3.1274 \(\int (a+b x)^8 (c+d x)^7 \, dx\)

Optimal. Leaf size=200 \[ \frac{7 d^6 (a+b x)^{15} (b c-a d)}{15 b^8}+\frac{3 d^5 (a+b x)^{14} (b c-a d)^2}{2 b^8}+\frac{35 d^4 (a+b x)^{13} (b c-a d)^3}{13 b^8}+\frac{35 d^3 (a+b x)^{12} (b c-a d)^4}{12 b^8}+\frac{21 d^2 (a+b x)^{11} (b c-a d)^5}{11 b^8}+\frac{7 d (a+b x)^{10} (b c-a d)^6}{10 b^8}+\frac{(a+b x)^9 (b c-a d)^7}{9 b^8}+\frac{d^7 (a+b x)^{16}}{16 b^8} \]

[Out]

((b*c - a*d)^7*(a + b*x)^9)/(9*b^8) + (7*d*(b*c - a*d)^6*(a + b*x)^10)/(10*b^8)
+ (21*d^2*(b*c - a*d)^5*(a + b*x)^11)/(11*b^8) + (35*d^3*(b*c - a*d)^4*(a + b*x)
^12)/(12*b^8) + (35*d^4*(b*c - a*d)^3*(a + b*x)^13)/(13*b^8) + (3*d^5*(b*c - a*d
)^2*(a + b*x)^14)/(2*b^8) + (7*d^6*(b*c - a*d)*(a + b*x)^15)/(15*b^8) + (d^7*(a
+ b*x)^16)/(16*b^8)

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Rubi [A]  time = 1.23807, 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 \[ \frac{7 d^6 (a+b x)^{15} (b c-a d)}{15 b^8}+\frac{3 d^5 (a+b x)^{14} (b c-a d)^2}{2 b^8}+\frac{35 d^4 (a+b x)^{13} (b c-a d)^3}{13 b^8}+\frac{35 d^3 (a+b x)^{12} (b c-a d)^4}{12 b^8}+\frac{21 d^2 (a+b x)^{11} (b c-a d)^5}{11 b^8}+\frac{7 d (a+b x)^{10} (b c-a d)^6}{10 b^8}+\frac{(a+b x)^9 (b c-a d)^7}{9 b^8}+\frac{d^7 (a+b x)^{16}}{16 b^8} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x)^8*(c + d*x)^7,x]

[Out]

((b*c - a*d)^7*(a + b*x)^9)/(9*b^8) + (7*d*(b*c - a*d)^6*(a + b*x)^10)/(10*b^8)
+ (21*d^2*(b*c - a*d)^5*(a + b*x)^11)/(11*b^8) + (35*d^3*(b*c - a*d)^4*(a + b*x)
^12)/(12*b^8) + (35*d^4*(b*c - a*d)^3*(a + b*x)^13)/(13*b^8) + (3*d^5*(b*c - a*d
)^2*(a + b*x)^14)/(2*b^8) + (7*d^6*(b*c - a*d)*(a + b*x)^15)/(15*b^8) + (d^7*(a
+ b*x)^16)/(16*b^8)

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Rubi in Sympy [A]  time = 123.539, size = 184, normalized size = 0.92 \[ \frac{d^{7} \left (a + b x\right )^{16}}{16 b^{8}} - \frac{7 d^{6} \left (a + b x\right )^{15} \left (a d - b c\right )}{15 b^{8}} + \frac{3 d^{5} \left (a + b x\right )^{14} \left (a d - b c\right )^{2}}{2 b^{8}} - \frac{35 d^{4} \left (a + b x\right )^{13} \left (a d - b c\right )^{3}}{13 b^{8}} + \frac{35 d^{3} \left (a + b x\right )^{12} \left (a d - b c\right )^{4}}{12 b^{8}} - \frac{21 d^{2} \left (a + b x\right )^{11} \left (a d - b c\right )^{5}}{11 b^{8}} + \frac{7 d \left (a + b x\right )^{10} \left (a d - b c\right )^{6}}{10 b^{8}} - \frac{\left (a + b x\right )^{9} \left (a d - b c\right )^{7}}{9 b^{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x+a)**8*(d*x+c)**7,x)

[Out]

d**7*(a + b*x)**16/(16*b**8) - 7*d**6*(a + b*x)**15*(a*d - b*c)/(15*b**8) + 3*d*
*5*(a + b*x)**14*(a*d - b*c)**2/(2*b**8) - 35*d**4*(a + b*x)**13*(a*d - b*c)**3/
(13*b**8) + 35*d**3*(a + b*x)**12*(a*d - b*c)**4/(12*b**8) - 21*d**2*(a + b*x)**
11*(a*d - b*c)**5/(11*b**8) + 7*d*(a + b*x)**10*(a*d - b*c)**6/(10*b**8) - (a +
b*x)**9*(a*d - b*c)**7/(9*b**8)

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Mathematica [B]  time = 0.193822, size = 897, normalized size = 4.48 \[ \frac{1}{16} b^8 d^7 x^{16}+\frac{1}{15} b^7 d^6 (7 b c+8 a d) x^{15}+\frac{1}{2} b^6 d^5 \left (3 b^2 c^2+8 a b d c+4 a^2 d^2\right ) x^{14}+\frac{7}{13} b^5 d^4 \left (5 b^3 c^3+24 a b^2 d c^2+28 a^2 b d^2 c+8 a^3 d^3\right ) x^{13}+\frac{7}{12} b^4 d^3 \left (5 b^4 c^4+40 a b^3 d c^3+84 a^2 b^2 d^2 c^2+56 a^3 b d^3 c+10 a^4 d^4\right ) x^{12}+\frac{7}{11} b^3 d^2 \left (3 b^5 c^5+40 a b^4 d c^4+140 a^2 b^3 d^2 c^3+168 a^3 b^2 d^3 c^2+70 a^4 b d^4 c+8 a^5 d^5\right ) x^{11}+\frac{7}{10} b^2 d \left (b^6 c^6+24 a b^5 d c^5+140 a^2 b^4 d^2 c^4+280 a^3 b^3 d^3 c^3+210 a^4 b^2 d^4 c^2+56 a^5 b d^5 c+4 a^6 d^6\right ) x^{10}+\frac{1}{9} b \left (b^7 c^7+56 a b^6 d c^6+588 a^2 b^5 d^2 c^5+1960 a^3 b^4 d^3 c^4+2450 a^4 b^3 d^4 c^3+1176 a^5 b^2 d^5 c^2+196 a^6 b d^6 c+8 a^7 d^7\right ) x^9+\frac{1}{8} a \left (8 b^7 c^7+196 a b^6 d c^6+1176 a^2 b^5 d^2 c^5+2450 a^3 b^4 d^3 c^4+1960 a^4 b^3 d^4 c^3+588 a^5 b^2 d^5 c^2+56 a^6 b d^6 c+a^7 d^7\right ) x^8+a^2 c \left (4 b^6 c^6+56 a b^5 d c^5+210 a^2 b^4 d^2 c^4+280 a^3 b^3 d^3 c^3+140 a^4 b^2 d^4 c^2+24 a^5 b d^5 c+a^6 d^6\right ) x^7+\frac{7}{6} a^3 c^2 \left (8 b^5 c^5+70 a b^4 d c^4+168 a^2 b^3 d^2 c^3+140 a^3 b^2 d^3 c^2+40 a^4 b d^4 c+3 a^5 d^5\right ) x^6+\frac{7}{5} a^4 c^3 \left (10 b^4 c^4+56 a b^3 d c^3+84 a^2 b^2 d^2 c^2+40 a^3 b d^3 c+5 a^4 d^4\right ) x^5+\frac{7}{4} a^5 c^4 \left (8 b^3 c^3+28 a b^2 d c^2+24 a^2 b d^2 c+5 a^3 d^3\right ) x^4+\frac{7}{3} a^6 c^5 \left (4 b^2 c^2+8 a b d c+3 a^2 d^2\right ) x^3+\frac{1}{2} a^7 c^6 (8 b c+7 a d) x^2+a^8 c^7 x \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x)^8*(c + d*x)^7,x]

[Out]

a^8*c^7*x + (a^7*c^6*(8*b*c + 7*a*d)*x^2)/2 + (7*a^6*c^5*(4*b^2*c^2 + 8*a*b*c*d
+ 3*a^2*d^2)*x^3)/3 + (7*a^5*c^4*(8*b^3*c^3 + 28*a*b^2*c^2*d + 24*a^2*b*c*d^2 +
5*a^3*d^3)*x^4)/4 + (7*a^4*c^3*(10*b^4*c^4 + 56*a*b^3*c^3*d + 84*a^2*b^2*c^2*d^2
+ 40*a^3*b*c*d^3 + 5*a^4*d^4)*x^5)/5 + (7*a^3*c^2*(8*b^5*c^5 + 70*a*b^4*c^4*d +
168*a^2*b^3*c^3*d^2 + 140*a^3*b^2*c^2*d^3 + 40*a^4*b*c*d^4 + 3*a^5*d^5)*x^6)/6
+ a^2*c*(4*b^6*c^6 + 56*a*b^5*c^5*d + 210*a^2*b^4*c^4*d^2 + 280*a^3*b^3*c^3*d^3
+ 140*a^4*b^2*c^2*d^4 + 24*a^5*b*c*d^5 + a^6*d^6)*x^7 + (a*(8*b^7*c^7 + 196*a*b^
6*c^6*d + 1176*a^2*b^5*c^5*d^2 + 2450*a^3*b^4*c^4*d^3 + 1960*a^4*b^3*c^3*d^4 + 5
88*a^5*b^2*c^2*d^5 + 56*a^6*b*c*d^6 + a^7*d^7)*x^8)/8 + (b*(b^7*c^7 + 56*a*b^6*c
^6*d + 588*a^2*b^5*c^5*d^2 + 1960*a^3*b^4*c^4*d^3 + 2450*a^4*b^3*c^3*d^4 + 1176*
a^5*b^2*c^2*d^5 + 196*a^6*b*c*d^6 + 8*a^7*d^7)*x^9)/9 + (7*b^2*d*(b^6*c^6 + 24*a
*b^5*c^5*d + 140*a^2*b^4*c^4*d^2 + 280*a^3*b^3*c^3*d^3 + 210*a^4*b^2*c^2*d^4 + 5
6*a^5*b*c*d^5 + 4*a^6*d^6)*x^10)/10 + (7*b^3*d^2*(3*b^5*c^5 + 40*a*b^4*c^4*d + 1
40*a^2*b^3*c^3*d^2 + 168*a^3*b^2*c^2*d^3 + 70*a^4*b*c*d^4 + 8*a^5*d^5)*x^11)/11
+ (7*b^4*d^3*(5*b^4*c^4 + 40*a*b^3*c^3*d + 84*a^2*b^2*c^2*d^2 + 56*a^3*b*c*d^3 +
10*a^4*d^4)*x^12)/12 + (7*b^5*d^4*(5*b^3*c^3 + 24*a*b^2*c^2*d + 28*a^2*b*c*d^2
+ 8*a^3*d^3)*x^13)/13 + (b^6*d^5*(3*b^2*c^2 + 8*a*b*c*d + 4*a^2*d^2)*x^14)/2 + (
b^7*d^6*(7*b*c + 8*a*d)*x^15)/15 + (b^8*d^7*x^16)/16

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Maple [B]  time = 0.004, size = 925, normalized size = 4.6 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x+a)^8*(d*x+c)^7,x)

[Out]

1/16*b^8*d^7*x^16+1/15*(8*a*b^7*d^7+7*b^8*c*d^6)*x^15+1/14*(28*a^2*b^6*d^7+56*a*
b^7*c*d^6+21*b^8*c^2*d^5)*x^14+1/13*(56*a^3*b^5*d^7+196*a^2*b^6*c*d^6+168*a*b^7*
c^2*d^5+35*b^8*c^3*d^4)*x^13+1/12*(70*a^4*b^4*d^7+392*a^3*b^5*c*d^6+588*a^2*b^6*
c^2*d^5+280*a*b^7*c^3*d^4+35*b^8*c^4*d^3)*x^12+1/11*(56*a^5*b^3*d^7+490*a^4*b^4*
c*d^6+1176*a^3*b^5*c^2*d^5+980*a^2*b^6*c^3*d^4+280*a*b^7*c^4*d^3+21*b^8*c^5*d^2)
*x^11+1/10*(28*a^6*b^2*d^7+392*a^5*b^3*c*d^6+1470*a^4*b^4*c^2*d^5+1960*a^3*b^5*c
^3*d^4+980*a^2*b^6*c^4*d^3+168*a*b^7*c^5*d^2+7*b^8*c^6*d)*x^10+1/9*(8*a^7*b*d^7+
196*a^6*b^2*c*d^6+1176*a^5*b^3*c^2*d^5+2450*a^4*b^4*c^3*d^4+1960*a^3*b^5*c^4*d^3
+588*a^2*b^6*c^5*d^2+56*a*b^7*c^6*d+b^8*c^7)*x^9+1/8*(a^8*d^7+56*a^7*b*c*d^6+588
*a^6*b^2*c^2*d^5+1960*a^5*b^3*c^3*d^4+2450*a^4*b^4*c^4*d^3+1176*a^3*b^5*c^5*d^2+
196*a^2*b^6*c^6*d+8*a*b^7*c^7)*x^8+1/7*(7*a^8*c*d^6+168*a^7*b*c^2*d^5+980*a^6*b^
2*c^3*d^4+1960*a^5*b^3*c^4*d^3+1470*a^4*b^4*c^5*d^2+392*a^3*b^5*c^6*d+28*a^2*b^6
*c^7)*x^7+1/6*(21*a^8*c^2*d^5+280*a^7*b*c^3*d^4+980*a^6*b^2*c^4*d^3+1176*a^5*b^3
*c^5*d^2+490*a^4*b^4*c^6*d+56*a^3*b^5*c^7)*x^6+1/5*(35*a^8*c^3*d^4+280*a^7*b*c^4
*d^3+588*a^6*b^2*c^5*d^2+392*a^5*b^3*c^6*d+70*a^4*b^4*c^7)*x^5+1/4*(35*a^8*c^4*d
^3+168*a^7*b*c^5*d^2+196*a^6*b^2*c^6*d+56*a^5*b^3*c^7)*x^4+1/3*(21*a^8*c^5*d^2+5
6*a^7*b*c^6*d+28*a^6*b^2*c^7)*x^3+1/2*(7*a^8*c^6*d+8*a^7*b*c^7)*x^2+a^8*c^7*x

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Maxima [A]  time = 1.36316, size = 1243, normalized size = 6.22 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x + a)^8*(d*x + c)^7,x, algorithm="maxima")

[Out]

1/16*b^8*d^7*x^16 + a^8*c^7*x + 1/15*(7*b^8*c*d^6 + 8*a*b^7*d^7)*x^15 + 1/2*(3*b
^8*c^2*d^5 + 8*a*b^7*c*d^6 + 4*a^2*b^6*d^7)*x^14 + 7/13*(5*b^8*c^3*d^4 + 24*a*b^
7*c^2*d^5 + 28*a^2*b^6*c*d^6 + 8*a^3*b^5*d^7)*x^13 + 7/12*(5*b^8*c^4*d^3 + 40*a*
b^7*c^3*d^4 + 84*a^2*b^6*c^2*d^5 + 56*a^3*b^5*c*d^6 + 10*a^4*b^4*d^7)*x^12 + 7/1
1*(3*b^8*c^5*d^2 + 40*a*b^7*c^4*d^3 + 140*a^2*b^6*c^3*d^4 + 168*a^3*b^5*c^2*d^5
+ 70*a^4*b^4*c*d^6 + 8*a^5*b^3*d^7)*x^11 + 7/10*(b^8*c^6*d + 24*a*b^7*c^5*d^2 +
140*a^2*b^6*c^4*d^3 + 280*a^3*b^5*c^3*d^4 + 210*a^4*b^4*c^2*d^5 + 56*a^5*b^3*c*d
^6 + 4*a^6*b^2*d^7)*x^10 + 1/9*(b^8*c^7 + 56*a*b^7*c^6*d + 588*a^2*b^6*c^5*d^2 +
1960*a^3*b^5*c^4*d^3 + 2450*a^4*b^4*c^3*d^4 + 1176*a^5*b^3*c^2*d^5 + 196*a^6*b^
2*c*d^6 + 8*a^7*b*d^7)*x^9 + 1/8*(8*a*b^7*c^7 + 196*a^2*b^6*c^6*d + 1176*a^3*b^5
*c^5*d^2 + 2450*a^4*b^4*c^4*d^3 + 1960*a^5*b^3*c^3*d^4 + 588*a^6*b^2*c^2*d^5 + 5
6*a^7*b*c*d^6 + a^8*d^7)*x^8 + (4*a^2*b^6*c^7 + 56*a^3*b^5*c^6*d + 210*a^4*b^4*c
^5*d^2 + 280*a^5*b^3*c^4*d^3 + 140*a^6*b^2*c^3*d^4 + 24*a^7*b*c^2*d^5 + a^8*c*d^
6)*x^7 + 7/6*(8*a^3*b^5*c^7 + 70*a^4*b^4*c^6*d + 168*a^5*b^3*c^5*d^2 + 140*a^6*b
^2*c^4*d^3 + 40*a^7*b*c^3*d^4 + 3*a^8*c^2*d^5)*x^6 + 7/5*(10*a^4*b^4*c^7 + 56*a^
5*b^3*c^6*d + 84*a^6*b^2*c^5*d^2 + 40*a^7*b*c^4*d^3 + 5*a^8*c^3*d^4)*x^5 + 7/4*(
8*a^5*b^3*c^7 + 28*a^6*b^2*c^6*d + 24*a^7*b*c^5*d^2 + 5*a^8*c^4*d^3)*x^4 + 7/3*(
4*a^6*b^2*c^7 + 8*a^7*b*c^6*d + 3*a^8*c^5*d^2)*x^3 + 1/2*(8*a^7*b*c^7 + 7*a^8*c^
6*d)*x^2

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Fricas [A]  time = 0.198929, 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)^8*(d*x + c)^7,x, algorithm="fricas")

[Out]

1/16*x^16*d^7*b^8 + 7/15*x^15*d^6*c*b^8 + 8/15*x^15*d^7*b^7*a + 3/2*x^14*d^5*c^2
*b^8 + 4*x^14*d^6*c*b^7*a + 2*x^14*d^7*b^6*a^2 + 35/13*x^13*d^4*c^3*b^8 + 168/13
*x^13*d^5*c^2*b^7*a + 196/13*x^13*d^6*c*b^6*a^2 + 56/13*x^13*d^7*b^5*a^3 + 35/12
*x^12*d^3*c^4*b^8 + 70/3*x^12*d^4*c^3*b^7*a + 49*x^12*d^5*c^2*b^6*a^2 + 98/3*x^1
2*d^6*c*b^5*a^3 + 35/6*x^12*d^7*b^4*a^4 + 21/11*x^11*d^2*c^5*b^8 + 280/11*x^11*d
^3*c^4*b^7*a + 980/11*x^11*d^4*c^3*b^6*a^2 + 1176/11*x^11*d^5*c^2*b^5*a^3 + 490/
11*x^11*d^6*c*b^4*a^4 + 56/11*x^11*d^7*b^3*a^5 + 7/10*x^10*d*c^6*b^8 + 84/5*x^10
*d^2*c^5*b^7*a + 98*x^10*d^3*c^4*b^6*a^2 + 196*x^10*d^4*c^3*b^5*a^3 + 147*x^10*d
^5*c^2*b^4*a^4 + 196/5*x^10*d^6*c*b^3*a^5 + 14/5*x^10*d^7*b^2*a^6 + 1/9*x^9*c^7*
b^8 + 56/9*x^9*d*c^6*b^7*a + 196/3*x^9*d^2*c^5*b^6*a^2 + 1960/9*x^9*d^3*c^4*b^5*
a^3 + 2450/9*x^9*d^4*c^3*b^4*a^4 + 392/3*x^9*d^5*c^2*b^3*a^5 + 196/9*x^9*d^6*c*b
^2*a^6 + 8/9*x^9*d^7*b*a^7 + x^8*c^7*b^7*a + 49/2*x^8*d*c^6*b^6*a^2 + 147*x^8*d^
2*c^5*b^5*a^3 + 1225/4*x^8*d^3*c^4*b^4*a^4 + 245*x^8*d^4*c^3*b^3*a^5 + 147/2*x^8
*d^5*c^2*b^2*a^6 + 7*x^8*d^6*c*b*a^7 + 1/8*x^8*d^7*a^8 + 4*x^7*c^7*b^6*a^2 + 56*
x^7*d*c^6*b^5*a^3 + 210*x^7*d^2*c^5*b^4*a^4 + 280*x^7*d^3*c^4*b^3*a^5 + 140*x^7*
d^4*c^3*b^2*a^6 + 24*x^7*d^5*c^2*b*a^7 + x^7*d^6*c*a^8 + 28/3*x^6*c^7*b^5*a^3 +
245/3*x^6*d*c^6*b^4*a^4 + 196*x^6*d^2*c^5*b^3*a^5 + 490/3*x^6*d^3*c^4*b^2*a^6 +
140/3*x^6*d^4*c^3*b*a^7 + 7/2*x^6*d^5*c^2*a^8 + 14*x^5*c^7*b^4*a^4 + 392/5*x^5*d
*c^6*b^3*a^5 + 588/5*x^5*d^2*c^5*b^2*a^6 + 56*x^5*d^3*c^4*b*a^7 + 7*x^5*d^4*c^3*
a^8 + 14*x^4*c^7*b^3*a^5 + 49*x^4*d*c^6*b^2*a^6 + 42*x^4*d^2*c^5*b*a^7 + 35/4*x^
4*d^3*c^4*a^8 + 28/3*x^3*c^7*b^2*a^6 + 56/3*x^3*d*c^6*b*a^7 + 7*x^3*d^2*c^5*a^8
+ 4*x^2*c^7*b*a^7 + 7/2*x^2*d*c^6*a^8 + x*c^7*a^8

_______________________________________________________________________________________

Sympy [A]  time = 0.493418, size = 1046, normalized size = 5.23 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x+a)**8*(d*x+c)**7,x)

[Out]

a**8*c**7*x + b**8*d**7*x**16/16 + x**15*(8*a*b**7*d**7/15 + 7*b**8*c*d**6/15) +
x**14*(2*a**2*b**6*d**7 + 4*a*b**7*c*d**6 + 3*b**8*c**2*d**5/2) + x**13*(56*a**
3*b**5*d**7/13 + 196*a**2*b**6*c*d**6/13 + 168*a*b**7*c**2*d**5/13 + 35*b**8*c**
3*d**4/13) + x**12*(35*a**4*b**4*d**7/6 + 98*a**3*b**5*c*d**6/3 + 49*a**2*b**6*c
**2*d**5 + 70*a*b**7*c**3*d**4/3 + 35*b**8*c**4*d**3/12) + x**11*(56*a**5*b**3*d
**7/11 + 490*a**4*b**4*c*d**6/11 + 1176*a**3*b**5*c**2*d**5/11 + 980*a**2*b**6*c
**3*d**4/11 + 280*a*b**7*c**4*d**3/11 + 21*b**8*c**5*d**2/11) + x**10*(14*a**6*b
**2*d**7/5 + 196*a**5*b**3*c*d**6/5 + 147*a**4*b**4*c**2*d**5 + 196*a**3*b**5*c*
*3*d**4 + 98*a**2*b**6*c**4*d**3 + 84*a*b**7*c**5*d**2/5 + 7*b**8*c**6*d/10) + x
**9*(8*a**7*b*d**7/9 + 196*a**6*b**2*c*d**6/9 + 392*a**5*b**3*c**2*d**5/3 + 2450
*a**4*b**4*c**3*d**4/9 + 1960*a**3*b**5*c**4*d**3/9 + 196*a**2*b**6*c**5*d**2/3
+ 56*a*b**7*c**6*d/9 + b**8*c**7/9) + x**8*(a**8*d**7/8 + 7*a**7*b*c*d**6 + 147*
a**6*b**2*c**2*d**5/2 + 245*a**5*b**3*c**3*d**4 + 1225*a**4*b**4*c**4*d**3/4 + 1
47*a**3*b**5*c**5*d**2 + 49*a**2*b**6*c**6*d/2 + a*b**7*c**7) + x**7*(a**8*c*d**
6 + 24*a**7*b*c**2*d**5 + 140*a**6*b**2*c**3*d**4 + 280*a**5*b**3*c**4*d**3 + 21
0*a**4*b**4*c**5*d**2 + 56*a**3*b**5*c**6*d + 4*a**2*b**6*c**7) + x**6*(7*a**8*c
**2*d**5/2 + 140*a**7*b*c**3*d**4/3 + 490*a**6*b**2*c**4*d**3/3 + 196*a**5*b**3*
c**5*d**2 + 245*a**4*b**4*c**6*d/3 + 28*a**3*b**5*c**7/3) + x**5*(7*a**8*c**3*d*
*4 + 56*a**7*b*c**4*d**3 + 588*a**6*b**2*c**5*d**2/5 + 392*a**5*b**3*c**6*d/5 +
14*a**4*b**4*c**7) + x**4*(35*a**8*c**4*d**3/4 + 42*a**7*b*c**5*d**2 + 49*a**6*b
**2*c**6*d + 14*a**5*b**3*c**7) + x**3*(7*a**8*c**5*d**2 + 56*a**7*b*c**6*d/3 +
28*a**6*b**2*c**7/3) + x**2*(7*a**8*c**6*d/2 + 4*a**7*b*c**7)

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GIAC/XCAS [A]  time = 0.21863, size = 1, normalized size = 0. \[ \mathit{Done} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x + a)^8*(d*x + c)^7,x, algorithm="giac")

[Out]

Done