3.7.99 \(\int x^m (a+b x)^{10} \, dx\) [699]
Optimal. Leaf size=187 \[ \frac {a^{10} x^{1+m}}{1+m}+\frac {10 a^9 b x^{2+m}}{2+m}+\frac {45 a^8 b^2 x^{3+m}}{3+m}+\frac {120 a^7 b^3 x^{4+m}}{4+m}+\frac {210 a^6 b^4 x^{5+m}}{5+m}+\frac {252 a^5 b^5 x^{6+m}}{6+m}+\frac {210 a^4 b^6 x^{7+m}}{7+m}+\frac {120 a^3 b^7 x^{8+m}}{8+m}+\frac {45 a^2 b^8 x^{9+m}}{9+m}+\frac {10 a b^9 x^{10+m}}{10+m}+\frac {b^{10} x^{11+m}}{11+m} \]
[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)
________________________________________________________________________________________
Rubi [A]
time = 0.06, 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 = {45}
\begin {gather*} \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} \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 45
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*}
________________________________________________________________________________________
Mathematica [A]
time = 0.18, size = 166, normalized size = 0.89 \begin {gather*} x^{1+m} \left (\frac {a^{10}}{1+m}+\frac {10 a^9 b x}{2+m}+\frac {45 a^8 b^2 x^2}{3+m}+\frac {120 a^7 b^3 x^3}{4+m}+\frac {210 a^6 b^4 x^4}{5+m}+\frac {252 a^5 b^5 x^5}{6+m}+\frac {210 a^4 b^6 x^6}{7+m}+\frac {120 a^3 b^7 x^7}{8+m}+\frac {45 a^2 b^8 x^8}{9+m}+\frac {10 a b^9 x^9}{10+m}+\frac {b^{10} x^{10}}{11+m}\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))
________________________________________________________________________________________
Mathics [C] Result contains higher order function than in optimal. Order 9 vs. order 3 in
optimal.
time = 8.78, size = 9691, normalized size = 51.82
result too large to display
Antiderivative was successfully verified.
[In]
mathics('Integrate[x^m*(a + b*x)^10,x]')
[Out]
Piecewise[{{(-252 a ^ 10 - 2800 a ^ 9 b x - 14175 a ^ 8 b ^ 2 x ^ 2 - 43200 a ^ 7 b ^ 3 x ^ 3 - 88200 a ^ 6 b
^ 4 x ^ 4 - 127008 a ^ 5 b ^ 5 x ^ 5 - 132300 a ^ 4 b ^ 6 x ^ 6 - 100800 a ^ 3 b ^ 7 x ^ 7 - 56700 a ^ 2 b ^ 8
x ^ 8 - 25200 a b ^ 9 x ^ 9 + 2520 b ^ 10 x ^ 10 Log[x]) / (2520 x ^ 10), 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, m == -10}, {(-7 a ^ 10 - 80 a ^ 9 b x - 420 a ^ 8 b ^ 2 x ^ 2 - 1344 a ^ 7 b ^ 3 x ^ 3 - 2940 a ^ 6 b
^ 4 x ^ 4 - 4704 a ^ 5 b ^ 5 x ^ 5 - 5880 a ^ 4 b ^ 6 x ^ 6 - 6720 a ^ 3 b ^ 7 x ^ 7 + 28 b ^ 8 x ^ 8 (90 a ^
2 Log[x] + 20 a b x + b ^ 2 x ^ 2)) / (56 x ^ 8), 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, m == -8}, {(-2 a ^ 10
- 24 a ^ 9 b x - 135 a ^ 8 b ^ 2 x ^ 2 - 480 a ^ 7 b ^ 3 x ^ 3 - 1260 a ^ 6 b ^ 4 x ^ 4 - 3024 a ^ 5 b ^ 5 x
^ 5 + b ^ 6 x ^ 6 (2520 a ^ 4 Log[x] + 1440 a ^ 3 b x + 270 a ^ 2 b ^ 2 x ^ 2 + 40 a b ^ 3 x ^ 3 + 3 b ^ 4 x ^
4)) / (12 x ^ 6), m == -7}, {(-2 a ^ 10 - 25 a ^ 9 b x - 150 a ^ 8 b ^ 2 x ^ 2 - 600 a ^ 7 b ^ 3 x ^ 3 - 2100
a ^ 6 b ^ 4 x ^ 4 + b ^ 5 x ^ 5 (2520 a ^ 5 Log[x] + 2100 a ^ 4 b x + 600 a ^ 3 b ^ 2 x ^ 2 + 150 a ^ 2 b ^ 3
x ^ 3 + 25 a b ^ 4 x ^ 4 + 2 b ^ 5 x ^ 5)) / (10 x ^ 5), m == -6}, {(-3 a ^ 10 - 40 a ^ 9 b x - 270 a ^ 8 b ^
2 x ^ 2 - 1440 a ^ 7 b ^ 3 x ^ 3 + b ^ 4 x ^ 4 (2520 a ^ 6 Log[x] + 3024 a ^ 5 b x + 1260 a ^ 4 b ^ 2 x ^ 2 +
480 a ^ 3 b ^ 3 x ^ 3 + 135 a ^ 2 b ^ 4 x ^ 4 + 24 a b ^ 5 x ^ 5 + 2 b ^ 6 x ^ 6)) / (12 x ^ 4), 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, m == -4}, {(-28 a ^ 10 - 560 a ^ 9 b x + b ^ 2 x ^ 2 (2520 a ^ 8 Log[x] + 6720 a ^ 7 b x +
5880 a ^ 6 b ^ 2 x ^ 2 + 4704 a ^ 5 b ^ 3 x ^ 3 + 2940 a ^ 4 b ^ 4 x ^ 4 + 1344 a ^ 3 b ^ 5 x ^ 5 + 420 a ^ 2
b ^ 6 x ^ 6 + 80 a b ^ 7 x ^ 7 + 7 b ^ 8 x ^ 8)) / (56 x ^ 2), m == -3}, {(-a ^ 10 + b x (2520 a ^ 9 Log[x] +
11340 a ^ 8 b x + 15120 a ^ 7 b ^ 2 x ^ 2 + 17640 a ^ 6 b ^ 3 x ^ 3 + 15876 a ^ 5 b ^ 4 x ^ 4 + 10584 a ^ 4 b
^ 5 x ^ 5 + 5040 a ^ 3 b ^ 6 x ^ 6 + 1620 a ^ 2 b ^ 7 x ^ 7 + 315 a b ^ 8 x ^ 8 + 28 b ^ 9 x ^ 9) / 252) / x,
m == -2}, {a ^ 10 Log[x] + 10 a ^ 9 b x + 45 a ^ 8 b ^ 2 x ^ 2 / 2 + 40 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, m == -1}}, 39916800 a ^ 10 x x ^ m / (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) + 80627040 a ^ 10 m x x ^ m / (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) + 70290936 a ^ 10 m ^ 2 x x ^ m / (39916800 + 120543840 m + 150917976 m ^ 2 + 10525807
6 m ^ 3 + 45995730 m ^ 4 + 13339535 m ^ 5 + 2637558 m ^ 6 + 357423 m ^ 7 + 32670 m ^ 8 + 1925 m ^ 9 + 66 m ^ 1
0 + m ^ 11) + 34967140 a ^ 10 m ^ 3 x x ^ m / (39916800 + 120543840 m + 150917976 m ^ 2 + 105258076 m ^ 3 + 45
995730 m ^ 4 + 13339535 m ^ 5 + 2637558 m ^ 6 + 357423 m ^ 7 + 32670 m ^ 8 + 1925 m ^ 9 + 66 m ^ 10 + m ^ 11)
+ 11028590 a ^ 10 m ^ 4 x x ^ m / (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) + 2310945 a
^ 10 m ^ 5 x x ^ m / (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) + 326613 a ^ 10 m ^ 6 x x
^ m / (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) + 30810 a ^ 10 m ^ 7 x x ^ m / (3991680
0 + 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) + 1860 a ^ 10 m ^ 8 x x ^ m / (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) + 65 a ^ 10 m ^ 9 x x ^ m / (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) + a ^ 10 m ^ 10 x x ^ m / (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
) + 199584000 a ^ 9 b x ^ 2 x ^ m / (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) + 50292720
0 a ^ 9 b m x ^ 2 x ^ m / (39916800 + 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) + 503126280 a ^ 9 b
m ^ 2 x ^ 2 x ^ m / (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) + 274727240 a ^ 9 b m ^ 3
x ^ 2 x ^ m / (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) + 92615030 a ^ 9 b m ^ 4 x ^ 2 x
^ m / (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) + 20390160 a ^ 9 b m ^ 5 x ^ 2 x ^ m /
(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) + 2992710 a ^ 9 b m ^ 6 x ^ 2 x ^ m / (3991680
0 + 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) + 290760 a ^ 9 b m ^ 7 x ^ 2 x ^ m / (39916800 + 12054
3840 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) + 17970 a ^ 9 b m ^ 8 x ^ 2 x ^ m / (39916800 + 120543840 m + 1
50917976 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) + 640 a ^ 9 b m ^ 9 x ^ 2 x ^ m / (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) + 10 a ^ 9 b m ^ 10 x ^ 2 x ^ m / (39916800 + 120543840 m + 150917976 m ^ 2 + 1052580
76 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) + 598752000 a ^ 8 b ^ 2 x ^ 3 x ^ m / (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) + 1608573600 a ^ 8 b ^ 2 m x ^ 3 x ^ m / (39916800 + 120543840 m + 150917976 m ^ 2 + 105258076 m ^ 3 + 45
995730 m ^ 4 + 13339535 m ^ 5 + 2637558 m ^ 6 + 357423 m ^ 7 + 32670 m ^ 8 + 1925 m ^ 9 + 66 m ^ 10 + m ^ 11)
+ 1727578440 a ^ 8 b ^ 2 m ^ 2 x ^ 3 x ^ m / (39916800 + 120543840 m + 150917976 m ^ 2 + 105258076 m ^ 3 + 459
95730 m ^ 4 + 13339535 m ^ 5 + 2637558 m ^ 6 + 357423 m ^ 7 + 32670 m ^ 8 + 1925 m ^ 9 + 66 m ^ 10 + m ^ 11) +
1003011660 a ^ 8 b ^ 2 m ^ 3 x ^ 3 x ^ m / (39916800 + 120543840 m + 150917976 m ^ 2 + 105258076 m ^ 3 + 4599
5730 m ^ 4 + 13339535 m ^ 5 + 2637558 m ^ 6 + 357423 m ^ 7 + 32670 m ^ 8 + 1925 m ^ 9 + 66 m ^ 10 + m ^ 11) +
355598730 a ^ 8 b ^ 2 m ^ 4 x ^ 3 x ^ m / (39916800 + 120543840 m + 150917976 m ^ 2 + 105258076 m ^ 3 + 459957
30 m ^ 4 + 13339535 m ^ 5 + 2637558 m ^ 6 + 357423 m ^ 7 + 32670 m ^ 8 + 1925 m ^ 9 + 66 m ^ 10 + m ^ 11) + 81
560115 a ^ 8 b ^ 2 m ^ 5 x ^ 3 x ^ m / (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) + 12376
665 a ^ 8 b ^ 2 m ^ 6 x ^ 3 x ^ m / (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) + 1235790
a ^ 8 b ^ 2 m ^ 7 x ^ 3 x ^ m / (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) + 78120 a ^ 8
b ^ 2 m ^ 8 x ^ 3 x ^ m / (39916800 + 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) + 2835 a ^ 8 b ^ 2 m
^ 9 x ^ 3 x ^ m / (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) + 45 a ^ 8 b ^ 2 m ^ 10 x ^
3 x ^ m / (39916800 + 120543840 m + 150917976 m ^ 2 + 105258076 m ^ 3 + 45995730 m ^ 4 + 13339535 m ^ 5 + 263
7558 m ^ 6 + 357423 m ^ 7 + 32670 m ^ 8 + 1925 m ^ 9 + 66 m ^ 10 + m ^ 11) + 1197504000 a ^ 7 b ^ 3 x ^ 4 x ^
m / (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) + 3316939200 a ^ 7 b ^ 3 m x ^ 4 x ^ m / (
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) + 3698304480 a ^ 7 b ^ 3 m ^ 2 x ^ 4 x ^ m / (3
9916800 + 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) + 2233166160 a ^ 7 b ^ 3 m ^ 3 x ^ 4 x ^ m / (39
916800 + 120543840 m + 150917976 m ^ 2 + 105258076 m ^ 3 + 45995730 m ^ 4 + 13339535 m ^ 5 + 2637558 m ^ 6 + 3
57423 m ^ 7 + 32670 m ^ 8 + 1925 m ^ 9 + 66 m ^ 10 + m ^ 11) + 821580360 a ^ 7 b ^ 3 m ^ 4 x ^ 4 x ^ m / (3991
6800 + 120543840 m + 150917976 m ^ 2 + 105258076 m ^ 3 + 45995730 m ^ 4 + 13339535 m ^ 5 + 2637558 m ^ 6 + 357
423 m ^ 7 + 32670 m ^ 8 + 1925 m ^ 9 + 66 m ^ 10 + m ^ 11) + 194790960 a ^ 7 b ^ 3 m ^ 5 x ^ 4 x ^ m / (399168
00 + 120543840 m + 150917976 m ^ 2 + 105258076 m ^ 3 + 45995730 m ^ 4 + 13339535 m ^ 5 + 2637558 m ^ 6 + 35742
3 m ^ 7 + 32670 m ^ 8 + 1925 m ^ 9 + 66 m ^ 10 + m ^ 11) + 30429000 a ^ 7 b ^ 3 m ^ 6 x ^ 4 x ^ m / (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) + 3115440 a ^ 7 b ^ 3 m ^ 7 x ^ 4 x ^ m / (39916800 + 12
0543840 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) + 201240 a ^ 7 b ^ 3 m ^ 8 x ^ 4 x ^ m / (39916800 + 1205438
40 m + 150917976 m ^ 2 + 105258076 m ^ 3 + 45995730 m ^ 4 + 13339535 m ^ 5 + 2637558 m ^ 6 + 357423 m ^ 7 + 32
670 m ^ 8 + 1925 m ^ 9 + 66 m ^ 10 + m ^ 11) + 7440 a ^ 7 b ^ 3 m ^ 9 x ^ 4 x ^ m / (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) + 120 a ^ 7 b ^ 3 m ^ 10 x ^ 4 x ^ m / (39916800 + 120543840 m + 1509179
76 m ^ 2 + 105258076 m ^ 3 + 45995730 m ^ 4 + 13339535 m ^ 5 + 2637558 m ^ 6 + 357423 m ^ 7 + 32670 m ^ 8 + 19
25 m ^ 9 + 66 m ^ 10 + m ^ 11) + 1676505600 a ^ 6 b ^ 4 x ^ 5 x ^ m / (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) + 4727540160 a ^ 6 b ^ 4 m x ^ 5 x ^ m / (39916800 + 120543840 m + 150917976 m ^ 2 + 1
05258076 m ^ 3 + 45995730 m ^ 4 + 13339535 m ^ 5 + 2637558 m ^ 6 + 357423 m ^ 7 + 32670 m ^ 8 + 1925 m ^ 9 + 6
6 m ^ 10 + m ^ 11) + 5393046960 a ^ 6 b ^ 4 m ^ 2 x ^ 5 x ^ m / (39916800 + 120543840 m + 150917976 m ^ 2 + 10
5258076 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) + 3342229800 a ^ 6 b ^ 4 m ^ 3 x ^ 5 x ^ m / (39916800 + 120543840 m + 150917976 m ^ 2 + 105
258076 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) + 1263374700 a ^ 6 b ^ 4 m ^ 4 x ^ 5 x ^ m / (39916800 + 120543840 m + 150917976 m ^ 2 + 1052
58076 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) + 307585530 a ^ 6 b ^ 4 m ^ 5 x ^ 5 x ^ m / (39916800 + 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) + 49260330 a ^ 6 b ^ 4 m ^ 6 x ^ 5 x ^ m / (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) + 5159700 a ^ 6 b ^ 4 m ^ 7 x ^ 5 x ^ m / (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) + 340200 a ^ 6 b ^ 4 m ^ 8 x ^ 5 x ^ m / (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
) + 12810 a ^ 6 b ^ 4 m ^ 9 x ^ 5 x ^ m / (39916800 + 120543840 m + 150917976 m ^ 2 + 105258076 m ^ 3 + 459957
30 m ^ 4 + 13339535 m ^ 5 + 2637558 m ^ 6 + 357423 m ^ 7 + 32670 m ^ 8 + 1925 m ^ 9 + 66 m ^ 10 + m ^ 11) + 21
0 a ^ 6 b ^ 4 m ^ 10 x ^ 5 x ^ m / (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) + 167650560
0 a ^ 5 b ^ 5 x ^ 6 x ^ m / (39916800 + 120543840 m + 150917976 m ^ 2 + 105258076 m ^ 3 + 45995730 m ^ 4 + 133
39535 m ^ 5 + 2637558 m ^ 6 + 357423 m ^ 7 + 32670 m ^ 8 + 1925 m ^ 9 + 66 m ^ 10 + m ^ 11) + 4783423680 a ^ 5
b ^ 5 m x ^ 6 x ^ m / (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) + 5541317712 a ^ 5 b ^
5 m ^ 2 x ^ 6 x ^ m / (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) + 3497286240 a ^ 5 b ^ 5
m ^ 3 x ^ 6 x ^ m / (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) + 1348939620 a ^ 5 b ^ 5
m ^ 4 x ^ 6 x ^ m / (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) + 335437200 a ^ 5 b ^ 5 m
^ 5 x ^ 6 x ^ m / (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) + 54871236 a ^ 5 b ^ 5 m ^ 6
x ^ 6 x ^ m / (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) + 5866560 a ^ 5 b ^ 5 m ^ 7 x ^
6 x ^ m / (39916800 + 120543840 m + 150917976 m ^ 2 + 105258076 m ^ 3 + 45995730 m ^ 4 + 13339535 m ^ 5 + 263
7558 m ^ 6 + 357423 m ^ 7 + 32670 m ^ 8 + 1925 m ^ 9 + 66 m ^ 10 + m ^ 11) + 394380 a ^ 5 b ^ 5 m ^ 8 x ^ 6 x
^ m / (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) + 15120 a ^ 5 b ^ 5 m ^ 9 x ^ 6 x ^ m /
(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) + 252 a ^ 5 b ^ 5 m ^ 10 x ^ 6 x ^ m / (399168
00 + 120543840 m + 150917976 m ^ 2 + 105258076 m ^ 3 + 45995730 m ^ 4 + 13339535 m ^ 5 + 2637558 m ^ 6 + 35742
3 m ^ 7 + 32670 m ^ 8 + 1925 m ^ 9 + 66 m ^ 10 + m ^ 11) + 1197504000 a ^ 4 b ^ 6 x ^ 7 x ^ m / (39916800 + 12
0543840 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) + 3445243200 a ^ 4 b ^ 6 m x ^ 7 x ^ m / (39916800 + 1205438
40 m + 150917976 m ^ 2 + 105258076 m ^ 3 + 45995730 m ^ 4 + 13339535 m ^ 5 + 2637558 m ^ 6 + 357423 m ^ 7 + 32
670 m ^ 8 + 1925 m ^ 9 + 66 m ^ 10 + m ^ 11) + 4035361680 a ^ 4 b ^ 6 m ^ 2 x ^ 7 x ^ m / (39916800 + 12054384
0 m + 150917976 m ^ 2 + 105258076 m ^ 3 + 45995730 m ^ 4 + 13339535 m ^ 5 + 2637558 m ^ 6 + 357423 m ^ 7 + 326
70 m ^ 8 + 1925 m ^ 9 + 66 m ^ 10 + m ^ 11) + 2581262040 a ^ 4 b ^ 6 m ^ 3 x ^ 7 x ^ m / (39916800 + 120543840
m + 150917976 m ^ 2 + 105258076 m ^ 3 + 45995730 m ^ 4 + 13339535 m ^ 5 + 2637558 m ^ 6 + 357423 m ^ 7 + 3267
0 m ^ 8 + 1925 m ^ 9 + 66 m ^ 10 + m ^ 11) + 1011120180 a ^ 4 b ^ 6 m ^ 4 x ^ 7 x ^ m / (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) + 255740310 a ^ 4 b ^ 6 m ^ 5 x ^ 7 x ^ m / (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) + 42592410 a ^ 4 b ^ 6 m ^ 6 x ^ 7 x ^ m / (39916800 + 120543840 m + 1
50917976 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) + 4638060 a ^ 4 b ^ 6 m ^ 7 x ^ 7 x ^ m / (39916800 + 120543840 m + 15091
7976 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) + 317520 a ^ 4 b ^ 6 m ^ 8 x ^ 7 x ^ m / (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) + 12390 a ^ 4 b ^ 6 m ^ 9 x ^ 7 x ^ m / (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) + 210 a ^ 4 b ^ 6 m ^ 10 x ^ 7 x ^ m / (39916800 + 120543840 m + 150917976 m ^ 2 + 10525
8076 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) + 598752000 a ^ 3 b ^ 7 x ^ 8 x ^ m / (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) + 1733313600 a ^ 3 b ^ 7 m x ^ 8 x ^ m / (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
) + 2047105440 a ^ 3 b ^ 7 m ^ 2 x ^ 8 x ^ m / (39916800 + 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)
+ 1322982960 a ^ 3 b ^ 7 m ^ 3 x ^ 8 x ^ m / (39916800 + 120543840 m + 150917976 m ^ 2 + 105258076 m ^ 3 + 45
995730 m ^ 4 + 13339535 m ^ 5 + 2637558 m ^ 6 + 357423 m ^ 7 + 32670 m ^ 8 + 1925 m ^ 9 + 66 m ^ 10 + m ^ 11)
+ 524563080 a ^ 3 b ^ 7 m ^ 4 x ^ 8 x ^ m / (39916800 + 120543840 m + 150917976 m ^ 2 + 105258076 m ^ 3 + 4599
5730 m ^ 4 + 13339535 m ^ 5 + 2637558 m ^ 6 + 357423 m ^ 7 + 32670 m ^ 8 + 1925 m ^ 9 + 66 m ^ 10 + m ^ 11) +
134522640 a ^ 3 b ^ 7 m ^ 5 x ^ 8 x ^ m / (39916800 + 120543840 m + 150917976 m ^ 2 + 105258076 m ^ 3 + 459957
30 m ^ 4 + 13339535 m ^ 5 + 2637558 m ^ 6 + 357423 m ^ 7 + 32670 m ^ 8 + 1925 m ^ 9 + 66 m ^ 10 + m ^ 11) + 22
748040 a ^ 3 b ^ 7 m ^ 6 x ^ 8 x ^ m / (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) + 25178
40 a ^ 3 b ^ 7 m ^ 7 x ^ 8 x ^ m / (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) + 175320 a
^ 3 b ^ 7 m ^ 8 x ^ 8 x ^ m / (39916800 + 120543840 m + 150917976 m ^ 2 + 105258076 m ^ 3 + 45995730 m ^ 4 + 1
3339535 m ^ 5 + 2637558 m ^ 6 + 357423 m ^ 7 + 32670 m ^ 8 + 1925 m ^ 9 + 66 m ^ 10 + m ^ 11) + 6960 a ^ 3 b ^
7 m ^ 9 x ^ 8 x ^ m / (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) + 120 a ^ 3 b ^ 7 m ^ 1
0 x ^ 8 x ^ m / (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) + 199584000 a ^ 2 b ^ 8 x ^ 9
x ^ m / (39916800 + 120543840 m + 150917976 m ^ 2 + 105258076 m ^ 3 + 45995730 m ^ 4 + 13339535 m ^ 5 + 263755
8 m ^ 6 + 357423 m ^ 7 + 32670 m ^ 8 + 1925 m ^ 9 + 66 m ^ 10 + m ^ 11) + 580543200 a ^ 2 b ^ 8 m x ^ 9 x ^ m
/ (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) + 690085080 a ^ 2 b ^ 8 m ^ 2 x ^ 9 x ^ m /
(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) + 449614260 a ^ 2 b ^ 8 m ^ 3 x ^ 9 x ^ m / (3
9916800 + 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) + 180021510 a ^ 2 b ^ 8 m ^ 4 x ^ 9 x ^ m / (399
16800 + 120543840 m + 150917976 m ^ 2 + 105258076 m ^ 3 + 45995730 m ^ 4 + 13339535 m ^ 5 + 2637558 m ^ 6 + 35
7423 m ^ 7 + 32670 m ^ 8 + 1925 m ^ 9 + 66 m ^ 10 + m ^ 11) + 46695285 a ^ 2 b ^ 8 m ^ 5 x ^ 9 x ^ m / (399168
00 + 120543840 m + 150917976 m ^ 2 + 105258076 m ^ 3 + 45995730 m ^ 4 + 13339535 m ^ 5 + 2637558 m ^ 6 + 35742
3 m ^ 7 + 32670 m ^ 8 + 1925 m ^ 9 + 66 m ^ 10 + m ^ 11) + 7999425 a ^ 2 b ^ 8 m ^ 6 x ^ 9 x ^ m / (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) + 898290 a ^ 2 b ^ 8 m ^ 7 x ^ 9 x ^ m / (39916800 + 1205
43840 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) + 63540 a ^ 2 b ^ 8 m ^ 8 x ^ 9 x ^ m / (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) + 2565 a ^ 2 b ^ 8 m ^ 9 x ^ 9 x ^ m / (39916800 + 120543840 m + 150
917976 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) + 45 a ^ 2 b ^ 8 m ^ 10 x ^ 9 x ^ m / (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 a b ^ 9 x ^ 10 x ^ m / (39916800 + 120543840 m + 150917976 m ^ 2 + 10525
8076 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) + 116552160 a b ^ 9 m x ^ 10 x ^ m / (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) + 139262760 a b ^ 9 m ^ 2 x ^ 10 x ^ m / (39916800 + 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)
+ 91331800 a b ^ 9 m ^ 3 x ^ 10 x ^ m / (39916800 + 120543840 m + 150917976 m ^ 2 + 105258076 m ^ 3 + 4599573
0 m ^ 4 + 13339535 m ^ 5 + 2637558 m ^ 6 + 357423 m ^ 7 + 32670 m ^ 8 + 1925 m ^ 9 + 66 m ^ 10 + m ^ 11) + 368
62550 a b ^ 9 m ^ 4 x ^ 10 x ^ m / (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) + 9653280 a
b ^ 9 m ^ 5 x ^ 10 x ^ m / (39916800 + 120543840 m + 150917976 m ^ 2 + 105258076 m ^ 3 + 45995730 m ^ 4 + 133
39535 m ^ 5 + 2637558 m ^ 6 + 357423 m ^ 7 + 32670 m ^ 8 + 1925 m ^ 9 + 66 m ^ 10 + m ^ 11) + 1672230 a b ^ 9
m ^ 6 x ^ 10 x ^ m / (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) + 190200 a b ^ 9 m ^ 7 x
^ 10 x ^ m / (39916800 + 120543840 m + 150917976 m ^ 2 + 105258076 m ^ 3 + 45995730 m ^ 4 + 13339535 m ^ 5 + 2
637558 m ^ 6 + 357423 m ^ 7 + 32670 m ^ 8 + 1925 m ^ 9 + 66 m ^ 10 + m ^ 11) + 13650 a b ^ 9 m ^ 8 x ^ 10 x ^
m / (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) + 560 a b ^ 9 m ^ 9 x ^ 10 x ^ m / (399168
00 + 120543840 m + 150917976 m ^ 2 + 105258076 m ^ 3 + 45995730 m ^ 4 + 13339535 m ^ 5 + 2637558 m ^ 6 + 35742
3 m ^ 7 + 32670 m ^ 8 + 1925 m ^ 9 + 66 m ^ 10 + m ^ 11) + 10 a b ^ 9 m ^ 10 x ^ 10 x ^ m / (39916800 + 120543
840 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) + 3628800 b ^ 10 x ^ 11 x ^ m / (39916800 + 120543840 m + 150917
976 m ^ 2 + 105258076 m ^ 3 + 45995730 m ^ 4 + 13339535 m ^ 5 + 2637558 m ^ 6 + 357423 m ^ 7 + 32670 m ^ 8 + 1
925 m ^ 9 + 66 m ^ 10 + m ^ 11) + 10628640 b ^ 10 m x ^ 11 x ^ m / (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) + 12753576 b ^ 10 m ^ 2 x ^ 11 x ^ m / (39916800 + 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) + 8409500 b ^ 10 m ^ 3 x ^ 11 x ^ m / (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) + 3416930 b ^ 10 m ^ 4 x ^ 11 x ^ m / (39916800 + 120543840 m + 150917976 m ^ 2 + 105258076 m ^ 3 + 4599
5730 m ^ 4 + 13339535 m ^ 5 + 2637558 m ^ 6 + 357423 m ^ 7 + 32670 m ^ 8 + 1925 m ^ 9 + 66 m ^ 10 + m ^ 11) +
902055 b ^ 10 m ^ 5 x ^ 11 x ^ m / (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) + 157773 b
^ 10 m ^ 6 x ^ 11 x ^ m / (39916800 + 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) + 18150 b ^ 10 m ^ 7
x ^ 11 x ^ m / (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) + 1320 b ^ 10 m ^ 8 x ^ 11 x ^
m / (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) + 55 b ^ 10 m ^ 9 x ^ 11 x ^ m / (3991680
0 + 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) + b ^ 10 m ^ 10 x ^ 11 x ^ m / (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)]
________________________________________________________________________________________
Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(1533\) vs.
\(2(187)=374\).
time = 0.11, size = 1534, normalized size = 8.20
| | |
| method |
result |
size |
| | |
| risch |
\(\text {Expression too large to display}\) |
\(1534\) |
| gosper |
\(\text {Expression too large to display}\) |
\(1535\) |
| | |
|
|
|
|
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(x^m*(b*x+a)^10,x,method=_RETURNVERBOSE)
[Out]
x*(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+6960*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+965328
0*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+463806
0*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+2557403
10*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+3354372
00*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+116552160*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+30
7585530*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+58054
3200*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+194790960*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+326
613*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+274727240*
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+50312
6280*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+5987520
00*a^8*b^2*x^2+80627040*a^10*m+199584000*a^9*b*x+39916800*a^10)*x^m/(11+m)/(10+m)/(9+m)/(8+m)/(7+m)/(6+m)/(5+m
)/(4+m)/(3+m)/(2+m)/(1+m)
________________________________________________________________________________________
Maxima [A]
time = 0.27, 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
)
________________________________________________________________________________________
Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 1277 vs.
\(2 (187) = 374\).
time = 0.33, 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)
________________________________________________________________________________________
Sympy [A]
time = 1.23, 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*
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95730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 45*a**2*b**8*m**10*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) + 2565*a**2*b**8*m**9*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 + 12
0543840*m + 39916800) + 63540*a**2*b**8*m**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 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) +
898290*a**2*b**8*m**7*x**9*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) + 7999425*a**2*b**8*m**
6*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) + 46695285*a**2*b**8*m**5*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) + 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
+ 120543840*m + 39916800) + 449614260*a**2*b**8*m**3*x**9*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) + 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
+ 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 1509
17976*m**2 + 120543840*m + 39916800) + 9653280*a*b**9*m**5*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) + 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 +
150917976*m**2 + 120543840*m + 39916800) + 8409500*b**10*m**3*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 + 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))
________________________________________________________________________________________
Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 1925 vs.
\(2 (187) = 374\).
time = 0.02, size = 2166, normalized size = 11.58
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]
(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)
________________________________________________________________________________________
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)
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