3.1055 \(\int (a+b x)^6 (A+B x) (d+e x)^4 \, dx\)

Optimal. Leaf size=204 \[ \frac{e^3 (a+b x)^{11} (-5 a B e+A b e+4 b B d)}{11 b^6}+\frac{e^2 (a+b x)^{10} (b d-a e) (-5 a B e+2 A b e+3 b B d)}{5 b^6}+\frac{2 e (a+b x)^9 (b d-a e)^2 (-5 a B e+3 A b e+2 b B d)}{9 b^6}+\frac{(a+b x)^8 (b d-a e)^3 (-5 a B e+4 A b e+b B d)}{8 b^6}+\frac{(a+b x)^7 (A b-a B) (b d-a e)^4}{7 b^6}+\frac{B e^4 (a+b x)^{12}}{12 b^6} \]

[Out]

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

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Rubi [A]  time = 0.626025, antiderivative size = 204, 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, Rules used = {77} \[ \frac{e^3 (a+b x)^{11} (-5 a B e+A b e+4 b B d)}{11 b^6}+\frac{e^2 (a+b x)^{10} (b d-a e) (-5 a B e+2 A b e+3 b B d)}{5 b^6}+\frac{2 e (a+b x)^9 (b d-a e)^2 (-5 a B e+3 A b e+2 b B d)}{9 b^6}+\frac{(a+b x)^8 (b d-a e)^3 (-5 a B e+4 A b e+b B d)}{8 b^6}+\frac{(a+b x)^7 (A b-a B) (b d-a e)^4}{7 b^6}+\frac{B e^4 (a+b x)^{12}}{12 b^6} \]

Antiderivative was successfully verified.

[In]

Int[(a + b*x)^6*(A + B*x)*(d + e*x)^4,x]

[Out]

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

Rule 77

Int[((a_.) + (b_.)*(x_))*((c_) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandIntegran
d[(a + b*x)*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, n}, x] && NeQ[b*c - a*d, 0] && ((ILtQ[
n, 0] && ILtQ[p, 0]) || EqQ[p, 1] || (IGtQ[p, 0] && ( !IntegerQ[n] || LeQ[9*p + 5*(n + 2), 0] || GeQ[n + p + 1
, 0] || (GeQ[n + p + 2, 0] && RationalQ[a, b, c, d, e, f]))))

Rubi steps

\begin{align*} \int (a+b x)^6 (A+B x) (d+e x)^4 \, dx &=\int \left (\frac{(A b-a B) (b d-a e)^4 (a+b x)^6}{b^5}+\frac{(b d-a e)^3 (b B d+4 A b e-5 a B e) (a+b x)^7}{b^5}+\frac{2 e (b d-a e)^2 (2 b B d+3 A b e-5 a B e) (a+b x)^8}{b^5}+\frac{2 e^2 (b d-a e) (3 b B d+2 A b e-5 a B e) (a+b x)^9}{b^5}+\frac{e^3 (4 b B d+A b e-5 a B e) (a+b x)^{10}}{b^5}+\frac{B e^4 (a+b x)^{11}}{b^5}\right ) \, dx\\ &=\frac{(A b-a B) (b d-a e)^4 (a+b x)^7}{7 b^6}+\frac{(b d-a e)^3 (b B d+4 A b e-5 a B e) (a+b x)^8}{8 b^6}+\frac{2 e (b d-a e)^2 (2 b B d+3 A b e-5 a B e) (a+b x)^9}{9 b^6}+\frac{e^2 (b d-a e) (3 b B d+2 A b e-5 a B e) (a+b x)^{10}}{5 b^6}+\frac{e^3 (4 b B d+A b e-5 a B e) (a+b x)^{11}}{11 b^6}+\frac{B e^4 (a+b x)^{12}}{12 b^6}\\ \end{align*}

Mathematica [B]  time = 0.248028, size = 762, normalized size = 3.74 \[ \frac{1}{9} b^3 e x^9 \left (15 a^2 b e^2 (A e+4 B d)+20 a^3 B e^3+12 a b^2 d e (2 A e+3 B d)+2 b^3 d^2 (3 A e+2 B d)\right )+\frac{1}{8} b^2 x^8 \left (30 a^2 b^2 d e^2 (2 A e+3 B d)+20 a^3 b e^3 (A e+4 B d)+15 a^4 B e^4+12 a b^3 d^2 e (3 A e+2 B d)+b^4 d^3 (4 A e+B d)\right )+\frac{1}{7} b x^7 \left (A b \left (90 a^2 b^2 d^2 e^2+80 a^3 b d e^3+15 a^4 e^4+24 a b^3 d^3 e+b^4 d^4\right )+6 a B \left (20 a^2 b^2 d^2 e^2+10 a^3 b d e^3+a^4 e^4+10 a b^3 d^3 e+b^4 d^4\right )\right )+\frac{1}{6} a x^6 \left (6 A b \left (20 a^2 b^2 d^2 e^2+10 a^3 b d e^3+a^4 e^4+10 a b^3 d^3 e+b^4 d^4\right )+a B \left (90 a^2 b^2 d^2 e^2+24 a^3 b d e^3+a^4 e^4+80 a b^3 d^3 e+15 b^4 d^4\right )\right )+\frac{1}{5} a^2 x^5 \left (A \left (90 a^2 b^2 d^2 e^2+24 a^3 b d e^3+a^4 e^4+80 a b^3 d^3 e+15 b^4 d^4\right )+4 a B d \left (9 a^2 b d e^2+a^3 e^3+15 a b^2 d^2 e+5 b^3 d^3\right )\right )+\frac{1}{4} a^3 d x^4 \left (4 A \left (9 a^2 b d e^2+a^3 e^3+15 a b^2 d^2 e+5 b^3 d^3\right )+3 a B d \left (2 a^2 e^2+8 a b d e+5 b^2 d^2\right )\right )+\frac{1}{3} a^4 d^2 x^3 \left (3 A \left (2 a^2 e^2+8 a b d e+5 b^2 d^2\right )+2 a B d (2 a e+3 b d)\right )+\frac{1}{10} b^4 e^2 x^{10} \left (15 a^2 B e^2+6 a b e (A e+4 B d)+2 b^2 d (2 A e+3 B d)\right )+\frac{1}{2} a^5 d^3 x^2 (4 a A e+a B d+6 A b d)+a^6 A d^4 x+\frac{1}{11} b^5 e^3 x^{11} (6 a B e+A b e+4 b B d)+\frac{1}{12} b^6 B e^4 x^{12} \]

Antiderivative was successfully verified.

[In]

Integrate[(a + b*x)^6*(A + B*x)*(d + e*x)^4,x]

[Out]

a^6*A*d^4*x + (a^5*d^3*(6*A*b*d + a*B*d + 4*a*A*e)*x^2)/2 + (a^4*d^2*(2*a*B*d*(3*b*d + 2*a*e) + 3*A*(5*b^2*d^2
+ 8*a*b*d*e + 2*a^2*e^2))*x^3)/3 + (a^3*d*(3*a*B*d*(5*b^2*d^2 + 8*a*b*d*e + 2*a^2*e^2) + 4*A*(5*b^3*d^3 + 15*
a*b^2*d^2*e + 9*a^2*b*d*e^2 + a^3*e^3))*x^4)/4 + (a^2*(4*a*B*d*(5*b^3*d^3 + 15*a*b^2*d^2*e + 9*a^2*b*d*e^2 + a
^3*e^3) + A*(15*b^4*d^4 + 80*a*b^3*d^3*e + 90*a^2*b^2*d^2*e^2 + 24*a^3*b*d*e^3 + a^4*e^4))*x^5)/5 + (a*(6*A*b*
(b^4*d^4 + 10*a*b^3*d^3*e + 20*a^2*b^2*d^2*e^2 + 10*a^3*b*d*e^3 + a^4*e^4) + a*B*(15*b^4*d^4 + 80*a*b^3*d^3*e
+ 90*a^2*b^2*d^2*e^2 + 24*a^3*b*d*e^3 + a^4*e^4))*x^6)/6 + (b*(6*a*B*(b^4*d^4 + 10*a*b^3*d^3*e + 20*a^2*b^2*d^
2*e^2 + 10*a^3*b*d*e^3 + a^4*e^4) + A*b*(b^4*d^4 + 24*a*b^3*d^3*e + 90*a^2*b^2*d^2*e^2 + 80*a^3*b*d*e^3 + 15*a
^4*e^4))*x^7)/7 + (b^2*(15*a^4*B*e^4 + 20*a^3*b*e^3*(4*B*d + A*e) + 30*a^2*b^2*d*e^2*(3*B*d + 2*A*e) + 12*a*b^
3*d^2*e*(2*B*d + 3*A*e) + b^4*d^3*(B*d + 4*A*e))*x^8)/8 + (b^3*e*(20*a^3*B*e^3 + 15*a^2*b*e^2*(4*B*d + A*e) +
12*a*b^2*d*e*(3*B*d + 2*A*e) + 2*b^3*d^2*(2*B*d + 3*A*e))*x^9)/9 + (b^4*e^2*(15*a^2*B*e^2 + 6*a*b*e*(4*B*d + A
*e) + 2*b^2*d*(3*B*d + 2*A*e))*x^10)/10 + (b^5*e^3*(4*b*B*d + A*b*e + 6*a*B*e)*x^11)/11 + (b^6*B*e^4*x^12)/12

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Maple [B]  time = 0.002, size = 821, normalized size = 4. \begin{align*} \text{result too large to display} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((b*x+a)^6*(B*x+A)*(e*x+d)^4,x)

[Out]

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

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Maxima [B]  time = 1.16229, size = 1118, normalized size = 5.48 \begin{align*} \text{result too large to display} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)^6*(B*x+A)*(e*x+d)^4,x, algorithm="maxima")

[Out]

1/12*B*b^6*e^4*x^12 + A*a^6*d^4*x + 1/11*(4*B*b^6*d*e^3 + (6*B*a*b^5 + A*b^6)*e^4)*x^11 + 1/10*(6*B*b^6*d^2*e^
2 + 4*(6*B*a*b^5 + A*b^6)*d*e^3 + 3*(5*B*a^2*b^4 + 2*A*a*b^5)*e^4)*x^10 + 1/9*(4*B*b^6*d^3*e + 6*(6*B*a*b^5 +
A*b^6)*d^2*e^2 + 12*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^3 + 5*(4*B*a^3*b^3 + 3*A*a^2*b^4)*e^4)*x^9 + 1/8*(B*b^6*d^4
+ 4*(6*B*a*b^5 + A*b^6)*d^3*e + 18*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^2 + 20*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d*e^3 +
5*(3*B*a^4*b^2 + 4*A*a^3*b^3)*e^4)*x^8 + 1/7*((6*B*a*b^5 + A*b^6)*d^4 + 12*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e + 3
0*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^2 + 20*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d*e^3 + 3*(2*B*a^5*b + 5*A*a^4*b^2)*e^4
)*x^7 + 1/6*(3*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4 + 20*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e + 30*(3*B*a^4*b^2 + 4*A*a^
3*b^3)*d^2*e^2 + 12*(2*B*a^5*b + 5*A*a^4*b^2)*d*e^3 + (B*a^6 + 6*A*a^5*b)*e^4)*x^6 + 1/5*(A*a^6*e^4 + 5*(4*B*a
^3*b^3 + 3*A*a^2*b^4)*d^4 + 20*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e + 18*(2*B*a^5*b + 5*A*a^4*b^2)*d^2*e^2 + 4*(B
*a^6 + 6*A*a^5*b)*d*e^3)*x^5 + 1/4*(4*A*a^6*d*e^3 + 5*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^4 + 12*(2*B*a^5*b + 5*A*a^
4*b^2)*d^3*e + 6*(B*a^6 + 6*A*a^5*b)*d^2*e^2)*x^4 + 1/3*(6*A*a^6*d^2*e^2 + 3*(2*B*a^5*b + 5*A*a^4*b^2)*d^4 + 4
*(B*a^6 + 6*A*a^5*b)*d^3*e)*x^3 + 1/2*(4*A*a^6*d^3*e + (B*a^6 + 6*A*a^5*b)*d^4)*x^2

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Fricas [B]  time = 1.58463, size = 2223, normalized size = 10.9 \begin{align*} \text{result too large to display} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)^6*(B*x+A)*(e*x+d)^4,x, algorithm="fricas")

[Out]

1/12*x^12*e^4*b^6*B + 4/11*x^11*e^3*d*b^6*B + 6/11*x^11*e^4*b^5*a*B + 1/11*x^11*e^4*b^6*A + 3/5*x^10*e^2*d^2*b
^6*B + 12/5*x^10*e^3*d*b^5*a*B + 3/2*x^10*e^4*b^4*a^2*B + 2/5*x^10*e^3*d*b^6*A + 3/5*x^10*e^4*b^5*a*A + 4/9*x^
9*e*d^3*b^6*B + 4*x^9*e^2*d^2*b^5*a*B + 20/3*x^9*e^3*d*b^4*a^2*B + 20/9*x^9*e^4*b^3*a^3*B + 2/3*x^9*e^2*d^2*b^
6*A + 8/3*x^9*e^3*d*b^5*a*A + 5/3*x^9*e^4*b^4*a^2*A + 1/8*x^8*d^4*b^6*B + 3*x^8*e*d^3*b^5*a*B + 45/4*x^8*e^2*d
^2*b^4*a^2*B + 10*x^8*e^3*d*b^3*a^3*B + 15/8*x^8*e^4*b^2*a^4*B + 1/2*x^8*e*d^3*b^6*A + 9/2*x^8*e^2*d^2*b^5*a*A
+ 15/2*x^8*e^3*d*b^4*a^2*A + 5/2*x^8*e^4*b^3*a^3*A + 6/7*x^7*d^4*b^5*a*B + 60/7*x^7*e*d^3*b^4*a^2*B + 120/7*x
^7*e^2*d^2*b^3*a^3*B + 60/7*x^7*e^3*d*b^2*a^4*B + 6/7*x^7*e^4*b*a^5*B + 1/7*x^7*d^4*b^6*A + 24/7*x^7*e*d^3*b^5
*a*A + 90/7*x^7*e^2*d^2*b^4*a^2*A + 80/7*x^7*e^3*d*b^3*a^3*A + 15/7*x^7*e^4*b^2*a^4*A + 5/2*x^6*d^4*b^4*a^2*B
+ 40/3*x^6*e*d^3*b^3*a^3*B + 15*x^6*e^2*d^2*b^2*a^4*B + 4*x^6*e^3*d*b*a^5*B + 1/6*x^6*e^4*a^6*B + x^6*d^4*b^5*
a*A + 10*x^6*e*d^3*b^4*a^2*A + 20*x^6*e^2*d^2*b^3*a^3*A + 10*x^6*e^3*d*b^2*a^4*A + x^6*e^4*b*a^5*A + 4*x^5*d^4
*b^3*a^3*B + 12*x^5*e*d^3*b^2*a^4*B + 36/5*x^5*e^2*d^2*b*a^5*B + 4/5*x^5*e^3*d*a^6*B + 3*x^5*d^4*b^4*a^2*A + 1
6*x^5*e*d^3*b^3*a^3*A + 18*x^5*e^2*d^2*b^2*a^4*A + 24/5*x^5*e^3*d*b*a^5*A + 1/5*x^5*e^4*a^6*A + 15/4*x^4*d^4*b
^2*a^4*B + 6*x^4*e*d^3*b*a^5*B + 3/2*x^4*e^2*d^2*a^6*B + 5*x^4*d^4*b^3*a^3*A + 15*x^4*e*d^3*b^2*a^4*A + 9*x^4*
e^2*d^2*b*a^5*A + x^4*e^3*d*a^6*A + 2*x^3*d^4*b*a^5*B + 4/3*x^3*e*d^3*a^6*B + 5*x^3*d^4*b^2*a^4*A + 8*x^3*e*d^
3*b*a^5*A + 2*x^3*e^2*d^2*a^6*A + 1/2*x^2*d^4*a^6*B + 3*x^2*d^4*b*a^5*A + 2*x^2*e*d^3*a^6*A + x*d^4*a^6*A

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Sympy [B]  time = 0.171595, size = 1035, normalized size = 5.07 \begin{align*} \text{result too large to display} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)**6*(B*x+A)*(e*x+d)**4,x)

[Out]

A*a**6*d**4*x + B*b**6*e**4*x**12/12 + x**11*(A*b**6*e**4/11 + 6*B*a*b**5*e**4/11 + 4*B*b**6*d*e**3/11) + x**1
0*(3*A*a*b**5*e**4/5 + 2*A*b**6*d*e**3/5 + 3*B*a**2*b**4*e**4/2 + 12*B*a*b**5*d*e**3/5 + 3*B*b**6*d**2*e**2/5)
+ x**9*(5*A*a**2*b**4*e**4/3 + 8*A*a*b**5*d*e**3/3 + 2*A*b**6*d**2*e**2/3 + 20*B*a**3*b**3*e**4/9 + 20*B*a**2
*b**4*d*e**3/3 + 4*B*a*b**5*d**2*e**2 + 4*B*b**6*d**3*e/9) + x**8*(5*A*a**3*b**3*e**4/2 + 15*A*a**2*b**4*d*e**
3/2 + 9*A*a*b**5*d**2*e**2/2 + A*b**6*d**3*e/2 + 15*B*a**4*b**2*e**4/8 + 10*B*a**3*b**3*d*e**3 + 45*B*a**2*b**
4*d**2*e**2/4 + 3*B*a*b**5*d**3*e + B*b**6*d**4/8) + x**7*(15*A*a**4*b**2*e**4/7 + 80*A*a**3*b**3*d*e**3/7 + 9
0*A*a**2*b**4*d**2*e**2/7 + 24*A*a*b**5*d**3*e/7 + A*b**6*d**4/7 + 6*B*a**5*b*e**4/7 + 60*B*a**4*b**2*d*e**3/7
+ 120*B*a**3*b**3*d**2*e**2/7 + 60*B*a**2*b**4*d**3*e/7 + 6*B*a*b**5*d**4/7) + x**6*(A*a**5*b*e**4 + 10*A*a**
4*b**2*d*e**3 + 20*A*a**3*b**3*d**2*e**2 + 10*A*a**2*b**4*d**3*e + A*a*b**5*d**4 + B*a**6*e**4/6 + 4*B*a**5*b*
d*e**3 + 15*B*a**4*b**2*d**2*e**2 + 40*B*a**3*b**3*d**3*e/3 + 5*B*a**2*b**4*d**4/2) + x**5*(A*a**6*e**4/5 + 24
*A*a**5*b*d*e**3/5 + 18*A*a**4*b**2*d**2*e**2 + 16*A*a**3*b**3*d**3*e + 3*A*a**2*b**4*d**4 + 4*B*a**6*d*e**3/5
+ 36*B*a**5*b*d**2*e**2/5 + 12*B*a**4*b**2*d**3*e + 4*B*a**3*b**3*d**4) + x**4*(A*a**6*d*e**3 + 9*A*a**5*b*d*
*2*e**2 + 15*A*a**4*b**2*d**3*e + 5*A*a**3*b**3*d**4 + 3*B*a**6*d**2*e**2/2 + 6*B*a**5*b*d**3*e + 15*B*a**4*b*
*2*d**4/4) + x**3*(2*A*a**6*d**2*e**2 + 8*A*a**5*b*d**3*e + 5*A*a**4*b**2*d**4 + 4*B*a**6*d**3*e/3 + 2*B*a**5*
b*d**4) + x**2*(2*A*a**6*d**3*e + 3*A*a**5*b*d**4 + B*a**6*d**4/2)

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Giac [B]  time = 2.21354, size = 1332, normalized size = 6.53 \begin{align*} \text{result too large to display} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)^6*(B*x+A)*(e*x+d)^4,x, algorithm="giac")

[Out]

1/12*B*b^6*x^12*e^4 + 4/11*B*b^6*d*x^11*e^3 + 3/5*B*b^6*d^2*x^10*e^2 + 4/9*B*b^6*d^3*x^9*e + 1/8*B*b^6*d^4*x^8
+ 6/11*B*a*b^5*x^11*e^4 + 1/11*A*b^6*x^11*e^4 + 12/5*B*a*b^5*d*x^10*e^3 + 2/5*A*b^6*d*x^10*e^3 + 4*B*a*b^5*d^
2*x^9*e^2 + 2/3*A*b^6*d^2*x^9*e^2 + 3*B*a*b^5*d^3*x^8*e + 1/2*A*b^6*d^3*x^8*e + 6/7*B*a*b^5*d^4*x^7 + 1/7*A*b^
6*d^4*x^7 + 3/2*B*a^2*b^4*x^10*e^4 + 3/5*A*a*b^5*x^10*e^4 + 20/3*B*a^2*b^4*d*x^9*e^3 + 8/3*A*a*b^5*d*x^9*e^3 +
45/4*B*a^2*b^4*d^2*x^8*e^2 + 9/2*A*a*b^5*d^2*x^8*e^2 + 60/7*B*a^2*b^4*d^3*x^7*e + 24/7*A*a*b^5*d^3*x^7*e + 5/
2*B*a^2*b^4*d^4*x^6 + A*a*b^5*d^4*x^6 + 20/9*B*a^3*b^3*x^9*e^4 + 5/3*A*a^2*b^4*x^9*e^4 + 10*B*a^3*b^3*d*x^8*e^
3 + 15/2*A*a^2*b^4*d*x^8*e^3 + 120/7*B*a^3*b^3*d^2*x^7*e^2 + 90/7*A*a^2*b^4*d^2*x^7*e^2 + 40/3*B*a^3*b^3*d^3*x
^6*e + 10*A*a^2*b^4*d^3*x^6*e + 4*B*a^3*b^3*d^4*x^5 + 3*A*a^2*b^4*d^4*x^5 + 15/8*B*a^4*b^2*x^8*e^4 + 5/2*A*a^3
*b^3*x^8*e^4 + 60/7*B*a^4*b^2*d*x^7*e^3 + 80/7*A*a^3*b^3*d*x^7*e^3 + 15*B*a^4*b^2*d^2*x^6*e^2 + 20*A*a^3*b^3*d
^2*x^6*e^2 + 12*B*a^4*b^2*d^3*x^5*e + 16*A*a^3*b^3*d^3*x^5*e + 15/4*B*a^4*b^2*d^4*x^4 + 5*A*a^3*b^3*d^4*x^4 +
6/7*B*a^5*b*x^7*e^4 + 15/7*A*a^4*b^2*x^7*e^4 + 4*B*a^5*b*d*x^6*e^3 + 10*A*a^4*b^2*d*x^6*e^3 + 36/5*B*a^5*b*d^2
*x^5*e^2 + 18*A*a^4*b^2*d^2*x^5*e^2 + 6*B*a^5*b*d^3*x^4*e + 15*A*a^4*b^2*d^3*x^4*e + 2*B*a^5*b*d^4*x^3 + 5*A*a
^4*b^2*d^4*x^3 + 1/6*B*a^6*x^6*e^4 + A*a^5*b*x^6*e^4 + 4/5*B*a^6*d*x^5*e^3 + 24/5*A*a^5*b*d*x^5*e^3 + 3/2*B*a^
6*d^2*x^4*e^2 + 9*A*a^5*b*d^2*x^4*e^2 + 4/3*B*a^6*d^3*x^3*e + 8*A*a^5*b*d^3*x^3*e + 1/2*B*a^6*d^4*x^2 + 3*A*a^
5*b*d^4*x^2 + 1/5*A*a^6*x^5*e^4 + A*a^6*d*x^4*e^3 + 2*A*a^6*d^2*x^3*e^2 + 2*A*a^6*d^3*x^2*e + A*a^6*d^4*x