3.14.4 \(\int (a+b x)^7 (c+d x)^{10} \, dx\) [1304]

Optimal. Leaf size=200 \[ -\frac {(b c-a d)^7 (c+d x)^{11}}{11 d^8}+\frac {7 b (b c-a d)^6 (c+d x)^{12}}{12 d^8}-\frac {21 b^2 (b c-a d)^5 (c+d x)^{13}}{13 d^8}+\frac {5 b^3 (b c-a d)^4 (c+d x)^{14}}{2 d^8}-\frac {7 b^4 (b c-a d)^3 (c+d x)^{15}}{3 d^8}+\frac {21 b^5 (b c-a d)^2 (c+d x)^{16}}{16 d^8}-\frac {7 b^6 (b c-a d) (c+d x)^{17}}{17 d^8}+\frac {b^7 (c+d x)^{18}}{18 d^8} \]

[Out]

-1/11*(-a*d+b*c)^7*(d*x+c)^11/d^8+7/12*b*(-a*d+b*c)^6*(d*x+c)^12/d^8-21/13*b^2*(-a*d+b*c)^5*(d*x+c)^13/d^8+5/2
*b^3*(-a*d+b*c)^4*(d*x+c)^14/d^8-7/3*b^4*(-a*d+b*c)^3*(d*x+c)^15/d^8+21/16*b^5*(-a*d+b*c)^2*(d*x+c)^16/d^8-7/1
7*b^6*(-a*d+b*c)*(d*x+c)^17/d^8+1/18*b^7*(d*x+c)^18/d^8

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Rubi [A]
time = 0.53, antiderivative size = 200, 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 {7 b^6 (c+d x)^{17} (b c-a d)}{17 d^8}+\frac {21 b^5 (c+d x)^{16} (b c-a d)^2}{16 d^8}-\frac {7 b^4 (c+d x)^{15} (b c-a d)^3}{3 d^8}+\frac {5 b^3 (c+d x)^{14} (b c-a d)^4}{2 d^8}-\frac {21 b^2 (c+d x)^{13} (b c-a d)^5}{13 d^8}+\frac {7 b (c+d x)^{12} (b c-a d)^6}{12 d^8}-\frac {(c+d x)^{11} (b c-a d)^7}{11 d^8}+\frac {b^7 (c+d x)^{18}}{18 d^8} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(a + b*x)^7*(c + d*x)^10,x]

[Out]

-1/11*((b*c - a*d)^7*(c + d*x)^11)/d^8 + (7*b*(b*c - a*d)^6*(c + d*x)^12)/(12*d^8) - (21*b^2*(b*c - a*d)^5*(c
+ d*x)^13)/(13*d^8) + (5*b^3*(b*c - a*d)^4*(c + d*x)^14)/(2*d^8) - (7*b^4*(b*c - a*d)^3*(c + d*x)^15)/(3*d^8)
+ (21*b^5*(b*c - a*d)^2*(c + d*x)^16)/(16*d^8) - (7*b^6*(b*c - a*d)*(c + d*x)^17)/(17*d^8) + (b^7*(c + d*x)^18
)/(18*d^8)

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

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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(1105\) vs. \(2(200)=400\).
time = 0.08, size = 1105, normalized size = 5.52 \begin {gather*} a^7 c^{10} x+\frac {1}{2} a^6 c^9 (7 b c+10 a d) x^2+\frac {1}{3} a^5 c^8 \left (21 b^2 c^2+70 a b c d+45 a^2 d^2\right ) x^3+\frac {5}{4} a^4 c^7 \left (7 b^3 c^3+42 a b^2 c^2 d+63 a^2 b c d^2+24 a^3 d^3\right ) x^4+7 a^3 c^6 \left (b^4 c^4+10 a b^3 c^3 d+27 a^2 b^2 c^2 d^2+24 a^3 b c d^3+6 a^4 d^4\right ) x^5+\frac {7}{6} a^2 c^5 \left (3 b^5 c^5+50 a b^4 c^4 d+225 a^2 b^3 c^3 d^2+360 a^3 b^2 c^2 d^3+210 a^4 b c d^4+36 a^5 d^5\right ) x^6+a c^4 \left (b^6 c^6+30 a b^5 c^5 d+225 a^2 b^4 c^4 d^2+600 a^3 b^3 c^3 d^3+630 a^4 b^2 c^2 d^4+252 a^5 b c d^5+30 a^6 d^6\right ) x^7+\frac {1}{8} c^3 \left (b^7 c^7+70 a b^6 c^6 d+945 a^2 b^5 c^5 d^2+4200 a^3 b^4 c^4 d^3+7350 a^4 b^3 c^3 d^4+5292 a^5 b^2 c^2 d^5+1470 a^6 b c d^6+120 a^7 d^7\right ) x^8+\frac {5}{9} c^2 d \left (2 b^7 c^7+63 a b^6 c^6 d+504 a^2 b^5 c^5 d^2+1470 a^3 b^4 c^4 d^3+1764 a^4 b^3 c^3 d^4+882 a^5 b^2 c^2 d^5+168 a^6 b c d^6+9 a^7 d^7\right ) x^9+\frac {1}{2} c d^2 \left (9 b^7 c^7+168 a b^6 c^6 d+882 a^2 b^5 c^5 d^2+1764 a^3 b^4 c^4 d^3+1470 a^4 b^3 c^3 d^4+504 a^5 b^2 c^2 d^5+63 a^6 b c d^6+2 a^7 d^7\right ) x^{10}+\frac {1}{11} d^3 \left (120 b^7 c^7+1470 a b^6 c^6 d+5292 a^2 b^5 c^5 d^2+7350 a^3 b^4 c^4 d^3+4200 a^4 b^3 c^3 d^4+945 a^5 b^2 c^2 d^5+70 a^6 b c d^6+a^7 d^7\right ) x^{11}+\frac {7}{12} b d^4 \left (30 b^6 c^6+252 a b^5 c^5 d+630 a^2 b^4 c^4 d^2+600 a^3 b^3 c^3 d^3+225 a^4 b^2 c^2 d^4+30 a^5 b c d^5+a^6 d^6\right ) x^{12}+\frac {7}{13} b^2 d^5 \left (36 b^5 c^5+210 a b^4 c^4 d+360 a^2 b^3 c^3 d^2+225 a^3 b^2 c^2 d^3+50 a^4 b c d^4+3 a^5 d^5\right ) x^{13}+\frac {5}{2} b^3 d^6 \left (6 b^4 c^4+24 a b^3 c^3 d+27 a^2 b^2 c^2 d^2+10 a^3 b c d^3+a^4 d^4\right ) x^{14}+\frac {1}{3} b^4 d^7 \left (24 b^3 c^3+63 a b^2 c^2 d+42 a^2 b c d^2+7 a^3 d^3\right ) x^{15}+\frac {1}{16} b^5 d^8 \left (45 b^2 c^2+70 a b c d+21 a^2 d^2\right ) x^{16}+\frac {1}{17} b^6 d^9 (10 b c+7 a d) x^{17}+\frac {1}{18} b^7 d^{10} x^{18} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(a + b*x)^7*(c + d*x)^10,x]

[Out]

a^7*c^10*x + (a^6*c^9*(7*b*c + 10*a*d)*x^2)/2 + (a^5*c^8*(21*b^2*c^2 + 70*a*b*c*d + 45*a^2*d^2)*x^3)/3 + (5*a^
4*c^7*(7*b^3*c^3 + 42*a*b^2*c^2*d + 63*a^2*b*c*d^2 + 24*a^3*d^3)*x^4)/4 + 7*a^3*c^6*(b^4*c^4 + 10*a*b^3*c^3*d
+ 27*a^2*b^2*c^2*d^2 + 24*a^3*b*c*d^3 + 6*a^4*d^4)*x^5 + (7*a^2*c^5*(3*b^5*c^5 + 50*a*b^4*c^4*d + 225*a^2*b^3*
c^3*d^2 + 360*a^3*b^2*c^2*d^3 + 210*a^4*b*c*d^4 + 36*a^5*d^5)*x^6)/6 + a*c^4*(b^6*c^6 + 30*a*b^5*c^5*d + 225*a
^2*b^4*c^4*d^2 + 600*a^3*b^3*c^3*d^3 + 630*a^4*b^2*c^2*d^4 + 252*a^5*b*c*d^5 + 30*a^6*d^6)*x^7 + (c^3*(b^7*c^7
+ 70*a*b^6*c^6*d + 945*a^2*b^5*c^5*d^2 + 4200*a^3*b^4*c^4*d^3 + 7350*a^4*b^3*c^3*d^4 + 5292*a^5*b^2*c^2*d^5 +
1470*a^6*b*c*d^6 + 120*a^7*d^7)*x^8)/8 + (5*c^2*d*(2*b^7*c^7 + 63*a*b^6*c^6*d + 504*a^2*b^5*c^5*d^2 + 1470*a^
3*b^4*c^4*d^3 + 1764*a^4*b^3*c^3*d^4 + 882*a^5*b^2*c^2*d^5 + 168*a^6*b*c*d^6 + 9*a^7*d^7)*x^9)/9 + (c*d^2*(9*b
^7*c^7 + 168*a*b^6*c^6*d + 882*a^2*b^5*c^5*d^2 + 1764*a^3*b^4*c^4*d^3 + 1470*a^4*b^3*c^3*d^4 + 504*a^5*b^2*c^2
*d^5 + 63*a^6*b*c*d^6 + 2*a^7*d^7)*x^10)/2 + (d^3*(120*b^7*c^7 + 1470*a*b^6*c^6*d + 5292*a^2*b^5*c^5*d^2 + 735
0*a^3*b^4*c^4*d^3 + 4200*a^4*b^3*c^3*d^4 + 945*a^5*b^2*c^2*d^5 + 70*a^6*b*c*d^6 + a^7*d^7)*x^11)/11 + (7*b*d^4
*(30*b^6*c^6 + 252*a*b^5*c^5*d + 630*a^2*b^4*c^4*d^2 + 600*a^3*b^3*c^3*d^3 + 225*a^4*b^2*c^2*d^4 + 30*a^5*b*c*
d^5 + a^6*d^6)*x^12)/12 + (7*b^2*d^5*(36*b^5*c^5 + 210*a*b^4*c^4*d + 360*a^2*b^3*c^3*d^2 + 225*a^3*b^2*c^2*d^3
+ 50*a^4*b*c*d^4 + 3*a^5*d^5)*x^13)/13 + (5*b^3*d^6*(6*b^4*c^4 + 24*a*b^3*c^3*d + 27*a^2*b^2*c^2*d^2 + 10*a^3
*b*c*d^3 + a^4*d^4)*x^14)/2 + (b^4*d^7*(24*b^3*c^3 + 63*a*b^2*c^2*d + 42*a^2*b*c*d^2 + 7*a^3*d^3)*x^15)/3 + (b
^5*d^8*(45*b^2*c^2 + 70*a*b*c*d + 21*a^2*d^2)*x^16)/16 + (b^6*d^9*(10*b*c + 7*a*d)*x^17)/17 + (b^7*d^10*x^18)/
18

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Mathics [B] Leaf count is larger than twice the leaf count of optimal. \(1072\) vs. \(2(200)=400\).
time = 10.35, size = 1070, normalized size = 5.35 \begin {gather*} \frac {x \left (350064 a^7 c^{10}+175032 a^6 c^9 x \left (10 a d+7 b c\right )+a^5 c^8 x^2 \left (5250960 a^2 d^2+8168160 a b c d+2450448 b^2 c^2\right )+a^4 c^7 x^3 \left (10501920 a^3 d^3+27567540 a^2 b c d^2+18378360 a b^2 c^2 d+3063060 b^3 c^3\right )+a^3 c^6 x^4 \left (14702688 a^4 d^4+58810752 a^3 b c d^3+66162096 a^2 b^2 c^2 d^2+24504480 a b^3 c^3 d+2450448 b^4 c^4\right )+a^2 c^5 x^5 \left (14702688 a^5 d^5+85765680 a^4 b c d^4+147026880 a^3 b^2 c^2 d^3+91891800 a^2 b^3 c^3 d^2+20420400 a b^4 c^4 d+1225224 b^5 c^5\right )+350064 a c^4 x^6 \left (30 a^6 d^6+252 a^5 b c d^5+630 a^4 b^2 c^2 d^4+600 a^3 b^3 c^3 d^3+225 a^2 b^4 c^4 d^2+30 a b^5 c^5 d+b^6 c^6\right )+204204 b d^4 x^{11} \left (a^6 d^6+30 a^5 b c d^5+225 a^4 b^2 c^2 d^4+600 a^3 b^3 c^3 d^3+630 a^2 b^4 c^4 d^2+252 a b^5 c^5 d+30 b^6 c^6\right )+b^4 d^7 x^{14} \left (816816 a^3 d^3+4900896 a^2 b c d^2+7351344 a b^2 c^2 d+2800512 b^3 c^3\right )+b^6 d^9 x^{16} \left (144144 a d+205920 b c\right )+c^3 x^7 \left (5250960 a^7 d^7+64324260 a^6 b c d^6+231567336 a^5 b^2 c^2 d^5+321621300 a^4 b^3 c^3 d^4+183783600 a^3 b^4 c^4 d^3+41351310 a^2 b^5 c^5 d^2+3063060 a b^6 c^6 d+43758 b^7 c^7\right )+d^3 x^{10} \left (31824 a^7 d^7+2227680 a^6 b c d^6+30073680 a^5 b^2 c^2 d^5+133660800 a^4 b^3 c^3 d^4+233906400 a^3 b^4 c^4 d^3+168412608 a^2 b^5 c^5 d^2+46781280 a b^6 c^6 d+3818880 b^7 c^7\right )+b^2 d^5 x^{12} \left (565488 a^5 d^5+9424800 a^4 b c d^4+42411600 a^3 b^2 c^2 d^3+67858560 a^2 b^3 c^3 d^2+39584160 a b^4 c^4 d+6785856 b^5 c^5\right )+b^3 d^6 x^{13} \left (875160 a^4 d^4+8751600 a^3 b c d^3+23629320 a^2 b^2 c^2 d^2+21003840 a b^3 c^3 d+5250960 b^4 c^4\right )+b^5 d^8 x^{15} \left (459459 a^2 d^2+1531530 a b c d+984555 b^2 c^2\right )+19448 b^7 d^{10} x^{17}+194480 c^2 d x^8 \left (9 a^7 d^7+168 a^6 b c d^6+882 a^5 b^2 c^2 d^5+1764 a^4 b^3 c^3 d^4+1470 a^3 b^4 c^4 d^3+504 a^2 b^5 c^5 d^2+63 a b^6 c^6 d+2 b^7 c^7\right )+175032 c d^2 x^9 \left (2 a^7 d^7+63 a^6 b c d^6+504 a^5 b^2 c^2 d^5+1470 a^4 b^3 c^3 d^4+1764 a^3 b^4 c^4 d^3+882 a^2 b^5 c^5 d^2+168 a b^6 c^6 d+9 b^7 c^7\right )\right )}{350064} \end {gather*}

Antiderivative was successfully verified.

[In]

mathics('Integrate[(a + b*x)^7*(c + d*x)^10,x]')

[Out]

x (350064 a ^ 7 c ^ 10 + 175032 a ^ 6 c ^ 9 x (10 a d + 7 b c) + a ^ 5 c ^ 8 x ^ 2 (5250960 a ^ 2 d ^ 2 + 8168
160 a b c d + 2450448 b ^ 2 c ^ 2) + a ^ 4 c ^ 7 x ^ 3 (10501920 a ^ 3 d ^ 3 + 27567540 a ^ 2 b c d ^ 2 + 1837
8360 a b ^ 2 c ^ 2 d + 3063060 b ^ 3 c ^ 3) + a ^ 3 c ^ 6 x ^ 4 (14702688 a ^ 4 d ^ 4 + 58810752 a ^ 3 b c d ^
3 + 66162096 a ^ 2 b ^ 2 c ^ 2 d ^ 2 + 24504480 a b ^ 3 c ^ 3 d + 2450448 b ^ 4 c ^ 4) + a ^ 2 c ^ 5 x ^ 5 (1
4702688 a ^ 5 d ^ 5 + 85765680 a ^ 4 b c d ^ 4 + 147026880 a ^ 3 b ^ 2 c ^ 2 d ^ 3 + 91891800 a ^ 2 b ^ 3 c ^
3 d ^ 2 + 20420400 a b ^ 4 c ^ 4 d + 1225224 b ^ 5 c ^ 5) + 350064 a c ^ 4 x ^ 6 (30 a ^ 6 d ^ 6 + 252 a ^ 5 b
c d ^ 5 + 630 a ^ 4 b ^ 2 c ^ 2 d ^ 4 + 600 a ^ 3 b ^ 3 c ^ 3 d ^ 3 + 225 a ^ 2 b ^ 4 c ^ 4 d ^ 2 + 30 a b ^
5 c ^ 5 d + b ^ 6 c ^ 6) + 204204 b d ^ 4 x ^ 11 (a ^ 6 d ^ 6 + 30 a ^ 5 b c d ^ 5 + 225 a ^ 4 b ^ 2 c ^ 2 d ^
4 + 600 a ^ 3 b ^ 3 c ^ 3 d ^ 3 + 630 a ^ 2 b ^ 4 c ^ 4 d ^ 2 + 252 a b ^ 5 c ^ 5 d + 30 b ^ 6 c ^ 6) + b ^ 4
d ^ 7 x ^ 14 (816816 a ^ 3 d ^ 3 + 4900896 a ^ 2 b c d ^ 2 + 7351344 a b ^ 2 c ^ 2 d + 2800512 b ^ 3 c ^ 3) +
b ^ 6 d ^ 9 x ^ 16 (144144 a d + 205920 b c) + c ^ 3 x ^ 7 (5250960 a ^ 7 d ^ 7 + 64324260 a ^ 6 b c d ^ 6 +
231567336 a ^ 5 b ^ 2 c ^ 2 d ^ 5 + 321621300 a ^ 4 b ^ 3 c ^ 3 d ^ 4 + 183783600 a ^ 3 b ^ 4 c ^ 4 d ^ 3 + 41
351310 a ^ 2 b ^ 5 c ^ 5 d ^ 2 + 3063060 a b ^ 6 c ^ 6 d + 43758 b ^ 7 c ^ 7) + d ^ 3 x ^ 10 (31824 a ^ 7 d ^
7 + 2227680 a ^ 6 b c d ^ 6 + 30073680 a ^ 5 b ^ 2 c ^ 2 d ^ 5 + 133660800 a ^ 4 b ^ 3 c ^ 3 d ^ 4 + 233906400
a ^ 3 b ^ 4 c ^ 4 d ^ 3 + 168412608 a ^ 2 b ^ 5 c ^ 5 d ^ 2 + 46781280 a b ^ 6 c ^ 6 d + 3818880 b ^ 7 c ^ 7)
+ b ^ 2 d ^ 5 x ^ 12 (565488 a ^ 5 d ^ 5 + 9424800 a ^ 4 b c d ^ 4 + 42411600 a ^ 3 b ^ 2 c ^ 2 d ^ 3 + 67858
560 a ^ 2 b ^ 3 c ^ 3 d ^ 2 + 39584160 a b ^ 4 c ^ 4 d + 6785856 b ^ 5 c ^ 5) + b ^ 3 d ^ 6 x ^ 13 (875160 a ^
4 d ^ 4 + 8751600 a ^ 3 b c d ^ 3 + 23629320 a ^ 2 b ^ 2 c ^ 2 d ^ 2 + 21003840 a b ^ 3 c ^ 3 d + 5250960 b ^
4 c ^ 4) + b ^ 5 d ^ 8 x ^ 15 (459459 a ^ 2 d ^ 2 + 1531530 a b c d + 984555 b ^ 2 c ^ 2) + 19448 b ^ 7 d ^ 1
0 x ^ 17 + 194480 c ^ 2 d x ^ 8 (9 a ^ 7 d ^ 7 + 168 a ^ 6 b c d ^ 6 + 882 a ^ 5 b ^ 2 c ^ 2 d ^ 5 + 1764 a ^
4 b ^ 3 c ^ 3 d ^ 4 + 1470 a ^ 3 b ^ 4 c ^ 4 d ^ 3 + 504 a ^ 2 b ^ 5 c ^ 5 d ^ 2 + 63 a b ^ 6 c ^ 6 d + 2 b ^
7 c ^ 7) + 175032 c d ^ 2 x ^ 9 (2 a ^ 7 d ^ 7 + 63 a ^ 6 b c d ^ 6 + 504 a ^ 5 b ^ 2 c ^ 2 d ^ 5 + 1470 a ^ 4
b ^ 3 c ^ 3 d ^ 4 + 1764 a ^ 3 b ^ 4 c ^ 4 d ^ 3 + 882 a ^ 2 b ^ 5 c ^ 5 d ^ 2 + 168 a b ^ 6 c ^ 6 d + 9 b ^
7 c ^ 7)) / 350064

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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(1140\) vs. \(2(184)=368\).
time = 0.13, size = 1141, normalized size = 5.70

method	result	size
norman	\(a^{7} c^{10} x +\left (5 a^{7} c^{9} d +\frac {7}{2} a^{6} b \,c^{10}\right ) x^{2}+\left (15 a^{7} c^{8} d^{2}+\frac {70}{3} a^{6} b \,c^{9} d +7 a^{5} b^{2} c^{10}\right ) x^{3}+\left (30 a^{7} c^{7} d^{3}+\frac {315}{4} a^{6} b \,c^{8} d^{2}+\frac {105}{2} a^{5} b^{2} c^{9} d +\frac {35}{4} a^{4} b^{3} c^{10}\right ) x^{4}+\left (42 a^{7} c^{6} d^{4}+168 a^{6} b \,c^{7} d^{3}+189 a^{5} b^{2} c^{8} d^{2}+70 a^{4} b^{3} c^{9} d +7 a^{3} b^{4} c^{10}\right ) x^{5}+\left (42 a^{7} c^{5} d^{5}+245 a^{6} b \,c^{6} d^{4}+420 a^{5} b^{2} c^{7} d^{3}+\frac {525}{2} a^{4} b^{3} c^{8} d^{2}+\frac {175}{3} a^{3} b^{4} c^{9} d +\frac {7}{2} a^{2} b^{5} c^{10}\right ) x^{6}+\left (30 a^{7} c^{4} d^{6}+252 a^{6} b \,c^{5} d^{5}+630 a^{5} b^{2} c^{6} d^{4}+600 a^{4} b^{3} c^{7} d^{3}+225 a^{3} b^{4} c^{8} d^{2}+30 a^{2} b^{5} c^{9} d +a \,b^{6} c^{10}\right ) x^{7}+\left (15 a^{7} c^{3} d^{7}+\frac {735}{4} a^{6} b \,c^{4} d^{6}+\frac {1323}{2} a^{5} b^{2} c^{5} d^{5}+\frac {3675}{4} a^{4} b^{3} c^{6} d^{4}+525 a^{3} b^{4} c^{7} d^{3}+\frac {945}{8} a^{2} b^{5} c^{8} d^{2}+\frac {35}{4} a \,b^{6} c^{9} d +\frac {1}{8} b^{7} c^{10}\right ) x^{8}+\left (5 a^{7} c^{2} d^{8}+\frac {280}{3} a^{6} b \,c^{3} d^{7}+490 a^{5} b^{2} c^{4} d^{6}+980 a^{4} b^{3} c^{5} d^{5}+\frac {2450}{3} a^{3} b^{4} c^{6} d^{4}+280 a^{2} b^{5} c^{7} d^{3}+35 a \,b^{6} c^{8} d^{2}+\frac {10}{9} b^{7} c^{9} d \right ) x^{9}+\left (a^{7} c \,d^{9}+\frac {63}{2} a^{6} b \,c^{2} d^{8}+252 a^{5} b^{2} c^{3} d^{7}+735 a^{4} b^{3} c^{4} d^{6}+882 a^{3} b^{4} c^{5} d^{5}+441 a^{2} b^{5} c^{6} d^{4}+84 a \,b^{6} c^{7} d^{3}+\frac {9}{2} b^{7} c^{8} d^{2}\right ) x^{10}+\left (\frac {1}{11} a^{7} d^{10}+\frac {70}{11} a^{6} b c \,d^{9}+\frac {945}{11} a^{5} b^{2} c^{2} d^{8}+\frac {4200}{11} a^{4} b^{3} c^{3} d^{7}+\frac {7350}{11} a^{3} b^{4} c^{4} d^{6}+\frac {5292}{11} a^{2} b^{5} c^{5} d^{5}+\frac {1470}{11} a \,b^{6} c^{6} d^{4}+\frac {120}{11} b^{7} c^{7} d^{3}\right ) x^{11}+\left (\frac {7}{12} a^{6} b \,d^{10}+\frac {35}{2} a^{5} b^{2} c \,d^{9}+\frac {525}{4} a^{4} b^{3} c^{2} d^{8}+350 a^{3} b^{4} c^{3} d^{7}+\frac {735}{2} a^{2} b^{5} c^{4} d^{6}+147 a \,b^{6} c^{5} d^{5}+\frac {35}{2} b^{7} c^{6} d^{4}\right ) x^{12}+\left (\frac {21}{13} a^{5} b^{2} d^{10}+\frac {350}{13} a^{4} b^{3} c \,d^{9}+\frac {1575}{13} a^{3} b^{4} c^{2} d^{8}+\frac {2520}{13} a^{2} b^{5} c^{3} d^{7}+\frac {1470}{13} a \,b^{6} c^{4} d^{6}+\frac {252}{13} b^{7} c^{5} d^{5}\right ) x^{13}+\left (\frac {5}{2} a^{4} b^{3} d^{10}+25 a^{3} b^{4} c \,d^{9}+\frac {135}{2} a^{2} b^{5} c^{2} d^{8}+60 a \,b^{6} c^{3} d^{7}+15 b^{7} c^{4} d^{6}\right ) x^{14}+\left (\frac {7}{3} a^{3} b^{4} d^{10}+14 a^{2} b^{5} c \,d^{9}+21 a \,b^{6} c^{2} d^{8}+8 b^{7} c^{3} d^{7}\right ) x^{15}+\left (\frac {21}{16} a^{2} b^{5} d^{10}+\frac {35}{8} a \,b^{6} c \,d^{9}+\frac {45}{16} b^{7} c^{2} d^{8}\right ) x^{16}+\left (\frac {7}{17} a \,b^{6} d^{10}+\frac {10}{17} b^{7} c \,d^{9}\right ) x^{17}+\frac {b^{7} d^{10} x^{18}}{18}\)	\(1125\)
default	\(\frac {b^{7} d^{10} x^{18}}{18}+\frac {\left (7 a \,b^{6} d^{10}+10 b^{7} c \,d^{9}\right ) x^{17}}{17}+\frac {\left (21 a^{2} b^{5} d^{10}+70 a \,b^{6} c \,d^{9}+45 b^{7} c^{2} d^{8}\right ) x^{16}}{16}+\frac {\left (35 a^{3} b^{4} d^{10}+210 a^{2} b^{5} c \,d^{9}+315 a \,b^{6} c^{2} d^{8}+120 b^{7} c^{3} d^{7}\right ) x^{15}}{15}+\frac {\left (35 a^{4} b^{3} d^{10}+350 a^{3} b^{4} c \,d^{9}+945 a^{2} b^{5} c^{2} d^{8}+840 a \,b^{6} c^{3} d^{7}+210 b^{7} c^{4} d^{6}\right ) x^{14}}{14}+\frac {\left (21 a^{5} b^{2} d^{10}+350 a^{4} b^{3} c \,d^{9}+1575 a^{3} b^{4} c^{2} d^{8}+2520 a^{2} b^{5} c^{3} d^{7}+1470 a \,b^{6} c^{4} d^{6}+252 b^{7} c^{5} d^{5}\right ) x^{13}}{13}+\frac {\left (7 a^{6} b \,d^{10}+210 a^{5} b^{2} c \,d^{9}+1575 a^{4} b^{3} c^{2} d^{8}+4200 a^{3} b^{4} c^{3} d^{7}+4410 a^{2} b^{5} c^{4} d^{6}+1764 a \,b^{6} c^{5} d^{5}+210 b^{7} c^{6} d^{4}\right ) x^{12}}{12}+\frac {\left (a^{7} d^{10}+70 a^{6} b c \,d^{9}+945 a^{5} b^{2} c^{2} d^{8}+4200 a^{4} b^{3} c^{3} d^{7}+7350 a^{3} b^{4} c^{4} d^{6}+5292 a^{2} b^{5} c^{5} d^{5}+1470 a \,b^{6} c^{6} d^{4}+120 b^{7} c^{7} d^{3}\right ) x^{11}}{11}+\frac {\left (10 a^{7} c \,d^{9}+315 a^{6} b \,c^{2} d^{8}+2520 a^{5} b^{2} c^{3} d^{7}+7350 a^{4} b^{3} c^{4} d^{6}+8820 a^{3} b^{4} c^{5} d^{5}+4410 a^{2} b^{5} c^{6} d^{4}+840 a \,b^{6} c^{7} d^{3}+45 b^{7} c^{8} d^{2}\right ) x^{10}}{10}+\frac {\left (45 a^{7} c^{2} d^{8}+840 a^{6} b \,c^{3} d^{7}+4410 a^{5} b^{2} c^{4} d^{6}+8820 a^{4} b^{3} c^{5} d^{5}+7350 a^{3} b^{4} c^{6} d^{4}+2520 a^{2} b^{5} c^{7} d^{3}+315 a \,b^{6} c^{8} d^{2}+10 b^{7} c^{9} d \right ) x^{9}}{9}+\frac {\left (120 a^{7} c^{3} d^{7}+1470 a^{6} b \,c^{4} d^{6}+5292 a^{5} b^{2} c^{5} d^{5}+7350 a^{4} b^{3} c^{6} d^{4}+4200 a^{3} b^{4} c^{7} d^{3}+945 a^{2} b^{5} c^{8} d^{2}+70 a \,b^{6} c^{9} d +b^{7} c^{10}\right ) x^{8}}{8}+\frac {\left (210 a^{7} c^{4} d^{6}+1764 a^{6} b \,c^{5} d^{5}+4410 a^{5} b^{2} c^{6} d^{4}+4200 a^{4} b^{3} c^{7} d^{3}+1575 a^{3} b^{4} c^{8} d^{2}+210 a^{2} b^{5} c^{9} d +7 a \,b^{6} c^{10}\right ) x^{7}}{7}+\frac {\left (252 a^{7} c^{5} d^{5}+1470 a^{6} b \,c^{6} d^{4}+2520 a^{5} b^{2} c^{7} d^{3}+1575 a^{4} b^{3} c^{8} d^{2}+350 a^{3} b^{4} c^{9} d +21 a^{2} b^{5} c^{10}\right ) x^{6}}{6}+\frac {\left (210 a^{7} c^{6} d^{4}+840 a^{6} b \,c^{7} d^{3}+945 a^{5} b^{2} c^{8} d^{2}+350 a^{4} b^{3} c^{9} d +35 a^{3} b^{4} c^{10}\right ) x^{5}}{5}+\frac {\left (120 a^{7} c^{7} d^{3}+315 a^{6} b \,c^{8} d^{2}+210 a^{5} b^{2} c^{9} d +35 a^{4} b^{3} c^{10}\right ) x^{4}}{4}+\frac {\left (45 a^{7} c^{8} d^{2}+70 a^{6} b \,c^{9} d +21 a^{5} b^{2} c^{10}\right ) x^{3}}{3}+\frac {\left (10 a^{7} c^{9} d +7 a^{6} b \,c^{10}\right ) x^{2}}{2}+a^{7} c^{10} x\)	\(1141\)
gosper	\(5 x^{9} a^{7} c^{2} d^{8}+5 x^{2} a^{7} c^{9} d +\frac {7}{2} x^{2} a^{6} b \,c^{10}+15 x^{3} a^{7} c^{8} d^{2}+7 x^{3} a^{5} b^{2} c^{10}+30 x^{4} a^{7} c^{7} d^{3}+\frac {35}{4} x^{4} a^{4} b^{3} c^{10}+42 x^{6} a^{7} c^{5} d^{5}+\frac {7}{2} x^{6} a^{2} b^{5} c^{10}+15 x^{8} a^{7} c^{3} d^{7}+15 x^{14} b^{7} c^{4} d^{6}+\frac {7}{3} x^{15} a^{3} b^{4} d^{10}+8 x^{15} b^{7} c^{3} d^{7}+\frac {21}{16} x^{16} a^{2} b^{5} d^{10}+\frac {45}{16} x^{16} b^{7} c^{2} d^{8}+\frac {7}{17} x^{17} a \,b^{6} d^{10}+\frac {10}{17} x^{17} b^{7} c \,d^{9}+42 a^{7} c^{6} d^{4} x^{5}+7 a^{3} b^{4} c^{10} x^{5}+30 a^{7} c^{4} d^{6} x^{7}+a \,b^{6} c^{10} x^{7}+\frac {10}{9} x^{9} b^{7} c^{9} d +x^{10} a^{7} c \,d^{9}+\frac {9}{2} x^{10} b^{7} c^{8} d^{2}+\frac {120}{11} x^{11} b^{7} c^{7} d^{3}+\frac {7}{12} x^{12} a^{6} b \,d^{10}+\frac {35}{2} x^{12} b^{7} c^{6} d^{4}+\frac {21}{13} x^{13} a^{5} b^{2} d^{10}+\frac {252}{13} x^{13} b^{7} c^{5} d^{5}+\frac {5}{2} x^{14} a^{4} b^{3} d^{10}+\frac {70}{3} x^{3} a^{6} b \,c^{9} d +\frac {315}{4} x^{4} a^{6} b \,c^{8} d^{2}+\frac {105}{2} x^{4} a^{5} b^{2} c^{9} d +245 x^{6} a^{6} b \,c^{6} d^{4}+420 x^{6} a^{5} b^{2} c^{7} d^{3}+\frac {525}{2} x^{6} a^{4} b^{3} c^{8} d^{2}+\frac {175}{3} x^{6} a^{3} b^{4} c^{9} d +\frac {735}{4} x^{8} a^{6} b \,c^{4} d^{6}+\frac {1323}{2} x^{8} a^{5} b^{2} c^{5} d^{5}+\frac {3675}{4} x^{8} a^{4} b^{3} c^{6} d^{4}+525 x^{8} a^{3} b^{4} c^{7} d^{3}+\frac {945}{8} x^{8} a^{2} b^{5} c^{8} d^{2}+\frac {35}{4} x^{8} a \,b^{6} c^{9} d +\frac {280}{3} x^{9} a^{6} b \,c^{3} d^{7}+a^{7} c^{10} x +\frac {1}{18} b^{7} d^{10} x^{18}+\frac {1}{8} x^{8} b^{7} c^{10}+\frac {1}{11} x^{11} a^{7} d^{10}+30 a^{2} b^{5} c^{9} d \,x^{7}+\frac {1470}{13} x^{13} a \,b^{6} c^{4} d^{6}+25 x^{14} a^{3} b^{4} c \,d^{9}+\frac {135}{2} x^{14} a^{2} b^{5} c^{2} d^{8}+60 x^{14} a \,b^{6} c^{3} d^{7}+14 x^{15} a^{2} b^{5} c \,d^{9}+21 x^{15} a \,b^{6} c^{2} d^{8}+\frac {35}{8} x^{16} a \,b^{6} c \,d^{9}+168 a^{6} b \,c^{7} d^{3} x^{5}+189 a^{5} b^{2} c^{8} d^{2} x^{5}+70 a^{4} b^{3} c^{9} d \,x^{5}+252 a^{6} b \,c^{5} d^{5} x^{7}+630 a^{5} b^{2} c^{6} d^{4} x^{7}+600 a^{4} b^{3} c^{7} d^{3} x^{7}+225 a^{3} b^{4} c^{8} d^{2} x^{7}+350 x^{12} a^{3} b^{4} c^{3} d^{7}+\frac {735}{2} x^{12} a^{2} b^{5} c^{4} d^{6}+147 x^{12} a \,b^{6} c^{5} d^{5}+\frac {350}{13} x^{13} a^{4} b^{3} c \,d^{9}+\frac {1575}{13} x^{13} a^{3} b^{4} c^{2} d^{8}+\frac {2520}{13} x^{13} a^{2} b^{5} c^{3} d^{7}+\frac {5292}{11} x^{11} a^{2} b^{5} c^{5} d^{5}+\frac {1470}{11} x^{11} a \,b^{6} c^{6} d^{4}+\frac {35}{2} x^{12} a^{5} b^{2} c \,d^{9}+\frac {525}{4} x^{12} a^{4} b^{3} c^{2} d^{8}+252 x^{10} a^{5} b^{2} c^{3} d^{7}+735 x^{10} a^{4} b^{3} c^{4} d^{6}+882 x^{10} a^{3} b^{4} c^{5} d^{5}+441 x^{10} a^{2} b^{5} c^{6} d^{4}+84 x^{10} a \,b^{6} c^{7} d^{3}+\frac {70}{11} x^{11} a^{6} b c \,d^{9}+\frac {945}{11} x^{11} a^{5} b^{2} c^{2} d^{8}+\frac {4200}{11} x^{11} a^{4} b^{3} c^{3} d^{7}+\frac {7350}{11} x^{11} a^{3} b^{4} c^{4} d^{6}+490 x^{9} a^{5} b^{2} c^{4} d^{6}+980 x^{9} a^{4} b^{3} c^{5} d^{5}+\frac {2450}{3} x^{9} a^{3} b^{4} c^{6} d^{4}+280 x^{9} a^{2} b^{5} c^{7} d^{3}+35 x^{9} a \,b^{6} c^{8} d^{2}+\frac {63}{2} x^{10} a^{6} b \,c^{2} d^{8}\)	\(1303\)
risch	\(5 x^{9} a^{7} c^{2} d^{8}+5 x^{2} a^{7} c^{9} d +\frac {7}{2} x^{2} a^{6} b \,c^{10}+15 x^{3} a^{7} c^{8} d^{2}+7 x^{3} a^{5} b^{2} c^{10}+30 x^{4} a^{7} c^{7} d^{3}+\frac {35}{4} x^{4} a^{4} b^{3} c^{10}+42 x^{6} a^{7} c^{5} d^{5}+\frac {7}{2} x^{6} a^{2} b^{5} c^{10}+15 x^{8} a^{7} c^{3} d^{7}+15 x^{14} b^{7} c^{4} d^{6}+\frac {7}{3} x^{15} a^{3} b^{4} d^{10}+8 x^{15} b^{7} c^{3} d^{7}+\frac {21}{16} x^{16} a^{2} b^{5} d^{10}+\frac {45}{16} x^{16} b^{7} c^{2} d^{8}+\frac {7}{17} x^{17} a \,b^{6} d^{10}+\frac {10}{17} x^{17} b^{7} c \,d^{9}+42 a^{7} c^{6} d^{4} x^{5}+7 a^{3} b^{4} c^{10} x^{5}+30 a^{7} c^{4} d^{6} x^{7}+a \,b^{6} c^{10} x^{7}+\frac {10}{9} x^{9} b^{7} c^{9} d +x^{10} a^{7} c \,d^{9}+\frac {9}{2} x^{10} b^{7} c^{8} d^{2}+\frac {120}{11} x^{11} b^{7} c^{7} d^{3}+\frac {7}{12} x^{12} a^{6} b \,d^{10}+\frac {35}{2} x^{12} b^{7} c^{6} d^{4}+\frac {21}{13} x^{13} a^{5} b^{2} d^{10}+\frac {252}{13} x^{13} b^{7} c^{5} d^{5}+\frac {5}{2} x^{14} a^{4} b^{3} d^{10}+\frac {70}{3} x^{3} a^{6} b \,c^{9} d +\frac {315}{4} x^{4} a^{6} b \,c^{8} d^{2}+\frac {105}{2} x^{4} a^{5} b^{2} c^{9} d +245 x^{6} a^{6} b \,c^{6} d^{4}+420 x^{6} a^{5} b^{2} c^{7} d^{3}+\frac {525}{2} x^{6} a^{4} b^{3} c^{8} d^{2}+\frac {175}{3} x^{6} a^{3} b^{4} c^{9} d +\frac {735}{4} x^{8} a^{6} b \,c^{4} d^{6}+\frac {1323}{2} x^{8} a^{5} b^{2} c^{5} d^{5}+\frac {3675}{4} x^{8} a^{4} b^{3} c^{6} d^{4}+525 x^{8} a^{3} b^{4} c^{7} d^{3}+\frac {945}{8} x^{8} a^{2} b^{5} c^{8} d^{2}+\frac {35}{4} x^{8} a \,b^{6} c^{9} d +\frac {280}{3} x^{9} a^{6} b \,c^{3} d^{7}+a^{7} c^{10} x +\frac {1}{18} b^{7} d^{10} x^{18}+\frac {1}{8} x^{8} b^{7} c^{10}+\frac {1}{11} x^{11} a^{7} d^{10}+30 a^{2} b^{5} c^{9} d \,x^{7}+\frac {1470}{13} x^{13} a \,b^{6} c^{4} d^{6}+25 x^{14} a^{3} b^{4} c \,d^{9}+\frac {135}{2} x^{14} a^{2} b^{5} c^{2} d^{8}+60 x^{14} a \,b^{6} c^{3} d^{7}+14 x^{15} a^{2} b^{5} c \,d^{9}+21 x^{15} a \,b^{6} c^{2} d^{8}+\frac {35}{8} x^{16} a \,b^{6} c \,d^{9}+168 a^{6} b \,c^{7} d^{3} x^{5}+189 a^{5} b^{2} c^{8} d^{2} x^{5}+70 a^{4} b^{3} c^{9} d \,x^{5}+252 a^{6} b \,c^{5} d^{5} x^{7}+630 a^{5} b^{2} c^{6} d^{4} x^{7}+600 a^{4} b^{3} c^{7} d^{3} x^{7}+225 a^{3} b^{4} c^{8} d^{2} x^{7}+350 x^{12} a^{3} b^{4} c^{3} d^{7}+\frac {735}{2} x^{12} a^{2} b^{5} c^{4} d^{6}+147 x^{12} a \,b^{6} c^{5} d^{5}+\frac {350}{13} x^{13} a^{4} b^{3} c \,d^{9}+\frac {1575}{13} x^{13} a^{3} b^{4} c^{2} d^{8}+\frac {2520}{13} x^{13} a^{2} b^{5} c^{3} d^{7}+\frac {5292}{11} x^{11} a^{2} b^{5} c^{5} d^{5}+\frac {1470}{11} x^{11} a \,b^{6} c^{6} d^{4}+\frac {35}{2} x^{12} a^{5} b^{2} c \,d^{9}+\frac {525}{4} x^{12} a^{4} b^{3} c^{2} d^{8}+252 x^{10} a^{5} b^{2} c^{3} d^{7}+735 x^{10} a^{4} b^{3} c^{4} d^{6}+882 x^{10} a^{3} b^{4} c^{5} d^{5}+441 x^{10} a^{2} b^{5} c^{6} d^{4}+84 x^{10} a \,b^{6} c^{7} d^{3}+\frac {70}{11} x^{11} a^{6} b c \,d^{9}+\frac {945}{11} x^{11} a^{5} b^{2} c^{2} d^{8}+\frac {4200}{11} x^{11} a^{4} b^{3} c^{3} d^{7}+\frac {7350}{11} x^{11} a^{3} b^{4} c^{4} d^{6}+490 x^{9} a^{5} b^{2} c^{4} d^{6}+980 x^{9} a^{4} b^{3} c^{5} d^{5}+\frac {2450}{3} x^{9} a^{3} b^{4} c^{6} d^{4}+280 x^{9} a^{2} b^{5} c^{7} d^{3}+35 x^{9} a \,b^{6} c^{8} d^{2}+\frac {63}{2} x^{10} a^{6} b \,c^{2} d^{8}\)	\(1303\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((b*x+a)^7*(d*x+c)^10,x,method=_RETURNVERBOSE)

[Out]

1/18*b^7*d^10*x^18+1/17*(7*a*b^6*d^10+10*b^7*c*d^9)*x^17+1/16*(21*a^2*b^5*d^10+70*a*b^6*c*d^9+45*b^7*c^2*d^8)*
x^16+1/15*(35*a^3*b^4*d^10+210*a^2*b^5*c*d^9+315*a*b^6*c^2*d^8+120*b^7*c^3*d^7)*x^15+1/14*(35*a^4*b^3*d^10+350
*a^3*b^4*c*d^9+945*a^2*b^5*c^2*d^8+840*a*b^6*c^3*d^7+210*b^7*c^4*d^6)*x^14+1/13*(21*a^5*b^2*d^10+350*a^4*b^3*c
*d^9+1575*a^3*b^4*c^2*d^8+2520*a^2*b^5*c^3*d^7+1470*a*b^6*c^4*d^6+252*b^7*c^5*d^5)*x^13+1/12*(7*a^6*b*d^10+210
*a^5*b^2*c*d^9+1575*a^4*b^3*c^2*d^8+4200*a^3*b^4*c^3*d^7+4410*a^2*b^5*c^4*d^6+1764*a*b^6*c^5*d^5+210*b^7*c^6*d
^4)*x^12+1/11*(a^7*d^10+70*a^6*b*c*d^9+945*a^5*b^2*c^2*d^8+4200*a^4*b^3*c^3*d^7+7350*a^3*b^4*c^4*d^6+5292*a^2*
b^5*c^5*d^5+1470*a*b^6*c^6*d^4+120*b^7*c^7*d^3)*x^11+1/10*(10*a^7*c*d^9+315*a^6*b*c^2*d^8+2520*a^5*b^2*c^3*d^7
+7350*a^4*b^3*c^4*d^6+8820*a^3*b^4*c^5*d^5+4410*a^2*b^5*c^6*d^4+840*a*b^6*c^7*d^3+45*b^7*c^8*d^2)*x^10+1/9*(45
*a^7*c^2*d^8+840*a^6*b*c^3*d^7+4410*a^5*b^2*c^4*d^6+8820*a^4*b^3*c^5*d^5+7350*a^3*b^4*c^6*d^4+2520*a^2*b^5*c^7
*d^3+315*a*b^6*c^8*d^2+10*b^7*c^9*d)*x^9+1/8*(120*a^7*c^3*d^7+1470*a^6*b*c^4*d^6+5292*a^5*b^2*c^5*d^5+7350*a^4
*b^3*c^6*d^4+4200*a^3*b^4*c^7*d^3+945*a^2*b^5*c^8*d^2+70*a*b^6*c^9*d+b^7*c^10)*x^8+1/7*(210*a^7*c^4*d^6+1764*a
^6*b*c^5*d^5+4410*a^5*b^2*c^6*d^4+4200*a^4*b^3*c^7*d^3+1575*a^3*b^4*c^8*d^2+210*a^2*b^5*c^9*d+7*a*b^6*c^10)*x^
7+1/6*(252*a^7*c^5*d^5+1470*a^6*b*c^6*d^4+2520*a^5*b^2*c^7*d^3+1575*a^4*b^3*c^8*d^2+350*a^3*b^4*c^9*d+21*a^2*b
^5*c^10)*x^6+1/5*(210*a^7*c^6*d^4+840*a^6*b*c^7*d^3+945*a^5*b^2*c^8*d^2+350*a^4*b^3*c^9*d+35*a^3*b^4*c^10)*x^5
+1/4*(120*a^7*c^7*d^3+315*a^6*b*c^8*d^2+210*a^5*b^2*c^9*d+35*a^4*b^3*c^10)*x^4+1/3*(45*a^7*c^8*d^2+70*a^6*b*c^
9*d+21*a^5*b^2*c^10)*x^3+1/2*(10*a^7*c^9*d+7*a^6*b*c^10)*x^2+a^7*c^10*x

________________________________________________________________________________________

Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 1135 vs. \(2 (184) = 368\).
time = 0.29, size = 1135, normalized size = 5.68

result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)^7*(d*x+c)^10,x, algorithm="maxima")

[Out]

1/18*b^7*d^10*x^18 + a^7*c^10*x + 1/17*(10*b^7*c*d^9 + 7*a*b^6*d^10)*x^17 + 1/16*(45*b^7*c^2*d^8 + 70*a*b^6*c*
d^9 + 21*a^2*b^5*d^10)*x^16 + 1/3*(24*b^7*c^3*d^7 + 63*a*b^6*c^2*d^8 + 42*a^2*b^5*c*d^9 + 7*a^3*b^4*d^10)*x^15
+ 5/2*(6*b^7*c^4*d^6 + 24*a*b^6*c^3*d^7 + 27*a^2*b^5*c^2*d^8 + 10*a^3*b^4*c*d^9 + a^4*b^3*d^10)*x^14 + 7/13*(
36*b^7*c^5*d^5 + 210*a*b^6*c^4*d^6 + 360*a^2*b^5*c^3*d^7 + 225*a^3*b^4*c^2*d^8 + 50*a^4*b^3*c*d^9 + 3*a^5*b^2*
d^10)*x^13 + 7/12*(30*b^7*c^6*d^4 + 252*a*b^6*c^5*d^5 + 630*a^2*b^5*c^4*d^6 + 600*a^3*b^4*c^3*d^7 + 225*a^4*b^
3*c^2*d^8 + 30*a^5*b^2*c*d^9 + a^6*b*d^10)*x^12 + 1/11*(120*b^7*c^7*d^3 + 1470*a*b^6*c^6*d^4 + 5292*a^2*b^5*c^
5*d^5 + 7350*a^3*b^4*c^4*d^6 + 4200*a^4*b^3*c^3*d^7 + 945*a^5*b^2*c^2*d^8 + 70*a^6*b*c*d^9 + a^7*d^10)*x^11 +
1/2*(9*b^7*c^8*d^2 + 168*a*b^6*c^7*d^3 + 882*a^2*b^5*c^6*d^4 + 1764*a^3*b^4*c^5*d^5 + 1470*a^4*b^3*c^4*d^6 + 5
04*a^5*b^2*c^3*d^7 + 63*a^6*b*c^2*d^8 + 2*a^7*c*d^9)*x^10 + 5/9*(2*b^7*c^9*d + 63*a*b^6*c^8*d^2 + 504*a^2*b^5*
c^7*d^3 + 1470*a^3*b^4*c^6*d^4 + 1764*a^4*b^3*c^5*d^5 + 882*a^5*b^2*c^4*d^6 + 168*a^6*b*c^3*d^7 + 9*a^7*c^2*d^
8)*x^9 + 1/8*(b^7*c^10 + 70*a*b^6*c^9*d + 945*a^2*b^5*c^8*d^2 + 4200*a^3*b^4*c^7*d^3 + 7350*a^4*b^3*c^6*d^4 +
5292*a^5*b^2*c^5*d^5 + 1470*a^6*b*c^4*d^6 + 120*a^7*c^3*d^7)*x^8 + (a*b^6*c^10 + 30*a^2*b^5*c^9*d + 225*a^3*b^
4*c^8*d^2 + 600*a^4*b^3*c^7*d^3 + 630*a^5*b^2*c^6*d^4 + 252*a^6*b*c^5*d^5 + 30*a^7*c^4*d^6)*x^7 + 7/6*(3*a^2*b
^5*c^10 + 50*a^3*b^4*c^9*d + 225*a^4*b^3*c^8*d^2 + 360*a^5*b^2*c^7*d^3 + 210*a^6*b*c^6*d^4 + 36*a^7*c^5*d^5)*x
^6 + 7*(a^3*b^4*c^10 + 10*a^4*b^3*c^9*d + 27*a^5*b^2*c^8*d^2 + 24*a^6*b*c^7*d^3 + 6*a^7*c^6*d^4)*x^5 + 5/4*(7*
a^4*b^3*c^10 + 42*a^5*b^2*c^9*d + 63*a^6*b*c^8*d^2 + 24*a^7*c^7*d^3)*x^4 + 1/3*(21*a^5*b^2*c^10 + 70*a^6*b*c^9
*d + 45*a^7*c^8*d^2)*x^3 + 1/2*(7*a^6*b*c^10 + 10*a^7*c^9*d)*x^2

________________________________________________________________________________________

Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 1135 vs. \(2 (184) = 368\).
time = 0.30, size = 1135, normalized size = 5.68

result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)^7*(d*x+c)^10,x, algorithm="fricas")

[Out]

1/18*b^7*d^10*x^18 + a^7*c^10*x + 1/17*(10*b^7*c*d^9 + 7*a*b^6*d^10)*x^17 + 1/16*(45*b^7*c^2*d^8 + 70*a*b^6*c*
d^9 + 21*a^2*b^5*d^10)*x^16 + 1/3*(24*b^7*c^3*d^7 + 63*a*b^6*c^2*d^8 + 42*a^2*b^5*c*d^9 + 7*a^3*b^4*d^10)*x^15
+ 5/2*(6*b^7*c^4*d^6 + 24*a*b^6*c^3*d^7 + 27*a^2*b^5*c^2*d^8 + 10*a^3*b^4*c*d^9 + a^4*b^3*d^10)*x^14 + 7/13*(
36*b^7*c^5*d^5 + 210*a*b^6*c^4*d^6 + 360*a^2*b^5*c^3*d^7 + 225*a^3*b^4*c^2*d^8 + 50*a^4*b^3*c*d^9 + 3*a^5*b^2*
d^10)*x^13 + 7/12*(30*b^7*c^6*d^4 + 252*a*b^6*c^5*d^5 + 630*a^2*b^5*c^4*d^6 + 600*a^3*b^4*c^3*d^7 + 225*a^4*b^
3*c^2*d^8 + 30*a^5*b^2*c*d^9 + a^6*b*d^10)*x^12 + 1/11*(120*b^7*c^7*d^3 + 1470*a*b^6*c^6*d^4 + 5292*a^2*b^5*c^
5*d^5 + 7350*a^3*b^4*c^4*d^6 + 4200*a^4*b^3*c^3*d^7 + 945*a^5*b^2*c^2*d^8 + 70*a^6*b*c*d^9 + a^7*d^10)*x^11 +
1/2*(9*b^7*c^8*d^2 + 168*a*b^6*c^7*d^3 + 882*a^2*b^5*c^6*d^4 + 1764*a^3*b^4*c^5*d^5 + 1470*a^4*b^3*c^4*d^6 + 5
04*a^5*b^2*c^3*d^7 + 63*a^6*b*c^2*d^8 + 2*a^7*c*d^9)*x^10 + 5/9*(2*b^7*c^9*d + 63*a*b^6*c^8*d^2 + 504*a^2*b^5*
c^7*d^3 + 1470*a^3*b^4*c^6*d^4 + 1764*a^4*b^3*c^5*d^5 + 882*a^5*b^2*c^4*d^6 + 168*a^6*b*c^3*d^7 + 9*a^7*c^2*d^
8)*x^9 + 1/8*(b^7*c^10 + 70*a*b^6*c^9*d + 945*a^2*b^5*c^8*d^2 + 4200*a^3*b^4*c^7*d^3 + 7350*a^4*b^3*c^6*d^4 +
5292*a^5*b^2*c^5*d^5 + 1470*a^6*b*c^4*d^6 + 120*a^7*c^3*d^7)*x^8 + (a*b^6*c^10 + 30*a^2*b^5*c^9*d + 225*a^3*b^
4*c^8*d^2 + 600*a^4*b^3*c^7*d^3 + 630*a^5*b^2*c^6*d^4 + 252*a^6*b*c^5*d^5 + 30*a^7*c^4*d^6)*x^7 + 7/6*(3*a^2*b
^5*c^10 + 50*a^3*b^4*c^9*d + 225*a^4*b^3*c^8*d^2 + 360*a^5*b^2*c^7*d^3 + 210*a^6*b*c^6*d^4 + 36*a^7*c^5*d^5)*x
^6 + 7*(a^3*b^4*c^10 + 10*a^4*b^3*c^9*d + 27*a^5*b^2*c^8*d^2 + 24*a^6*b*c^7*d^3 + 6*a^7*c^6*d^4)*x^5 + 5/4*(7*
a^4*b^3*c^10 + 42*a^5*b^2*c^9*d + 63*a^6*b*c^8*d^2 + 24*a^7*c^7*d^3)*x^4 + 1/3*(21*a^5*b^2*c^10 + 70*a^6*b*c^9
*d + 45*a^7*c^8*d^2)*x^3 + 1/2*(7*a^6*b*c^10 + 10*a^7*c^9*d)*x^2

________________________________________________________________________________________

Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 1280 vs. \(2 (184) = 368\).
time = 0.12, size = 1280, normalized size = 6.40

result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)**7*(d*x+c)**10,x)

[Out]

a**7*c**10*x + b**7*d**10*x**18/18 + x**17*(7*a*b**6*d**10/17 + 10*b**7*c*d**9/17) + x**16*(21*a**2*b**5*d**10
/16 + 35*a*b**6*c*d**9/8 + 45*b**7*c**2*d**8/16) + x**15*(7*a**3*b**4*d**10/3 + 14*a**2*b**5*c*d**9 + 21*a*b**
6*c**2*d**8 + 8*b**7*c**3*d**7) + x**14*(5*a**4*b**3*d**10/2 + 25*a**3*b**4*c*d**9 + 135*a**2*b**5*c**2*d**8/2
+ 60*a*b**6*c**3*d**7 + 15*b**7*c**4*d**6) + x**13*(21*a**5*b**2*d**10/13 + 350*a**4*b**3*c*d**9/13 + 1575*a*
*3*b**4*c**2*d**8/13 + 2520*a**2*b**5*c**3*d**7/13 + 1470*a*b**6*c**4*d**6/13 + 252*b**7*c**5*d**5/13) + x**12
*(7*a**6*b*d**10/12 + 35*a**5*b**2*c*d**9/2 + 525*a**4*b**3*c**2*d**8/4 + 350*a**3*b**4*c**3*d**7 + 735*a**2*b
**5*c**4*d**6/2 + 147*a*b**6*c**5*d**5 + 35*b**7*c**6*d**4/2) + x**11*(a**7*d**10/11 + 70*a**6*b*c*d**9/11 + 9
45*a**5*b**2*c**2*d**8/11 + 4200*a**4*b**3*c**3*d**7/11 + 7350*a**3*b**4*c**4*d**6/11 + 5292*a**2*b**5*c**5*d*
*5/11 + 1470*a*b**6*c**6*d**4/11 + 120*b**7*c**7*d**3/11) + x**10*(a**7*c*d**9 + 63*a**6*b*c**2*d**8/2 + 252*a
**5*b**2*c**3*d**7 + 735*a**4*b**3*c**4*d**6 + 882*a**3*b**4*c**5*d**5 + 441*a**2*b**5*c**6*d**4 + 84*a*b**6*c
**7*d**3 + 9*b**7*c**8*d**2/2) + x**9*(5*a**7*c**2*d**8 + 280*a**6*b*c**3*d**7/3 + 490*a**5*b**2*c**4*d**6 + 9
80*a**4*b**3*c**5*d**5 + 2450*a**3*b**4*c**6*d**4/3 + 280*a**2*b**5*c**7*d**3 + 35*a*b**6*c**8*d**2 + 10*b**7*
c**9*d/9) + x**8*(15*a**7*c**3*d**7 + 735*a**6*b*c**4*d**6/4 + 1323*a**5*b**2*c**5*d**5/2 + 3675*a**4*b**3*c**
6*d**4/4 + 525*a**3*b**4*c**7*d**3 + 945*a**2*b**5*c**8*d**2/8 + 35*a*b**6*c**9*d/4 + b**7*c**10/8) + x**7*(30
*a**7*c**4*d**6 + 252*a**6*b*c**5*d**5 + 630*a**5*b**2*c**6*d**4 + 600*a**4*b**3*c**7*d**3 + 225*a**3*b**4*c**
8*d**2 + 30*a**2*b**5*c**9*d + a*b**6*c**10) + x**6*(42*a**7*c**5*d**5 + 245*a**6*b*c**6*d**4 + 420*a**5*b**2*
c**7*d**3 + 525*a**4*b**3*c**8*d**2/2 + 175*a**3*b**4*c**9*d/3 + 7*a**2*b**5*c**10/2) + x**5*(42*a**7*c**6*d**
4 + 168*a**6*b*c**7*d**3 + 189*a**5*b**2*c**8*d**2 + 70*a**4*b**3*c**9*d + 7*a**3*b**4*c**10) + x**4*(30*a**7*
c**7*d**3 + 315*a**6*b*c**8*d**2/4 + 105*a**5*b**2*c**9*d/2 + 35*a**4*b**3*c**10/4) + x**3*(15*a**7*c**8*d**2
+ 70*a**6*b*c**9*d/3 + 7*a**5*b**2*c**10) + x**2*(5*a**7*c**9*d + 7*a**6*b*c**10/2)

________________________________________________________________________________________

Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 1302 vs. \(2 (184) = 368\).
time = 0.00, size = 1396, normalized size = 6.98

result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)^7*(d*x+c)^10,x)

[Out]

1/18*b^7*d^10*x^18 + 10/17*b^7*c*d^9*x^17 + 7/17*a*b^6*d^10*x^17 + 45/16*b^7*c^2*d^8*x^16 + 35/8*a*b^6*c*d^9*x
^16 + 21/16*a^2*b^5*d^10*x^16 + 8*b^7*c^3*d^7*x^15 + 21*a*b^6*c^2*d^8*x^15 + 14*a^2*b^5*c*d^9*x^15 + 7/3*a^3*b
^4*d^10*x^15 + 15*b^7*c^4*d^6*x^14 + 60*a*b^6*c^3*d^7*x^14 + 135/2*a^2*b^5*c^2*d^8*x^14 + 25*a^3*b^4*c*d^9*x^1
4 + 5/2*a^4*b^3*d^10*x^14 + 252/13*b^7*c^5*d^5*x^13 + 1470/13*a*b^6*c^4*d^6*x^13 + 2520/13*a^2*b^5*c^3*d^7*x^1
3 + 1575/13*a^3*b^4*c^2*d^8*x^13 + 350/13*a^4*b^3*c*d^9*x^13 + 21/13*a^5*b^2*d^10*x^13 + 35/2*b^7*c^6*d^4*x^12
+ 147*a*b^6*c^5*d^5*x^12 + 735/2*a^2*b^5*c^4*d^6*x^12 + 350*a^3*b^4*c^3*d^7*x^12 + 525/4*a^4*b^3*c^2*d^8*x^12
+ 35/2*a^5*b^2*c*d^9*x^12 + 7/12*a^6*b*d^10*x^12 + 120/11*b^7*c^7*d^3*x^11 + 1470/11*a*b^6*c^6*d^4*x^11 + 529
2/11*a^2*b^5*c^5*d^5*x^11 + 7350/11*a^3*b^4*c^4*d^6*x^11 + 4200/11*a^4*b^3*c^3*d^7*x^11 + 945/11*a^5*b^2*c^2*d
^8*x^11 + 70/11*a^6*b*c*d^9*x^11 + 1/11*a^7*d^10*x^11 + 9/2*b^7*c^8*d^2*x^10 + 84*a*b^6*c^7*d^3*x^10 + 441*a^2
*b^5*c^6*d^4*x^10 + 882*a^3*b^4*c^5*d^5*x^10 + 735*a^4*b^3*c^4*d^6*x^10 + 252*a^5*b^2*c^3*d^7*x^10 + 63/2*a^6*
b*c^2*d^8*x^10 + a^7*c*d^9*x^10 + 10/9*b^7*c^9*d*x^9 + 35*a*b^6*c^8*d^2*x^9 + 280*a^2*b^5*c^7*d^3*x^9 + 2450/3
*a^3*b^4*c^6*d^4*x^9 + 980*a^4*b^3*c^5*d^5*x^9 + 490*a^5*b^2*c^4*d^6*x^9 + 280/3*a^6*b*c^3*d^7*x^9 + 5*a^7*c^2
*d^8*x^9 + 1/8*b^7*c^10*x^8 + 35/4*a*b^6*c^9*d*x^8 + 945/8*a^2*b^5*c^8*d^2*x^8 + 525*a^3*b^4*c^7*d^3*x^8 + 367
5/4*a^4*b^3*c^6*d^4*x^8 + 1323/2*a^5*b^2*c^5*d^5*x^8 + 735/4*a^6*b*c^4*d^6*x^8 + 15*a^7*c^3*d^7*x^8 + a*b^6*c^
10*x^7 + 30*a^2*b^5*c^9*d*x^7 + 225*a^3*b^4*c^8*d^2*x^7 + 600*a^4*b^3*c^7*d^3*x^7 + 630*a^5*b^2*c^6*d^4*x^7 +
252*a^6*b*c^5*d^5*x^7 + 30*a^7*c^4*d^6*x^7 + 7/2*a^2*b^5*c^10*x^6 + 175/3*a^3*b^4*c^9*d*x^6 + 525/2*a^4*b^3*c^
8*d^2*x^6 + 420*a^5*b^2*c^7*d^3*x^6 + 245*a^6*b*c^6*d^4*x^6 + 42*a^7*c^5*d^5*x^6 + 7*a^3*b^4*c^10*x^5 + 70*a^4
*b^3*c^9*d*x^5 + 189*a^5*b^2*c^8*d^2*x^5 + 168*a^6*b*c^7*d^3*x^5 + 42*a^7*c^6*d^4*x^5 + 35/4*a^4*b^3*c^10*x^4
+ 105/2*a^5*b^2*c^9*d*x^4 + 315/4*a^6*b*c^8*d^2*x^4 + 30*a^7*c^7*d^3*x^4 + 7*a^5*b^2*c^10*x^3 + 70/3*a^6*b*c^9
*d*x^3 + 15*a^7*c^8*d^2*x^3 + 7/2*a^6*b*c^10*x^2 + 5*a^7*c^9*d*x^2 + a^7*c^10*x

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Mupad [B]
time = 0.61, size = 1106, normalized size = 5.53 \begin {gather*} x^{10}\,\left (a^7\,c\,d^9+\frac {63\,a^6\,b\,c^2\,d^8}{2}+252\,a^5\,b^2\,c^3\,d^7+735\,a^4\,b^3\,c^4\,d^6+882\,a^3\,b^4\,c^5\,d^5+441\,a^2\,b^5\,c^6\,d^4+84\,a\,b^6\,c^7\,d^3+\frac {9\,b^7\,c^8\,d^2}{2}\right )+x^9\,\left (5\,a^7\,c^2\,d^8+\frac {280\,a^6\,b\,c^3\,d^7}{3}+490\,a^5\,b^2\,c^4\,d^6+980\,a^4\,b^3\,c^5\,d^5+\frac {2450\,a^3\,b^4\,c^6\,d^4}{3}+280\,a^2\,b^5\,c^7\,d^3+35\,a\,b^6\,c^8\,d^2+\frac {10\,b^7\,c^9\,d}{9}\right )+x^5\,\left (42\,a^7\,c^6\,d^4+168\,a^6\,b\,c^7\,d^3+189\,a^5\,b^2\,c^8\,d^2+70\,a^4\,b^3\,c^9\,d+7\,a^3\,b^4\,c^{10}\right )+x^{14}\,\left (\frac {5\,a^4\,b^3\,d^{10}}{2}+25\,a^3\,b^4\,c\,d^9+\frac {135\,a^2\,b^5\,c^2\,d^8}{2}+60\,a\,b^6\,c^3\,d^7+15\,b^7\,c^4\,d^6\right )+x^8\,\left (15\,a^7\,c^3\,d^7+\frac {735\,a^6\,b\,c^4\,d^6}{4}+\frac {1323\,a^5\,b^2\,c^5\,d^5}{2}+\frac {3675\,a^4\,b^3\,c^6\,d^4}{4}+525\,a^3\,b^4\,c^7\,d^3+\frac {945\,a^2\,b^5\,c^8\,d^2}{8}+\frac {35\,a\,b^6\,c^9\,d}{4}+\frac {b^7\,c^{10}}{8}\right )+x^{11}\,\left (\frac {a^7\,d^{10}}{11}+\frac {70\,a^6\,b\,c\,d^9}{11}+\frac {945\,a^5\,b^2\,c^2\,d^8}{11}+\frac {4200\,a^4\,b^3\,c^3\,d^7}{11}+\frac {7350\,a^3\,b^4\,c^4\,d^6}{11}+\frac {5292\,a^2\,b^5\,c^5\,d^5}{11}+\frac {1470\,a\,b^6\,c^6\,d^4}{11}+\frac {120\,b^7\,c^7\,d^3}{11}\right )+x^6\,\left (42\,a^7\,c^5\,d^5+245\,a^6\,b\,c^6\,d^4+420\,a^5\,b^2\,c^7\,d^3+\frac {525\,a^4\,b^3\,c^8\,d^2}{2}+\frac {175\,a^3\,b^4\,c^9\,d}{3}+\frac {7\,a^2\,b^5\,c^{10}}{2}\right )+x^{13}\,\left (\frac {21\,a^5\,b^2\,d^{10}}{13}+\frac {350\,a^4\,b^3\,c\,d^9}{13}+\frac {1575\,a^3\,b^4\,c^2\,d^8}{13}+\frac {2520\,a^2\,b^5\,c^3\,d^7}{13}+\frac {1470\,a\,b^6\,c^4\,d^6}{13}+\frac {252\,b^7\,c^5\,d^5}{13}\right )+x^7\,\left (30\,a^7\,c^4\,d^6+252\,a^6\,b\,c^5\,d^5+630\,a^5\,b^2\,c^6\,d^4+600\,a^4\,b^3\,c^7\,d^3+225\,a^3\,b^4\,c^8\,d^2+30\,a^2\,b^5\,c^9\,d+a\,b^6\,c^{10}\right )+x^{12}\,\left (\frac {7\,a^6\,b\,d^{10}}{12}+\frac {35\,a^5\,b^2\,c\,d^9}{2}+\frac {525\,a^4\,b^3\,c^2\,d^8}{4}+350\,a^3\,b^4\,c^3\,d^7+\frac {735\,a^2\,b^5\,c^4\,d^6}{2}+147\,a\,b^6\,c^5\,d^5+\frac {35\,b^7\,c^6\,d^4}{2}\right )+a^7\,c^{10}\,x+\frac {b^7\,d^{10}\,x^{18}}{18}+\frac {5\,a^4\,c^7\,x^4\,\left (24\,a^3\,d^3+63\,a^2\,b\,c\,d^2+42\,a\,b^2\,c^2\,d+7\,b^3\,c^3\right )}{4}+\frac {b^4\,d^7\,x^{15}\,\left (7\,a^3\,d^3+42\,a^2\,b\,c\,d^2+63\,a\,b^2\,c^2\,d+24\,b^3\,c^3\right )}{3}+\frac {a^6\,c^9\,x^2\,\left (10\,a\,d+7\,b\,c\right )}{2}+\frac {b^6\,d^9\,x^{17}\,\left (7\,a\,d+10\,b\,c\right )}{17}+\frac {a^5\,c^8\,x^3\,\left (45\,a^2\,d^2+70\,a\,b\,c\,d+21\,b^2\,c^2\right )}{3}+\frac {b^5\,d^8\,x^{16}\,\left (21\,a^2\,d^2+70\,a\,b\,c\,d+45\,b^2\,c^2\right )}{16} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a + b*x)^7*(c + d*x)^10,x)

[Out]

x^10*(a^7*c*d^9 + (9*b^7*c^8*d^2)/2 + 84*a*b^6*c^7*d^3 + (63*a^6*b*c^2*d^8)/2 + 441*a^2*b^5*c^6*d^4 + 882*a^3*
b^4*c^5*d^5 + 735*a^4*b^3*c^4*d^6 + 252*a^5*b^2*c^3*d^7) + x^9*((10*b^7*c^9*d)/9 + 5*a^7*c^2*d^8 + 35*a*b^6*c^
8*d^2 + (280*a^6*b*c^3*d^7)/3 + 280*a^2*b^5*c^7*d^3 + (2450*a^3*b^4*c^6*d^4)/3 + 980*a^4*b^3*c^5*d^5 + 490*a^5
*b^2*c^4*d^6) + x^5*(7*a^3*b^4*c^10 + 42*a^7*c^6*d^4 + 70*a^4*b^3*c^9*d + 168*a^6*b*c^7*d^3 + 189*a^5*b^2*c^8*
d^2) + x^14*((5*a^4*b^3*d^10)/2 + 15*b^7*c^4*d^6 + 60*a*b^6*c^3*d^7 + 25*a^3*b^4*c*d^9 + (135*a^2*b^5*c^2*d^8)
/2) + x^8*((b^7*c^10)/8 + 15*a^7*c^3*d^7 + (735*a^6*b*c^4*d^6)/4 + (945*a^2*b^5*c^8*d^2)/8 + 525*a^3*b^4*c^7*d
^3 + (3675*a^4*b^3*c^6*d^4)/4 + (1323*a^5*b^2*c^5*d^5)/2 + (35*a*b^6*c^9*d)/4) + x^11*((a^7*d^10)/11 + (120*b^
7*c^7*d^3)/11 + (1470*a*b^6*c^6*d^4)/11 + (5292*a^2*b^5*c^5*d^5)/11 + (7350*a^3*b^4*c^4*d^6)/11 + (4200*a^4*b^
3*c^3*d^7)/11 + (945*a^5*b^2*c^2*d^8)/11 + (70*a^6*b*c*d^9)/11) + x^6*((7*a^2*b^5*c^10)/2 + 42*a^7*c^5*d^5 + (
175*a^3*b^4*c^9*d)/3 + 245*a^6*b*c^6*d^4 + (525*a^4*b^3*c^8*d^2)/2 + 420*a^5*b^2*c^7*d^3) + x^13*((21*a^5*b^2*
d^10)/13 + (252*b^7*c^5*d^5)/13 + (1470*a*b^6*c^4*d^6)/13 + (350*a^4*b^3*c*d^9)/13 + (2520*a^2*b^5*c^3*d^7)/13
+ (1575*a^3*b^4*c^2*d^8)/13) + x^7*(a*b^6*c^10 + 30*a^7*c^4*d^6 + 30*a^2*b^5*c^9*d + 252*a^6*b*c^5*d^5 + 225*
a^3*b^4*c^8*d^2 + 600*a^4*b^3*c^7*d^3 + 630*a^5*b^2*c^6*d^4) + x^12*((7*a^6*b*d^10)/12 + (35*b^7*c^6*d^4)/2 +
147*a*b^6*c^5*d^5 + (35*a^5*b^2*c*d^9)/2 + (735*a^2*b^5*c^4*d^6)/2 + 350*a^3*b^4*c^3*d^7 + (525*a^4*b^3*c^2*d^
8)/4) + a^7*c^10*x + (b^7*d^10*x^18)/18 + (5*a^4*c^7*x^4*(24*a^3*d^3 + 7*b^3*c^3 + 42*a*b^2*c^2*d + 63*a^2*b*c
*d^2))/4 + (b^4*d^7*x^15*(7*a^3*d^3 + 24*b^3*c^3 + 63*a*b^2*c^2*d + 42*a^2*b*c*d^2))/3 + (a^6*c^9*x^2*(10*a*d
+ 7*b*c))/2 + (b^6*d^9*x^17*(7*a*d + 10*b*c))/17 + (a^5*c^8*x^3*(45*a^2*d^2 + 21*b^2*c^2 + 70*a*b*c*d))/3 + (b
^5*d^8*x^16*(21*a^2*d^2 + 45*b^2*c^2 + 70*a*b*c*d))/16

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