^10*x^9+55*b^10*m^9*x^10+45*a^2*b^8*m^10*x^8+560*a*b^9*m^9*x^9+1320*b^10*m^8
*x^10+120*a^3*b^7*m^10*x^7+2565*a^2*b^8*m^9*x^8+13650*a*b^9*m^8*x^9+18150*b^10*m^7*x^10+210*a^4*b^6*m^10*x^6+6
960*a^3*b^7*m^9*x^7+63540*a^2*b^8*m^8*x^8+190200*a*b^9*m^7*x^9+157773*b^10*m^6*x^10+252*a^5*b^5*m^10*x^5+12390
*a^4*b^6*m^9*x^6+175320*a^3*b^7*m^8*x^7+898290*a^2*b^8*m^7*x^8+1672230*a*b^9*m^6*x^9+902055*b^10*m^5*x^10+210*
a^6*b^4*m^10*x^4+15120*a^5*b^5*m^9*x^5+317520*a^4*b^6*m^8*x^6+2517840*a^3*b^7*m^7*x^7+7999425*a^2*b^8*m^6*x^8+
9653280*a*b^9*m^5*x^9+3416930*b^10*m^4*x^10+120*a^7*b^3*m^10*x^3+12810*a^6*b^4*m^9*x^4+394380*a^5*b^5*m^8*x^5+
4638060*a^4*b^6*m^7*x^6+22748040*a^3*b^7*m^6*x^7+46695285*a^2*b^8*m^5*x^8+36862550*a*b^9*m^4*x^9+8409500*b^10*
m^3*x^10+45*a^8*b^2*m^10*x^2+7440*a^7*b^3*m^9*x^3+340200*a^6*b^4*m^8*x^4+5866560*a^5*b^5*m^7*x^5+42592410*a^4*
b^6*m^6*x^6+134522640*a^3*b^7*m^5*x^7+180021510*a^2*b^8*m^4*x^8+91331800*a*b^9*m^3*x^9+12753576*b^10*m^2*x^10+
10*a^9*b*m^10*x+2835*a^8*b^2*m^9*x^2+201240*a^7*b^3*m^8*x^3+5159700*a^6*b^4*m^7*x^4+54871236*a^5*b^5*m^6*x^5+2
55740310*a^4*b^6*m^5*x^6+524563080*a^3*b^7*m^4*x^7+449614260*a^2*b^8*m^3*x^8+139262760*a*b^9*m^2*x^9+10628640*
b^10*m*x^10+a^10*m^10+640*a^9*b*m^9*x+78120*a^8*b^2*m^8*x^2+3115440*a^7*b^3*m^7*x^3+49260330*a^6*b^4*m^6*x^4+3
35437200*a^5*b^5*m^5*x^5+1011120180*a^4*b^6*m^4*x^6+1322982960*a^3*b^7*m^3*x^7+690085080*a^2*b^8*m^2*x^8+11655
2160*a*b^9*m*x^9+3628800*b^10*x^10+65*a^10*m^9+17970*a^9*b*m^8*x+1235790*a^8*b^2*m^7*x^2+30429000*a^7*b^3*m^6*
x^3+307585530*a^6*b^4*m^5*x^4+1348939620*a^5*b^5*m^4*x^5+2581262040*a^4*b^6*m^3*x^6+2047105440*a^3*b^7*m^2*x^7
+580543200*a^2*b^8*m*x^8+39916800*a*b^9*x^9+1860*a^10*m^8+290760*a^9*b*m^7*x+12376665*a^8*b^2*m^6*x^2+19479096
0*a^7*b^3*m^5*x^3+1263374700*a^6*b^4*m^4*x^4+3497286240*a^5*b^5*m^3*x^5+4035361680*a^4*b^6*m^2*x^6+1733313600*
a^3*b^7*m*x^7+199584000*a^2*b^8*x^8+30810*a^10*m^7+2992710*a^9*b*m^6*x+81560115*a^8*b^2*m^5*x^2+821580360*a^7*
b^3*m^4*x^3+3342229800*a^6*b^4*m^3*x^4+5541317712*a^5*b^5*m^2*x^5+3445243200*a^4*b^6*m*x^6+598752000*a^3*b^7*x
^7+326613*a^10*m^6+20390160*a^9*b*m^5*x+355598730*a^8*b^2*m^4*x^2+2233166160*a^7*b^3*m^3*x^3+5393046960*a^6*b^
4*m^2*x^4+4783423680*a^5*b^5*m*x^5+1197504000*a^4*b^6*x^6+2310945*a^10*m^5+92615030*a^9*b*m^4*x+1003011660*a^8
*b^2*m^3*x^2+3698304480*a^7*b^3*m^2*x^3+4727540160*a^6*b^4*m*x^4+1676505600*a^5*b^5*x^5+11028590*a^10*m^4+2747
27240*a^9*b*m^3*x+1727578440*a^8*b^2*m^2*x^2+3316939200*a^7*b^3*m*x^3+1676505600*a^6*b^4*x^4+34967140*a^10*m^3
+503126280*a^9*b*m^2*x+1608573600*a^8*b^2*m*x^2+1197504000*a^7*b^3*x^3+70290936*a^10*m^2+502927200*a^9*b*m*x+5
98752000*a^8*b^2*x^2+80627040*a^10*m+199584000*a^9*b*x+39916800*a^10)/(11+m)/(10+m)/(9+m)/(8+m)/(7+m)/(6+m)/(5
+m)/(m+4)/(m+3)/(m+2)/(m+1)
________________________________________________________________________________________
maxima [A] time = 1.39, size = 187, normalized size = 1.00 \begin {gather*} \frac {b^{10} x^{m + 11}}{m + 11} + \frac {10 \, a b^{9} x^{m + 10}}{m + 10} + \frac {45 \, a^{2} b^{8} x^{m + 9}}{m + 9} + \frac {120 \, a^{3} b^{7} x^{m + 8}}{m + 8} + \frac {210 \, a^{4} b^{6} x^{m + 7}}{m + 7} + \frac {252 \, a^{5} b^{5} x^{m + 6}}{m + 6} + \frac {210 \, a^{6} b^{4} x^{m + 5}}{m + 5} + \frac {120 \, a^{7} b^{3} x^{m + 4}}{m + 4} + \frac {45 \, a^{8} b^{2} x^{m + 3}}{m + 3} + \frac {10 \, a^{9} b x^{m + 2}}{m + 2} + \frac {a^{10} x^{m + 1}}{m + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(x^m*(b*x+a)^10,x, algorithm="maxima")
[Out]
b^10*x^(m + 11)/(m + 11) + 10*a*b^9*x^(m + 10)/(m + 10) + 45*a^2*b^8*x^(m + 9)/(m + 9) + 120*a^3*b^7*x^(m + 8)
/(m + 8) + 210*a^4*b^6*x^(m + 7)/(m + 7) + 252*a^5*b^5*x^(m + 6)/(m + 6) + 210*a^6*b^4*x^(m + 5)/(m + 5) + 120
*a^7*b^3*x^(m + 4)/(m + 4) + 45*a^8*b^2*x^(m + 3)/(m + 3) + 10*a^9*b*x^(m + 2)/(m + 2) + a^10*x^(m + 1)/(m + 1
)
________________________________________________________________________________________
mupad [B] time = 1.37, size = 1274, normalized size = 6.81
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(x^m*(a + b*x)^10,x)
[Out]
(a^10*x*x^m*(80627040*m + 70290936*m^2 + 34967140*m^3 + 11028590*m^4 + 2310945*m^5 + 326613*m^6 + 30810*m^7 +
1860*m^8 + 65*m^9 + m^10 + 39916800))/(120543840*m + 150917976*m^2 + 105258076*m^3 + 45995730*m^4 + 13339535*m
^5 + 2637558*m^6 + 357423*m^7 + 32670*m^8 + 1925*m^9 + 66*m^10 + m^11 + 39916800) + (b^10*x^m*x^11*(10628640*m
+ 12753576*m^2 + 8409500*m^3 + 3416930*m^4 + 902055*m^5 + 157773*m^6 + 18150*m^7 + 1320*m^8 + 55*m^9 + m^10 +
3628800))/(120543840*m + 150917976*m^2 + 105258076*m^3 + 45995730*m^4 + 13339535*m^5 + 2637558*m^6 + 357423*m
^7 + 32670*m^8 + 1925*m^9 + 66*m^10 + m^11 + 39916800) + (45*a^2*b^8*x^m*x^9*(12900960*m + 15335224*m^2 + 9991
428*m^3 + 4000478*m^4 + 1037673*m^5 + 177765*m^6 + 19962*m^7 + 1412*m^8 + 57*m^9 + m^10 + 4435200))/(120543840
*m + 150917976*m^2 + 105258076*m^3 + 45995730*m^4 + 13339535*m^5 + 2637558*m^6 + 357423*m^7 + 32670*m^8 + 1925
*m^9 + 66*m^10 + m^11 + 39916800) + (120*a^3*b^7*x^m*x^8*(14444280*m + 17059212*m^2 + 11024858*m^3 + 4371359*m
^4 + 1121022*m^5 + 189567*m^6 + 20982*m^7 + 1461*m^8 + 58*m^9 + m^10 + 4989600))/(120543840*m + 150917976*m^2
+ 105258076*m^3 + 45995730*m^4 + 13339535*m^5 + 2637558*m^6 + 357423*m^7 + 32670*m^8 + 1925*m^9 + 66*m^10 + m^
11 + 39916800) + (210*a^4*b^6*x^m*x^7*(16405920*m + 19216008*m^2 + 12291724*m^3 + 4814858*m^4 + 1217811*m^5 +
202821*m^6 + 22086*m^7 + 1512*m^8 + 59*m^9 + m^10 + 5702400))/(120543840*m + 150917976*m^2 + 105258076*m^3 + 4
5995730*m^4 + 13339535*m^5 + 2637558*m^6 + 357423*m^7 + 32670*m^8 + 1925*m^9 + 66*m^10 + m^11 + 39916800) + (2
52*a^5*b^5*x^m*x^6*(18981840*m + 21989356*m^2 + 13878120*m^3 + 5352935*m^4 + 1331100*m^5 + 217743*m^6 + 23280*
m^7 + 1565*m^8 + 60*m^9 + m^10 + 6652800))/(120543840*m + 150917976*m^2 + 105258076*m^3 + 45995730*m^4 + 13339
535*m^5 + 2637558*m^6 + 357423*m^7 + 32670*m^8 + 1925*m^9 + 66*m^10 + m^11 + 39916800) + (210*a^6*b^4*x^m*x^5*
(22512096*m + 25681176*m^2 + 15915380*m^3 + 6016070*m^4 + 1464693*m^5 + 234573*m^6 + 24570*m^7 + 1620*m^8 + 61
*m^9 + m^10 + 7983360))/(120543840*m + 150917976*m^2 + 105258076*m^3 + 45995730*m^4 + 13339535*m^5 + 2637558*m
^6 + 357423*m^7 + 32670*m^8 + 1925*m^9 + 66*m^10 + m^11 + 39916800) + (120*a^7*b^3*x^m*x^4*(27641160*m + 30819
204*m^2 + 18609718*m^3 + 6846503*m^4 + 1623258*m^5 + 253575*m^6 + 25962*m^7 + 1677*m^8 + 62*m^9 + m^10 + 99792
00))/(120543840*m + 150917976*m^2 + 105258076*m^3 + 45995730*m^4 + 13339535*m^5 + 2637558*m^6 + 357423*m^7 + 3
2670*m^8 + 1925*m^9 + 66*m^10 + m^11 + 39916800) + (45*a^8*b^2*x^m*x^3*(35746080*m + 38390632*m^2 + 22289148*m
^3 + 7902194*m^4 + 1812447*m^5 + 275037*m^6 + 27462*m^7 + 1736*m^8 + 63*m^9 + m^10 + 13305600))/(120543840*m +
150917976*m^2 + 105258076*m^3 + 45995730*m^4 + 13339535*m^5 + 2637558*m^6 + 357423*m^7 + 32670*m^8 + 1925*m^9
+ 66*m^10 + m^11 + 39916800) + (10*a*b^9*x^m*x^10*(11655216*m + 13926276*m^2 + 9133180*m^3 + 3686255*m^4 + 96
5328*m^5 + 167223*m^6 + 19020*m^7 + 1365*m^8 + 56*m^9 + m^10 + 3991680))/(120543840*m + 150917976*m^2 + 105258
076*m^3 + 45995730*m^4 + 13339535*m^5 + 2637558*m^6 + 357423*m^7 + 32670*m^8 + 1925*m^9 + 66*m^10 + m^11 + 399
16800) + (10*a^9*b*x^m*x^2*(50292720*m + 50312628*m^2 + 27472724*m^3 + 9261503*m^4 + 2039016*m^5 + 299271*m^6
+ 29076*m^7 + 1797*m^8 + 64*m^9 + m^10 + 19958400))/(120543840*m + 150917976*m^2 + 105258076*m^3 + 45995730*m^
4 + 13339535*m^5 + 2637558*m^6 + 357423*m^7 + 32670*m^8 + 1925*m^9 + 66*m^10 + m^11 + 39916800)
________________________________________________________________________________________
sympy [A] time = 6.93, size = 9996, normalized size = 53.45
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(x**m*(b*x+a)**10,x)
[Out]
Piecewise((-a**10/(10*x**10) - 10*a**9*b/(9*x**9) - 45*a**8*b**2/(8*x**8) - 120*a**7*b**3/(7*x**7) - 35*a**6*b
**4/x**6 - 252*a**5*b**5/(5*x**5) - 105*a**4*b**6/(2*x**4) - 40*a**3*b**7/x**3 - 45*a**2*b**8/(2*x**2) - 10*a*
b**9/x + b**10*log(x), Eq(m, -11)), (-a**10/(9*x**9) - 5*a**9*b/(4*x**8) - 45*a**8*b**2/(7*x**7) - 20*a**7*b**
3/x**6 - 42*a**6*b**4/x**5 - 63*a**5*b**5/x**4 - 70*a**4*b**6/x**3 - 60*a**3*b**7/x**2 - 45*a**2*b**8/x + 10*a
*b**9*log(x) + b**10*x, Eq(m, -10)), (-a**10/(8*x**8) - 10*a**9*b/(7*x**7) - 15*a**8*b**2/(2*x**6) - 24*a**7*b
**3/x**5 - 105*a**6*b**4/(2*x**4) - 84*a**5*b**5/x**3 - 105*a**4*b**6/x**2 - 120*a**3*b**7/x + 45*a**2*b**8*lo
g(x) + 10*a*b**9*x + b**10*x**2/2, Eq(m, -9)), (-a**10/(7*x**7) - 5*a**9*b/(3*x**6) - 9*a**8*b**2/x**5 - 30*a*
*7*b**3/x**4 - 70*a**6*b**4/x**3 - 126*a**5*b**5/x**2 - 210*a**4*b**6/x + 120*a**3*b**7*log(x) + 45*a**2*b**8*
x + 5*a*b**9*x**2 + b**10*x**3/3, Eq(m, -8)), (-a**10/(6*x**6) - 2*a**9*b/x**5 - 45*a**8*b**2/(4*x**4) - 40*a*
*7*b**3/x**3 - 105*a**6*b**4/x**2 - 252*a**5*b**5/x + 210*a**4*b**6*log(x) + 120*a**3*b**7*x + 45*a**2*b**8*x*
*2/2 + 10*a*b**9*x**3/3 + b**10*x**4/4, Eq(m, -7)), (-a**10/(5*x**5) - 5*a**9*b/(2*x**4) - 15*a**8*b**2/x**3 -
60*a**7*b**3/x**2 - 210*a**6*b**4/x + 252*a**5*b**5*log(x) + 210*a**4*b**6*x + 60*a**3*b**7*x**2 + 15*a**2*b*
*8*x**3 + 5*a*b**9*x**4/2 + b**10*x**5/5, Eq(m, -6)), (-a**10/(4*x**4) - 10*a**9*b/(3*x**3) - 45*a**8*b**2/(2*
x**2) - 120*a**7*b**3/x + 210*a**6*b**4*log(x) + 252*a**5*b**5*x + 105*a**4*b**6*x**2 + 40*a**3*b**7*x**3 + 45
*a**2*b**8*x**4/4 + 2*a*b**9*x**5 + b**10*x**6/6, Eq(m, -5)), (-a**10/(3*x**3) - 5*a**9*b/x**2 - 45*a**8*b**2/
x + 120*a**7*b**3*log(x) + 210*a**6*b**4*x + 126*a**5*b**5*x**2 + 70*a**4*b**6*x**3 + 30*a**3*b**7*x**4 + 9*a*
*2*b**8*x**5 + 5*a*b**9*x**6/3 + b**10*x**7/7, Eq(m, -4)), (-a**10/(2*x**2) - 10*a**9*b/x + 45*a**8*b**2*log(x
) + 120*a**7*b**3*x + 105*a**6*b**4*x**2 + 84*a**5*b**5*x**3 + 105*a**4*b**6*x**4/2 + 24*a**3*b**7*x**5 + 15*a
**2*b**8*x**6/2 + 10*a*b**9*x**7/7 + b**10*x**8/8, Eq(m, -3)), (-a**10/x + 10*a**9*b*log(x) + 45*a**8*b**2*x +
60*a**7*b**3*x**2 + 70*a**6*b**4*x**3 + 63*a**5*b**5*x**4 + 42*a**4*b**6*x**5 + 20*a**3*b**7*x**6 + 45*a**2*b
**8*x**7/7 + 5*a*b**9*x**8/4 + b**10*x**9/9, Eq(m, -2)), (a**10*log(x) + 10*a**9*b*x + 45*a**8*b**2*x**2/2 + 4
0*a**7*b**3*x**3 + 105*a**6*b**4*x**4/2 + 252*a**5*b**5*x**5/5 + 35*a**4*b**6*x**6 + 120*a**3*b**7*x**7/7 + 45
*a**2*b**8*x**8/8 + 10*a*b**9*x**9/9 + b**10*x**10/10, Eq(m, -1)), (a**10*m**10*x*x**m/(m**11 + 66*m**10 + 192
5*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*
m**2 + 120543840*m + 39916800) + 65*a**10*m**9*x*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7
+ 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) +
1860*a**10*m**8*x*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5
+ 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 30810*a**10*m**7*x*x**m/(m**11
+ 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m
**3 + 150917976*m**2 + 120543840*m + 39916800) + 326613*a**10*m**6*x*x**m/(m**11 + 66*m**10 + 1925*m**9 + 3267
0*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543
840*m + 39916800) + 2310945*a**10*m**5*x*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 26375
58*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 11028590
*a**10*m**4*x*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 4
5995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 34967140*a**10*m**3*x*x**m/(m**11 +
66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m*
*3 + 150917976*m**2 + 120543840*m + 39916800) + 70290936*a**10*m**2*x*x**m/(m**11 + 66*m**10 + 1925*m**9 + 326
70*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 12054
3840*m + 39916800) + 80627040*a**10*m*x*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 263755
8*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 39916800*
a**10*x*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 4599573
0*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 10*a**9*b*m**10*x**2*x**m/(m**11 + 66*m**
10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 15
0917976*m**2 + 120543840*m + 39916800) + 640*a**9*b*m**9*x**2*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8
+ 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m +
39916800) + 17970*a**9*b*m**8*x**2*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m*
*6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 290760*a**9*b
*m**7*x**2*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 4599
5730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 2992710*a**9*b*m**6*x**2*x**m/(m**11 +
66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m*
*3 + 150917976*m**2 + 120543840*m + 39916800) + 20390160*a**9*b*m**5*x**2*x**m/(m**11 + 66*m**10 + 1925*m**9 +
32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 1
20543840*m + 39916800) + 92615030*a**9*b*m**4*x**2*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m*
*7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800)
+ 274727240*a**9*b*m**3*x**2*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13
339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 503126280*a**9*b*m**
2*x**2*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730
*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 502927200*a**9*b*m*x**2*x**m/(m**11 + 66*m
**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 +
150917976*m**2 + 120543840*m + 39916800) + 199584000*a**9*b*x**2*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m*
*8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*
m + 39916800) + 45*a**8*b**2*m**10*x**3*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 263755
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*3 + 150917976*m**2 + 120543840*m + 39916800) + 180021510*a**2*b**8*m**4*x**9*x**m/(m**11 + 66*m**10 + 1925*m*
*9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2
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57423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39
916800) + 690085080*a**2*b**8*m**2*x**9*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 263755
8*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 580543200
*a**2*b**8*m*x**9*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5
+ 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 199584000*a**2*b**8*x**9*x**m/(
m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 10525
8076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 10*a*b**9*m**10*x**10*x**m/(m**11 + 66*m**10 + 1925*m**
9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2
+ 120543840*m + 39916800) + 560*a*b**9*m**9*x**10*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**
7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) +
13650*a*b**9*m**8*x**10*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 133395
35*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 190200*a*b**9*m**7*x**10
*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4
+ 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 1672230*a*b**9*m**6*x**10*x**m/(m**11 + 66*m**10
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*8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*
m + 39916800) + 36862550*a*b**9*m**4*x**10*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 263
7558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 913318
00*a*b**9*m**3*x**10*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m
**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 139262760*a*b**9*m**2*x**10*
x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 +
105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 116552160*a*b**9*m*x**10*x**m/(m**11 + 66*m**10 +
1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917
976*m**2 + 120543840*m + 39916800) + 39916800*a*b**9*x**10*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 3
57423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39
916800) + b**10*m**10*x**11*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 133
39535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 55*b**10*m**9*x**11*x
**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 +
105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 1320*b**10*m**8*x**11*x**m/(m**11 + 66*m**10 + 192
5*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*
m**2 + 120543840*m + 39916800) + 18150*b**10*m**7*x**11*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 3574
23*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916
800) + 157773*b**10*m**6*x**11*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 +
13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 902055*b**10*m**5*
x**11*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*
m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 3416930*b**10*m**4*x**11*x**m/(m**11 + 66*m
**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 +
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*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 1205438
40*m + 39916800) + 12753576*b**10*m**2*x**11*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2
637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 1062
8640*b**10*m*x**11*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**
5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 3628800*b**10*x**11*x**m/(m**1
1 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076
*m**3 + 150917976*m**2 + 120543840*m + 39916800), True))
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