3.1036 \(\int (a+b x)^6 (A+B x) (d+e x)^6 \, dx\)

Optimal. Leaf size=290 \[ \frac{e^5 (a+b x)^{13} (-7 a B e+A b e+6 b B d)}{13 b^8}+\frac{e^4 (a+b x)^{12} (b d-a e) (-7 a B e+2 A b e+5 b B d)}{4 b^8}+\frac{5 e^3 (a+b x)^{11} (b d-a e)^2 (-7 a B e+3 A b e+4 b B d)}{11 b^8}+\frac{e^2 (a+b x)^{10} (b d-a e)^3 (-7 a B e+4 A b e+3 b B d)}{2 b^8}+\frac{e (a+b x)^9 (b d-a e)^4 (-7 a B e+5 A b e+2 b B d)}{3 b^8}+\frac{(a+b x)^8 (b d-a e)^5 (-7 a B e+6 A b e+b B d)}{8 b^8}+\frac{(a+b x)^7 (A b-a B) (b d-a e)^6}{7 b^8}+\frac{B e^6 (a+b x)^{14}}{14 b^8} \]

[Out]

((A*b - a*B)*(b*d - a*e)^6*(a + b*x)^7)/(7*b^8) + ((b*d - a*e)^5*(b*B*d + 6*A*b*
e - 7*a*B*e)*(a + b*x)^8)/(8*b^8) + (e*(b*d - a*e)^4*(2*b*B*d + 5*A*b*e - 7*a*B*
e)*(a + b*x)^9)/(3*b^8) + (e^2*(b*d - a*e)^3*(3*b*B*d + 4*A*b*e - 7*a*B*e)*(a +
b*x)^10)/(2*b^8) + (5*e^3*(b*d - a*e)^2*(4*b*B*d + 3*A*b*e - 7*a*B*e)*(a + b*x)^
11)/(11*b^8) + (e^4*(b*d - a*e)*(5*b*B*d + 2*A*b*e - 7*a*B*e)*(a + b*x)^12)/(4*b
^8) + (e^5*(6*b*B*d + A*b*e - 7*a*B*e)*(a + b*x)^13)/(13*b^8) + (B*e^6*(a + b*x)
^14)/(14*b^8)

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Rubi [A]  time = 3.21046, antiderivative size = 290, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ \frac{e^5 (a+b x)^{13} (-7 a B e+A b e+6 b B d)}{13 b^8}+\frac{e^4 (a+b x)^{12} (b d-a e) (-7 a B e+2 A b e+5 b B d)}{4 b^8}+\frac{5 e^3 (a+b x)^{11} (b d-a e)^2 (-7 a B e+3 A b e+4 b B d)}{11 b^8}+\frac{e^2 (a+b x)^{10} (b d-a e)^3 (-7 a B e+4 A b e+3 b B d)}{2 b^8}+\frac{e (a+b x)^9 (b d-a e)^4 (-7 a B e+5 A b e+2 b B d)}{3 b^8}+\frac{(a+b x)^8 (b d-a e)^5 (-7 a B e+6 A b e+b B d)}{8 b^8}+\frac{(a+b x)^7 (A b-a B) (b d-a e)^6}{7 b^8}+\frac{B e^6 (a+b x)^{14}}{14 b^8} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x)^6*(A + B*x)*(d + e*x)^6,x]

[Out]

((A*b - a*B)*(b*d - a*e)^6*(a + b*x)^7)/(7*b^8) + ((b*d - a*e)^5*(b*B*d + 6*A*b*
e - 7*a*B*e)*(a + b*x)^8)/(8*b^8) + (e*(b*d - a*e)^4*(2*b*B*d + 5*A*b*e - 7*a*B*
e)*(a + b*x)^9)/(3*b^8) + (e^2*(b*d - a*e)^3*(3*b*B*d + 4*A*b*e - 7*a*B*e)*(a +
b*x)^10)/(2*b^8) + (5*e^3*(b*d - a*e)^2*(4*b*B*d + 3*A*b*e - 7*a*B*e)*(a + b*x)^
11)/(11*b^8) + (e^4*(b*d - a*e)*(5*b*B*d + 2*A*b*e - 7*a*B*e)*(a + b*x)^12)/(4*b
^8) + (e^5*(6*b*B*d + A*b*e - 7*a*B*e)*(a + b*x)^13)/(13*b^8) + (B*e^6*(a + b*x)
^14)/(14*b^8)

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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)**6*(B*x+A)*(e*x+d)**6,x)

[Out]

Timed out

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Mathematica [B]  time = 0.804869, size = 1069, normalized size = 3.69 \[ \frac{1}{14} b^6 B e^6 x^{14}+\frac{1}{13} b^5 e^5 (6 b B d+A b e+6 a B e) x^{13}+\frac{1}{4} b^4 e^4 \left (d (5 B d+2 A e) b^2+2 a e (6 B d+A e) b+5 a^2 B e^2\right ) x^{12}+\frac{1}{11} b^3 e^3 \left (5 d^2 (4 B d+3 A e) b^3+18 a d e (5 B d+2 A e) b^2+15 a^2 e^2 (6 B d+A e) b+20 a^3 B e^3\right ) x^{11}+\frac{1}{2} b^2 e^2 \left (d^3 (3 B d+4 A e) b^4+6 a d^2 e (4 B d+3 A e) b^3+9 a^2 d e^2 (5 B d+2 A e) b^2+4 a^3 e^3 (6 B d+A e) b+3 a^4 B e^4\right ) x^{10}+\frac{1}{3} b e \left (d^4 (2 B d+5 A e) b^5+10 a d^3 e (3 B d+4 A e) b^4+25 a^2 d^2 e^2 (4 B d+3 A e) b^3+20 a^3 d e^3 (5 B d+2 A e) b^2+5 a^4 e^4 (6 B d+A e) b+2 a^5 B e^5\right ) x^9+\frac{1}{8} \left (d^5 (B d+6 A e) b^6+18 a d^4 e (2 B d+5 A e) b^5+75 a^2 d^3 e^2 (3 B d+4 A e) b^4+100 a^3 d^2 e^3 (4 B d+3 A e) b^3+45 a^4 d e^4 (5 B d+2 A e) b^2+6 a^5 e^5 (6 B d+A e) b+a^6 B e^6\right ) x^8+\frac{1}{7} \left (6 a B d \left (b^5 d^5+15 a b^4 e d^4+50 a^2 b^3 e^2 d^3+50 a^3 b^2 e^3 d^2+15 a^4 b e^4 d+a^5 e^5\right )+A \left (b^6 d^6+36 a b^5 e d^5+225 a^2 b^4 e^2 d^4+400 a^3 b^3 e^3 d^3+225 a^4 b^2 e^4 d^2+36 a^5 b e^5 d+a^6 e^6\right )\right ) x^7+\frac{1}{2} a d \left (5 a B d \left (b^4 d^4+8 a b^3 e d^3+15 a^2 b^2 e^2 d^2+8 a^3 b e^3 d+a^4 e^4\right )+2 A \left (b^5 d^5+15 a b^4 e d^4+50 a^2 b^3 e^2 d^3+50 a^3 b^2 e^3 d^2+15 a^4 b e^4 d+a^5 e^5\right )\right ) x^6+a^2 d^2 \left (2 a B d \left (2 b^3 d^3+9 a b^2 e d^2+9 a^2 b e^2 d+2 a^3 e^3\right )+3 A \left (b^4 d^4+8 a b^3 e d^3+15 a^2 b^2 e^2 d^2+8 a^3 b e^3 d+a^4 e^4\right )\right ) x^5+\frac{1}{4} a^3 d^3 \left (3 a B d \left (5 b^2 d^2+12 a b e d+5 a^2 e^2\right )+10 A \left (2 b^3 d^3+9 a b^2 e d^2+9 a^2 b e^2 d+2 a^3 e^3\right )\right ) x^4+a^4 d^4 \left (2 a B d (b d+a e)+A \left (5 b^2 d^2+12 a b e d+5 a^2 e^2\right )\right ) x^3+\frac{1}{2} a^5 d^5 (a B d+6 A (b d+a e)) x^2+a^6 A d^6 x \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x)^6*(A + B*x)*(d + e*x)^6,x]

[Out]

a^6*A*d^6*x + (a^5*d^5*(a*B*d + 6*A*(b*d + a*e))*x^2)/2 + a^4*d^4*(2*a*B*d*(b*d
+ a*e) + A*(5*b^2*d^2 + 12*a*b*d*e + 5*a^2*e^2))*x^3 + (a^3*d^3*(3*a*B*d*(5*b^2*
d^2 + 12*a*b*d*e + 5*a^2*e^2) + 10*A*(2*b^3*d^3 + 9*a*b^2*d^2*e + 9*a^2*b*d*e^2
+ 2*a^3*e^3))*x^4)/4 + a^2*d^2*(2*a*B*d*(2*b^3*d^3 + 9*a*b^2*d^2*e + 9*a^2*b*d*e
^2 + 2*a^3*e^3) + 3*A*(b^4*d^4 + 8*a*b^3*d^3*e + 15*a^2*b^2*d^2*e^2 + 8*a^3*b*d*
e^3 + a^4*e^4))*x^5 + (a*d*(5*a*B*d*(b^4*d^4 + 8*a*b^3*d^3*e + 15*a^2*b^2*d^2*e^
2 + 8*a^3*b*d*e^3 + a^4*e^4) + 2*A*(b^5*d^5 + 15*a*b^4*d^4*e + 50*a^2*b^3*d^3*e^
2 + 50*a^3*b^2*d^2*e^3 + 15*a^4*b*d*e^4 + a^5*e^5))*x^6)/2 + ((6*a*B*d*(b^5*d^5
+ 15*a*b^4*d^4*e + 50*a^2*b^3*d^3*e^2 + 50*a^3*b^2*d^2*e^3 + 15*a^4*b*d*e^4 + a^
5*e^5) + A*(b^6*d^6 + 36*a*b^5*d^5*e + 225*a^2*b^4*d^4*e^2 + 400*a^3*b^3*d^3*e^3
+ 225*a^4*b^2*d^2*e^4 + 36*a^5*b*d*e^5 + a^6*e^6))*x^7)/7 + ((a^6*B*e^6 + 6*a^5
*b*e^5*(6*B*d + A*e) + 45*a^4*b^2*d*e^4*(5*B*d + 2*A*e) + 100*a^3*b^3*d^2*e^3*(4
*B*d + 3*A*e) + 75*a^2*b^4*d^3*e^2*(3*B*d + 4*A*e) + 18*a*b^5*d^4*e*(2*B*d + 5*A
*e) + b^6*d^5*(B*d + 6*A*e))*x^8)/8 + (b*e*(2*a^5*B*e^5 + 5*a^4*b*e^4*(6*B*d + A
*e) + 20*a^3*b^2*d*e^3*(5*B*d + 2*A*e) + 25*a^2*b^3*d^2*e^2*(4*B*d + 3*A*e) + 10
*a*b^4*d^3*e*(3*B*d + 4*A*e) + b^5*d^4*(2*B*d + 5*A*e))*x^9)/3 + (b^2*e^2*(3*a^4
*B*e^4 + 4*a^3*b*e^3*(6*B*d + A*e) + 9*a^2*b^2*d*e^2*(5*B*d + 2*A*e) + 6*a*b^3*d
^2*e*(4*B*d + 3*A*e) + b^4*d^3*(3*B*d + 4*A*e))*x^10)/2 + (b^3*e^3*(20*a^3*B*e^3
+ 15*a^2*b*e^2*(6*B*d + A*e) + 18*a*b^2*d*e*(5*B*d + 2*A*e) + 5*b^3*d^2*(4*B*d
+ 3*A*e))*x^11)/11 + (b^4*e^4*(5*a^2*B*e^2 + 2*a*b*e*(6*B*d + A*e) + b^2*d*(5*B*
d + 2*A*e))*x^12)/4 + (b^5*e^5*(6*b*B*d + A*b*e + 6*a*B*e)*x^13)/13 + (b^6*B*e^6
*x^14)/14

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Maple [B]  time = 0.003, size = 1173, normalized size = 4. \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x+a)^6*(B*x+A)*(e*x+d)^6,x)

[Out]

1/14*b^6*B*e^6*x^14+1/13*((A*b^6+6*B*a*b^5)*e^6+6*b^6*B*d*e^5)*x^13+1/12*((6*A*a
*b^5+15*B*a^2*b^4)*e^6+6*(A*b^6+6*B*a*b^5)*d*e^5+15*b^6*B*d^2*e^4)*x^12+1/11*((1
5*A*a^2*b^4+20*B*a^3*b^3)*e^6+6*(6*A*a*b^5+15*B*a^2*b^4)*d*e^5+15*(A*b^6+6*B*a*b
^5)*d^2*e^4+20*b^6*B*d^3*e^3)*x^11+1/10*((20*A*a^3*b^3+15*B*a^4*b^2)*e^6+6*(15*A
*a^2*b^4+20*B*a^3*b^3)*d*e^5+15*(6*A*a*b^5+15*B*a^2*b^4)*d^2*e^4+20*(A*b^6+6*B*a
*b^5)*d^3*e^3+15*b^6*B*d^4*e^2)*x^10+1/9*((15*A*a^4*b^2+6*B*a^5*b)*e^6+6*(20*A*a
^3*b^3+15*B*a^4*b^2)*d*e^5+15*(15*A*a^2*b^4+20*B*a^3*b^3)*d^2*e^4+20*(6*A*a*b^5+
15*B*a^2*b^4)*d^3*e^3+15*(A*b^6+6*B*a*b^5)*d^4*e^2+6*b^6*B*d^5*e)*x^9+1/8*((6*A*
a^5*b+B*a^6)*e^6+6*(15*A*a^4*b^2+6*B*a^5*b)*d*e^5+15*(20*A*a^3*b^3+15*B*a^4*b^2)
*d^2*e^4+20*(15*A*a^2*b^4+20*B*a^3*b^3)*d^3*e^3+15*(6*A*a*b^5+15*B*a^2*b^4)*d^4*
e^2+6*(A*b^6+6*B*a*b^5)*d^5*e+b^6*B*d^6)*x^8+1/7*(a^6*A*e^6+6*(6*A*a^5*b+B*a^6)*
d*e^5+15*(15*A*a^4*b^2+6*B*a^5*b)*d^2*e^4+20*(20*A*a^3*b^3+15*B*a^4*b^2)*d^3*e^3
+15*(15*A*a^2*b^4+20*B*a^3*b^3)*d^4*e^2+6*(6*A*a*b^5+15*B*a^2*b^4)*d^5*e+(A*b^6+
6*B*a*b^5)*d^6)*x^7+1/6*(6*a^6*A*d*e^5+15*(6*A*a^5*b+B*a^6)*d^2*e^4+20*(15*A*a^4
*b^2+6*B*a^5*b)*d^3*e^3+15*(20*A*a^3*b^3+15*B*a^4*b^2)*d^4*e^2+6*(15*A*a^2*b^4+2
0*B*a^3*b^3)*d^5*e+(6*A*a*b^5+15*B*a^2*b^4)*d^6)*x^6+1/5*(15*a^6*A*d^2*e^4+20*(6
*A*a^5*b+B*a^6)*d^3*e^3+15*(15*A*a^4*b^2+6*B*a^5*b)*d^4*e^2+6*(20*A*a^3*b^3+15*B
*a^4*b^2)*d^5*e+(15*A*a^2*b^4+20*B*a^3*b^3)*d^6)*x^5+1/4*(20*a^6*A*d^3*e^3+15*(6
*A*a^5*b+B*a^6)*d^4*e^2+6*(15*A*a^4*b^2+6*B*a^5*b)*d^5*e+(20*A*a^3*b^3+15*B*a^4*
b^2)*d^6)*x^4+1/3*(15*a^6*A*d^4*e^2+6*(6*A*a^5*b+B*a^6)*d^5*e+(15*A*a^4*b^2+6*B*
a^5*b)*d^6)*x^3+1/2*(6*a^6*A*d^5*e+(6*A*a^5*b+B*a^6)*d^6)*x^2+a^6*A*d^6*x

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Maxima [A]  time = 1.37574, size = 1582, normalized size = 5.46 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((B*x + A)*(b*x + a)^6*(e*x + d)^6,x, algorithm="maxima")

[Out]

1/14*B*b^6*e^6*x^14 + A*a^6*d^6*x + 1/13*(6*B*b^6*d*e^5 + (6*B*a*b^5 + A*b^6)*e^
6)*x^13 + 1/4*(5*B*b^6*d^2*e^4 + 2*(6*B*a*b^5 + A*b^6)*d*e^5 + (5*B*a^2*b^4 + 2*
A*a*b^5)*e^6)*x^12 + 1/11*(20*B*b^6*d^3*e^3 + 15*(6*B*a*b^5 + A*b^6)*d^2*e^4 + 1
8*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^5 + 5*(4*B*a^3*b^3 + 3*A*a^2*b^4)*e^6)*x^11 + 1/
2*(3*B*b^6*d^4*e^2 + 4*(6*B*a*b^5 + A*b^6)*d^3*e^3 + 9*(5*B*a^2*b^4 + 2*A*a*b^5)
*d^2*e^4 + 6*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d*e^5 + (3*B*a^4*b^2 + 4*A*a^3*b^3)*e^6
)*x^10 + 1/3*(2*B*b^6*d^5*e + 5*(6*B*a*b^5 + A*b^6)*d^4*e^2 + 20*(5*B*a^2*b^4 +
2*A*a*b^5)*d^3*e^3 + 25*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^4 + 10*(3*B*a^4*b^2 +
4*A*a^3*b^3)*d*e^5 + (2*B*a^5*b + 5*A*a^4*b^2)*e^6)*x^9 + 1/8*(B*b^6*d^6 + 6*(6*
B*a*b^5 + A*b^6)*d^5*e + 45*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^2 + 100*(4*B*a^3*b^3
+ 3*A*a^2*b^4)*d^3*e^3 + 75*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^4 + 18*(2*B*a^5*b
+ 5*A*a^4*b^2)*d*e^5 + (B*a^6 + 6*A*a^5*b)*e^6)*x^8 + 1/7*(A*a^6*e^6 + (6*B*a*b
^5 + A*b^6)*d^6 + 18*(5*B*a^2*b^4 + 2*A*a*b^5)*d^5*e + 75*(4*B*a^3*b^3 + 3*A*a^2
*b^4)*d^4*e^2 + 100*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^3 + 45*(2*B*a^5*b + 5*A*a^
4*b^2)*d^2*e^4 + 6*(B*a^6 + 6*A*a^5*b)*d*e^5)*x^7 + 1/2*(2*A*a^6*d*e^5 + (5*B*a^
2*b^4 + 2*A*a*b^5)*d^6 + 10*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^5*e + 25*(3*B*a^4*b^2
+ 4*A*a^3*b^3)*d^4*e^2 + 20*(2*B*a^5*b + 5*A*a^4*b^2)*d^3*e^3 + 5*(B*a^6 + 6*A*a
^5*b)*d^2*e^4)*x^6 + (3*A*a^6*d^2*e^4 + (4*B*a^3*b^3 + 3*A*a^2*b^4)*d^6 + 6*(3*B
*a^4*b^2 + 4*A*a^3*b^3)*d^5*e + 9*(2*B*a^5*b + 5*A*a^4*b^2)*d^4*e^2 + 4*(B*a^6 +
6*A*a^5*b)*d^3*e^3)*x^5 + 1/4*(20*A*a^6*d^3*e^3 + 5*(3*B*a^4*b^2 + 4*A*a^3*b^3)
*d^6 + 18*(2*B*a^5*b + 5*A*a^4*b^2)*d^5*e + 15*(B*a^6 + 6*A*a^5*b)*d^4*e^2)*x^4
+ (5*A*a^6*d^4*e^2 + (2*B*a^5*b + 5*A*a^4*b^2)*d^6 + 2*(B*a^6 + 6*A*a^5*b)*d^5*e
)*x^3 + 1/2*(6*A*a^6*d^5*e + (B*a^6 + 6*A*a^5*b)*d^6)*x^2

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Fricas [A]  time = 0.195779, 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)*(b*x + a)^6*(e*x + d)^6,x, algorithm="fricas")

[Out]

1/14*x^14*e^6*b^6*B + 6/13*x^13*e^5*d*b^6*B + 6/13*x^13*e^6*b^5*a*B + 1/13*x^13*
e^6*b^6*A + 5/4*x^12*e^4*d^2*b^6*B + 3*x^12*e^5*d*b^5*a*B + 5/4*x^12*e^6*b^4*a^2
*B + 1/2*x^12*e^5*d*b^6*A + 1/2*x^12*e^6*b^5*a*A + 20/11*x^11*e^3*d^3*b^6*B + 90
/11*x^11*e^4*d^2*b^5*a*B + 90/11*x^11*e^5*d*b^4*a^2*B + 20/11*x^11*e^6*b^3*a^3*B
+ 15/11*x^11*e^4*d^2*b^6*A + 36/11*x^11*e^5*d*b^5*a*A + 15/11*x^11*e^6*b^4*a^2*
A + 3/2*x^10*e^2*d^4*b^6*B + 12*x^10*e^3*d^3*b^5*a*B + 45/2*x^10*e^4*d^2*b^4*a^2
*B + 12*x^10*e^5*d*b^3*a^3*B + 3/2*x^10*e^6*b^2*a^4*B + 2*x^10*e^3*d^3*b^6*A + 9
*x^10*e^4*d^2*b^5*a*A + 9*x^10*e^5*d*b^4*a^2*A + 2*x^10*e^6*b^3*a^3*A + 2/3*x^9*
e*d^5*b^6*B + 10*x^9*e^2*d^4*b^5*a*B + 100/3*x^9*e^3*d^3*b^4*a^2*B + 100/3*x^9*e
^4*d^2*b^3*a^3*B + 10*x^9*e^5*d*b^2*a^4*B + 2/3*x^9*e^6*b*a^5*B + 5/3*x^9*e^2*d^
4*b^6*A + 40/3*x^9*e^3*d^3*b^5*a*A + 25*x^9*e^4*d^2*b^4*a^2*A + 40/3*x^9*e^5*d*b
^3*a^3*A + 5/3*x^9*e^6*b^2*a^4*A + 1/8*x^8*d^6*b^6*B + 9/2*x^8*e*d^5*b^5*a*B + 2
25/8*x^8*e^2*d^4*b^4*a^2*B + 50*x^8*e^3*d^3*b^3*a^3*B + 225/8*x^8*e^4*d^2*b^2*a^
4*B + 9/2*x^8*e^5*d*b*a^5*B + 1/8*x^8*e^6*a^6*B + 3/4*x^8*e*d^5*b^6*A + 45/4*x^8
*e^2*d^4*b^5*a*A + 75/2*x^8*e^3*d^3*b^4*a^2*A + 75/2*x^8*e^4*d^2*b^3*a^3*A + 45/
4*x^8*e^5*d*b^2*a^4*A + 3/4*x^8*e^6*b*a^5*A + 6/7*x^7*d^6*b^5*a*B + 90/7*x^7*e*d
^5*b^4*a^2*B + 300/7*x^7*e^2*d^4*b^3*a^3*B + 300/7*x^7*e^3*d^3*b^2*a^4*B + 90/7*
x^7*e^4*d^2*b*a^5*B + 6/7*x^7*e^5*d*a^6*B + 1/7*x^7*d^6*b^6*A + 36/7*x^7*e*d^5*b
^5*a*A + 225/7*x^7*e^2*d^4*b^4*a^2*A + 400/7*x^7*e^3*d^3*b^3*a^3*A + 225/7*x^7*e
^4*d^2*b^2*a^4*A + 36/7*x^7*e^5*d*b*a^5*A + 1/7*x^7*e^6*a^6*A + 5/2*x^6*d^6*b^4*
a^2*B + 20*x^6*e*d^5*b^3*a^3*B + 75/2*x^6*e^2*d^4*b^2*a^4*B + 20*x^6*e^3*d^3*b*a
^5*B + 5/2*x^6*e^4*d^2*a^6*B + x^6*d^6*b^5*a*A + 15*x^6*e*d^5*b^4*a^2*A + 50*x^6
*e^2*d^4*b^3*a^3*A + 50*x^6*e^3*d^3*b^2*a^4*A + 15*x^6*e^4*d^2*b*a^5*A + x^6*e^5
*d*a^6*A + 4*x^5*d^6*b^3*a^3*B + 18*x^5*e*d^5*b^2*a^4*B + 18*x^5*e^2*d^4*b*a^5*B
+ 4*x^5*e^3*d^3*a^6*B + 3*x^5*d^6*b^4*a^2*A + 24*x^5*e*d^5*b^3*a^3*A + 45*x^5*e
^2*d^4*b^2*a^4*A + 24*x^5*e^3*d^3*b*a^5*A + 3*x^5*e^4*d^2*a^6*A + 15/4*x^4*d^6*b
^2*a^4*B + 9*x^4*e*d^5*b*a^5*B + 15/4*x^4*e^2*d^4*a^6*B + 5*x^4*d^6*b^3*a^3*A +
45/2*x^4*e*d^5*b^2*a^4*A + 45/2*x^4*e^2*d^4*b*a^5*A + 5*x^4*e^3*d^3*a^6*A + 2*x^
3*d^6*b*a^5*B + 2*x^3*e*d^5*a^6*B + 5*x^3*d^6*b^2*a^4*A + 12*x^3*e*d^5*b*a^5*A +
5*x^3*e^2*d^4*a^6*A + 1/2*x^2*d^6*a^6*B + 3*x^2*d^6*b*a^5*A + 3*x^2*e*d^5*a^6*A
+ x*d^6*a^6*A

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Sympy [A]  time = 0.703402, size = 1504, normalized size = 5.19 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x+a)**6*(B*x+A)*(e*x+d)**6,x)

[Out]

A*a**6*d**6*x + B*b**6*e**6*x**14/14 + x**13*(A*b**6*e**6/13 + 6*B*a*b**5*e**6/1
3 + 6*B*b**6*d*e**5/13) + x**12*(A*a*b**5*e**6/2 + A*b**6*d*e**5/2 + 5*B*a**2*b*
*4*e**6/4 + 3*B*a*b**5*d*e**5 + 5*B*b**6*d**2*e**4/4) + x**11*(15*A*a**2*b**4*e*
*6/11 + 36*A*a*b**5*d*e**5/11 + 15*A*b**6*d**2*e**4/11 + 20*B*a**3*b**3*e**6/11
+ 90*B*a**2*b**4*d*e**5/11 + 90*B*a*b**5*d**2*e**4/11 + 20*B*b**6*d**3*e**3/11)
+ x**10*(2*A*a**3*b**3*e**6 + 9*A*a**2*b**4*d*e**5 + 9*A*a*b**5*d**2*e**4 + 2*A*
b**6*d**3*e**3 + 3*B*a**4*b**2*e**6/2 + 12*B*a**3*b**3*d*e**5 + 45*B*a**2*b**4*d
**2*e**4/2 + 12*B*a*b**5*d**3*e**3 + 3*B*b**6*d**4*e**2/2) + x**9*(5*A*a**4*b**2
*e**6/3 + 40*A*a**3*b**3*d*e**5/3 + 25*A*a**2*b**4*d**2*e**4 + 40*A*a*b**5*d**3*
e**3/3 + 5*A*b**6*d**4*e**2/3 + 2*B*a**5*b*e**6/3 + 10*B*a**4*b**2*d*e**5 + 100*
B*a**3*b**3*d**2*e**4/3 + 100*B*a**2*b**4*d**3*e**3/3 + 10*B*a*b**5*d**4*e**2 +
2*B*b**6*d**5*e/3) + x**8*(3*A*a**5*b*e**6/4 + 45*A*a**4*b**2*d*e**5/4 + 75*A*a*
*3*b**3*d**2*e**4/2 + 75*A*a**2*b**4*d**3*e**3/2 + 45*A*a*b**5*d**4*e**2/4 + 3*A
*b**6*d**5*e/4 + B*a**6*e**6/8 + 9*B*a**5*b*d*e**5/2 + 225*B*a**4*b**2*d**2*e**4
/8 + 50*B*a**3*b**3*d**3*e**3 + 225*B*a**2*b**4*d**4*e**2/8 + 9*B*a*b**5*d**5*e/
2 + B*b**6*d**6/8) + x**7*(A*a**6*e**6/7 + 36*A*a**5*b*d*e**5/7 + 225*A*a**4*b**
2*d**2*e**4/7 + 400*A*a**3*b**3*d**3*e**3/7 + 225*A*a**2*b**4*d**4*e**2/7 + 36*A
*a*b**5*d**5*e/7 + A*b**6*d**6/7 + 6*B*a**6*d*e**5/7 + 90*B*a**5*b*d**2*e**4/7 +
300*B*a**4*b**2*d**3*e**3/7 + 300*B*a**3*b**3*d**4*e**2/7 + 90*B*a**2*b**4*d**5
*e/7 + 6*B*a*b**5*d**6/7) + x**6*(A*a**6*d*e**5 + 15*A*a**5*b*d**2*e**4 + 50*A*a
**4*b**2*d**3*e**3 + 50*A*a**3*b**3*d**4*e**2 + 15*A*a**2*b**4*d**5*e + A*a*b**5
*d**6 + 5*B*a**6*d**2*e**4/2 + 20*B*a**5*b*d**3*e**3 + 75*B*a**4*b**2*d**4*e**2/
2 + 20*B*a**3*b**3*d**5*e + 5*B*a**2*b**4*d**6/2) + x**5*(3*A*a**6*d**2*e**4 + 2
4*A*a**5*b*d**3*e**3 + 45*A*a**4*b**2*d**4*e**2 + 24*A*a**3*b**3*d**5*e + 3*A*a*
*2*b**4*d**6 + 4*B*a**6*d**3*e**3 + 18*B*a**5*b*d**4*e**2 + 18*B*a**4*b**2*d**5*
e + 4*B*a**3*b**3*d**6) + x**4*(5*A*a**6*d**3*e**3 + 45*A*a**5*b*d**4*e**2/2 + 4
5*A*a**4*b**2*d**5*e/2 + 5*A*a**3*b**3*d**6 + 15*B*a**6*d**4*e**2/4 + 9*B*a**5*b
*d**5*e + 15*B*a**4*b**2*d**6/4) + x**3*(5*A*a**6*d**4*e**2 + 12*A*a**5*b*d**5*e
+ 5*A*a**4*b**2*d**6 + 2*B*a**6*d**5*e + 2*B*a**5*b*d**6) + x**2*(3*A*a**6*d**5
*e + 3*A*a**5*b*d**6 + B*a**6*d**6/2)

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GIAC/XCAS [A]  time = 0.225089, size = 1, normalized size = 0. \[ \mathit{Done} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((B*x + A)*(b*x + a)^6*(e*x + d)^6,x, algorithm="giac")

[Out]

Done