3.1673 \(\int (A+B x) (d+e x)^7 \left (a^2+2 a b x+b^2 x^2\right )^2 \, dx\)
Optimal. Leaf size=206 \[ -\frac{b^3 (d+e x)^{12} (-4 a B e-A b e+5 b B d)}{12 e^6}+\frac{2 b^2 (d+e x)^{11} (b d-a e) (-3 a B e-2 A b e+5 b B d)}{11 e^6}-\frac{b (d+e x)^{10} (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{5 e^6}+\frac{(d+e x)^9 (b d-a e)^3 (-a B e-4 A b e+5 b B d)}{9 e^6}-\frac{(d+e x)^8 (b d-a e)^4 (B d-A e)}{8 e^6}+\frac{b^4 B (d+e x)^{13}}{13 e^6} \]
[Out]
-((b*d - a*e)^4*(B*d - A*e)*(d + e*x)^8)/(8*e^6) + ((b*d - a*e)^3*(5*b*B*d - 4*A
*b*e - a*B*e)*(d + e*x)^9)/(9*e^6) - (b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B
*e)*(d + e*x)^10)/(5*e^6) + (2*b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e)*(d
+ e*x)^11)/(11*e^6) - (b^3*(5*b*B*d - A*b*e - 4*a*B*e)*(d + e*x)^12)/(12*e^6) +
(b^4*B*(d + e*x)^13)/(13*e^6)
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Rubi [A] time = 2.23219, antiderivative size = 206, normalized size of antiderivative = 1.,
number of steps used = 3, number of rules used = 2, integrand size = 31, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.065
\[ -\frac{b^3 (d+e x)^{12} (-4 a B e-A b e+5 b B d)}{12 e^6}+\frac{2 b^2 (d+e x)^{11} (b d-a e) (-3 a B e-2 A b e+5 b B d)}{11 e^6}-\frac{b (d+e x)^{10} (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{5 e^6}+\frac{(d+e x)^9 (b d-a e)^3 (-a B e-4 A b e+5 b B d)}{9 e^6}-\frac{(d+e x)^8 (b d-a e)^4 (B d-A e)}{8 e^6}+\frac{b^4 B (d+e x)^{13}}{13 e^6} \]
Antiderivative was successfully verified.
[In] Int[(A + B*x)*(d + e*x)^7*(a^2 + 2*a*b*x + b^2*x^2)^2,x]
[Out]
-((b*d - a*e)^4*(B*d - A*e)*(d + e*x)^8)/(8*e^6) + ((b*d - a*e)^3*(5*b*B*d - 4*A
*b*e - a*B*e)*(d + e*x)^9)/(9*e^6) - (b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B
*e)*(d + e*x)^10)/(5*e^6) + (2*b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e)*(d
+ e*x)^11)/(11*e^6) - (b^3*(5*b*B*d - A*b*e - 4*a*B*e)*(d + e*x)^12)/(12*e^6) +
(b^4*B*(d + e*x)^13)/(13*e^6)
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Rubi in Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)*(e*x+d)**7*(b**2*x**2+2*a*b*x+a**2)**2,x)
[Out]
Timed out
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Mathematica [B] time = 0.594742, size = 823, normalized size = 4. \[ \frac{1}{13} b^4 B e^7 x^{13}+\frac{1}{12} b^3 e^6 (7 b B d+A b e+4 a B e) x^{12}+\frac{1}{11} b^2 e^5 \left (7 d (3 B d+A e) b^2+4 a e (7 B d+A e) b+6 a^2 B e^2\right ) x^{11}+\frac{1}{10} b e^4 \left (7 d^2 (5 B d+3 A e) b^3+28 a d e (3 B d+A e) b^2+6 a^2 e^2 (7 B d+A e) b+4 a^3 B e^3\right ) x^{10}+\frac{1}{9} e^3 \left (35 d^3 (B d+A e) b^4+28 a d^2 e (5 B d+3 A e) b^3+42 a^2 d e^2 (3 B d+A e) b^2+4 a^3 e^3 (7 B d+A e) b+a^4 B e^4\right ) x^9+\frac{1}{8} e^2 \left (7 b^4 (3 B d+5 A e) d^4+140 a b^3 e (B d+A e) d^3+42 a^2 b^2 e^2 (5 B d+3 A e) d^2+28 a^3 b e^3 (3 B d+A e) d+a^4 e^4 (7 B d+A e)\right ) x^8+d e \left (b^4 (B d+3 A e) d^4+4 a b^3 e (3 B d+5 A e) d^3+30 a^2 b^2 e^2 (B d+A e) d^2+4 a^3 b e^3 (5 B d+3 A e) d+a^4 e^4 (3 B d+A e)\right ) x^7+\frac{1}{6} d^2 \left (b^4 (B d+7 A e) d^4+28 a b^3 e (B d+3 A e) d^3+42 a^2 b^2 e^2 (3 B d+5 A e) d^2+140 a^3 b e^3 (B d+A e) d+7 a^4 e^4 (5 B d+3 A e)\right ) x^6+\frac{1}{5} d^3 \left (a B d \left (4 b^3 d^3+42 a b^2 e d^2+84 a^2 b e^2 d+35 a^3 e^3\right )+A \left (b^4 d^4+28 a b^3 e d^3+126 a^2 b^2 e^2 d^2+140 a^3 b e^3 d+35 a^4 e^4\right )\right ) x^5+\frac{1}{4} a d^4 \left (a B d \left (6 b^2 d^2+28 a b e d+21 a^2 e^2\right )+A \left (4 b^3 d^3+42 a b^2 e d^2+84 a^2 b e^2 d+35 a^3 e^3\right )\right ) x^4+\frac{1}{3} a^2 d^5 \left (a B d (4 b d+7 a e)+A \left (6 b^2 d^2+28 a b e d+21 a^2 e^2\right )\right ) x^3+\frac{1}{2} a^3 d^6 (4 A b d+a B d+7 a A e) x^2+a^4 A d^7 x \]
Antiderivative was successfully verified.
[In] Integrate[(A + B*x)*(d + e*x)^7*(a^2 + 2*a*b*x + b^2*x^2)^2,x]
[Out]
a^4*A*d^7*x + (a^3*d^6*(4*A*b*d + a*B*d + 7*a*A*e)*x^2)/2 + (a^2*d^5*(a*B*d*(4*b
*d + 7*a*e) + A*(6*b^2*d^2 + 28*a*b*d*e + 21*a^2*e^2))*x^3)/3 + (a*d^4*(a*B*d*(6
*b^2*d^2 + 28*a*b*d*e + 21*a^2*e^2) + A*(4*b^3*d^3 + 42*a*b^2*d^2*e + 84*a^2*b*d
*e^2 + 35*a^3*e^3))*x^4)/4 + (d^3*(a*B*d*(4*b^3*d^3 + 42*a*b^2*d^2*e + 84*a^2*b*
d*e^2 + 35*a^3*e^3) + A*(b^4*d^4 + 28*a*b^3*d^3*e + 126*a^2*b^2*d^2*e^2 + 140*a^
3*b*d*e^3 + 35*a^4*e^4))*x^5)/5 + (d^2*(140*a^3*b*d*e^3*(B*d + A*e) + 28*a*b^3*d
^3*e*(B*d + 3*A*e) + 7*a^4*e^4*(5*B*d + 3*A*e) + 42*a^2*b^2*d^2*e^2*(3*B*d + 5*A
*e) + b^4*d^4*(B*d + 7*A*e))*x^6)/6 + d*e*(30*a^2*b^2*d^2*e^2*(B*d + A*e) + a^4*
e^4*(3*B*d + A*e) + b^4*d^4*(B*d + 3*A*e) + 4*a^3*b*d*e^3*(5*B*d + 3*A*e) + 4*a*
b^3*d^3*e*(3*B*d + 5*A*e))*x^7 + (e^2*(140*a*b^3*d^3*e*(B*d + A*e) + 28*a^3*b*d*
e^3*(3*B*d + A*e) + a^4*e^4*(7*B*d + A*e) + 42*a^2*b^2*d^2*e^2*(5*B*d + 3*A*e) +
7*b^4*d^4*(3*B*d + 5*A*e))*x^8)/8 + (e^3*(a^4*B*e^4 + 35*b^4*d^3*(B*d + A*e) +
42*a^2*b^2*d*e^2*(3*B*d + A*e) + 4*a^3*b*e^3*(7*B*d + A*e) + 28*a*b^3*d^2*e*(5*B
*d + 3*A*e))*x^9)/9 + (b*e^4*(4*a^3*B*e^3 + 28*a*b^2*d*e*(3*B*d + A*e) + 6*a^2*b
*e^2*(7*B*d + A*e) + 7*b^3*d^2*(5*B*d + 3*A*e))*x^10)/10 + (b^2*e^5*(6*a^2*B*e^2
+ 7*b^2*d*(3*B*d + A*e) + 4*a*b*e*(7*B*d + A*e))*x^11)/11 + (b^3*e^6*(7*b*B*d +
A*b*e + 4*a*B*e)*x^12)/12 + (b^4*B*e^7*x^13)/13
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Maple [B] time = 0.003, size = 950, 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)*(e*x+d)^7*(b^2*x^2+2*a*b*x+a^2)^2,x)
[Out]
1/13*B*e^7*b^4*x^13+1/12*((A*e^7+7*B*d*e^6)*b^4+4*B*e^7*a*b^3)*x^12+1/11*((7*A*d
*e^6+21*B*d^2*e^5)*b^4+4*(A*e^7+7*B*d*e^6)*a*b^3+6*B*e^7*a^2*b^2)*x^11+1/10*((21
*A*d^2*e^5+35*B*d^3*e^4)*b^4+4*(7*A*d*e^6+21*B*d^2*e^5)*a*b^3+6*(A*e^7+7*B*d*e^6
)*a^2*b^2+4*B*e^7*a^3*b)*x^10+1/9*((35*A*d^3*e^4+35*B*d^4*e^3)*b^4+4*(21*A*d^2*e
^5+35*B*d^3*e^4)*a*b^3+6*(7*A*d*e^6+21*B*d^2*e^5)*a^2*b^2+4*(A*e^7+7*B*d*e^6)*a^
3*b+B*e^7*a^4)*x^9+1/8*((35*A*d^4*e^3+21*B*d^5*e^2)*b^4+4*(35*A*d^3*e^4+35*B*d^4
*e^3)*a*b^3+6*(21*A*d^2*e^5+35*B*d^3*e^4)*a^2*b^2+4*(7*A*d*e^6+21*B*d^2*e^5)*a^3
*b+(A*e^7+7*B*d*e^6)*a^4)*x^8+1/7*((21*A*d^5*e^2+7*B*d^6*e)*b^4+4*(35*A*d^4*e^3+
21*B*d^5*e^2)*a*b^3+6*(35*A*d^3*e^4+35*B*d^4*e^3)*a^2*b^2+4*(21*A*d^2*e^5+35*B*d
^3*e^4)*a^3*b+(7*A*d*e^6+21*B*d^2*e^5)*a^4)*x^7+1/6*((7*A*d^6*e+B*d^7)*b^4+4*(21
*A*d^5*e^2+7*B*d^6*e)*a*b^3+6*(35*A*d^4*e^3+21*B*d^5*e^2)*a^2*b^2+4*(35*A*d^3*e^
4+35*B*d^4*e^3)*a^3*b+(21*A*d^2*e^5+35*B*d^3*e^4)*a^4)*x^6+1/5*(A*d^7*b^4+4*(7*A
*d^6*e+B*d^7)*a*b^3+6*(21*A*d^5*e^2+7*B*d^6*e)*a^2*b^2+4*(35*A*d^4*e^3+21*B*d^5*
e^2)*a^3*b+(35*A*d^3*e^4+35*B*d^4*e^3)*a^4)*x^5+1/4*(4*A*d^7*a*b^3+6*(7*A*d^6*e+
B*d^7)*a^2*b^2+4*(21*A*d^5*e^2+7*B*d^6*e)*a^3*b+(35*A*d^4*e^3+21*B*d^5*e^2)*a^4)
*x^4+1/3*(6*A*d^7*a^2*b^2+4*(7*A*d^6*e+B*d^7)*a^3*b+(21*A*d^5*e^2+7*B*d^6*e)*a^4
)*x^3+1/2*(4*A*d^7*a^3*b+(7*A*d^6*e+B*d^7)*a^4)*x^2+A*d^7*a^4*x
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Maxima [A] time = 0.701337, size = 1254, normalized size = 6.09 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)^2*(B*x + A)*(e*x + d)^7,x, algorithm="maxima")
[Out]
1/13*B*b^4*e^7*x^13 + A*a^4*d^7*x + 1/12*(7*B*b^4*d*e^6 + (4*B*a*b^3 + A*b^4)*e^
7)*x^12 + 1/11*(21*B*b^4*d^2*e^5 + 7*(4*B*a*b^3 + A*b^4)*d*e^6 + 2*(3*B*a^2*b^2
+ 2*A*a*b^3)*e^7)*x^11 + 1/10*(35*B*b^4*d^3*e^4 + 21*(4*B*a*b^3 + A*b^4)*d^2*e^5
+ 14*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^6 + 2*(2*B*a^3*b + 3*A*a^2*b^2)*e^7)*x^10 +
1/9*(35*B*b^4*d^4*e^3 + 35*(4*B*a*b^3 + A*b^4)*d^3*e^4 + 42*(3*B*a^2*b^2 + 2*A*a
*b^3)*d^2*e^5 + 14*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^6 + (B*a^4 + 4*A*a^3*b)*e^7)*x^
9 + 1/8*(21*B*b^4*d^5*e^2 + A*a^4*e^7 + 35*(4*B*a*b^3 + A*b^4)*d^4*e^3 + 70*(3*B
*a^2*b^2 + 2*A*a*b^3)*d^3*e^4 + 42*(2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^5 + 7*(B*a^4
+ 4*A*a^3*b)*d*e^6)*x^8 + (B*b^4*d^6*e + A*a^4*d*e^6 + 3*(4*B*a*b^3 + A*b^4)*d^5
*e^2 + 10*(3*B*a^2*b^2 + 2*A*a*b^3)*d^4*e^3 + 10*(2*B*a^3*b + 3*A*a^2*b^2)*d^3*e
^4 + 3*(B*a^4 + 4*A*a^3*b)*d^2*e^5)*x^7 + 1/6*(B*b^4*d^7 + 21*A*a^4*d^2*e^5 + 7*
(4*B*a*b^3 + A*b^4)*d^6*e + 42*(3*B*a^2*b^2 + 2*A*a*b^3)*d^5*e^2 + 70*(2*B*a^3*b
+ 3*A*a^2*b^2)*d^4*e^3 + 35*(B*a^4 + 4*A*a^3*b)*d^3*e^4)*x^6 + 1/5*(35*A*a^4*d^
3*e^4 + (4*B*a*b^3 + A*b^4)*d^7 + 14*(3*B*a^2*b^2 + 2*A*a*b^3)*d^6*e + 42*(2*B*a
^3*b + 3*A*a^2*b^2)*d^5*e^2 + 35*(B*a^4 + 4*A*a^3*b)*d^4*e^3)*x^5 + 1/4*(35*A*a^
4*d^4*e^3 + 2*(3*B*a^2*b^2 + 2*A*a*b^3)*d^7 + 14*(2*B*a^3*b + 3*A*a^2*b^2)*d^6*e
+ 21*(B*a^4 + 4*A*a^3*b)*d^5*e^2)*x^4 + 1/3*(21*A*a^4*d^5*e^2 + 2*(2*B*a^3*b +
3*A*a^2*b^2)*d^7 + 7*(B*a^4 + 4*A*a^3*b)*d^6*e)*x^3 + 1/2*(7*A*a^4*d^6*e + (B*a^
4 + 4*A*a^3*b)*d^7)*x^2
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Fricas [A] time = 0.257377, size = 1, normalized size = 0. \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)^2*(B*x + A)*(e*x + d)^7,x, algorithm="fricas")
[Out]
1/13*x^13*e^7*b^4*B + 7/12*x^12*e^6*d*b^4*B + 1/3*x^12*e^7*b^3*a*B + 1/12*x^12*e
^7*b^4*A + 21/11*x^11*e^5*d^2*b^4*B + 28/11*x^11*e^6*d*b^3*a*B + 6/11*x^11*e^7*b
^2*a^2*B + 7/11*x^11*e^6*d*b^4*A + 4/11*x^11*e^7*b^3*a*A + 7/2*x^10*e^4*d^3*b^4*
B + 42/5*x^10*e^5*d^2*b^3*a*B + 21/5*x^10*e^6*d*b^2*a^2*B + 2/5*x^10*e^7*b*a^3*B
+ 21/10*x^10*e^5*d^2*b^4*A + 14/5*x^10*e^6*d*b^3*a*A + 3/5*x^10*e^7*b^2*a^2*A +
35/9*x^9*e^3*d^4*b^4*B + 140/9*x^9*e^4*d^3*b^3*a*B + 14*x^9*e^5*d^2*b^2*a^2*B +
28/9*x^9*e^6*d*b*a^3*B + 1/9*x^9*e^7*a^4*B + 35/9*x^9*e^4*d^3*b^4*A + 28/3*x^9*
e^5*d^2*b^3*a*A + 14/3*x^9*e^6*d*b^2*a^2*A + 4/9*x^9*e^7*b*a^3*A + 21/8*x^8*e^2*
d^5*b^4*B + 35/2*x^8*e^3*d^4*b^3*a*B + 105/4*x^8*e^4*d^3*b^2*a^2*B + 21/2*x^8*e^
5*d^2*b*a^3*B + 7/8*x^8*e^6*d*a^4*B + 35/8*x^8*e^3*d^4*b^4*A + 35/2*x^8*e^4*d^3*
b^3*a*A + 63/4*x^8*e^5*d^2*b^2*a^2*A + 7/2*x^8*e^6*d*b*a^3*A + 1/8*x^8*e^7*a^4*A
+ x^7*e*d^6*b^4*B + 12*x^7*e^2*d^5*b^3*a*B + 30*x^7*e^3*d^4*b^2*a^2*B + 20*x^7*
e^4*d^3*b*a^3*B + 3*x^7*e^5*d^2*a^4*B + 3*x^7*e^2*d^5*b^4*A + 20*x^7*e^3*d^4*b^3
*a*A + 30*x^7*e^4*d^3*b^2*a^2*A + 12*x^7*e^5*d^2*b*a^3*A + x^7*e^6*d*a^4*A + 1/6
*x^6*d^7*b^4*B + 14/3*x^6*e*d^6*b^3*a*B + 21*x^6*e^2*d^5*b^2*a^2*B + 70/3*x^6*e^
3*d^4*b*a^3*B + 35/6*x^6*e^4*d^3*a^4*B + 7/6*x^6*e*d^6*b^4*A + 14*x^6*e^2*d^5*b^
3*a*A + 35*x^6*e^3*d^4*b^2*a^2*A + 70/3*x^6*e^4*d^3*b*a^3*A + 7/2*x^6*e^5*d^2*a^
4*A + 4/5*x^5*d^7*b^3*a*B + 42/5*x^5*e*d^6*b^2*a^2*B + 84/5*x^5*e^2*d^5*b*a^3*B
+ 7*x^5*e^3*d^4*a^4*B + 1/5*x^5*d^7*b^4*A + 28/5*x^5*e*d^6*b^3*a*A + 126/5*x^5*e
^2*d^5*b^2*a^2*A + 28*x^5*e^3*d^4*b*a^3*A + 7*x^5*e^4*d^3*a^4*A + 3/2*x^4*d^7*b^
2*a^2*B + 7*x^4*e*d^6*b*a^3*B + 21/4*x^4*e^2*d^5*a^4*B + x^4*d^7*b^3*a*A + 21/2*
x^4*e*d^6*b^2*a^2*A + 21*x^4*e^2*d^5*b*a^3*A + 35/4*x^4*e^3*d^4*a^4*A + 4/3*x^3*
d^7*b*a^3*B + 7/3*x^3*e*d^6*a^4*B + 2*x^3*d^7*b^2*a^2*A + 28/3*x^3*e*d^6*b*a^3*A
+ 7*x^3*e^2*d^5*a^4*A + 1/2*x^2*d^7*a^4*B + 2*x^2*d^7*b*a^3*A + 7/2*x^2*e*d^6*a
^4*A + x*d^7*a^4*A
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Sympy [A] time = 0.572197, size = 1210, normalized size = 5.87 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)*(e*x+d)**7*(b**2*x**2+2*a*b*x+a**2)**2,x)
[Out]
A*a**4*d**7*x + B*b**4*e**7*x**13/13 + x**12*(A*b**4*e**7/12 + B*a*b**3*e**7/3 +
7*B*b**4*d*e**6/12) + x**11*(4*A*a*b**3*e**7/11 + 7*A*b**4*d*e**6/11 + 6*B*a**2
*b**2*e**7/11 + 28*B*a*b**3*d*e**6/11 + 21*B*b**4*d**2*e**5/11) + x**10*(3*A*a**
2*b**2*e**7/5 + 14*A*a*b**3*d*e**6/5 + 21*A*b**4*d**2*e**5/10 + 2*B*a**3*b*e**7/
5 + 21*B*a**2*b**2*d*e**6/5 + 42*B*a*b**3*d**2*e**5/5 + 7*B*b**4*d**3*e**4/2) +
x**9*(4*A*a**3*b*e**7/9 + 14*A*a**2*b**2*d*e**6/3 + 28*A*a*b**3*d**2*e**5/3 + 35
*A*b**4*d**3*e**4/9 + B*a**4*e**7/9 + 28*B*a**3*b*d*e**6/9 + 14*B*a**2*b**2*d**2
*e**5 + 140*B*a*b**3*d**3*e**4/9 + 35*B*b**4*d**4*e**3/9) + x**8*(A*a**4*e**7/8
+ 7*A*a**3*b*d*e**6/2 + 63*A*a**2*b**2*d**2*e**5/4 + 35*A*a*b**3*d**3*e**4/2 + 3
5*A*b**4*d**4*e**3/8 + 7*B*a**4*d*e**6/8 + 21*B*a**3*b*d**2*e**5/2 + 105*B*a**2*
b**2*d**3*e**4/4 + 35*B*a*b**3*d**4*e**3/2 + 21*B*b**4*d**5*e**2/8) + x**7*(A*a*
*4*d*e**6 + 12*A*a**3*b*d**2*e**5 + 30*A*a**2*b**2*d**3*e**4 + 20*A*a*b**3*d**4*
e**3 + 3*A*b**4*d**5*e**2 + 3*B*a**4*d**2*e**5 + 20*B*a**3*b*d**3*e**4 + 30*B*a*
*2*b**2*d**4*e**3 + 12*B*a*b**3*d**5*e**2 + B*b**4*d**6*e) + x**6*(7*A*a**4*d**2
*e**5/2 + 70*A*a**3*b*d**3*e**4/3 + 35*A*a**2*b**2*d**4*e**3 + 14*A*a*b**3*d**5*
e**2 + 7*A*b**4*d**6*e/6 + 35*B*a**4*d**3*e**4/6 + 70*B*a**3*b*d**4*e**3/3 + 21*
B*a**2*b**2*d**5*e**2 + 14*B*a*b**3*d**6*e/3 + B*b**4*d**7/6) + x**5*(7*A*a**4*d
**3*e**4 + 28*A*a**3*b*d**4*e**3 + 126*A*a**2*b**2*d**5*e**2/5 + 28*A*a*b**3*d**
6*e/5 + A*b**4*d**7/5 + 7*B*a**4*d**4*e**3 + 84*B*a**3*b*d**5*e**2/5 + 42*B*a**2
*b**2*d**6*e/5 + 4*B*a*b**3*d**7/5) + x**4*(35*A*a**4*d**4*e**3/4 + 21*A*a**3*b*
d**5*e**2 + 21*A*a**2*b**2*d**6*e/2 + A*a*b**3*d**7 + 21*B*a**4*d**5*e**2/4 + 7*
B*a**3*b*d**6*e + 3*B*a**2*b**2*d**7/2) + x**3*(7*A*a**4*d**5*e**2 + 28*A*a**3*b
*d**6*e/3 + 2*A*a**2*b**2*d**7 + 7*B*a**4*d**6*e/3 + 4*B*a**3*b*d**7/3) + x**2*(
7*A*a**4*d**6*e/2 + 2*A*a**3*b*d**7 + B*a**4*d**7/2)
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.282623, size = 1, normalized size = 0. \[ \mathit{Done} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)^2*(B*x + A)*(e*x + d)^7,x, algorithm="giac")
[Out]
Done