3.13.100 \(\int (a+b x)^{11} (c+d x)^{10} \, dx\) [1300]

Optimal. Leaf size=279 \[ \frac {(b c-a d)^{10} (a+b x)^{12}}{12 b^{11}}+\frac {10 d (b c-a d)^9 (a+b x)^{13}}{13 b^{11}}+\frac {45 d^2 (b c-a d)^8 (a+b x)^{14}}{14 b^{11}}+\frac {8 d^3 (b c-a d)^7 (a+b x)^{15}}{b^{11}}+\frac {105 d^4 (b c-a d)^6 (a+b x)^{16}}{8 b^{11}}+\frac {252 d^5 (b c-a d)^5 (a+b x)^{17}}{17 b^{11}}+\frac {35 d^6 (b c-a d)^4 (a+b x)^{18}}{3 b^{11}}+\frac {120 d^7 (b c-a d)^3 (a+b x)^{19}}{19 b^{11}}+\frac {9 d^8 (b c-a d)^2 (a+b x)^{20}}{4 b^{11}}+\frac {10 d^9 (b c-a d) (a+b x)^{21}}{21 b^{11}}+\frac {d^{10} (a+b x)^{22}}{22 b^{11}} \]

[Out]

1/12*(-a*d+b*c)^10*(b*x+a)^12/b^11+10/13*d*(-a*d+b*c)^9*(b*x+a)^13/b^11+45/14*d^2*(-a*d+b*c)^8*(b*x+a)^14/b^11
+8*d^3*(-a*d+b*c)^7*(b*x+a)^15/b^11+105/8*d^4*(-a*d+b*c)^6*(b*x+a)^16/b^11+252/17*d^5*(-a*d+b*c)^5*(b*x+a)^17/
b^11+35/3*d^6*(-a*d+b*c)^4*(b*x+a)^18/b^11+120/19*d^7*(-a*d+b*c)^3*(b*x+a)^19/b^11+9/4*d^8*(-a*d+b*c)^2*(b*x+a
)^20/b^11+10/21*d^9*(-a*d+b*c)*(b*x+a)^21/b^11+1/22*d^10*(b*x+a)^22/b^11

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Rubi [A]
time = 0.88, antiderivative size = 279, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {45} \begin {gather*} \frac {10 d^9 (a+b x)^{21} (b c-a d)}{21 b^{11}}+\frac {9 d^8 (a+b x)^{20} (b c-a d)^2}{4 b^{11}}+\frac {120 d^7 (a+b x)^{19} (b c-a d)^3}{19 b^{11}}+\frac {35 d^6 (a+b x)^{18} (b c-a d)^4}{3 b^{11}}+\frac {252 d^5 (a+b x)^{17} (b c-a d)^5}{17 b^{11}}+\frac {105 d^4 (a+b x)^{16} (b c-a d)^6}{8 b^{11}}+\frac {8 d^3 (a+b x)^{15} (b c-a d)^7}{b^{11}}+\frac {45 d^2 (a+b x)^{14} (b c-a d)^8}{14 b^{11}}+\frac {10 d (a+b x)^{13} (b c-a d)^9}{13 b^{11}}+\frac {(a+b x)^{12} (b c-a d)^{10}}{12 b^{11}}+\frac {d^{10} (a+b x)^{22}}{22 b^{11}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(a + b*x)^11*(c + d*x)^10,x]

[Out]

((b*c - a*d)^10*(a + b*x)^12)/(12*b^11) + (10*d*(b*c - a*d)^9*(a + b*x)^13)/(13*b^11) + (45*d^2*(b*c - a*d)^8*
(a + b*x)^14)/(14*b^11) + (8*d^3*(b*c - a*d)^7*(a + b*x)^15)/b^11 + (105*d^4*(b*c - a*d)^6*(a + b*x)^16)/(8*b^
11) + (252*d^5*(b*c - a*d)^5*(a + b*x)^17)/(17*b^11) + (35*d^6*(b*c - a*d)^4*(a + b*x)^18)/(3*b^11) + (120*d^7
*(b*c - a*d)^3*(a + b*x)^19)/(19*b^11) + (9*d^8*(b*c - a*d)^2*(a + b*x)^20)/(4*b^11) + (10*d^9*(b*c - a*d)*(a
+ b*x)^21)/(21*b^11) + (d^10*(a + b*x)^22)/(22*b^11)

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 (a+b x)^{11} (c+d x)^{10} \, dx &=\int \left (\frac {(b c-a d)^{10} (a+b x)^{11}}{b^{10}}+\frac {10 d (b c-a d)^9 (a+b x)^{12}}{b^{10}}+\frac {45 d^2 (b c-a d)^8 (a+b x)^{13}}{b^{10}}+\frac {120 d^3 (b c-a d)^7 (a+b x)^{14}}{b^{10}}+\frac {210 d^4 (b c-a d)^6 (a+b x)^{15}}{b^{10}}+\frac {252 d^5 (b c-a d)^5 (a+b x)^{16}}{b^{10}}+\frac {210 d^6 (b c-a d)^4 (a+b x)^{17}}{b^{10}}+\frac {120 d^7 (b c-a d)^3 (a+b x)^{18}}{b^{10}}+\frac {45 d^8 (b c-a d)^2 (a+b x)^{19}}{b^{10}}+\frac {10 d^9 (b c-a d) (a+b x)^{20}}{b^{10}}+\frac {d^{10} (a+b x)^{21}}{b^{10}}\right ) \, dx\\ &=\frac {(b c-a d)^{10} (a+b x)^{12}}{12 b^{11}}+\frac {10 d (b c-a d)^9 (a+b x)^{13}}{13 b^{11}}+\frac {45 d^2 (b c-a d)^8 (a+b x)^{14}}{14 b^{11}}+\frac {8 d^3 (b c-a d)^7 (a+b x)^{15}}{b^{11}}+\frac {105 d^4 (b c-a d)^6 (a+b x)^{16}}{8 b^{11}}+\frac {252 d^5 (b c-a d)^5 (a+b x)^{17}}{17 b^{11}}+\frac {35 d^6 (b c-a d)^4 (a+b x)^{18}}{3 b^{11}}+\frac {120 d^7 (b c-a d)^3 (a+b x)^{19}}{19 b^{11}}+\frac {9 d^8 (b c-a d)^2 (a+b x)^{20}}{4 b^{11}}+\frac {10 d^9 (b c-a d) (a+b x)^{21}}{21 b^{11}}+\frac {d^{10} (a+b x)^{22}}{22 b^{11}}\\ \end {align*}

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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(1702\) vs. \(2(279)=558\).
time = 0.13, size = 1702, normalized size = 6.10 \begin {gather*} a^{11} c^{10} x+\frac {1}{2} a^{10} c^9 (11 b c+10 a d) x^2+\frac {5}{3} a^9 c^8 \left (11 b^2 c^2+22 a b c d+9 a^2 d^2\right ) x^3+\frac {5}{4} a^8 c^7 \left (33 b^3 c^3+110 a b^2 c^2 d+99 a^2 b c d^2+24 a^3 d^3\right ) x^4+3 a^7 c^6 \left (22 b^4 c^4+110 a b^3 c^3 d+165 a^2 b^2 c^2 d^2+88 a^3 b c d^3+14 a^4 d^4\right ) x^5+\frac {1}{2} a^6 c^5 \left (154 b^5 c^5+1100 a b^4 c^4 d+2475 a^2 b^3 c^3 d^2+2200 a^3 b^2 c^2 d^3+770 a^4 b c d^4+84 a^5 d^5\right ) x^6+\frac {6}{7} a^5 c^4 \left (77 b^6 c^6+770 a b^5 c^5 d+2475 a^2 b^4 c^4 d^2+3300 a^3 b^3 c^3 d^3+1925 a^4 b^2 c^2 d^4+462 a^5 b c d^5+35 a^6 d^6\right ) x^7+\frac {15}{4} a^4 c^3 \left (11 b^7 c^7+154 a b^6 c^6 d+693 a^2 b^5 c^5 d^2+1320 a^3 b^4 c^4 d^3+1155 a^4 b^3 c^3 d^4+462 a^5 b^2 c^2 d^5+77 a^6 b c d^6+4 a^7 d^7\right ) x^8+\frac {5}{3} a^3 c^2 \left (11 b^8 c^8+220 a b^7 c^7 d+1386 a^2 b^6 c^6 d^2+3696 a^3 b^5 c^5 d^3+4620 a^4 b^4 c^4 d^4+2772 a^5 b^3 c^3 d^5+770 a^6 b^2 c^2 d^6+88 a^7 b c d^7+3 a^8 d^8\right ) x^9+\frac {1}{2} a^2 c \left (11 b^9 c^9+330 a b^8 c^8 d+2970 a^2 b^7 c^7 d^2+11088 a^3 b^6 c^6 d^3+19404 a^4 b^5 c^5 d^4+16632 a^5 b^4 c^4 d^5+6930 a^6 b^3 c^3 d^6+1320 a^7 b^2 c^2 d^7+99 a^8 b c d^8+2 a^9 d^9\right ) x^{10}+\frac {1}{11} a \left (11 b^{10} c^{10}+550 a b^9 c^9 d+7425 a^2 b^8 c^8 d^2+39600 a^3 b^7 c^7 d^3+97020 a^4 b^6 c^6 d^4+116424 a^5 b^5 c^5 d^5+69300 a^6 b^4 c^4 d^6+19800 a^7 b^3 c^3 d^7+2475 a^8 b^2 c^2 d^8+110 a^9 b c d^9+a^{10} d^{10}\right ) x^{11}+\frac {1}{12} b \left (b^{10} c^{10}+110 a b^9 c^9 d+2475 a^2 b^8 c^8 d^2+19800 a^3 b^7 c^7 d^3+69300 a^4 b^6 c^6 d^4+116424 a^5 b^5 c^5 d^5+97020 a^6 b^4 c^4 d^6+39600 a^7 b^3 c^3 d^7+7425 a^8 b^2 c^2 d^8+550 a^9 b c d^9+11 a^{10} d^{10}\right ) x^{12}+\frac {5}{13} b^2 d \left (2 b^9 c^9+99 a b^8 c^8 d+1320 a^2 b^7 c^7 d^2+6930 a^3 b^6 c^6 d^3+16632 a^4 b^5 c^5 d^4+19404 a^5 b^4 c^4 d^5+11088 a^6 b^3 c^3 d^6+2970 a^7 b^2 c^2 d^7+330 a^8 b c d^8+11 a^9 d^9\right ) x^{13}+\frac {15}{14} b^3 d^2 \left (3 b^8 c^8+88 a b^7 c^7 d+770 a^2 b^6 c^6 d^2+2772 a^3 b^5 c^5 d^3+4620 a^4 b^4 c^4 d^4+3696 a^5 b^3 c^3 d^5+1386 a^6 b^2 c^2 d^6+220 a^7 b c d^7+11 a^8 d^8\right ) x^{14}+2 b^4 d^3 \left (4 b^7 c^7+77 a b^6 c^6 d+462 a^2 b^5 c^5 d^2+1155 a^3 b^4 c^4 d^3+1320 a^4 b^3 c^3 d^4+693 a^5 b^2 c^2 d^5+154 a^6 b c d^6+11 a^7 d^7\right ) x^{15}+\frac {3}{8} b^5 d^4 \left (35 b^6 c^6+462 a b^5 c^5 d+1925 a^2 b^4 c^4 d^2+3300 a^3 b^3 c^3 d^3+2475 a^4 b^2 c^2 d^4+770 a^5 b c d^5+77 a^6 d^6\right ) x^{16}+\frac {3}{17} b^6 d^5 \left (84 b^5 c^5+770 a b^4 c^4 d+2200 a^2 b^3 c^3 d^2+2475 a^3 b^2 c^2 d^3+1100 a^4 b c d^4+154 a^5 d^5\right ) x^{17}+\frac {5}{6} b^7 d^6 \left (14 b^4 c^4+88 a b^3 c^3 d+165 a^2 b^2 c^2 d^2+110 a^3 b c d^3+22 a^4 d^4\right ) x^{18}+\frac {5}{19} b^8 d^7 \left (24 b^3 c^3+99 a b^2 c^2 d+110 a^2 b c d^2+33 a^3 d^3\right ) x^{19}+\frac {1}{4} b^9 d^8 \left (9 b^2 c^2+22 a b c d+11 a^2 d^2\right ) x^{20}+\frac {1}{21} b^{10} d^9 (10 b c+11 a d) x^{21}+\frac {1}{22} b^{11} d^{10} x^{22} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(a + b*x)^11*(c + d*x)^10,x]

[Out]

a^11*c^10*x + (a^10*c^9*(11*b*c + 10*a*d)*x^2)/2 + (5*a^9*c^8*(11*b^2*c^2 + 22*a*b*c*d + 9*a^2*d^2)*x^3)/3 + (
5*a^8*c^7*(33*b^3*c^3 + 110*a*b^2*c^2*d + 99*a^2*b*c*d^2 + 24*a^3*d^3)*x^4)/4 + 3*a^7*c^6*(22*b^4*c^4 + 110*a*
b^3*c^3*d + 165*a^2*b^2*c^2*d^2 + 88*a^3*b*c*d^3 + 14*a^4*d^4)*x^5 + (a^6*c^5*(154*b^5*c^5 + 1100*a*b^4*c^4*d
+ 2475*a^2*b^3*c^3*d^2 + 2200*a^3*b^2*c^2*d^3 + 770*a^4*b*c*d^4 + 84*a^5*d^5)*x^6)/2 + (6*a^5*c^4*(77*b^6*c^6
+ 770*a*b^5*c^5*d + 2475*a^2*b^4*c^4*d^2 + 3300*a^3*b^3*c^3*d^3 + 1925*a^4*b^2*c^2*d^4 + 462*a^5*b*c*d^5 + 35*
a^6*d^6)*x^7)/7 + (15*a^4*c^3*(11*b^7*c^7 + 154*a*b^6*c^6*d + 693*a^2*b^5*c^5*d^2 + 1320*a^3*b^4*c^4*d^3 + 115
5*a^4*b^3*c^3*d^4 + 462*a^5*b^2*c^2*d^5 + 77*a^6*b*c*d^6 + 4*a^7*d^7)*x^8)/4 + (5*a^3*c^2*(11*b^8*c^8 + 220*a*
b^7*c^7*d + 1386*a^2*b^6*c^6*d^2 + 3696*a^3*b^5*c^5*d^3 + 4620*a^4*b^4*c^4*d^4 + 2772*a^5*b^3*c^3*d^5 + 770*a^
6*b^2*c^2*d^6 + 88*a^7*b*c*d^7 + 3*a^8*d^8)*x^9)/3 + (a^2*c*(11*b^9*c^9 + 330*a*b^8*c^8*d + 2970*a^2*b^7*c^7*d
^2 + 11088*a^3*b^6*c^6*d^3 + 19404*a^4*b^5*c^5*d^4 + 16632*a^5*b^4*c^4*d^5 + 6930*a^6*b^3*c^3*d^6 + 1320*a^7*b
^2*c^2*d^7 + 99*a^8*b*c*d^8 + 2*a^9*d^9)*x^10)/2 + (a*(11*b^10*c^10 + 550*a*b^9*c^9*d + 7425*a^2*b^8*c^8*d^2 +
39600*a^3*b^7*c^7*d^3 + 97020*a^4*b^6*c^6*d^4 + 116424*a^5*b^5*c^5*d^5 + 69300*a^6*b^4*c^4*d^6 + 19800*a^7*b^
3*c^3*d^7 + 2475*a^8*b^2*c^2*d^8 + 110*a^9*b*c*d^9 + a^10*d^10)*x^11)/11 + (b*(b^10*c^10 + 110*a*b^9*c^9*d + 2
475*a^2*b^8*c^8*d^2 + 19800*a^3*b^7*c^7*d^3 + 69300*a^4*b^6*c^6*d^4 + 116424*a^5*b^5*c^5*d^5 + 97020*a^6*b^4*c
^4*d^6 + 39600*a^7*b^3*c^3*d^7 + 7425*a^8*b^2*c^2*d^8 + 550*a^9*b*c*d^9 + 11*a^10*d^10)*x^12)/12 + (5*b^2*d*(2
*b^9*c^9 + 99*a*b^8*c^8*d + 1320*a^2*b^7*c^7*d^2 + 6930*a^3*b^6*c^6*d^3 + 16632*a^4*b^5*c^5*d^4 + 19404*a^5*b^
4*c^4*d^5 + 11088*a^6*b^3*c^3*d^6 + 2970*a^7*b^2*c^2*d^7 + 330*a^8*b*c*d^8 + 11*a^9*d^9)*x^13)/13 + (15*b^3*d^
2*(3*b^8*c^8 + 88*a*b^7*c^7*d + 770*a^2*b^6*c^6*d^2 + 2772*a^3*b^5*c^5*d^3 + 4620*a^4*b^4*c^4*d^4 + 3696*a^5*b
^3*c^3*d^5 + 1386*a^6*b^2*c^2*d^6 + 220*a^7*b*c*d^7 + 11*a^8*d^8)*x^14)/14 + 2*b^4*d^3*(4*b^7*c^7 + 77*a*b^6*c
^6*d + 462*a^2*b^5*c^5*d^2 + 1155*a^3*b^4*c^4*d^3 + 1320*a^4*b^3*c^3*d^4 + 693*a^5*b^2*c^2*d^5 + 154*a^6*b*c*d
^6 + 11*a^7*d^7)*x^15 + (3*b^5*d^4*(35*b^6*c^6 + 462*a*b^5*c^5*d + 1925*a^2*b^4*c^4*d^2 + 3300*a^3*b^3*c^3*d^3
+ 2475*a^4*b^2*c^2*d^4 + 770*a^5*b*c*d^5 + 77*a^6*d^6)*x^16)/8 + (3*b^6*d^5*(84*b^5*c^5 + 770*a*b^4*c^4*d + 2
200*a^2*b^3*c^3*d^2 + 2475*a^3*b^2*c^2*d^3 + 1100*a^4*b*c*d^4 + 154*a^5*d^5)*x^17)/17 + (5*b^7*d^6*(14*b^4*c^4
+ 88*a*b^3*c^3*d + 165*a^2*b^2*c^2*d^2 + 110*a^3*b*c*d^3 + 22*a^4*d^4)*x^18)/6 + (5*b^8*d^7*(24*b^3*c^3 + 99*
a*b^2*c^2*d + 110*a^2*b*c*d^2 + 33*a^3*d^3)*x^19)/19 + (b^9*d^8*(9*b^2*c^2 + 22*a*b*c*d + 11*a^2*d^2)*x^20)/4
+ (b^10*d^9*(10*b*c + 11*a*d)*x^21)/21 + (b^11*d^10*x^22)/22

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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(1740\) vs. \(2(259)=518\).
time = 0.14, size = 1741, normalized size = 6.24

method	result	size
norman	\(\text {Expression too large to display}\)	\(1721\)
default	\(\text {Expression too large to display}\)	\(1741\)
gosper	\(\text {Expression too large to display}\)	\(2011\)
risch	\(\text {Expression too large to display}\)	\(2011\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((b*x+a)^11*(d*x+c)^10,x,method=_RETURNVERBOSE)

[Out]

1/22*b^11*d^10*x^22+1/21*(11*a*b^10*d^10+10*b^11*c*d^9)*x^21+1/20*(55*a^2*b^9*d^10+110*a*b^10*c*d^9+45*b^11*c^
2*d^8)*x^20+1/19*(165*a^3*b^8*d^10+550*a^2*b^9*c*d^9+495*a*b^10*c^2*d^8+120*b^11*c^3*d^7)*x^19+1/18*(330*a^4*b
^7*d^10+1650*a^3*b^8*c*d^9+2475*a^2*b^9*c^2*d^8+1320*a*b^10*c^3*d^7+210*b^11*c^4*d^6)*x^18+1/17*(462*a^5*b^6*d
^10+3300*a^4*b^7*c*d^9+7425*a^3*b^8*c^2*d^8+6600*a^2*b^9*c^3*d^7+2310*a*b^10*c^4*d^6+252*b^11*c^5*d^5)*x^17+1/
16*(462*a^6*b^5*d^10+4620*a^5*b^6*c*d^9+14850*a^4*b^7*c^2*d^8+19800*a^3*b^8*c^3*d^7+11550*a^2*b^9*c^4*d^6+2772
*a*b^10*c^5*d^5+210*b^11*c^6*d^4)*x^16+1/15*(330*a^7*b^4*d^10+4620*a^6*b^5*c*d^9+20790*a^5*b^6*c^2*d^8+39600*a
^4*b^7*c^3*d^7+34650*a^3*b^8*c^4*d^6+13860*a^2*b^9*c^5*d^5+2310*a*b^10*c^6*d^4+120*b^11*c^7*d^3)*x^15+1/14*(16
5*a^8*b^3*d^10+3300*a^7*b^4*c*d^9+20790*a^6*b^5*c^2*d^8+55440*a^5*b^6*c^3*d^7+69300*a^4*b^7*c^4*d^6+41580*a^3*
b^8*c^5*d^5+11550*a^2*b^9*c^6*d^4+1320*a*b^10*c^7*d^3+45*b^11*c^8*d^2)*x^14+1/13*(55*a^9*b^2*d^10+1650*a^8*b^3
*c*d^9+14850*a^7*b^4*c^2*d^8+55440*a^6*b^5*c^3*d^7+97020*a^5*b^6*c^4*d^6+83160*a^4*b^7*c^5*d^5+34650*a^3*b^8*c
^6*d^4+6600*a^2*b^9*c^7*d^3+495*a*b^10*c^8*d^2+10*b^11*c^9*d)*x^13+1/12*(11*a^10*b*d^10+550*a^9*b^2*c*d^9+7425
*a^8*b^3*c^2*d^8+39600*a^7*b^4*c^3*d^7+97020*a^6*b^5*c^4*d^6+116424*a^5*b^6*c^5*d^5+69300*a^4*b^7*c^6*d^4+1980
0*a^3*b^8*c^7*d^3+2475*a^2*b^9*c^8*d^2+110*a*b^10*c^9*d+b^11*c^10)*x^12+1/11*(a^11*d^10+110*a^10*b*c*d^9+2475*
a^9*b^2*c^2*d^8+19800*a^8*b^3*c^3*d^7+69300*a^7*b^4*c^4*d^6+116424*a^6*b^5*c^5*d^5+97020*a^5*b^6*c^6*d^4+39600
*a^4*b^7*c^7*d^3+7425*a^3*b^8*c^8*d^2+550*a^2*b^9*c^9*d+11*a*b^10*c^10)*x^11+1/10*(10*a^11*c*d^9+495*a^10*b*c^
2*d^8+6600*a^9*b^2*c^3*d^7+34650*a^8*b^3*c^4*d^6+83160*a^7*b^4*c^5*d^5+97020*a^6*b^5*c^6*d^4+55440*a^5*b^6*c^7
*d^3+14850*a^4*b^7*c^8*d^2+1650*a^3*b^8*c^9*d+55*a^2*b^9*c^10)*x^10+1/9*(45*a^11*c^2*d^8+1320*a^10*b*c^3*d^7+1
1550*a^9*b^2*c^4*d^6+41580*a^8*b^3*c^5*d^5+69300*a^7*b^4*c^6*d^4+55440*a^6*b^5*c^7*d^3+20790*a^5*b^6*c^8*d^2+3
300*a^4*b^7*c^9*d+165*a^3*b^8*c^10)*x^9+1/8*(120*a^11*c^3*d^7+2310*a^10*b*c^4*d^6+13860*a^9*b^2*c^5*d^5+34650*
a^8*b^3*c^6*d^4+39600*a^7*b^4*c^7*d^3+20790*a^6*b^5*c^8*d^2+4620*a^5*b^6*c^9*d+330*a^4*b^7*c^10)*x^8+1/7*(210*
a^11*c^4*d^6+2772*a^10*b*c^5*d^5+11550*a^9*b^2*c^6*d^4+19800*a^8*b^3*c^7*d^3+14850*a^7*b^4*c^8*d^2+4620*a^6*b^
5*c^9*d+462*a^5*b^6*c^10)*x^7+1/6*(252*a^11*c^5*d^5+2310*a^10*b*c^6*d^4+6600*a^9*b^2*c^7*d^3+7425*a^8*b^3*c^8*
d^2+3300*a^7*b^4*c^9*d+462*a^6*b^5*c^10)*x^6+1/5*(210*a^11*c^6*d^4+1320*a^10*b*c^7*d^3+2475*a^9*b^2*c^8*d^2+16
50*a^8*b^3*c^9*d+330*a^7*b^4*c^10)*x^5+1/4*(120*a^11*c^7*d^3+495*a^10*b*c^8*d^2+550*a^9*b^2*c^9*d+165*a^8*b^3*
c^10)*x^4+1/3*(45*a^11*c^8*d^2+110*a^10*b*c^9*d+55*a^9*b^2*c^10)*x^3+1/2*(10*a^11*c^9*d+11*a^10*b*c^10)*x^2+a^
11*c^10*x

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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 1740 vs. \(2 (259) = 518\).
time = 0.29, size = 1740, normalized size = 6.24 \begin {gather*} \frac {1}{22} \, b^{11} d^{10} x^{22} + a^{11} c^{10} x + \frac {1}{21} \, {\left (10 \, b^{11} c d^{9} + 11 \, a b^{10} d^{10}\right )} x^{21} + \frac {1}{4} \, {\left (9 \, b^{11} c^{2} d^{8} + 22 \, a b^{10} c d^{9} + 11 \, a^{2} b^{9} d^{10}\right )} x^{20} + \frac {5}{19} \, {\left (24 \, b^{11} c^{3} d^{7} + 99 \, a b^{10} c^{2} d^{8} + 110 \, a^{2} b^{9} c d^{9} + 33 \, a^{3} b^{8} d^{10}\right )} x^{19} + \frac {5}{6} \, {\left (14 \, b^{11} c^{4} d^{6} + 88 \, a b^{10} c^{3} d^{7} + 165 \, a^{2} b^{9} c^{2} d^{8} + 110 \, a^{3} b^{8} c d^{9} + 22 \, a^{4} b^{7} d^{10}\right )} x^{18} + \frac {3}{17} \, {\left (84 \, b^{11} c^{5} d^{5} + 770 \, a b^{10} c^{4} d^{6} + 2200 \, a^{2} b^{9} c^{3} d^{7} + 2475 \, a^{3} b^{8} c^{2} d^{8} + 1100 \, a^{4} b^{7} c d^{9} + 154 \, a^{5} b^{6} d^{10}\right )} x^{17} + \frac {3}{8} \, {\left (35 \, b^{11} c^{6} d^{4} + 462 \, a b^{10} c^{5} d^{5} + 1925 \, a^{2} b^{9} c^{4} d^{6} + 3300 \, a^{3} b^{8} c^{3} d^{7} + 2475 \, a^{4} b^{7} c^{2} d^{8} + 770 \, a^{5} b^{6} c d^{9} + 77 \, a^{6} b^{5} d^{10}\right )} x^{16} + 2 \, {\left (4 \, b^{11} c^{7} d^{3} + 77 \, a b^{10} c^{6} d^{4} + 462 \, a^{2} b^{9} c^{5} d^{5} + 1155 \, a^{3} b^{8} c^{4} d^{6} + 1320 \, a^{4} b^{7} c^{3} d^{7} + 693 \, a^{5} b^{6} c^{2} d^{8} + 154 \, a^{6} b^{5} c d^{9} + 11 \, a^{7} b^{4} d^{10}\right )} x^{15} + \frac {15}{14} \, {\left (3 \, b^{11} c^{8} d^{2} + 88 \, a b^{10} c^{7} d^{3} + 770 \, a^{2} b^{9} c^{6} d^{4} + 2772 \, a^{3} b^{8} c^{5} d^{5} + 4620 \, a^{4} b^{7} c^{4} d^{6} + 3696 \, a^{5} b^{6} c^{3} d^{7} + 1386 \, a^{6} b^{5} c^{2} d^{8} + 220 \, a^{7} b^{4} c d^{9} + 11 \, a^{8} b^{3} d^{10}\right )} x^{14} + \frac {5}{13} \, {\left (2 \, b^{11} c^{9} d + 99 \, a b^{10} c^{8} d^{2} + 1320 \, a^{2} b^{9} c^{7} d^{3} + 6930 \, a^{3} b^{8} c^{6} d^{4} + 16632 \, a^{4} b^{7} c^{5} d^{5} + 19404 \, a^{5} b^{6} c^{4} d^{6} + 11088 \, a^{6} b^{5} c^{3} d^{7} + 2970 \, a^{7} b^{4} c^{2} d^{8} + 330 \, a^{8} b^{3} c d^{9} + 11 \, a^{9} b^{2} d^{10}\right )} x^{13} + \frac {1}{12} \, {\left (b^{11} c^{10} + 110 \, a b^{10} c^{9} d + 2475 \, a^{2} b^{9} c^{8} d^{2} + 19800 \, a^{3} b^{8} c^{7} d^{3} + 69300 \, a^{4} b^{7} c^{6} d^{4} + 116424 \, a^{5} b^{6} c^{5} d^{5} + 97020 \, a^{6} b^{5} c^{4} d^{6} + 39600 \, a^{7} b^{4} c^{3} d^{7} + 7425 \, a^{8} b^{3} c^{2} d^{8} + 550 \, a^{9} b^{2} c d^{9} + 11 \, a^{10} b d^{10}\right )} x^{12} + \frac {1}{11} \, {\left (11 \, a b^{10} c^{10} + 550 \, a^{2} b^{9} c^{9} d + 7425 \, a^{3} b^{8} c^{8} d^{2} + 39600 \, a^{4} b^{7} c^{7} d^{3} + 97020 \, a^{5} b^{6} c^{6} d^{4} + 116424 \, a^{6} b^{5} c^{5} d^{5} + 69300 \, a^{7} b^{4} c^{4} d^{6} + 19800 \, a^{8} b^{3} c^{3} d^{7} + 2475 \, a^{9} b^{2} c^{2} d^{8} + 110 \, a^{10} b c d^{9} + a^{11} d^{10}\right )} x^{11} + \frac {1}{2} \, {\left (11 \, a^{2} b^{9} c^{10} + 330 \, a^{3} b^{8} c^{9} d + 2970 \, a^{4} b^{7} c^{8} d^{2} + 11088 \, a^{5} b^{6} c^{7} d^{3} + 19404 \, a^{6} b^{5} c^{6} d^{4} + 16632 \, a^{7} b^{4} c^{5} d^{5} + 6930 \, a^{8} b^{3} c^{4} d^{6} + 1320 \, a^{9} b^{2} c^{3} d^{7} + 99 \, a^{10} b c^{2} d^{8} + 2 \, a^{11} c d^{9}\right )} x^{10} + \frac {5}{3} \, {\left (11 \, a^{3} b^{8} c^{10} + 220 \, a^{4} b^{7} c^{9} d + 1386 \, a^{5} b^{6} c^{8} d^{2} + 3696 \, a^{6} b^{5} c^{7} d^{3} + 4620 \, a^{7} b^{4} c^{6} d^{4} + 2772 \, a^{8} b^{3} c^{5} d^{5} + 770 \, a^{9} b^{2} c^{4} d^{6} + 88 \, a^{10} b c^{3} d^{7} + 3 \, a^{11} c^{2} d^{8}\right )} x^{9} + \frac {15}{4} \, {\left (11 \, a^{4} b^{7} c^{10} + 154 \, a^{5} b^{6} c^{9} d + 693 \, a^{6} b^{5} c^{8} d^{2} + 1320 \, a^{7} b^{4} c^{7} d^{3} + 1155 \, a^{8} b^{3} c^{6} d^{4} + 462 \, a^{9} b^{2} c^{5} d^{5} + 77 \, a^{10} b c^{4} d^{6} + 4 \, a^{11} c^{3} d^{7}\right )} x^{8} + \frac {6}{7} \, {\left (77 \, a^{5} b^{6} c^{10} + 770 \, a^{6} b^{5} c^{9} d + 2475 \, a^{7} b^{4} c^{8} d^{2} + 3300 \, a^{8} b^{3} c^{7} d^{3} + 1925 \, a^{9} b^{2} c^{6} d^{4} + 462 \, a^{10} b c^{5} d^{5} + 35 \, a^{11} c^{4} d^{6}\right )} x^{7} + \frac {1}{2} \, {\left (154 \, a^{6} b^{5} c^{10} + 1100 \, a^{7} b^{4} c^{9} d + 2475 \, a^{8} b^{3} c^{8} d^{2} + 2200 \, a^{9} b^{2} c^{7} d^{3} + 770 \, a^{10} b c^{6} d^{4} + 84 \, a^{11} c^{5} d^{5}\right )} x^{6} + 3 \, {\left (22 \, a^{7} b^{4} c^{10} + 110 \, a^{8} b^{3} c^{9} d + 165 \, a^{9} b^{2} c^{8} d^{2} + 88 \, a^{10} b c^{7} d^{3} + 14 \, a^{11} c^{6} d^{4}\right )} x^{5} + \frac {5}{4} \, {\left (33 \, a^{8} b^{3} c^{10} + 110 \, a^{9} b^{2} c^{9} d + 99 \, a^{10} b c^{8} d^{2} + 24 \, a^{11} c^{7} d^{3}\right )} x^{4} + \frac {5}{3} \, {\left (11 \, a^{9} b^{2} c^{10} + 22 \, a^{10} b c^{9} d + 9 \, a^{11} c^{8} d^{2}\right )} x^{3} + \frac {1}{2} \, {\left (11 \, a^{10} b c^{10} + 10 \, a^{11} c^{9} d\right )} x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)^11*(d*x+c)^10,x, algorithm="maxima")

[Out]

1/22*b^11*d^10*x^22 + a^11*c^10*x + 1/21*(10*b^11*c*d^9 + 11*a*b^10*d^10)*x^21 + 1/4*(9*b^11*c^2*d^8 + 22*a*b^
10*c*d^9 + 11*a^2*b^9*d^10)*x^20 + 5/19*(24*b^11*c^3*d^7 + 99*a*b^10*c^2*d^8 + 110*a^2*b^9*c*d^9 + 33*a^3*b^8*
d^10)*x^19 + 5/6*(14*b^11*c^4*d^6 + 88*a*b^10*c^3*d^7 + 165*a^2*b^9*c^2*d^8 + 110*a^3*b^8*c*d^9 + 22*a^4*b^7*d
^10)*x^18 + 3/17*(84*b^11*c^5*d^5 + 770*a*b^10*c^4*d^6 + 2200*a^2*b^9*c^3*d^7 + 2475*a^3*b^8*c^2*d^8 + 1100*a^
4*b^7*c*d^9 + 154*a^5*b^6*d^10)*x^17 + 3/8*(35*b^11*c^6*d^4 + 462*a*b^10*c^5*d^5 + 1925*a^2*b^9*c^4*d^6 + 3300
*a^3*b^8*c^3*d^7 + 2475*a^4*b^7*c^2*d^8 + 770*a^5*b^6*c*d^9 + 77*a^6*b^5*d^10)*x^16 + 2*(4*b^11*c^7*d^3 + 77*a
*b^10*c^6*d^4 + 462*a^2*b^9*c^5*d^5 + 1155*a^3*b^8*c^4*d^6 + 1320*a^4*b^7*c^3*d^7 + 693*a^5*b^6*c^2*d^8 + 154*
a^6*b^5*c*d^9 + 11*a^7*b^4*d^10)*x^15 + 15/14*(3*b^11*c^8*d^2 + 88*a*b^10*c^7*d^3 + 770*a^2*b^9*c^6*d^4 + 2772
*a^3*b^8*c^5*d^5 + 4620*a^4*b^7*c^4*d^6 + 3696*a^5*b^6*c^3*d^7 + 1386*a^6*b^5*c^2*d^8 + 220*a^7*b^4*c*d^9 + 11
*a^8*b^3*d^10)*x^14 + 5/13*(2*b^11*c^9*d + 99*a*b^10*c^8*d^2 + 1320*a^2*b^9*c^7*d^3 + 6930*a^3*b^8*c^6*d^4 + 1
6632*a^4*b^7*c^5*d^5 + 19404*a^5*b^6*c^4*d^6 + 11088*a^6*b^5*c^3*d^7 + 2970*a^7*b^4*c^2*d^8 + 330*a^8*b^3*c*d^
9 + 11*a^9*b^2*d^10)*x^13 + 1/12*(b^11*c^10 + 110*a*b^10*c^9*d + 2475*a^2*b^9*c^8*d^2 + 19800*a^3*b^8*c^7*d^3
+ 69300*a^4*b^7*c^6*d^4 + 116424*a^5*b^6*c^5*d^5 + 97020*a^6*b^5*c^4*d^6 + 39600*a^7*b^4*c^3*d^7 + 7425*a^8*b^
3*c^2*d^8 + 550*a^9*b^2*c*d^9 + 11*a^10*b*d^10)*x^12 + 1/11*(11*a*b^10*c^10 + 550*a^2*b^9*c^9*d + 7425*a^3*b^8
*c^8*d^2 + 39600*a^4*b^7*c^7*d^3 + 97020*a^5*b^6*c^6*d^4 + 116424*a^6*b^5*c^5*d^5 + 69300*a^7*b^4*c^4*d^6 + 19
800*a^8*b^3*c^3*d^7 + 2475*a^9*b^2*c^2*d^8 + 110*a^10*b*c*d^9 + a^11*d^10)*x^11 + 1/2*(11*a^2*b^9*c^10 + 330*a
^3*b^8*c^9*d + 2970*a^4*b^7*c^8*d^2 + 11088*a^5*b^6*c^7*d^3 + 19404*a^6*b^5*c^6*d^4 + 16632*a^7*b^4*c^5*d^5 +
6930*a^8*b^3*c^4*d^6 + 1320*a^9*b^2*c^3*d^7 + 99*a^10*b*c^2*d^8 + 2*a^11*c*d^9)*x^10 + 5/3*(11*a^3*b^8*c^10 +
220*a^4*b^7*c^9*d + 1386*a^5*b^6*c^8*d^2 + 3696*a^6*b^5*c^7*d^3 + 4620*a^7*b^4*c^6*d^4 + 2772*a^8*b^3*c^5*d^5
+ 770*a^9*b^2*c^4*d^6 + 88*a^10*b*c^3*d^7 + 3*a^11*c^2*d^8)*x^9 + 15/4*(11*a^4*b^7*c^10 + 154*a^5*b^6*c^9*d +
693*a^6*b^5*c^8*d^2 + 1320*a^7*b^4*c^7*d^3 + 1155*a^8*b^3*c^6*d^4 + 462*a^9*b^2*c^5*d^5 + 77*a^10*b*c^4*d^6 +
4*a^11*c^3*d^7)*x^8 + 6/7*(77*a^5*b^6*c^10 + 770*a^6*b^5*c^9*d + 2475*a^7*b^4*c^8*d^2 + 3300*a^8*b^3*c^7*d^3 +
1925*a^9*b^2*c^6*d^4 + 462*a^10*b*c^5*d^5 + 35*a^11*c^4*d^6)*x^7 + 1/2*(154*a^6*b^5*c^10 + 1100*a^7*b^4*c^9*d
+ 2475*a^8*b^3*c^8*d^2 + 2200*a^9*b^2*c^7*d^3 + 770*a^10*b*c^6*d^4 + 84*a^11*c^5*d^5)*x^6 + 3*(22*a^7*b^4*c^1
0 + 110*a^8*b^3*c^9*d + 165*a^9*b^2*c^8*d^2 + 88*a^10*b*c^7*d^3 + 14*a^11*c^6*d^4)*x^5 + 5/4*(33*a^8*b^3*c^10
+ 110*a^9*b^2*c^9*d + 99*a^10*b*c^8*d^2 + 24*a^11*c^7*d^3)*x^4 + 5/3*(11*a^9*b^2*c^10 + 22*a^10*b*c^9*d + 9*a^
11*c^8*d^2)*x^3 + 1/2*(11*a^10*b*c^10 + 10*a^11*c^9*d)*x^2

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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 1740 vs. \(2 (259) = 518\).
time = 0.52, size = 1740, normalized size = 6.24 \begin {gather*} \frac {1}{22} \, b^{11} d^{10} x^{22} + a^{11} c^{10} x + \frac {1}{21} \, {\left (10 \, b^{11} c d^{9} + 11 \, a b^{10} d^{10}\right )} x^{21} + \frac {1}{4} \, {\left (9 \, b^{11} c^{2} d^{8} + 22 \, a b^{10} c d^{9} + 11 \, a^{2} b^{9} d^{10}\right )} x^{20} + \frac {5}{19} \, {\left (24 \, b^{11} c^{3} d^{7} + 99 \, a b^{10} c^{2} d^{8} + 110 \, a^{2} b^{9} c d^{9} + 33 \, a^{3} b^{8} d^{10}\right )} x^{19} + \frac {5}{6} \, {\left (14 \, b^{11} c^{4} d^{6} + 88 \, a b^{10} c^{3} d^{7} + 165 \, a^{2} b^{9} c^{2} d^{8} + 110 \, a^{3} b^{8} c d^{9} + 22 \, a^{4} b^{7} d^{10}\right )} x^{18} + \frac {3}{17} \, {\left (84 \, b^{11} c^{5} d^{5} + 770 \, a b^{10} c^{4} d^{6} + 2200 \, a^{2} b^{9} c^{3} d^{7} + 2475 \, a^{3} b^{8} c^{2} d^{8} + 1100 \, a^{4} b^{7} c d^{9} + 154 \, a^{5} b^{6} d^{10}\right )} x^{17} + \frac {3}{8} \, {\left (35 \, b^{11} c^{6} d^{4} + 462 \, a b^{10} c^{5} d^{5} + 1925 \, a^{2} b^{9} c^{4} d^{6} + 3300 \, a^{3} b^{8} c^{3} d^{7} + 2475 \, a^{4} b^{7} c^{2} d^{8} + 770 \, a^{5} b^{6} c d^{9} + 77 \, a^{6} b^{5} d^{10}\right )} x^{16} + 2 \, {\left (4 \, b^{11} c^{7} d^{3} + 77 \, a b^{10} c^{6} d^{4} + 462 \, a^{2} b^{9} c^{5} d^{5} + 1155 \, a^{3} b^{8} c^{4} d^{6} + 1320 \, a^{4} b^{7} c^{3} d^{7} + 693 \, a^{5} b^{6} c^{2} d^{8} + 154 \, a^{6} b^{5} c d^{9} + 11 \, a^{7} b^{4} d^{10}\right )} x^{15} + \frac {15}{14} \, {\left (3 \, b^{11} c^{8} d^{2} + 88 \, a b^{10} c^{7} d^{3} + 770 \, a^{2} b^{9} c^{6} d^{4} + 2772 \, a^{3} b^{8} c^{5} d^{5} + 4620 \, a^{4} b^{7} c^{4} d^{6} + 3696 \, a^{5} b^{6} c^{3} d^{7} + 1386 \, a^{6} b^{5} c^{2} d^{8} + 220 \, a^{7} b^{4} c d^{9} + 11 \, a^{8} b^{3} d^{10}\right )} x^{14} + \frac {5}{13} \, {\left (2 \, b^{11} c^{9} d + 99 \, a b^{10} c^{8} d^{2} + 1320 \, a^{2} b^{9} c^{7} d^{3} + 6930 \, a^{3} b^{8} c^{6} d^{4} + 16632 \, a^{4} b^{7} c^{5} d^{5} + 19404 \, a^{5} b^{6} c^{4} d^{6} + 11088 \, a^{6} b^{5} c^{3} d^{7} + 2970 \, a^{7} b^{4} c^{2} d^{8} + 330 \, a^{8} b^{3} c d^{9} + 11 \, a^{9} b^{2} d^{10}\right )} x^{13} + \frac {1}{12} \, {\left (b^{11} c^{10} + 110 \, a b^{10} c^{9} d + 2475 \, a^{2} b^{9} c^{8} d^{2} + 19800 \, a^{3} b^{8} c^{7} d^{3} + 69300 \, a^{4} b^{7} c^{6} d^{4} + 116424 \, a^{5} b^{6} c^{5} d^{5} + 97020 \, a^{6} b^{5} c^{4} d^{6} + 39600 \, a^{7} b^{4} c^{3} d^{7} + 7425 \, a^{8} b^{3} c^{2} d^{8} + 550 \, a^{9} b^{2} c d^{9} + 11 \, a^{10} b d^{10}\right )} x^{12} + \frac {1}{11} \, {\left (11 \, a b^{10} c^{10} + 550 \, a^{2} b^{9} c^{9} d + 7425 \, a^{3} b^{8} c^{8} d^{2} + 39600 \, a^{4} b^{7} c^{7} d^{3} + 97020 \, a^{5} b^{6} c^{6} d^{4} + 116424 \, a^{6} b^{5} c^{5} d^{5} + 69300 \, a^{7} b^{4} c^{4} d^{6} + 19800 \, a^{8} b^{3} c^{3} d^{7} + 2475 \, a^{9} b^{2} c^{2} d^{8} + 110 \, a^{10} b c d^{9} + a^{11} d^{10}\right )} x^{11} + \frac {1}{2} \, {\left (11 \, a^{2} b^{9} c^{10} + 330 \, a^{3} b^{8} c^{9} d + 2970 \, a^{4} b^{7} c^{8} d^{2} + 11088 \, a^{5} b^{6} c^{7} d^{3} + 19404 \, a^{6} b^{5} c^{6} d^{4} + 16632 \, a^{7} b^{4} c^{5} d^{5} + 6930 \, a^{8} b^{3} c^{4} d^{6} + 1320 \, a^{9} b^{2} c^{3} d^{7} + 99 \, a^{10} b c^{2} d^{8} + 2 \, a^{11} c d^{9}\right )} x^{10} + \frac {5}{3} \, {\left (11 \, a^{3} b^{8} c^{10} + 220 \, a^{4} b^{7} c^{9} d + 1386 \, a^{5} b^{6} c^{8} d^{2} + 3696 \, a^{6} b^{5} c^{7} d^{3} + 4620 \, a^{7} b^{4} c^{6} d^{4} + 2772 \, a^{8} b^{3} c^{5} d^{5} + 770 \, a^{9} b^{2} c^{4} d^{6} + 88 \, a^{10} b c^{3} d^{7} + 3 \, a^{11} c^{2} d^{8}\right )} x^{9} + \frac {15}{4} \, {\left (11 \, a^{4} b^{7} c^{10} + 154 \, a^{5} b^{6} c^{9} d + 693 \, a^{6} b^{5} c^{8} d^{2} + 1320 \, a^{7} b^{4} c^{7} d^{3} + 1155 \, a^{8} b^{3} c^{6} d^{4} + 462 \, a^{9} b^{2} c^{5} d^{5} + 77 \, a^{10} b c^{4} d^{6} + 4 \, a^{11} c^{3} d^{7}\right )} x^{8} + \frac {6}{7} \, {\left (77 \, a^{5} b^{6} c^{10} + 770 \, a^{6} b^{5} c^{9} d + 2475 \, a^{7} b^{4} c^{8} d^{2} + 3300 \, a^{8} b^{3} c^{7} d^{3} + 1925 \, a^{9} b^{2} c^{6} d^{4} + 462 \, a^{10} b c^{5} d^{5} + 35 \, a^{11} c^{4} d^{6}\right )} x^{7} + \frac {1}{2} \, {\left (154 \, a^{6} b^{5} c^{10} + 1100 \, a^{7} b^{4} c^{9} d + 2475 \, a^{8} b^{3} c^{8} d^{2} + 2200 \, a^{9} b^{2} c^{7} d^{3} + 770 \, a^{10} b c^{6} d^{4} + 84 \, a^{11} c^{5} d^{5}\right )} x^{6} + 3 \, {\left (22 \, a^{7} b^{4} c^{10} + 110 \, a^{8} b^{3} c^{9} d + 165 \, a^{9} b^{2} c^{8} d^{2} + 88 \, a^{10} b c^{7} d^{3} + 14 \, a^{11} c^{6} d^{4}\right )} x^{5} + \frac {5}{4} \, {\left (33 \, a^{8} b^{3} c^{10} + 110 \, a^{9} b^{2} c^{9} d + 99 \, a^{10} b c^{8} d^{2} + 24 \, a^{11} c^{7} d^{3}\right )} x^{4} + \frac {5}{3} \, {\left (11 \, a^{9} b^{2} c^{10} + 22 \, a^{10} b c^{9} d + 9 \, a^{11} c^{8} d^{2}\right )} x^{3} + \frac {1}{2} \, {\left (11 \, a^{10} b c^{10} + 10 \, a^{11} c^{9} d\right )} x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)^11*(d*x+c)^10,x, algorithm="fricas")

[Out]

1/22*b^11*d^10*x^22 + a^11*c^10*x + 1/21*(10*b^11*c*d^9 + 11*a*b^10*d^10)*x^21 + 1/4*(9*b^11*c^2*d^8 + 22*a*b^
10*c*d^9 + 11*a^2*b^9*d^10)*x^20 + 5/19*(24*b^11*c^3*d^7 + 99*a*b^10*c^2*d^8 + 110*a^2*b^9*c*d^9 + 33*a^3*b^8*
d^10)*x^19 + 5/6*(14*b^11*c^4*d^6 + 88*a*b^10*c^3*d^7 + 165*a^2*b^9*c^2*d^8 + 110*a^3*b^8*c*d^9 + 22*a^4*b^7*d
^10)*x^18 + 3/17*(84*b^11*c^5*d^5 + 770*a*b^10*c^4*d^6 + 2200*a^2*b^9*c^3*d^7 + 2475*a^3*b^8*c^2*d^8 + 1100*a^
4*b^7*c*d^9 + 154*a^5*b^6*d^10)*x^17 + 3/8*(35*b^11*c^6*d^4 + 462*a*b^10*c^5*d^5 + 1925*a^2*b^9*c^4*d^6 + 3300
*a^3*b^8*c^3*d^7 + 2475*a^4*b^7*c^2*d^8 + 770*a^5*b^6*c*d^9 + 77*a^6*b^5*d^10)*x^16 + 2*(4*b^11*c^7*d^3 + 77*a
*b^10*c^6*d^4 + 462*a^2*b^9*c^5*d^5 + 1155*a^3*b^8*c^4*d^6 + 1320*a^4*b^7*c^3*d^7 + 693*a^5*b^6*c^2*d^8 + 154*
a^6*b^5*c*d^9 + 11*a^7*b^4*d^10)*x^15 + 15/14*(3*b^11*c^8*d^2 + 88*a*b^10*c^7*d^3 + 770*a^2*b^9*c^6*d^4 + 2772
*a^3*b^8*c^5*d^5 + 4620*a^4*b^7*c^4*d^6 + 3696*a^5*b^6*c^3*d^7 + 1386*a^6*b^5*c^2*d^8 + 220*a^7*b^4*c*d^9 + 11
*a^8*b^3*d^10)*x^14 + 5/13*(2*b^11*c^9*d + 99*a*b^10*c^8*d^2 + 1320*a^2*b^9*c^7*d^3 + 6930*a^3*b^8*c^6*d^4 + 1
6632*a^4*b^7*c^5*d^5 + 19404*a^5*b^6*c^4*d^6 + 11088*a^6*b^5*c^3*d^7 + 2970*a^7*b^4*c^2*d^8 + 330*a^8*b^3*c*d^
9 + 11*a^9*b^2*d^10)*x^13 + 1/12*(b^11*c^10 + 110*a*b^10*c^9*d + 2475*a^2*b^9*c^8*d^2 + 19800*a^3*b^8*c^7*d^3
+ 69300*a^4*b^7*c^6*d^4 + 116424*a^5*b^6*c^5*d^5 + 97020*a^6*b^5*c^4*d^6 + 39600*a^7*b^4*c^3*d^7 + 7425*a^8*b^
3*c^2*d^8 + 550*a^9*b^2*c*d^9 + 11*a^10*b*d^10)*x^12 + 1/11*(11*a*b^10*c^10 + 550*a^2*b^9*c^9*d + 7425*a^3*b^8
*c^8*d^2 + 39600*a^4*b^7*c^7*d^3 + 97020*a^5*b^6*c^6*d^4 + 116424*a^6*b^5*c^5*d^5 + 69300*a^7*b^4*c^4*d^6 + 19
800*a^8*b^3*c^3*d^7 + 2475*a^9*b^2*c^2*d^8 + 110*a^10*b*c*d^9 + a^11*d^10)*x^11 + 1/2*(11*a^2*b^9*c^10 + 330*a
^3*b^8*c^9*d + 2970*a^4*b^7*c^8*d^2 + 11088*a^5*b^6*c^7*d^3 + 19404*a^6*b^5*c^6*d^4 + 16632*a^7*b^4*c^5*d^5 +
6930*a^8*b^3*c^4*d^6 + 1320*a^9*b^2*c^3*d^7 + 99*a^10*b*c^2*d^8 + 2*a^11*c*d^9)*x^10 + 5/3*(11*a^3*b^8*c^10 +
220*a^4*b^7*c^9*d + 1386*a^5*b^6*c^8*d^2 + 3696*a^6*b^5*c^7*d^3 + 4620*a^7*b^4*c^6*d^4 + 2772*a^8*b^3*c^5*d^5
+ 770*a^9*b^2*c^4*d^6 + 88*a^10*b*c^3*d^7 + 3*a^11*c^2*d^8)*x^9 + 15/4*(11*a^4*b^7*c^10 + 154*a^5*b^6*c^9*d +
693*a^6*b^5*c^8*d^2 + 1320*a^7*b^4*c^7*d^3 + 1155*a^8*b^3*c^6*d^4 + 462*a^9*b^2*c^5*d^5 + 77*a^10*b*c^4*d^6 +
4*a^11*c^3*d^7)*x^8 + 6/7*(77*a^5*b^6*c^10 + 770*a^6*b^5*c^9*d + 2475*a^7*b^4*c^8*d^2 + 3300*a^8*b^3*c^7*d^3 +
1925*a^9*b^2*c^6*d^4 + 462*a^10*b*c^5*d^5 + 35*a^11*c^4*d^6)*x^7 + 1/2*(154*a^6*b^5*c^10 + 1100*a^7*b^4*c^9*d
+ 2475*a^8*b^3*c^8*d^2 + 2200*a^9*b^2*c^7*d^3 + 770*a^10*b*c^6*d^4 + 84*a^11*c^5*d^5)*x^6 + 3*(22*a^7*b^4*c^1
0 + 110*a^8*b^3*c^9*d + 165*a^9*b^2*c^8*d^2 + 88*a^10*b*c^7*d^3 + 14*a^11*c^6*d^4)*x^5 + 5/4*(33*a^8*b^3*c^10
+ 110*a^9*b^2*c^9*d + 99*a^10*b*c^8*d^2 + 24*a^11*c^7*d^3)*x^4 + 5/3*(11*a^9*b^2*c^10 + 22*a^10*b*c^9*d + 9*a^
11*c^8*d^2)*x^3 + 1/2*(11*a^10*b*c^10 + 10*a^11*c^9*d)*x^2

________________________________________________________________________________________

Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 1965 vs. \(2 (258) = 516\).
time = 0.13, size = 1965, normalized size = 7.04 \begin {gather*} a^{11} c^{10} x + \frac {b^{11} d^{10} x^{22}}{22} + x^{21} \cdot \left (\frac {11 a b^{10} d^{10}}{21} + \frac {10 b^{11} c d^{9}}{21}\right ) + x^{20} \cdot \left (\frac {11 a^{2} b^{9} d^{10}}{4} + \frac {11 a b^{10} c d^{9}}{2} + \frac {9 b^{11} c^{2} d^{8}}{4}\right ) + x^{19} \cdot \left (\frac {165 a^{3} b^{8} d^{10}}{19} + \frac {550 a^{2} b^{9} c d^{9}}{19} + \frac {495 a b^{10} c^{2} d^{8}}{19} + \frac {120 b^{11} c^{3} d^{7}}{19}\right ) + x^{18} \cdot \left (\frac {55 a^{4} b^{7} d^{10}}{3} + \frac {275 a^{3} b^{8} c d^{9}}{3} + \frac {275 a^{2} b^{9} c^{2} d^{8}}{2} + \frac {220 a b^{10} c^{3} d^{7}}{3} + \frac {35 b^{11} c^{4} d^{6}}{3}\right ) + x^{17} \cdot \left (\frac {462 a^{5} b^{6} d^{10}}{17} + \frac {3300 a^{4} b^{7} c d^{9}}{17} + \frac {7425 a^{3} b^{8} c^{2} d^{8}}{17} + \frac {6600 a^{2} b^{9} c^{3} d^{7}}{17} + \frac {2310 a b^{10} c^{4} d^{6}}{17} + \frac {252 b^{11} c^{5} d^{5}}{17}\right ) + x^{16} \cdot \left (\frac {231 a^{6} b^{5} d^{10}}{8} + \frac {1155 a^{5} b^{6} c d^{9}}{4} + \frac {7425 a^{4} b^{7} c^{2} d^{8}}{8} + \frac {2475 a^{3} b^{8} c^{3} d^{7}}{2} + \frac {5775 a^{2} b^{9} c^{4} d^{6}}{8} + \frac {693 a b^{10} c^{5} d^{5}}{4} + \frac {105 b^{11} c^{6} d^{4}}{8}\right ) + x^{15} \cdot \left (22 a^{7} b^{4} d^{10} + 308 a^{6} b^{5} c d^{9} + 1386 a^{5} b^{6} c^{2} d^{8} + 2640 a^{4} b^{7} c^{3} d^{7} + 2310 a^{3} b^{8} c^{4} d^{6} + 924 a^{2} b^{9} c^{5} d^{5} + 154 a b^{10} c^{6} d^{4} + 8 b^{11} c^{7} d^{3}\right ) + x^{14} \cdot \left (\frac {165 a^{8} b^{3} d^{10}}{14} + \frac {1650 a^{7} b^{4} c d^{9}}{7} + 1485 a^{6} b^{5} c^{2} d^{8} + 3960 a^{5} b^{6} c^{3} d^{7} + 4950 a^{4} b^{7} c^{4} d^{6} + 2970 a^{3} b^{8} c^{5} d^{5} + 825 a^{2} b^{9} c^{6} d^{4} + \frac {660 a b^{10} c^{7} d^{3}}{7} + \frac {45 b^{11} c^{8} d^{2}}{14}\right ) + x^{13} \cdot \left (\frac {55 a^{9} b^{2} d^{10}}{13} + \frac {1650 a^{8} b^{3} c d^{9}}{13} + \frac {14850 a^{7} b^{4} c^{2} d^{8}}{13} + \frac {55440 a^{6} b^{5} c^{3} d^{7}}{13} + \frac {97020 a^{5} b^{6} c^{4} d^{6}}{13} + \frac {83160 a^{4} b^{7} c^{5} d^{5}}{13} + \frac {34650 a^{3} b^{8} c^{6} d^{4}}{13} + \frac {6600 a^{2} b^{9} c^{7} d^{3}}{13} + \frac {495 a b^{10} c^{8} d^{2}}{13} + \frac {10 b^{11} c^{9} d}{13}\right ) + x^{12} \cdot \left (\frac {11 a^{10} b d^{10}}{12} + \frac {275 a^{9} b^{2} c d^{9}}{6} + \frac {2475 a^{8} b^{3} c^{2} d^{8}}{4} + 3300 a^{7} b^{4} c^{3} d^{7} + 8085 a^{6} b^{5} c^{4} d^{6} + 9702 a^{5} b^{6} c^{5} d^{5} + 5775 a^{4} b^{7} c^{6} d^{4} + 1650 a^{3} b^{8} c^{7} d^{3} + \frac {825 a^{2} b^{9} c^{8} d^{2}}{4} + \frac {55 a b^{10} c^{9} d}{6} + \frac {b^{11} c^{10}}{12}\right ) + x^{11} \left (\frac {a^{11} d^{10}}{11} + 10 a^{10} b c d^{9} + 225 a^{9} b^{2} c^{2} d^{8} + 1800 a^{8} b^{3} c^{3} d^{7} + 6300 a^{7} b^{4} c^{4} d^{6} + 10584 a^{6} b^{5} c^{5} d^{5} + 8820 a^{5} b^{6} c^{6} d^{4} + 3600 a^{4} b^{7} c^{7} d^{3} + 675 a^{3} b^{8} c^{8} d^{2} + 50 a^{2} b^{9} c^{9} d + a b^{10} c^{10}\right ) + x^{10} \left (a^{11} c d^{9} + \frac {99 a^{10} b c^{2} d^{8}}{2} + 660 a^{9} b^{2} c^{3} d^{7} + 3465 a^{8} b^{3} c^{4} d^{6} + 8316 a^{7} b^{4} c^{5} d^{5} + 9702 a^{6} b^{5} c^{6} d^{4} + 5544 a^{5} b^{6} c^{7} d^{3} + 1485 a^{4} b^{7} c^{8} d^{2} + 165 a^{3} b^{8} c^{9} d + \frac {11 a^{2} b^{9} c^{10}}{2}\right ) + x^{9} \cdot \left (5 a^{11} c^{2} d^{8} + \frac {440 a^{10} b c^{3} d^{7}}{3} + \frac {3850 a^{9} b^{2} c^{4} d^{6}}{3} + 4620 a^{8} b^{3} c^{5} d^{5} + 7700 a^{7} b^{4} c^{6} d^{4} + 6160 a^{6} b^{5} c^{7} d^{3} + 2310 a^{5} b^{6} c^{8} d^{2} + \frac {1100 a^{4} b^{7} c^{9} d}{3} + \frac {55 a^{3} b^{8} c^{10}}{3}\right ) + x^{8} \cdot \left (15 a^{11} c^{3} d^{7} + \frac {1155 a^{10} b c^{4} d^{6}}{4} + \frac {3465 a^{9} b^{2} c^{5} d^{5}}{2} + \frac {17325 a^{8} b^{3} c^{6} d^{4}}{4} + 4950 a^{7} b^{4} c^{7} d^{3} + \frac {10395 a^{6} b^{5} c^{8} d^{2}}{4} + \frac {1155 a^{5} b^{6} c^{9} d}{2} + \frac {165 a^{4} b^{7} c^{10}}{4}\right ) + x^{7} \cdot \left (30 a^{11} c^{4} d^{6} + 396 a^{10} b c^{5} d^{5} + 1650 a^{9} b^{2} c^{6} d^{4} + \frac {19800 a^{8} b^{3} c^{7} d^{3}}{7} + \frac {14850 a^{7} b^{4} c^{8} d^{2}}{7} + 660 a^{6} b^{5} c^{9} d + 66 a^{5} b^{6} c^{10}\right ) + x^{6} \cdot \left (42 a^{11} c^{5} d^{5} + 385 a^{10} b c^{6} d^{4} + 1100 a^{9} b^{2} c^{7} d^{3} + \frac {2475 a^{8} b^{3} c^{8} d^{2}}{2} + 550 a^{7} b^{4} c^{9} d + 77 a^{6} b^{5} c^{10}\right ) + x^{5} \cdot \left (42 a^{11} c^{6} d^{4} + 264 a^{10} b c^{7} d^{3} + 495 a^{9} b^{2} c^{8} d^{2} + 330 a^{8} b^{3} c^{9} d + 66 a^{7} b^{4} c^{10}\right ) + x^{4} \cdot \left (30 a^{11} c^{7} d^{3} + \frac {495 a^{10} b c^{8} d^{2}}{4} + \frac {275 a^{9} b^{2} c^{9} d}{2} + \frac {165 a^{8} b^{3} c^{10}}{4}\right ) + x^{3} \cdot \left (15 a^{11} c^{8} d^{2} + \frac {110 a^{10} b c^{9} d}{3} + \frac {55 a^{9} b^{2} c^{10}}{3}\right ) + x^{2} \cdot \left (5 a^{11} c^{9} d + \frac {11 a^{10} b c^{10}}{2}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)**11*(d*x+c)**10,x)

[Out]

a**11*c**10*x + b**11*d**10*x**22/22 + x**21*(11*a*b**10*d**10/21 + 10*b**11*c*d**9/21) + x**20*(11*a**2*b**9*
d**10/4 + 11*a*b**10*c*d**9/2 + 9*b**11*c**2*d**8/4) + x**19*(165*a**3*b**8*d**10/19 + 550*a**2*b**9*c*d**9/19
+ 495*a*b**10*c**2*d**8/19 + 120*b**11*c**3*d**7/19) + x**18*(55*a**4*b**7*d**10/3 + 275*a**3*b**8*c*d**9/3 +
275*a**2*b**9*c**2*d**8/2 + 220*a*b**10*c**3*d**7/3 + 35*b**11*c**4*d**6/3) + x**17*(462*a**5*b**6*d**10/17 +
3300*a**4*b**7*c*d**9/17 + 7425*a**3*b**8*c**2*d**8/17 + 6600*a**2*b**9*c**3*d**7/17 + 2310*a*b**10*c**4*d**6
/17 + 252*b**11*c**5*d**5/17) + x**16*(231*a**6*b**5*d**10/8 + 1155*a**5*b**6*c*d**9/4 + 7425*a**4*b**7*c**2*d
**8/8 + 2475*a**3*b**8*c**3*d**7/2 + 5775*a**2*b**9*c**4*d**6/8 + 693*a*b**10*c**5*d**5/4 + 105*b**11*c**6*d**
4/8) + x**15*(22*a**7*b**4*d**10 + 308*a**6*b**5*c*d**9 + 1386*a**5*b**6*c**2*d**8 + 2640*a**4*b**7*c**3*d**7
+ 2310*a**3*b**8*c**4*d**6 + 924*a**2*b**9*c**5*d**5 + 154*a*b**10*c**6*d**4 + 8*b**11*c**7*d**3) + x**14*(165
*a**8*b**3*d**10/14 + 1650*a**7*b**4*c*d**9/7 + 1485*a**6*b**5*c**2*d**8 + 3960*a**5*b**6*c**3*d**7 + 4950*a**
4*b**7*c**4*d**6 + 2970*a**3*b**8*c**5*d**5 + 825*a**2*b**9*c**6*d**4 + 660*a*b**10*c**7*d**3/7 + 45*b**11*c**
8*d**2/14) + x**13*(55*a**9*b**2*d**10/13 + 1650*a**8*b**3*c*d**9/13 + 14850*a**7*b**4*c**2*d**8/13 + 55440*a*
*6*b**5*c**3*d**7/13 + 97020*a**5*b**6*c**4*d**6/13 + 83160*a**4*b**7*c**5*d**5/13 + 34650*a**3*b**8*c**6*d**4
/13 + 6600*a**2*b**9*c**7*d**3/13 + 495*a*b**10*c**8*d**2/13 + 10*b**11*c**9*d/13) + x**12*(11*a**10*b*d**10/1
2 + 275*a**9*b**2*c*d**9/6 + 2475*a**8*b**3*c**2*d**8/4 + 3300*a**7*b**4*c**3*d**7 + 8085*a**6*b**5*c**4*d**6
+ 9702*a**5*b**6*c**5*d**5 + 5775*a**4*b**7*c**6*d**4 + 1650*a**3*b**8*c**7*d**3 + 825*a**2*b**9*c**8*d**2/4 +
55*a*b**10*c**9*d/6 + b**11*c**10/12) + x**11*(a**11*d**10/11 + 10*a**10*b*c*d**9 + 225*a**9*b**2*c**2*d**8 +
1800*a**8*b**3*c**3*d**7 + 6300*a**7*b**4*c**4*d**6 + 10584*a**6*b**5*c**5*d**5 + 8820*a**5*b**6*c**6*d**4 +
3600*a**4*b**7*c**7*d**3 + 675*a**3*b**8*c**8*d**2 + 50*a**2*b**9*c**9*d + a*b**10*c**10) + x**10*(a**11*c*d**
9 + 99*a**10*b*c**2*d**8/2 + 660*a**9*b**2*c**3*d**7 + 3465*a**8*b**3*c**4*d**6 + 8316*a**7*b**4*c**5*d**5 + 9
702*a**6*b**5*c**6*d**4 + 5544*a**5*b**6*c**7*d**3 + 1485*a**4*b**7*c**8*d**2 + 165*a**3*b**8*c**9*d + 11*a**2
*b**9*c**10/2) + x**9*(5*a**11*c**2*d**8 + 440*a**10*b*c**3*d**7/3 + 3850*a**9*b**2*c**4*d**6/3 + 4620*a**8*b*
*3*c**5*d**5 + 7700*a**7*b**4*c**6*d**4 + 6160*a**6*b**5*c**7*d**3 + 2310*a**5*b**6*c**8*d**2 + 1100*a**4*b**7
*c**9*d/3 + 55*a**3*b**8*c**10/3) + x**8*(15*a**11*c**3*d**7 + 1155*a**10*b*c**4*d**6/4 + 3465*a**9*b**2*c**5*
d**5/2 + 17325*a**8*b**3*c**6*d**4/4 + 4950*a**7*b**4*c**7*d**3 + 10395*a**6*b**5*c**8*d**2/4 + 1155*a**5*b**6
*c**9*d/2 + 165*a**4*b**7*c**10/4) + x**7*(30*a**11*c**4*d**6 + 396*a**10*b*c**5*d**5 + 1650*a**9*b**2*c**6*d*
*4 + 19800*a**8*b**3*c**7*d**3/7 + 14850*a**7*b**4*c**8*d**2/7 + 660*a**6*b**5*c**9*d + 66*a**5*b**6*c**10) +
x**6*(42*a**11*c**5*d**5 + 385*a**10*b*c**6*d**4 + 1100*a**9*b**2*c**7*d**3 + 2475*a**8*b**3*c**8*d**2/2 + 550
*a**7*b**4*c**9*d + 77*a**6*b**5*c**10) + x**5*(42*a**11*c**6*d**4 + 264*a**10*b*c**7*d**3 + 495*a**9*b**2*c**
8*d**2 + 330*a**8*b**3*c**9*d + 66*a**7*b**4*c**10) + x**4*(30*a**11*c**7*d**3 + 495*a**10*b*c**8*d**2/4 + 275
*a**9*b**2*c**9*d/2 + 165*a**8*b**3*c**10/4) + x**3*(15*a**11*c**8*d**2 + 110*a**10*b*c**9*d/3 + 55*a**9*b**2*
c**10/3) + x**2*(5*a**11*c**9*d + 11*a**10*b*c**10/2)

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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 2010 vs. \(2 (259) = 518\).
time = 1.33, size = 2010, normalized size = 7.20 \begin {gather*} \text {Too large to display} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)^11*(d*x+c)^10,x, algorithm="giac")

[Out]

1/22*b^11*d^10*x^22 + 10/21*b^11*c*d^9*x^21 + 11/21*a*b^10*d^10*x^21 + 9/4*b^11*c^2*d^8*x^20 + 11/2*a*b^10*c*d
^9*x^20 + 11/4*a^2*b^9*d^10*x^20 + 120/19*b^11*c^3*d^7*x^19 + 495/19*a*b^10*c^2*d^8*x^19 + 550/19*a^2*b^9*c*d^
9*x^19 + 165/19*a^3*b^8*d^10*x^19 + 35/3*b^11*c^4*d^6*x^18 + 220/3*a*b^10*c^3*d^7*x^18 + 275/2*a^2*b^9*c^2*d^8
*x^18 + 275/3*a^3*b^8*c*d^9*x^18 + 55/3*a^4*b^7*d^10*x^18 + 252/17*b^11*c^5*d^5*x^17 + 2310/17*a*b^10*c^4*d^6*
x^17 + 6600/17*a^2*b^9*c^3*d^7*x^17 + 7425/17*a^3*b^8*c^2*d^8*x^17 + 3300/17*a^4*b^7*c*d^9*x^17 + 462/17*a^5*b
^6*d^10*x^17 + 105/8*b^11*c^6*d^4*x^16 + 693/4*a*b^10*c^5*d^5*x^16 + 5775/8*a^2*b^9*c^4*d^6*x^16 + 2475/2*a^3*
b^8*c^3*d^7*x^16 + 7425/8*a^4*b^7*c^2*d^8*x^16 + 1155/4*a^5*b^6*c*d^9*x^16 + 231/8*a^6*b^5*d^10*x^16 + 8*b^11*
c^7*d^3*x^15 + 154*a*b^10*c^6*d^4*x^15 + 924*a^2*b^9*c^5*d^5*x^15 + 2310*a^3*b^8*c^4*d^6*x^15 + 2640*a^4*b^7*c
^3*d^7*x^15 + 1386*a^5*b^6*c^2*d^8*x^15 + 308*a^6*b^5*c*d^9*x^15 + 22*a^7*b^4*d^10*x^15 + 45/14*b^11*c^8*d^2*x
^14 + 660/7*a*b^10*c^7*d^3*x^14 + 825*a^2*b^9*c^6*d^4*x^14 + 2970*a^3*b^8*c^5*d^5*x^14 + 4950*a^4*b^7*c^4*d^6*
x^14 + 3960*a^5*b^6*c^3*d^7*x^14 + 1485*a^6*b^5*c^2*d^8*x^14 + 1650/7*a^7*b^4*c*d^9*x^14 + 165/14*a^8*b^3*d^10
*x^14 + 10/13*b^11*c^9*d*x^13 + 495/13*a*b^10*c^8*d^2*x^13 + 6600/13*a^2*b^9*c^7*d^3*x^13 + 34650/13*a^3*b^8*c
^6*d^4*x^13 + 83160/13*a^4*b^7*c^5*d^5*x^13 + 97020/13*a^5*b^6*c^4*d^6*x^13 + 55440/13*a^6*b^5*c^3*d^7*x^13 +
14850/13*a^7*b^4*c^2*d^8*x^13 + 1650/13*a^8*b^3*c*d^9*x^13 + 55/13*a^9*b^2*d^10*x^13 + 1/12*b^11*c^10*x^12 + 5
5/6*a*b^10*c^9*d*x^12 + 825/4*a^2*b^9*c^8*d^2*x^12 + 1650*a^3*b^8*c^7*d^3*x^12 + 5775*a^4*b^7*c^6*d^4*x^12 + 9
702*a^5*b^6*c^5*d^5*x^12 + 8085*a^6*b^5*c^4*d^6*x^12 + 3300*a^7*b^4*c^3*d^7*x^12 + 2475/4*a^8*b^3*c^2*d^8*x^12
+ 275/6*a^9*b^2*c*d^9*x^12 + 11/12*a^10*b*d^10*x^12 + a*b^10*c^10*x^11 + 50*a^2*b^9*c^9*d*x^11 + 675*a^3*b^8*
c^8*d^2*x^11 + 3600*a^4*b^7*c^7*d^3*x^11 + 8820*a^5*b^6*c^6*d^4*x^11 + 10584*a^6*b^5*c^5*d^5*x^11 + 6300*a^7*b
^4*c^4*d^6*x^11 + 1800*a^8*b^3*c^3*d^7*x^11 + 225*a^9*b^2*c^2*d^8*x^11 + 10*a^10*b*c*d^9*x^11 + 1/11*a^11*d^10
*x^11 + 11/2*a^2*b^9*c^10*x^10 + 165*a^3*b^8*c^9*d*x^10 + 1485*a^4*b^7*c^8*d^2*x^10 + 5544*a^5*b^6*c^7*d^3*x^1
0 + 9702*a^6*b^5*c^6*d^4*x^10 + 8316*a^7*b^4*c^5*d^5*x^10 + 3465*a^8*b^3*c^4*d^6*x^10 + 660*a^9*b^2*c^3*d^7*x^
10 + 99/2*a^10*b*c^2*d^8*x^10 + a^11*c*d^9*x^10 + 55/3*a^3*b^8*c^10*x^9 + 1100/3*a^4*b^7*c^9*d*x^9 + 2310*a^5*
b^6*c^8*d^2*x^9 + 6160*a^6*b^5*c^7*d^3*x^9 + 7700*a^7*b^4*c^6*d^4*x^9 + 4620*a^8*b^3*c^5*d^5*x^9 + 3850/3*a^9*
b^2*c^4*d^6*x^9 + 440/3*a^10*b*c^3*d^7*x^9 + 5*a^11*c^2*d^8*x^9 + 165/4*a^4*b^7*c^10*x^8 + 1155/2*a^5*b^6*c^9*
d*x^8 + 10395/4*a^6*b^5*c^8*d^2*x^8 + 4950*a^7*b^4*c^7*d^3*x^8 + 17325/4*a^8*b^3*c^6*d^4*x^8 + 3465/2*a^9*b^2*
c^5*d^5*x^8 + 1155/4*a^10*b*c^4*d^6*x^8 + 15*a^11*c^3*d^7*x^8 + 66*a^5*b^6*c^10*x^7 + 660*a^6*b^5*c^9*d*x^7 +
14850/7*a^7*b^4*c^8*d^2*x^7 + 19800/7*a^8*b^3*c^7*d^3*x^7 + 1650*a^9*b^2*c^6*d^4*x^7 + 396*a^10*b*c^5*d^5*x^7
+ 30*a^11*c^4*d^6*x^7 + 77*a^6*b^5*c^10*x^6 + 550*a^7*b^4*c^9*d*x^6 + 2475/2*a^8*b^3*c^8*d^2*x^6 + 1100*a^9*b^
2*c^7*d^3*x^6 + 385*a^10*b*c^6*d^4*x^6 + 42*a^11*c^5*d^5*x^6 + 66*a^7*b^4*c^10*x^5 + 330*a^8*b^3*c^9*d*x^5 + 4
95*a^9*b^2*c^8*d^2*x^5 + 264*a^10*b*c^7*d^3*x^5 + 42*a^11*c^6*d^4*x^5 + 165/4*a^8*b^3*c^10*x^4 + 275/2*a^9*b^2
*c^9*d*x^4 + 495/4*a^10*b*c^8*d^2*x^4 + 30*a^11*c^7*d^3*x^4 + 55/3*a^9*b^2*c^10*x^3 + 110/3*a^10*b*c^9*d*x^3 +
15*a^11*c^8*d^2*x^3 + 11/2*a^10*b*c^10*x^2 + 5*a^11*c^9*d*x^2 + a^11*c^10*x

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Mupad [B]
time = 1.03, size = 1702, normalized size = 6.10 \begin {gather*} x^7\,\left (30\,a^{11}\,c^4\,d^6+396\,a^{10}\,b\,c^5\,d^5+1650\,a^9\,b^2\,c^6\,d^4+\frac {19800\,a^8\,b^3\,c^7\,d^3}{7}+\frac {14850\,a^7\,b^4\,c^8\,d^2}{7}+660\,a^6\,b^5\,c^9\,d+66\,a^5\,b^6\,c^{10}\right )+x^{16}\,\left (\frac {231\,a^6\,b^5\,d^{10}}{8}+\frac {1155\,a^5\,b^6\,c\,d^9}{4}+\frac {7425\,a^4\,b^7\,c^2\,d^8}{8}+\frac {2475\,a^3\,b^8\,c^3\,d^7}{2}+\frac {5775\,a^2\,b^9\,c^4\,d^6}{8}+\frac {693\,a\,b^{10}\,c^5\,d^5}{4}+\frac {105\,b^{11}\,c^6\,d^4}{8}\right )+x^{11}\,\left (\frac {a^{11}\,d^{10}}{11}+10\,a^{10}\,b\,c\,d^9+225\,a^9\,b^2\,c^2\,d^8+1800\,a^8\,b^3\,c^3\,d^7+6300\,a^7\,b^4\,c^4\,d^6+10584\,a^6\,b^5\,c^5\,d^5+8820\,a^5\,b^6\,c^6\,d^4+3600\,a^4\,b^7\,c^7\,d^3+675\,a^3\,b^8\,c^8\,d^2+50\,a^2\,b^9\,c^9\,d+a\,b^{10}\,c^{10}\right )+x^{12}\,\left (\frac {11\,a^{10}\,b\,d^{10}}{12}+\frac {275\,a^9\,b^2\,c\,d^9}{6}+\frac {2475\,a^8\,b^3\,c^2\,d^8}{4}+3300\,a^7\,b^4\,c^3\,d^7+8085\,a^6\,b^5\,c^4\,d^6+9702\,a^5\,b^6\,c^5\,d^5+5775\,a^4\,b^7\,c^6\,d^4+1650\,a^3\,b^8\,c^7\,d^3+\frac {825\,a^2\,b^9\,c^8\,d^2}{4}+\frac {55\,a\,b^{10}\,c^9\,d}{6}+\frac {b^{11}\,c^{10}}{12}\right )+x^5\,\left (42\,a^{11}\,c^6\,d^4+264\,a^{10}\,b\,c^7\,d^3+495\,a^9\,b^2\,c^8\,d^2+330\,a^8\,b^3\,c^9\,d+66\,a^7\,b^4\,c^{10}\right )+x^{18}\,\left (\frac {55\,a^4\,b^7\,d^{10}}{3}+\frac {275\,a^3\,b^8\,c\,d^9}{3}+\frac {275\,a^2\,b^9\,c^2\,d^8}{2}+\frac {220\,a\,b^{10}\,c^3\,d^7}{3}+\frac {35\,b^{11}\,c^4\,d^6}{3}\right )+x^8\,\left (15\,a^{11}\,c^3\,d^7+\frac {1155\,a^{10}\,b\,c^4\,d^6}{4}+\frac {3465\,a^9\,b^2\,c^5\,d^5}{2}+\frac {17325\,a^8\,b^3\,c^6\,d^4}{4}+4950\,a^7\,b^4\,c^7\,d^3+\frac {10395\,a^6\,b^5\,c^8\,d^2}{4}+\frac {1155\,a^5\,b^6\,c^9\,d}{2}+\frac {165\,a^4\,b^7\,c^{10}}{4}\right )+x^{15}\,\left (22\,a^7\,b^4\,d^{10}+308\,a^6\,b^5\,c\,d^9+1386\,a^5\,b^6\,c^2\,d^8+2640\,a^4\,b^7\,c^3\,d^7+2310\,a^3\,b^8\,c^4\,d^6+924\,a^2\,b^9\,c^5\,d^5+154\,a\,b^{10}\,c^6\,d^4+8\,b^{11}\,c^7\,d^3\right )+x^6\,\left (42\,a^{11}\,c^5\,d^5+385\,a^{10}\,b\,c^6\,d^4+1100\,a^9\,b^2\,c^7\,d^3+\frac {2475\,a^8\,b^3\,c^8\,d^2}{2}+550\,a^7\,b^4\,c^9\,d+77\,a^6\,b^5\,c^{10}\right )+x^{17}\,\left (\frac {462\,a^5\,b^6\,d^{10}}{17}+\frac {3300\,a^4\,b^7\,c\,d^9}{17}+\frac {7425\,a^3\,b^8\,c^2\,d^8}{17}+\frac {6600\,a^2\,b^9\,c^3\,d^7}{17}+\frac {2310\,a\,b^{10}\,c^4\,d^6}{17}+\frac {252\,b^{11}\,c^5\,d^5}{17}\right )+x^9\,\left (5\,a^{11}\,c^2\,d^8+\frac {440\,a^{10}\,b\,c^3\,d^7}{3}+\frac {3850\,a^9\,b^2\,c^4\,d^6}{3}+4620\,a^8\,b^3\,c^5\,d^5+7700\,a^7\,b^4\,c^6\,d^4+6160\,a^6\,b^5\,c^7\,d^3+2310\,a^5\,b^6\,c^8\,d^2+\frac {1100\,a^4\,b^7\,c^9\,d}{3}+\frac {55\,a^3\,b^8\,c^{10}}{3}\right )+x^{14}\,\left (\frac {165\,a^8\,b^3\,d^{10}}{14}+\frac {1650\,a^7\,b^4\,c\,d^9}{7}+1485\,a^6\,b^5\,c^2\,d^8+3960\,a^5\,b^6\,c^3\,d^7+4950\,a^4\,b^7\,c^4\,d^6+2970\,a^3\,b^8\,c^5\,d^5+825\,a^2\,b^9\,c^6\,d^4+\frac {660\,a\,b^{10}\,c^7\,d^3}{7}+\frac {45\,b^{11}\,c^8\,d^2}{14}\right )+x^{10}\,\left (a^{11}\,c\,d^9+\frac {99\,a^{10}\,b\,c^2\,d^8}{2}+660\,a^9\,b^2\,c^3\,d^7+3465\,a^8\,b^3\,c^4\,d^6+8316\,a^7\,b^4\,c^5\,d^5+9702\,a^6\,b^5\,c^6\,d^4+5544\,a^5\,b^6\,c^7\,d^3+1485\,a^4\,b^7\,c^8\,d^2+165\,a^3\,b^8\,c^9\,d+\frac {11\,a^2\,b^9\,c^{10}}{2}\right )+x^{13}\,\left (\frac {55\,a^9\,b^2\,d^{10}}{13}+\frac {1650\,a^8\,b^3\,c\,d^9}{13}+\frac {14850\,a^7\,b^4\,c^2\,d^8}{13}+\frac {55440\,a^6\,b^5\,c^3\,d^7}{13}+\frac {97020\,a^5\,b^6\,c^4\,d^6}{13}+\frac {83160\,a^4\,b^7\,c^5\,d^5}{13}+\frac {34650\,a^3\,b^8\,c^6\,d^4}{13}+\frac {6600\,a^2\,b^9\,c^7\,d^3}{13}+\frac {495\,a\,b^{10}\,c^8\,d^2}{13}+\frac {10\,b^{11}\,c^9\,d}{13}\right )+a^{11}\,c^{10}\,x+\frac {b^{11}\,d^{10}\,x^{22}}{22}+\frac {5\,a^8\,c^7\,x^4\,\left (24\,a^3\,d^3+99\,a^2\,b\,c\,d^2+110\,a\,b^2\,c^2\,d+33\,b^3\,c^3\right )}{4}+\frac {5\,b^8\,d^7\,x^{19}\,\left (33\,a^3\,d^3+110\,a^2\,b\,c\,d^2+99\,a\,b^2\,c^2\,d+24\,b^3\,c^3\right )}{19}+\frac {a^{10}\,c^9\,x^2\,\left (10\,a\,d+11\,b\,c\right )}{2}+\frac {b^{10}\,d^9\,x^{21}\,\left (11\,a\,d+10\,b\,c\right )}{21}+\frac {5\,a^9\,c^8\,x^3\,\left (9\,a^2\,d^2+22\,a\,b\,c\,d+11\,b^2\,c^2\right )}{3}+\frac {b^9\,d^8\,x^{20}\,\left (11\,a^2\,d^2+22\,a\,b\,c\,d+9\,b^2\,c^2\right )}{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a + b*x)^11*(c + d*x)^10,x)

[Out]

x^7*(66*a^5*b^6*c^10 + 30*a^11*c^4*d^6 + 660*a^6*b^5*c^9*d + 396*a^10*b*c^5*d^5 + (14850*a^7*b^4*c^8*d^2)/7 +
(19800*a^8*b^3*c^7*d^3)/7 + 1650*a^9*b^2*c^6*d^4) + x^16*((231*a^6*b^5*d^10)/8 + (105*b^11*c^6*d^4)/8 + (693*a
*b^10*c^5*d^5)/4 + (1155*a^5*b^6*c*d^9)/4 + (5775*a^2*b^9*c^4*d^6)/8 + (2475*a^3*b^8*c^3*d^7)/2 + (7425*a^4*b^
7*c^2*d^8)/8) + x^11*((a^11*d^10)/11 + a*b^10*c^10 + 50*a^2*b^9*c^9*d + 675*a^3*b^8*c^8*d^2 + 3600*a^4*b^7*c^7
*d^3 + 8820*a^5*b^6*c^6*d^4 + 10584*a^6*b^5*c^5*d^5 + 6300*a^7*b^4*c^4*d^6 + 1800*a^8*b^3*c^3*d^7 + 225*a^9*b^
2*c^2*d^8 + 10*a^10*b*c*d^9) + x^12*((b^11*c^10)/12 + (11*a^10*b*d^10)/12 + (275*a^9*b^2*c*d^9)/6 + (825*a^2*b
^9*c^8*d^2)/4 + 1650*a^3*b^8*c^7*d^3 + 5775*a^4*b^7*c^6*d^4 + 9702*a^5*b^6*c^5*d^5 + 8085*a^6*b^5*c^4*d^6 + 33
00*a^7*b^4*c^3*d^7 + (2475*a^8*b^3*c^2*d^8)/4 + (55*a*b^10*c^9*d)/6) + x^5*(66*a^7*b^4*c^10 + 42*a^11*c^6*d^4
+ 330*a^8*b^3*c^9*d + 264*a^10*b*c^7*d^3 + 495*a^9*b^2*c^8*d^2) + x^18*((55*a^4*b^7*d^10)/3 + (35*b^11*c^4*d^6
)/3 + (220*a*b^10*c^3*d^7)/3 + (275*a^3*b^8*c*d^9)/3 + (275*a^2*b^9*c^2*d^8)/2) + x^8*((165*a^4*b^7*c^10)/4 +
15*a^11*c^3*d^7 + (1155*a^5*b^6*c^9*d)/2 + (1155*a^10*b*c^4*d^6)/4 + (10395*a^6*b^5*c^8*d^2)/4 + 4950*a^7*b^4*
c^7*d^3 + (17325*a^8*b^3*c^6*d^4)/4 + (3465*a^9*b^2*c^5*d^5)/2) + x^15*(22*a^7*b^4*d^10 + 8*b^11*c^7*d^3 + 154
*a*b^10*c^6*d^4 + 308*a^6*b^5*c*d^9 + 924*a^2*b^9*c^5*d^5 + 2310*a^3*b^8*c^4*d^6 + 2640*a^4*b^7*c^3*d^7 + 1386
*a^5*b^6*c^2*d^8) + x^6*(77*a^6*b^5*c^10 + 42*a^11*c^5*d^5 + 550*a^7*b^4*c^9*d + 385*a^10*b*c^6*d^4 + (2475*a^
8*b^3*c^8*d^2)/2 + 1100*a^9*b^2*c^7*d^3) + x^17*((462*a^5*b^6*d^10)/17 + (252*b^11*c^5*d^5)/17 + (2310*a*b^10*
c^4*d^6)/17 + (3300*a^4*b^7*c*d^9)/17 + (6600*a^2*b^9*c^3*d^7)/17 + (7425*a^3*b^8*c^2*d^8)/17) + x^9*((55*a^3*
b^8*c^10)/3 + 5*a^11*c^2*d^8 + (1100*a^4*b^7*c^9*d)/3 + (440*a^10*b*c^3*d^7)/3 + 2310*a^5*b^6*c^8*d^2 + 6160*a
^6*b^5*c^7*d^3 + 7700*a^7*b^4*c^6*d^4 + 4620*a^8*b^3*c^5*d^5 + (3850*a^9*b^2*c^4*d^6)/3) + x^14*((165*a^8*b^3*
d^10)/14 + (45*b^11*c^8*d^2)/14 + (660*a*b^10*c^7*d^3)/7 + (1650*a^7*b^4*c*d^9)/7 + 825*a^2*b^9*c^6*d^4 + 2970
*a^3*b^8*c^5*d^5 + 4950*a^4*b^7*c^4*d^6 + 3960*a^5*b^6*c^3*d^7 + 1485*a^6*b^5*c^2*d^8) + x^10*(a^11*c*d^9 + (1
1*a^2*b^9*c^10)/2 + 165*a^3*b^8*c^9*d + (99*a^10*b*c^2*d^8)/2 + 1485*a^4*b^7*c^8*d^2 + 5544*a^5*b^6*c^7*d^3 +
9702*a^6*b^5*c^6*d^4 + 8316*a^7*b^4*c^5*d^5 + 3465*a^8*b^3*c^4*d^6 + 660*a^9*b^2*c^3*d^7) + x^13*((10*b^11*c^9
*d)/13 + (55*a^9*b^2*d^10)/13 + (495*a*b^10*c^8*d^2)/13 + (1650*a^8*b^3*c*d^9)/13 + (6600*a^2*b^9*c^7*d^3)/13
+ (34650*a^3*b^8*c^6*d^4)/13 + (83160*a^4*b^7*c^5*d^5)/13 + (97020*a^5*b^6*c^4*d^6)/13 + (55440*a^6*b^5*c^3*d^
7)/13 + (14850*a^7*b^4*c^2*d^8)/13) + a^11*c^10*x + (b^11*d^10*x^22)/22 + (5*a^8*c^7*x^4*(24*a^3*d^3 + 33*b^3*
c^3 + 110*a*b^2*c^2*d + 99*a^2*b*c*d^2))/4 + (5*b^8*d^7*x^19*(33*a^3*d^3 + 24*b^3*c^3 + 99*a*b^2*c^2*d + 110*a
^2*b*c*d^2))/19 + (a^10*c^9*x^2*(10*a*d + 11*b*c))/2 + (b^10*d^9*x^21*(11*a*d + 10*b*c))/21 + (5*a^9*c^8*x^3*(
9*a^2*d^2 + 11*b^2*c^2 + 22*a*b*c*d))/3 + (b^9*d^8*x^20*(11*a^2*d^2 + 9*b^2*c^2 + 22*a*b*c*d))/4

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