3.1273 \(\int (a+b x)^9 (c+d x)^7 \, dx\)
Optimal. Leaf size=200 \[ \frac{7 d^6 (a+b x)^{16} (b c-a d)}{16 b^8}+\frac{7 d^5 (a+b x)^{15} (b c-a d)^2}{5 b^8}+\frac{5 d^4 (a+b x)^{14} (b c-a d)^3}{2 b^8}+\frac{35 d^3 (a+b x)^{13} (b c-a d)^4}{13 b^8}+\frac{7 d^2 (a+b x)^{12} (b c-a d)^5}{4 b^8}+\frac{7 d (a+b x)^{11} (b c-a d)^6}{11 b^8}+\frac{(a+b x)^{10} (b c-a d)^7}{10 b^8}+\frac{d^7 (a+b x)^{17}}{17 b^8} \]
[Out]
((b*c - a*d)^7*(a + b*x)^10)/(10*b^8) + (7*d*(b*c - a*d)^6*(a + b*x)^11)/(11*b^8
) + (7*d^2*(b*c - a*d)^5*(a + b*x)^12)/(4*b^8) + (35*d^3*(b*c - a*d)^4*(a + b*x)
^13)/(13*b^8) + (5*d^4*(b*c - a*d)^3*(a + b*x)^14)/(2*b^8) + (7*d^5*(b*c - a*d)^
2*(a + b*x)^15)/(5*b^8) + (7*d^6*(b*c - a*d)*(a + b*x)^16)/(16*b^8) + (d^7*(a +
b*x)^17)/(17*b^8)
_______________________________________________________________________________________
Rubi [A] time = 1.37335, antiderivative size = 200, normalized size of antiderivative = 1.,
number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067
\[ \frac{7 d^6 (a+b x)^{16} (b c-a d)}{16 b^8}+\frac{7 d^5 (a+b x)^{15} (b c-a d)^2}{5 b^8}+\frac{5 d^4 (a+b x)^{14} (b c-a d)^3}{2 b^8}+\frac{35 d^3 (a+b x)^{13} (b c-a d)^4}{13 b^8}+\frac{7 d^2 (a+b x)^{12} (b c-a d)^5}{4 b^8}+\frac{7 d (a+b x)^{11} (b c-a d)^6}{11 b^8}+\frac{(a+b x)^{10} (b c-a d)^7}{10 b^8}+\frac{d^7 (a+b x)^{17}}{17 b^8} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^9*(c + d*x)^7,x]
[Out]
((b*c - a*d)^7*(a + b*x)^10)/(10*b^8) + (7*d*(b*c - a*d)^6*(a + b*x)^11)/(11*b^8
) + (7*d^2*(b*c - a*d)^5*(a + b*x)^12)/(4*b^8) + (35*d^3*(b*c - a*d)^4*(a + b*x)
^13)/(13*b^8) + (5*d^4*(b*c - a*d)^3*(a + b*x)^14)/(2*b^8) + (7*d^5*(b*c - a*d)^
2*(a + b*x)^15)/(5*b^8) + (7*d^6*(b*c - a*d)*(a + b*x)^16)/(16*b^8) + (d^7*(a +
b*x)^17)/(17*b^8)
_______________________________________________________________________________________
Rubi in Sympy [A] time = 138.645, size = 184, normalized size = 0.92 \[ \frac{d^{7} \left (a + b x\right )^{17}}{17 b^{8}} - \frac{7 d^{6} \left (a + b x\right )^{16} \left (a d - b c\right )}{16 b^{8}} + \frac{7 d^{5} \left (a + b x\right )^{15} \left (a d - b c\right )^{2}}{5 b^{8}} - \frac{5 d^{4} \left (a + b x\right )^{14} \left (a d - b c\right )^{3}}{2 b^{8}} + \frac{35 d^{3} \left (a + b x\right )^{13} \left (a d - b c\right )^{4}}{13 b^{8}} - \frac{7 d^{2} \left (a + b x\right )^{12} \left (a d - b c\right )^{5}}{4 b^{8}} + \frac{7 d \left (a + b x\right )^{11} \left (a d - b c\right )^{6}}{11 b^{8}} - \frac{\left (a + b x\right )^{10} \left (a d - b c\right )^{7}}{10 b^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**9*(d*x+c)**7,x)
[Out]
d**7*(a + b*x)**17/(17*b**8) - 7*d**6*(a + b*x)**16*(a*d - b*c)/(16*b**8) + 7*d*
*5*(a + b*x)**15*(a*d - b*c)**2/(5*b**8) - 5*d**4*(a + b*x)**14*(a*d - b*c)**3/(
2*b**8) + 35*d**3*(a + b*x)**13*(a*d - b*c)**4/(13*b**8) - 7*d**2*(a + b*x)**12*
(a*d - b*c)**5/(4*b**8) + 7*d*(a + b*x)**11*(a*d - b*c)**6/(11*b**8) - (a + b*x)
**10*(a*d - b*c)**7/(10*b**8)
_______________________________________________________________________________________
Mathematica [B] time = 0.218364, size = 993, normalized size = 4.96 \[ \frac{1}{17} b^9 d^7 x^{17}+\frac{1}{16} b^8 d^6 (7 b c+9 a d) x^{16}+\frac{1}{5} b^7 d^5 \left (7 b^2 c^2+21 a b d c+12 a^2 d^2\right ) x^{15}+\frac{1}{2} b^6 d^4 \left (5 b^3 c^3+27 a b^2 d c^2+36 a^2 b d^2 c+12 a^3 d^3\right ) x^{14}+\frac{7}{13} b^5 d^3 \left (5 b^4 c^4+45 a b^3 d c^3+108 a^2 b^2 d^2 c^2+84 a^3 b d^3 c+18 a^4 d^4\right ) x^{13}+\frac{7}{4} b^4 d^2 \left (b^5 c^5+15 a b^4 d c^4+60 a^2 b^3 d^2 c^3+84 a^3 b^2 d^3 c^2+42 a^4 b d^4 c+6 a^5 d^5\right ) x^{12}+\frac{7}{11} b^3 d \left (b^6 c^6+27 a b^5 d c^5+180 a^2 b^4 d^2 c^4+420 a^3 b^3 d^3 c^3+378 a^4 b^2 d^4 c^2+126 a^5 b d^5 c+12 a^6 d^6\right ) x^{11}+\frac{1}{10} b^2 \left (b^7 c^7+63 a b^6 d c^6+756 a^2 b^5 d^2 c^5+2940 a^3 b^4 d^3 c^4+4410 a^4 b^3 d^4 c^3+2646 a^5 b^2 d^5 c^2+588 a^6 b d^6 c+36 a^7 d^7\right ) x^{10}+a b \left (b^7 c^7+28 a b^6 d c^6+196 a^2 b^5 d^2 c^5+490 a^3 b^4 d^3 c^4+490 a^4 b^3 d^4 c^3+196 a^5 b^2 d^5 c^2+28 a^6 b d^6 c+a^7 d^7\right ) x^9+\frac{1}{8} a^2 \left (36 b^7 c^7+588 a b^6 d c^6+2646 a^2 b^5 d^2 c^5+4410 a^3 b^4 d^3 c^4+2940 a^4 b^3 d^4 c^3+756 a^5 b^2 d^5 c^2+63 a^6 b d^6 c+a^7 d^7\right ) x^8+a^3 c \left (12 b^6 c^6+126 a b^5 d c^5+378 a^2 b^4 d^2 c^4+420 a^3 b^3 d^3 c^3+180 a^4 b^2 d^4 c^2+27 a^5 b d^5 c+a^6 d^6\right ) x^7+\frac{7}{2} a^4 c^2 \left (6 b^5 c^5+42 a b^4 d c^4+84 a^2 b^3 d^2 c^3+60 a^3 b^2 d^3 c^2+15 a^4 b d^4 c+a^5 d^5\right ) x^6+\frac{7}{5} a^5 c^3 \left (18 b^4 c^4+84 a b^3 d c^3+108 a^2 b^2 d^2 c^2+45 a^3 b d^3 c+5 a^4 d^4\right ) x^5+\frac{7}{4} a^6 c^4 \left (12 b^3 c^3+36 a b^2 d c^2+27 a^2 b d^2 c+5 a^3 d^3\right ) x^4+a^7 c^5 \left (12 b^2 c^2+21 a b d c+7 a^2 d^2\right ) x^3+\frac{1}{2} a^8 c^6 (9 b c+7 a d) x^2+a^9 c^7 x \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^9*(c + d*x)^7,x]
[Out]
a^9*c^7*x + (a^8*c^6*(9*b*c + 7*a*d)*x^2)/2 + a^7*c^5*(12*b^2*c^2 + 21*a*b*c*d +
7*a^2*d^2)*x^3 + (7*a^6*c^4*(12*b^3*c^3 + 36*a*b^2*c^2*d + 27*a^2*b*c*d^2 + 5*a
^3*d^3)*x^4)/4 + (7*a^5*c^3*(18*b^4*c^4 + 84*a*b^3*c^3*d + 108*a^2*b^2*c^2*d^2 +
45*a^3*b*c*d^3 + 5*a^4*d^4)*x^5)/5 + (7*a^4*c^2*(6*b^5*c^5 + 42*a*b^4*c^4*d + 8
4*a^2*b^3*c^3*d^2 + 60*a^3*b^2*c^2*d^3 + 15*a^4*b*c*d^4 + a^5*d^5)*x^6)/2 + a^3*
c*(12*b^6*c^6 + 126*a*b^5*c^5*d + 378*a^2*b^4*c^4*d^2 + 420*a^3*b^3*c^3*d^3 + 18
0*a^4*b^2*c^2*d^4 + 27*a^5*b*c*d^5 + a^6*d^6)*x^7 + (a^2*(36*b^7*c^7 + 588*a*b^6
*c^6*d + 2646*a^2*b^5*c^5*d^2 + 4410*a^3*b^4*c^4*d^3 + 2940*a^4*b^3*c^3*d^4 + 75
6*a^5*b^2*c^2*d^5 + 63*a^6*b*c*d^6 + a^7*d^7)*x^8)/8 + a*b*(b^7*c^7 + 28*a*b^6*c
^6*d + 196*a^2*b^5*c^5*d^2 + 490*a^3*b^4*c^4*d^3 + 490*a^4*b^3*c^3*d^4 + 196*a^5
*b^2*c^2*d^5 + 28*a^6*b*c*d^6 + a^7*d^7)*x^9 + (b^2*(b^7*c^7 + 63*a*b^6*c^6*d +
756*a^2*b^5*c^5*d^2 + 2940*a^3*b^4*c^4*d^3 + 4410*a^4*b^3*c^3*d^4 + 2646*a^5*b^2
*c^2*d^5 + 588*a^6*b*c*d^6 + 36*a^7*d^7)*x^10)/10 + (7*b^3*d*(b^6*c^6 + 27*a*b^5
*c^5*d + 180*a^2*b^4*c^4*d^2 + 420*a^3*b^3*c^3*d^3 + 378*a^4*b^2*c^2*d^4 + 126*a
^5*b*c*d^5 + 12*a^6*d^6)*x^11)/11 + (7*b^4*d^2*(b^5*c^5 + 15*a*b^4*c^4*d + 60*a^
2*b^3*c^3*d^2 + 84*a^3*b^2*c^2*d^3 + 42*a^4*b*c*d^4 + 6*a^5*d^5)*x^12)/4 + (7*b^
5*d^3*(5*b^4*c^4 + 45*a*b^3*c^3*d + 108*a^2*b^2*c^2*d^2 + 84*a^3*b*c*d^3 + 18*a^
4*d^4)*x^13)/13 + (b^6*d^4*(5*b^3*c^3 + 27*a*b^2*c^2*d + 36*a^2*b*c*d^2 + 12*a^3
*d^3)*x^14)/2 + (b^7*d^5*(7*b^2*c^2 + 21*a*b*c*d + 12*a^2*d^2)*x^15)/5 + (b^8*d^
6*(7*b*c + 9*a*d)*x^16)/16 + (b^9*d^7*x^17)/17
_______________________________________________________________________________________
Maple [B] time = 0.005, size = 1033, normalized size = 5.2 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^9*(d*x+c)^7,x)
[Out]
1/17*b^9*d^7*x^17+1/16*(9*a*b^8*d^7+7*b^9*c*d^6)*x^16+1/15*(36*a^2*b^7*d^7+63*a*
b^8*c*d^6+21*b^9*c^2*d^5)*x^15+1/14*(84*a^3*b^6*d^7+252*a^2*b^7*c*d^6+189*a*b^8*
c^2*d^5+35*b^9*c^3*d^4)*x^14+1/13*(126*a^4*b^5*d^7+588*a^3*b^6*c*d^6+756*a^2*b^7
*c^2*d^5+315*a*b^8*c^3*d^4+35*b^9*c^4*d^3)*x^13+1/12*(126*a^5*b^4*d^7+882*a^4*b^
5*c*d^6+1764*a^3*b^6*c^2*d^5+1260*a^2*b^7*c^3*d^4+315*a*b^8*c^4*d^3+21*b^9*c^5*d
^2)*x^12+1/11*(84*a^6*b^3*d^7+882*a^5*b^4*c*d^6+2646*a^4*b^5*c^2*d^5+2940*a^3*b^
6*c^3*d^4+1260*a^2*b^7*c^4*d^3+189*a*b^8*c^5*d^2+7*b^9*c^6*d)*x^11+1/10*(36*a^7*
b^2*d^7+588*a^6*b^3*c*d^6+2646*a^5*b^4*c^2*d^5+4410*a^4*b^5*c^3*d^4+2940*a^3*b^6
*c^4*d^3+756*a^2*b^7*c^5*d^2+63*a*b^8*c^6*d+b^9*c^7)*x^10+1/9*(9*a^8*b*d^7+252*a
^7*b^2*c*d^6+1764*a^6*b^3*c^2*d^5+4410*a^5*b^4*c^3*d^4+4410*a^4*b^5*c^4*d^3+1764
*a^3*b^6*c^5*d^2+252*a^2*b^7*c^6*d+9*a*b^8*c^7)*x^9+1/8*(a^9*d^7+63*a^8*b*c*d^6+
756*a^7*b^2*c^2*d^5+2940*a^6*b^3*c^3*d^4+4410*a^5*b^4*c^4*d^3+2646*a^4*b^5*c^5*d
^2+588*a^3*b^6*c^6*d+36*a^2*b^7*c^7)*x^8+1/7*(7*a^9*c*d^6+189*a^8*b*c^2*d^5+1260
*a^7*b^2*c^3*d^4+2940*a^6*b^3*c^4*d^3+2646*a^5*b^4*c^5*d^2+882*a^4*b^5*c^6*d+84*
a^3*b^6*c^7)*x^7+1/6*(21*a^9*c^2*d^5+315*a^8*b*c^3*d^4+1260*a^7*b^2*c^4*d^3+1764
*a^6*b^3*c^5*d^2+882*a^5*b^4*c^6*d+126*a^4*b^5*c^7)*x^6+1/5*(35*a^9*c^3*d^4+315*
a^8*b*c^4*d^3+756*a^7*b^2*c^5*d^2+588*a^6*b^3*c^6*d+126*a^5*b^4*c^7)*x^5+1/4*(35
*a^9*c^4*d^3+189*a^8*b*c^5*d^2+252*a^7*b^2*c^6*d+84*a^6*b^3*c^7)*x^4+1/3*(21*a^9
*c^5*d^2+63*a^8*b*c^6*d+36*a^7*b^2*c^7)*x^3+1/2*(7*a^9*c^6*d+9*a^8*b*c^7)*x^2+a^
9*c^7*x
_______________________________________________________________________________________
Maxima [A] time = 1.35715, size = 1381, normalized size = 6.9 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^9*(d*x + c)^7,x, algorithm="maxima")
[Out]
1/17*b^9*d^7*x^17 + a^9*c^7*x + 1/16*(7*b^9*c*d^6 + 9*a*b^8*d^7)*x^16 + 1/5*(7*b
^9*c^2*d^5 + 21*a*b^8*c*d^6 + 12*a^2*b^7*d^7)*x^15 + 1/2*(5*b^9*c^3*d^4 + 27*a*b
^8*c^2*d^5 + 36*a^2*b^7*c*d^6 + 12*a^3*b^6*d^7)*x^14 + 7/13*(5*b^9*c^4*d^3 + 45*
a*b^8*c^3*d^4 + 108*a^2*b^7*c^2*d^5 + 84*a^3*b^6*c*d^6 + 18*a^4*b^5*d^7)*x^13 +
7/4*(b^9*c^5*d^2 + 15*a*b^8*c^4*d^3 + 60*a^2*b^7*c^3*d^4 + 84*a^3*b^6*c^2*d^5 +
42*a^4*b^5*c*d^6 + 6*a^5*b^4*d^7)*x^12 + 7/11*(b^9*c^6*d + 27*a*b^8*c^5*d^2 + 18
0*a^2*b^7*c^4*d^3 + 420*a^3*b^6*c^3*d^4 + 378*a^4*b^5*c^2*d^5 + 126*a^5*b^4*c*d^
6 + 12*a^6*b^3*d^7)*x^11 + 1/10*(b^9*c^7 + 63*a*b^8*c^6*d + 756*a^2*b^7*c^5*d^2
+ 2940*a^3*b^6*c^4*d^3 + 4410*a^4*b^5*c^3*d^4 + 2646*a^5*b^4*c^2*d^5 + 588*a^6*b
^3*c*d^6 + 36*a^7*b^2*d^7)*x^10 + (a*b^8*c^7 + 28*a^2*b^7*c^6*d + 196*a^3*b^6*c^
5*d^2 + 490*a^4*b^5*c^4*d^3 + 490*a^5*b^4*c^3*d^4 + 196*a^6*b^3*c^2*d^5 + 28*a^7
*b^2*c*d^6 + a^8*b*d^7)*x^9 + 1/8*(36*a^2*b^7*c^7 + 588*a^3*b^6*c^6*d + 2646*a^4
*b^5*c^5*d^2 + 4410*a^5*b^4*c^4*d^3 + 2940*a^6*b^3*c^3*d^4 + 756*a^7*b^2*c^2*d^5
+ 63*a^8*b*c*d^6 + a^9*d^7)*x^8 + (12*a^3*b^6*c^7 + 126*a^4*b^5*c^6*d + 378*a^5
*b^4*c^5*d^2 + 420*a^6*b^3*c^4*d^3 + 180*a^7*b^2*c^3*d^4 + 27*a^8*b*c^2*d^5 + a^
9*c*d^6)*x^7 + 7/2*(6*a^4*b^5*c^7 + 42*a^5*b^4*c^6*d + 84*a^6*b^3*c^5*d^2 + 60*a
^7*b^2*c^4*d^3 + 15*a^8*b*c^3*d^4 + a^9*c^2*d^5)*x^6 + 7/5*(18*a^5*b^4*c^7 + 84*
a^6*b^3*c^6*d + 108*a^7*b^2*c^5*d^2 + 45*a^8*b*c^4*d^3 + 5*a^9*c^3*d^4)*x^5 + 7/
4*(12*a^6*b^3*c^7 + 36*a^7*b^2*c^6*d + 27*a^8*b*c^5*d^2 + 5*a^9*c^4*d^3)*x^4 + (
12*a^7*b^2*c^7 + 21*a^8*b*c^6*d + 7*a^9*c^5*d^2)*x^3 + 1/2*(9*a^8*b*c^7 + 7*a^9*
c^6*d)*x^2
_______________________________________________________________________________________
Fricas [A] time = 0.210706, size = 1, normalized size = 0. \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^9*(d*x + c)^7,x, algorithm="fricas")
[Out]
1/17*x^17*d^7*b^9 + 7/16*x^16*d^6*c*b^9 + 9/16*x^16*d^7*b^8*a + 7/5*x^15*d^5*c^2
*b^9 + 21/5*x^15*d^6*c*b^8*a + 12/5*x^15*d^7*b^7*a^2 + 5/2*x^14*d^4*c^3*b^9 + 27
/2*x^14*d^5*c^2*b^8*a + 18*x^14*d^6*c*b^7*a^2 + 6*x^14*d^7*b^6*a^3 + 35/13*x^13*
d^3*c^4*b^9 + 315/13*x^13*d^4*c^3*b^8*a + 756/13*x^13*d^5*c^2*b^7*a^2 + 588/13*x
^13*d^6*c*b^6*a^3 + 126/13*x^13*d^7*b^5*a^4 + 7/4*x^12*d^2*c^5*b^9 + 105/4*x^12*
d^3*c^4*b^8*a + 105*x^12*d^4*c^3*b^7*a^2 + 147*x^12*d^5*c^2*b^6*a^3 + 147/2*x^12
*d^6*c*b^5*a^4 + 21/2*x^12*d^7*b^4*a^5 + 7/11*x^11*d*c^6*b^9 + 189/11*x^11*d^2*c
^5*b^8*a + 1260/11*x^11*d^3*c^4*b^7*a^2 + 2940/11*x^11*d^4*c^3*b^6*a^3 + 2646/11
*x^11*d^5*c^2*b^5*a^4 + 882/11*x^11*d^6*c*b^4*a^5 + 84/11*x^11*d^7*b^3*a^6 + 1/1
0*x^10*c^7*b^9 + 63/10*x^10*d*c^6*b^8*a + 378/5*x^10*d^2*c^5*b^7*a^2 + 294*x^10*
d^3*c^4*b^6*a^3 + 441*x^10*d^4*c^3*b^5*a^4 + 1323/5*x^10*d^5*c^2*b^4*a^5 + 294/5
*x^10*d^6*c*b^3*a^6 + 18/5*x^10*d^7*b^2*a^7 + x^9*c^7*b^8*a + 28*x^9*d*c^6*b^7*a
^2 + 196*x^9*d^2*c^5*b^6*a^3 + 490*x^9*d^3*c^4*b^5*a^4 + 490*x^9*d^4*c^3*b^4*a^5
+ 196*x^9*d^5*c^2*b^3*a^6 + 28*x^9*d^6*c*b^2*a^7 + x^9*d^7*b*a^8 + 9/2*x^8*c^7*
b^7*a^2 + 147/2*x^8*d*c^6*b^6*a^3 + 1323/4*x^8*d^2*c^5*b^5*a^4 + 2205/4*x^8*d^3*
c^4*b^4*a^5 + 735/2*x^8*d^4*c^3*b^3*a^6 + 189/2*x^8*d^5*c^2*b^2*a^7 + 63/8*x^8*d
^6*c*b*a^8 + 1/8*x^8*d^7*a^9 + 12*x^7*c^7*b^6*a^3 + 126*x^7*d*c^6*b^5*a^4 + 378*
x^7*d^2*c^5*b^4*a^5 + 420*x^7*d^3*c^4*b^3*a^6 + 180*x^7*d^4*c^3*b^2*a^7 + 27*x^7
*d^5*c^2*b*a^8 + x^7*d^6*c*a^9 + 21*x^6*c^7*b^5*a^4 + 147*x^6*d*c^6*b^4*a^5 + 29
4*x^6*d^2*c^5*b^3*a^6 + 210*x^6*d^3*c^4*b^2*a^7 + 105/2*x^6*d^4*c^3*b*a^8 + 7/2*
x^6*d^5*c^2*a^9 + 126/5*x^5*c^7*b^4*a^5 + 588/5*x^5*d*c^6*b^3*a^6 + 756/5*x^5*d^
2*c^5*b^2*a^7 + 63*x^5*d^3*c^4*b*a^8 + 7*x^5*d^4*c^3*a^9 + 21*x^4*c^7*b^3*a^6 +
63*x^4*d*c^6*b^2*a^7 + 189/4*x^4*d^2*c^5*b*a^8 + 35/4*x^4*d^3*c^4*a^9 + 12*x^3*c
^7*b^2*a^7 + 21*x^3*d*c^6*b*a^8 + 7*x^3*d^2*c^5*a^9 + 9/2*x^2*c^7*b*a^8 + 7/2*x^
2*d*c^6*a^9 + x*c^7*a^9
_______________________________________________________________________________________
Sympy [A] time = 0.547523, size = 1163, normalized size = 5.82 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**9*(d*x+c)**7,x)
[Out]
a**9*c**7*x + b**9*d**7*x**17/17 + x**16*(9*a*b**8*d**7/16 + 7*b**9*c*d**6/16) +
x**15*(12*a**2*b**7*d**7/5 + 21*a*b**8*c*d**6/5 + 7*b**9*c**2*d**5/5) + x**14*(
6*a**3*b**6*d**7 + 18*a**2*b**7*c*d**6 + 27*a*b**8*c**2*d**5/2 + 5*b**9*c**3*d**
4/2) + x**13*(126*a**4*b**5*d**7/13 + 588*a**3*b**6*c*d**6/13 + 756*a**2*b**7*c*
*2*d**5/13 + 315*a*b**8*c**3*d**4/13 + 35*b**9*c**4*d**3/13) + x**12*(21*a**5*b*
*4*d**7/2 + 147*a**4*b**5*c*d**6/2 + 147*a**3*b**6*c**2*d**5 + 105*a**2*b**7*c**
3*d**4 + 105*a*b**8*c**4*d**3/4 + 7*b**9*c**5*d**2/4) + x**11*(84*a**6*b**3*d**7
/11 + 882*a**5*b**4*c*d**6/11 + 2646*a**4*b**5*c**2*d**5/11 + 2940*a**3*b**6*c**
3*d**4/11 + 1260*a**2*b**7*c**4*d**3/11 + 189*a*b**8*c**5*d**2/11 + 7*b**9*c**6*
d/11) + x**10*(18*a**7*b**2*d**7/5 + 294*a**6*b**3*c*d**6/5 + 1323*a**5*b**4*c**
2*d**5/5 + 441*a**4*b**5*c**3*d**4 + 294*a**3*b**6*c**4*d**3 + 378*a**2*b**7*c**
5*d**2/5 + 63*a*b**8*c**6*d/10 + b**9*c**7/10) + x**9*(a**8*b*d**7 + 28*a**7*b**
2*c*d**6 + 196*a**6*b**3*c**2*d**5 + 490*a**5*b**4*c**3*d**4 + 490*a**4*b**5*c**
4*d**3 + 196*a**3*b**6*c**5*d**2 + 28*a**2*b**7*c**6*d + a*b**8*c**7) + x**8*(a*
*9*d**7/8 + 63*a**8*b*c*d**6/8 + 189*a**7*b**2*c**2*d**5/2 + 735*a**6*b**3*c**3*
d**4/2 + 2205*a**5*b**4*c**4*d**3/4 + 1323*a**4*b**5*c**5*d**2/4 + 147*a**3*b**6
*c**6*d/2 + 9*a**2*b**7*c**7/2) + x**7*(a**9*c*d**6 + 27*a**8*b*c**2*d**5 + 180*
a**7*b**2*c**3*d**4 + 420*a**6*b**3*c**4*d**3 + 378*a**5*b**4*c**5*d**2 + 126*a*
*4*b**5*c**6*d + 12*a**3*b**6*c**7) + x**6*(7*a**9*c**2*d**5/2 + 105*a**8*b*c**3
*d**4/2 + 210*a**7*b**2*c**4*d**3 + 294*a**6*b**3*c**5*d**2 + 147*a**5*b**4*c**6
*d + 21*a**4*b**5*c**7) + x**5*(7*a**9*c**3*d**4 + 63*a**8*b*c**4*d**3 + 756*a**
7*b**2*c**5*d**2/5 + 588*a**6*b**3*c**6*d/5 + 126*a**5*b**4*c**7/5) + x**4*(35*a
**9*c**4*d**3/4 + 189*a**8*b*c**5*d**2/4 + 63*a**7*b**2*c**6*d + 21*a**6*b**3*c*
*7) + x**3*(7*a**9*c**5*d**2 + 21*a**8*b*c**6*d + 12*a**7*b**2*c**7) + x**2*(7*a
**9*c**6*d/2 + 9*a**8*b*c**7/2)
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.22065, size = 1, normalized size = 0. \[ \mathit{Done} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^9*(d*x + c)^7,x, algorithm="giac")
[Out]
Done