Integrand size = 20, antiderivative size = 292 \[ \int (a+b x)^6 (A+B x) (d+e x)^7 \, dx=-\frac {(b d-a e)^6 (B d-A e) (d+e x)^8}{8 e^8}+\frac {(b d-a e)^5 (7 b B d-6 A b e-a B e) (d+e x)^9}{9 e^8}-\frac {3 b (b d-a e)^4 (7 b B d-5 A b e-2 a B e) (d+e x)^{10}}{10 e^8}+\frac {5 b^2 (b d-a e)^3 (7 b B d-4 A b e-3 a B e) (d+e x)^{11}}{11 e^8}-\frac {5 b^3 (b d-a e)^2 (7 b B d-3 A b e-4 a B e) (d+e x)^{12}}{12 e^8}+\frac {3 b^4 (b d-a e) (7 b B d-2 A b e-5 a B e) (d+e x)^{13}}{13 e^8}-\frac {b^5 (7 b B d-A b e-6 a B e) (d+e x)^{14}}{14 e^8}+\frac {b^6 B (d+e x)^{15}}{15 e^8} \]
-1/8*(-a*e+b*d)^6*(-A*e+B*d)*(e*x+d)^8/e^8+1/9*(-a*e+b*d)^5*(-6*A*b*e-B*a* e+7*B*b*d)*(e*x+d)^9/e^8-3/10*b*(-a*e+b*d)^4*(-5*A*b*e-2*B*a*e+7*B*b*d)*(e *x+d)^10/e^8+5/11*b^2*(-a*e+b*d)^3*(-4*A*b*e-3*B*a*e+7*B*b*d)*(e*x+d)^11/e ^8-5/12*b^3*(-a*e+b*d)^2*(-3*A*b*e-4*B*a*e+7*B*b*d)*(e*x+d)^12/e^8+3/13*b^ 4*(-a*e+b*d)*(-2*A*b*e-5*B*a*e+7*B*b*d)*(e*x+d)^13/e^8-1/14*b^5*(-A*b*e-6* B*a*e+7*B*b*d)*(e*x+d)^14/e^8+1/15*b^6*B*(e*x+d)^15/e^8
Leaf count is larger than twice the leaf count of optimal. \(1224\) vs. \(2(292)=584\).
Time = 0.30 (sec) , antiderivative size = 1224, normalized size of antiderivative = 4.19 \[ \int (a+b x)^6 (A+B x) (d+e x)^7 \, dx=a^6 A d^7 x+\frac {1}{2} a^5 d^6 (6 A b d+a B d+7 a A e) x^2+\frac {1}{3} a^4 d^5 \left (a B d (6 b d+7 a e)+3 A \left (5 b^2 d^2+14 a b d e+7 a^2 e^2\right )\right ) x^3+\frac {1}{4} a^3 d^4 \left (3 a B d \left (5 b^2 d^2+14 a b d e+7 a^2 e^2\right )+A \left (20 b^3 d^3+105 a b^2 d^2 e+126 a^2 b d e^2+35 a^3 e^3\right )\right ) x^4+\frac {1}{5} a^2 d^3 \left (a B d \left (20 b^3 d^3+105 a b^2 d^2 e+126 a^2 b d e^2+35 a^3 e^3\right )+5 A \left (3 b^4 d^4+28 a b^3 d^3 e+63 a^2 b^2 d^2 e^2+42 a^3 b d e^3+7 a^4 e^4\right )\right ) x^5+\frac {1}{6} a d^2 \left (5 a B d \left (3 b^4 d^4+28 a b^3 d^3 e+63 a^2 b^2 d^2 e^2+42 a^3 b d e^3+7 a^4 e^4\right )+3 A \left (2 b^5 d^5+35 a b^4 d^4 e+140 a^2 b^3 d^3 e^2+175 a^3 b^2 d^2 e^3+70 a^4 b d e^4+7 a^5 e^5\right )\right ) x^6+\frac {1}{7} d \left (3 a B d \left (2 b^5 d^5+35 a b^4 d^4 e+140 a^2 b^3 d^3 e^2+175 a^3 b^2 d^2 e^3+70 a^4 b d e^4+7 a^5 e^5\right )+A \left (b^6 d^6+42 a b^5 d^5 e+315 a^2 b^4 d^4 e^2+700 a^3 b^3 d^3 e^3+525 a^4 b^2 d^2 e^4+126 a^5 b d e^5+7 a^6 e^6\right )\right ) x^7+\frac {1}{8} \left (700 a^3 b^3 d^3 e^3 (B d+A e)+42 a^5 b d e^5 (3 B d+A e)+a^6 e^6 (7 B d+A e)+42 a b^5 d^5 e (B d+3 A e)+105 a^4 b^2 d^2 e^4 (5 B d+3 A e)+105 a^2 b^4 d^4 e^2 (3 B d+5 A e)+b^6 d^6 (B d+7 A e)\right ) x^8+\frac {1}{9} e \left (a^6 B e^6+525 a^2 b^4 d^3 e^2 (B d+A e)+105 a^4 b^2 d e^4 (3 B d+A e)+6 a^5 b e^5 (7 B d+A e)+7 b^6 d^5 (B d+3 A e)+140 a^3 b^3 d^2 e^3 (5 B d+3 A e)+42 a b^5 d^4 e (3 B d+5 A e)\right ) x^9+\frac {1}{10} b e^2 \left (6 a^5 B e^5+210 a b^4 d^3 e (B d+A e)+140 a^3 b^2 d e^3 (3 B d+A e)+15 a^4 b e^4 (7 B d+A e)+105 a^2 b^3 d^2 e^2 (5 B d+3 A e)+7 b^5 d^4 (3 B d+5 A e)\right ) x^{10}+\frac {1}{11} b^2 e^3 \left (15 a^4 B e^4+35 b^4 d^3 (B d+A e)+105 a^2 b^2 d e^2 (3 B d+A e)+20 a^3 b e^3 (7 B d+A e)+42 a b^3 d^2 e (5 B d+3 A e)\right ) x^{11}+\frac {1}{12} b^3 e^4 \left (20 a^3 B e^3+42 a b^2 d e (3 B d+A e)+15 a^2 b e^2 (7 B d+A e)+7 b^3 d^2 (5 B d+3 A e)\right ) x^{12}+\frac {1}{13} b^4 e^5 \left (15 a^2 B e^2+7 b^2 d (3 B d+A e)+6 a b e (7 B d+A e)\right ) x^{13}+\frac {1}{14} b^5 e^6 (7 b B d+A b e+6 a B e) x^{14}+\frac {1}{15} b^6 B e^7 x^{15} \]
a^6*A*d^7*x + (a^5*d^6*(6*A*b*d + a*B*d + 7*a*A*e)*x^2)/2 + (a^4*d^5*(a*B* d*(6*b*d + 7*a*e) + 3*A*(5*b^2*d^2 + 14*a*b*d*e + 7*a^2*e^2))*x^3)/3 + (a^ 3*d^4*(3*a*B*d*(5*b^2*d^2 + 14*a*b*d*e + 7*a^2*e^2) + A*(20*b^3*d^3 + 105* a*b^2*d^2*e + 126*a^2*b*d*e^2 + 35*a^3*e^3))*x^4)/4 + (a^2*d^3*(a*B*d*(20* b^3*d^3 + 105*a*b^2*d^2*e + 126*a^2*b*d*e^2 + 35*a^3*e^3) + 5*A*(3*b^4*d^4 + 28*a*b^3*d^3*e + 63*a^2*b^2*d^2*e^2 + 42*a^3*b*d*e^3 + 7*a^4*e^4))*x^5) /5 + (a*d^2*(5*a*B*d*(3*b^4*d^4 + 28*a*b^3*d^3*e + 63*a^2*b^2*d^2*e^2 + 42 *a^3*b*d*e^3 + 7*a^4*e^4) + 3*A*(2*b^5*d^5 + 35*a*b^4*d^4*e + 140*a^2*b^3* d^3*e^2 + 175*a^3*b^2*d^2*e^3 + 70*a^4*b*d*e^4 + 7*a^5*e^5))*x^6)/6 + (d*( 3*a*B*d*(2*b^5*d^5 + 35*a*b^4*d^4*e + 140*a^2*b^3*d^3*e^2 + 175*a^3*b^2*d^ 2*e^3 + 70*a^4*b*d*e^4 + 7*a^5*e^5) + A*(b^6*d^6 + 42*a*b^5*d^5*e + 315*a^ 2*b^4*d^4*e^2 + 700*a^3*b^3*d^3*e^3 + 525*a^4*b^2*d^2*e^4 + 126*a^5*b*d*e^ 5 + 7*a^6*e^6))*x^7)/7 + ((700*a^3*b^3*d^3*e^3*(B*d + A*e) + 42*a^5*b*d*e^ 5*(3*B*d + A*e) + a^6*e^6*(7*B*d + A*e) + 42*a*b^5*d^5*e*(B*d + 3*A*e) + 1 05*a^4*b^2*d^2*e^4*(5*B*d + 3*A*e) + 105*a^2*b^4*d^4*e^2*(3*B*d + 5*A*e) + b^6*d^6*(B*d + 7*A*e))*x^8)/8 + (e*(a^6*B*e^6 + 525*a^2*b^4*d^3*e^2*(B*d + A*e) + 105*a^4*b^2*d*e^4*(3*B*d + A*e) + 6*a^5*b*e^5*(7*B*d + A*e) + 7*b ^6*d^5*(B*d + 3*A*e) + 140*a^3*b^3*d^2*e^3*(5*B*d + 3*A*e) + 42*a*b^5*d^4* e*(3*B*d + 5*A*e))*x^9)/9 + (b*e^2*(6*a^5*B*e^5 + 210*a*b^4*d^3*e*(B*d + A *e) + 140*a^3*b^2*d*e^3*(3*B*d + A*e) + 15*a^4*b*e^4*(7*B*d + A*e) + 10...
Time = 1.16 (sec) , antiderivative size = 292, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {86, 2009}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int (a+b x)^6 (A+B x) (d+e x)^7 \, dx\) |
| \(\Big \downarrow \) 86 |
| \(\displaystyle \int \left (\frac {b^5 (d+e x)^{13} (6 a B e+A b e-7 b B d)}{e^7}-\frac {3 b^4 (d+e x)^{12} (b d-a e) (5 a B e+2 A b e-7 b B d)}{e^7}+\frac {5 b^3 (d+e x)^{11} (b d-a e)^2 (4 a B e+3 A b e-7 b B d)}{e^7}-\frac {5 b^2 (d+e x)^{10} (b d-a e)^3 (3 a B e+4 A b e-7 b B d)}{e^7}+\frac {3 b (d+e x)^9 (b d-a e)^4 (2 a B e+5 A b e-7 b B d)}{e^7}+\frac {(d+e x)^8 (a e-b d)^5 (a B e+6 A b e-7 b B d)}{e^7}+\frac {(d+e x)^7 (a e-b d)^6 (A e-B d)}{e^7}+\frac {b^6 B (d+e x)^{14}}{e^7}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\frac {b^5 (d+e x)^{14} (-6 a B e-A b e+7 b B d)}{14 e^8}+\frac {3 b^4 (d+e x)^{13} (b d-a e) (-5 a B e-2 A b e+7 b B d)}{13 e^8}-\frac {5 b^3 (d+e x)^{12} (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{12 e^8}+\frac {5 b^2 (d+e x)^{11} (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{11 e^8}-\frac {3 b (d+e x)^{10} (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{10 e^8}+\frac {(d+e x)^9 (b d-a e)^5 (-a B e-6 A b e+7 b B d)}{9 e^8}-\frac {(d+e x)^8 (b d-a e)^6 (B d-A e)}{8 e^8}+\frac {b^6 B (d+e x)^{15}}{15 e^8}\) |
-1/8*((b*d - a*e)^6*(B*d - A*e)*(d + e*x)^8)/e^8 + ((b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e)*(d + e*x)^9)/(9*e^8) - (3*b*(b*d - a*e)^4*(7*b*B*d - 5 *A*b*e - 2*a*B*e)*(d + e*x)^10)/(10*e^8) + (5*b^2*(b*d - a*e)^3*(7*b*B*d - 4*A*b*e - 3*a*B*e)*(d + e*x)^11)/(11*e^8) - (5*b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e - 4*a*B*e)*(d + e*x)^12)/(12*e^8) + (3*b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e)*(d + e*x)^13)/(13*e^8) - (b^5*(7*b*B*d - A*b*e - 6*a *B*e)*(d + e*x)^14)/(14*e^8) + (b^6*B*(d + e*x)^15)/(15*e^8)
3.11.52.3.1 Defintions of rubi rules used
Int[((a_.) + (b_.)*(x_))*((c_) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_ .), x_] :> Int[ExpandIntegrand[(a + b*x)*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, n}, x] && ((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]))))
Leaf count of result is larger than twice the leaf count of optimal. \(1348\) vs. \(2(276)=552\).
Time = 2.05 (sec) , antiderivative size = 1349, normalized size of antiderivative = 4.62
| method | result | size |
| default | \(\text {Expression too large to display}\) | \(1349\) |
| norman | \(\text {Expression too large to display}\) | \(1448\) |
| gosper | \(\text {Expression too large to display}\) | \(1713\) |
| risch | \(\text {Expression too large to display}\) | \(1713\) |
| parallelrisch | \(\text {Expression too large to display}\) | \(1713\) |
1/15*b^6*B*e^7*x^15+1/14*((A*b^6+6*B*a*b^5)*e^7+7*b^6*B*d*e^6)*x^14+1/13*( (6*A*a*b^5+15*B*a^2*b^4)*e^7+7*(A*b^6+6*B*a*b^5)*d*e^6+21*b^6*B*d^2*e^5)*x ^13+1/12*((15*A*a^2*b^4+20*B*a^3*b^3)*e^7+7*(6*A*a*b^5+15*B*a^2*b^4)*d*e^6 +21*(A*b^6+6*B*a*b^5)*d^2*e^5+35*b^6*B*d^3*e^4)*x^12+1/11*((20*A*a^3*b^3+1 5*B*a^4*b^2)*e^7+7*(15*A*a^2*b^4+20*B*a^3*b^3)*d*e^6+21*(6*A*a*b^5+15*B*a^ 2*b^4)*d^2*e^5+35*(A*b^6+6*B*a*b^5)*d^3*e^4+35*b^6*B*d^4*e^3)*x^11+1/10*(( 15*A*a^4*b^2+6*B*a^5*b)*e^7+7*(20*A*a^3*b^3+15*B*a^4*b^2)*d*e^6+21*(15*A*a ^2*b^4+20*B*a^3*b^3)*d^2*e^5+35*(6*A*a*b^5+15*B*a^2*b^4)*d^3*e^4+35*(A*b^6 +6*B*a*b^5)*d^4*e^3+21*b^6*B*d^5*e^2)*x^10+1/9*((6*A*a^5*b+B*a^6)*e^7+7*(1 5*A*a^4*b^2+6*B*a^5*b)*d*e^6+21*(20*A*a^3*b^3+15*B*a^4*b^2)*d^2*e^5+35*(15 *A*a^2*b^4+20*B*a^3*b^3)*d^3*e^4+35*(6*A*a*b^5+15*B*a^2*b^4)*d^4*e^3+21*(A *b^6+6*B*a*b^5)*d^5*e^2+7*b^6*B*d^6*e)*x^9+1/8*(A*a^6*e^7+7*(6*A*a^5*b+B*a ^6)*d*e^6+21*(15*A*a^4*b^2+6*B*a^5*b)*d^2*e^5+35*(20*A*a^3*b^3+15*B*a^4*b^ 2)*d^3*e^4+35*(15*A*a^2*b^4+20*B*a^3*b^3)*d^4*e^3+21*(6*A*a*b^5+15*B*a^2*b ^4)*d^5*e^2+7*(A*b^6+6*B*a*b^5)*d^6*e+b^6*B*d^7)*x^8+1/7*(7*A*a^6*d*e^6+21 *(6*A*a^5*b+B*a^6)*d^2*e^5+35*(15*A*a^4*b^2+6*B*a^5*b)*d^3*e^4+35*(20*A*a^ 3*b^3+15*B*a^4*b^2)*d^4*e^3+21*(15*A*a^2*b^4+20*B*a^3*b^3)*d^5*e^2+7*(6*A* a*b^5+15*B*a^2*b^4)*d^6*e+(A*b^6+6*B*a*b^5)*d^7)*x^7+1/6*(21*A*a^6*d^2*e^5 +35*(6*A*a^5*b+B*a^6)*d^3*e^4+35*(15*A*a^4*b^2+6*B*a^5*b)*d^4*e^3+21*(20*A *a^3*b^3+15*B*a^4*b^2)*d^5*e^2+7*(15*A*a^2*b^4+20*B*a^3*b^3)*d^6*e+(6*A...
Leaf count of result is larger than twice the leaf count of optimal. 1356 vs. \(2 (276) = 552\).
Time = 0.23 (sec) , antiderivative size = 1356, normalized size of antiderivative = 4.64 \[ \int (a+b x)^6 (A+B x) (d+e x)^7 \, dx=\text {Too large to display} \]
1/15*B*b^6*e^7*x^15 + A*a^6*d^7*x + 1/14*(7*B*b^6*d*e^6 + (6*B*a*b^5 + A*b ^6)*e^7)*x^14 + 1/13*(21*B*b^6*d^2*e^5 + 7*(6*B*a*b^5 + A*b^6)*d*e^6 + 3*( 5*B*a^2*b^4 + 2*A*a*b^5)*e^7)*x^13 + 1/12*(35*B*b^6*d^3*e^4 + 21*(6*B*a*b^ 5 + A*b^6)*d^2*e^5 + 21*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^6 + 5*(4*B*a^3*b^3 + 3*A*a^2*b^4)*e^7)*x^12 + 1/11*(35*B*b^6*d^4*e^3 + 35*(6*B*a*b^5 + A*b^6)* d^3*e^4 + 63*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^5 + 35*(4*B*a^3*b^3 + 3*A*a^2 *b^4)*d*e^6 + 5*(3*B*a^4*b^2 + 4*A*a^3*b^3)*e^7)*x^11 + 1/10*(21*B*b^6*d^5 *e^2 + 35*(6*B*a*b^5 + A*b^6)*d^4*e^3 + 105*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3* e^4 + 105*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^5 + 35*(3*B*a^4*b^2 + 4*A*a^3* b^3)*d*e^6 + 3*(2*B*a^5*b + 5*A*a^4*b^2)*e^7)*x^10 + 1/9*(7*B*b^6*d^6*e + 21*(6*B*a*b^5 + A*b^6)*d^5*e^2 + 105*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^3 + 1 75*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^4 + 105*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d ^2*e^5 + 21*(2*B*a^5*b + 5*A*a^4*b^2)*d*e^6 + (B*a^6 + 6*A*a^5*b)*e^7)*x^9 + 1/8*(B*b^6*d^7 + A*a^6*e^7 + 7*(6*B*a*b^5 + A*b^6)*d^6*e + 63*(5*B*a^2* b^4 + 2*A*a*b^5)*d^5*e^2 + 175*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^3 + 175*( 3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^4 + 63*(2*B*a^5*b + 5*A*a^4*b^2)*d^2*e^5 + 7*(B*a^6 + 6*A*a^5*b)*d*e^6)*x^8 + 1/7*(7*A*a^6*d*e^6 + (6*B*a*b^5 + A*b ^6)*d^7 + 21*(5*B*a^2*b^4 + 2*A*a*b^5)*d^6*e + 105*(4*B*a^3*b^3 + 3*A*a^2* b^4)*d^5*e^2 + 175*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^4*e^3 + 105*(2*B*a^5*b + 5*A*a^4*b^2)*d^3*e^4 + 21*(B*a^6 + 6*A*a^5*b)*d^2*e^5)*x^7 + 1/6*(21*A*...
Leaf count of result is larger than twice the leaf count of optimal. 1756 vs. \(2 (296) = 592\).
Time = 0.11 (sec) , antiderivative size = 1756, normalized size of antiderivative = 6.01 \[ \int (a+b x)^6 (A+B x) (d+e x)^7 \, dx=\text {Too large to display} \]
A*a**6*d**7*x + B*b**6*e**7*x**15/15 + x**14*(A*b**6*e**7/14 + 3*B*a*b**5* e**7/7 + B*b**6*d*e**6/2) + x**13*(6*A*a*b**5*e**7/13 + 7*A*b**6*d*e**6/13 + 15*B*a**2*b**4*e**7/13 + 42*B*a*b**5*d*e**6/13 + 21*B*b**6*d**2*e**5/13 ) + x**12*(5*A*a**2*b**4*e**7/4 + 7*A*a*b**5*d*e**6/2 + 7*A*b**6*d**2*e**5 /4 + 5*B*a**3*b**3*e**7/3 + 35*B*a**2*b**4*d*e**6/4 + 21*B*a*b**5*d**2*e** 5/2 + 35*B*b**6*d**3*e**4/12) + x**11*(20*A*a**3*b**3*e**7/11 + 105*A*a**2 *b**4*d*e**6/11 + 126*A*a*b**5*d**2*e**5/11 + 35*A*b**6*d**3*e**4/11 + 15* B*a**4*b**2*e**7/11 + 140*B*a**3*b**3*d*e**6/11 + 315*B*a**2*b**4*d**2*e** 5/11 + 210*B*a*b**5*d**3*e**4/11 + 35*B*b**6*d**4*e**3/11) + x**10*(3*A*a* *4*b**2*e**7/2 + 14*A*a**3*b**3*d*e**6 + 63*A*a**2*b**4*d**2*e**5/2 + 21*A *a*b**5*d**3*e**4 + 7*A*b**6*d**4*e**3/2 + 3*B*a**5*b*e**7/5 + 21*B*a**4*b **2*d*e**6/2 + 42*B*a**3*b**3*d**2*e**5 + 105*B*a**2*b**4*d**3*e**4/2 + 21 *B*a*b**5*d**4*e**3 + 21*B*b**6*d**5*e**2/10) + x**9*(2*A*a**5*b*e**7/3 + 35*A*a**4*b**2*d*e**6/3 + 140*A*a**3*b**3*d**2*e**5/3 + 175*A*a**2*b**4*d* *3*e**4/3 + 70*A*a*b**5*d**4*e**3/3 + 7*A*b**6*d**5*e**2/3 + B*a**6*e**7/9 + 14*B*a**5*b*d*e**6/3 + 35*B*a**4*b**2*d**2*e**5 + 700*B*a**3*b**3*d**3* e**4/9 + 175*B*a**2*b**4*d**4*e**3/3 + 14*B*a*b**5*d**5*e**2 + 7*B*b**6*d* *6*e/9) + x**8*(A*a**6*e**7/8 + 21*A*a**5*b*d*e**6/4 + 315*A*a**4*b**2*d** 2*e**5/8 + 175*A*a**3*b**3*d**3*e**4/2 + 525*A*a**2*b**4*d**4*e**3/8 + 63* A*a*b**5*d**5*e**2/4 + 7*A*b**6*d**6*e/8 + 7*B*a**6*d*e**6/8 + 63*B*a**...
Leaf count of result is larger than twice the leaf count of optimal. 1356 vs. \(2 (276) = 552\).
Time = 0.25 (sec) , antiderivative size = 1356, normalized size of antiderivative = 4.64 \[ \int (a+b x)^6 (A+B x) (d+e x)^7 \, dx=\text {Too large to display} \]
1/15*B*b^6*e^7*x^15 + A*a^6*d^7*x + 1/14*(7*B*b^6*d*e^6 + (6*B*a*b^5 + A*b ^6)*e^7)*x^14 + 1/13*(21*B*b^6*d^2*e^5 + 7*(6*B*a*b^5 + A*b^6)*d*e^6 + 3*( 5*B*a^2*b^4 + 2*A*a*b^5)*e^7)*x^13 + 1/12*(35*B*b^6*d^3*e^4 + 21*(6*B*a*b^ 5 + A*b^6)*d^2*e^5 + 21*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^6 + 5*(4*B*a^3*b^3 + 3*A*a^2*b^4)*e^7)*x^12 + 1/11*(35*B*b^6*d^4*e^3 + 35*(6*B*a*b^5 + A*b^6)* d^3*e^4 + 63*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^5 + 35*(4*B*a^3*b^3 + 3*A*a^2 *b^4)*d*e^6 + 5*(3*B*a^4*b^2 + 4*A*a^3*b^3)*e^7)*x^11 + 1/10*(21*B*b^6*d^5 *e^2 + 35*(6*B*a*b^5 + A*b^6)*d^4*e^3 + 105*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3* e^4 + 105*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^5 + 35*(3*B*a^4*b^2 + 4*A*a^3* b^3)*d*e^6 + 3*(2*B*a^5*b + 5*A*a^4*b^2)*e^7)*x^10 + 1/9*(7*B*b^6*d^6*e + 21*(6*B*a*b^5 + A*b^6)*d^5*e^2 + 105*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^3 + 1 75*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^4 + 105*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d ^2*e^5 + 21*(2*B*a^5*b + 5*A*a^4*b^2)*d*e^6 + (B*a^6 + 6*A*a^5*b)*e^7)*x^9 + 1/8*(B*b^6*d^7 + A*a^6*e^7 + 7*(6*B*a*b^5 + A*b^6)*d^6*e + 63*(5*B*a^2* b^4 + 2*A*a*b^5)*d^5*e^2 + 175*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^3 + 175*( 3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^4 + 63*(2*B*a^5*b + 5*A*a^4*b^2)*d^2*e^5 + 7*(B*a^6 + 6*A*a^5*b)*d*e^6)*x^8 + 1/7*(7*A*a^6*d*e^6 + (6*B*a*b^5 + A*b ^6)*d^7 + 21*(5*B*a^2*b^4 + 2*A*a*b^5)*d^6*e + 105*(4*B*a^3*b^3 + 3*A*a^2* b^4)*d^5*e^2 + 175*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^4*e^3 + 105*(2*B*a^5*b + 5*A*a^4*b^2)*d^3*e^4 + 21*(B*a^6 + 6*A*a^5*b)*d^2*e^5)*x^7 + 1/6*(21*A*...
Leaf count of result is larger than twice the leaf count of optimal. 1712 vs. \(2 (276) = 552\).
Time = 0.32 (sec) , antiderivative size = 1712, normalized size of antiderivative = 5.86 \[ \int (a+b x)^6 (A+B x) (d+e x)^7 \, dx=\text {Too large to display} \]
1/15*B*b^6*e^7*x^15 + 1/2*B*b^6*d*e^6*x^14 + 3/7*B*a*b^5*e^7*x^14 + 1/14*A *b^6*e^7*x^14 + 21/13*B*b^6*d^2*e^5*x^13 + 42/13*B*a*b^5*d*e^6*x^13 + 7/13 *A*b^6*d*e^6*x^13 + 15/13*B*a^2*b^4*e^7*x^13 + 6/13*A*a*b^5*e^7*x^13 + 35/ 12*B*b^6*d^3*e^4*x^12 + 21/2*B*a*b^5*d^2*e^5*x^12 + 7/4*A*b^6*d^2*e^5*x^12 + 35/4*B*a^2*b^4*d*e^6*x^12 + 7/2*A*a*b^5*d*e^6*x^12 + 5/3*B*a^3*b^3*e^7* x^12 + 5/4*A*a^2*b^4*e^7*x^12 + 35/11*B*b^6*d^4*e^3*x^11 + 210/11*B*a*b^5* d^3*e^4*x^11 + 35/11*A*b^6*d^3*e^4*x^11 + 315/11*B*a^2*b^4*d^2*e^5*x^11 + 126/11*A*a*b^5*d^2*e^5*x^11 + 140/11*B*a^3*b^3*d*e^6*x^11 + 105/11*A*a^2*b ^4*d*e^6*x^11 + 15/11*B*a^4*b^2*e^7*x^11 + 20/11*A*a^3*b^3*e^7*x^11 + 21/1 0*B*b^6*d^5*e^2*x^10 + 21*B*a*b^5*d^4*e^3*x^10 + 7/2*A*b^6*d^4*e^3*x^10 + 105/2*B*a^2*b^4*d^3*e^4*x^10 + 21*A*a*b^5*d^3*e^4*x^10 + 42*B*a^3*b^3*d^2* e^5*x^10 + 63/2*A*a^2*b^4*d^2*e^5*x^10 + 21/2*B*a^4*b^2*d*e^6*x^10 + 14*A* a^3*b^3*d*e^6*x^10 + 3/5*B*a^5*b*e^7*x^10 + 3/2*A*a^4*b^2*e^7*x^10 + 7/9*B *b^6*d^6*e*x^9 + 14*B*a*b^5*d^5*e^2*x^9 + 7/3*A*b^6*d^5*e^2*x^9 + 175/3*B* a^2*b^4*d^4*e^3*x^9 + 70/3*A*a*b^5*d^4*e^3*x^9 + 700/9*B*a^3*b^3*d^3*e^4*x ^9 + 175/3*A*a^2*b^4*d^3*e^4*x^9 + 35*B*a^4*b^2*d^2*e^5*x^9 + 140/3*A*a^3* b^3*d^2*e^5*x^9 + 14/3*B*a^5*b*d*e^6*x^9 + 35/3*A*a^4*b^2*d*e^6*x^9 + 1/9* B*a^6*e^7*x^9 + 2/3*A*a^5*b*e^7*x^9 + 1/8*B*b^6*d^7*x^8 + 21/4*B*a*b^5*d^6 *e*x^8 + 7/8*A*b^6*d^6*e*x^8 + 315/8*B*a^2*b^4*d^5*e^2*x^8 + 63/4*A*a*b^5* d^5*e^2*x^8 + 175/2*B*a^3*b^3*d^4*e^3*x^8 + 525/8*A*a^2*b^4*d^4*e^3*x^8...
Time = 1.64 (sec) , antiderivative size = 1431, normalized size of antiderivative = 4.90 \[ \int (a+b x)^6 (A+B x) (d+e x)^7 \, dx=\text {Too large to display} \]
x^6*(A*a*b^5*d^7 + (5*B*a^2*b^4*d^7)/2 + (7*A*a^6*d^2*e^5)/2 + (35*B*a^6*d ^3*e^4)/6 + (35*A*a^2*b^4*d^6*e)/2 + 35*A*a^5*b*d^3*e^4 + (70*B*a^3*b^3*d^ 6*e)/3 + 35*B*a^5*b*d^4*e^3 + 70*A*a^3*b^3*d^5*e^2 + (175*A*a^4*b^2*d^4*e^ 3)/2 + (105*B*a^4*b^2*d^5*e^2)/2) + x^10*((3*B*a^5*b*e^7)/5 + (3*A*a^4*b^2 *e^7)/2 + (7*A*b^6*d^4*e^3)/2 + (21*B*b^6*d^5*e^2)/10 + 21*A*a*b^5*d^3*e^4 + 14*A*a^3*b^3*d*e^6 + 21*B*a*b^5*d^4*e^3 + (21*B*a^4*b^2*d*e^6)/2 + (63* A*a^2*b^4*d^2*e^5)/2 + (105*B*a^2*b^4*d^3*e^4)/2 + 42*B*a^3*b^3*d^2*e^5) + x^5*(3*A*a^2*b^4*d^7 + 4*B*a^3*b^3*d^7 + 7*A*a^6*d^3*e^4 + 7*B*a^6*d^4*e^ 3 + 28*A*a^3*b^3*d^6*e + 42*A*a^5*b*d^4*e^3 + 21*B*a^4*b^2*d^6*e + (126*B* a^5*b*d^5*e^2)/5 + 63*A*a^4*b^2*d^5*e^2) + x^11*((20*A*a^3*b^3*e^7)/11 + ( 15*B*a^4*b^2*e^7)/11 + (35*A*b^6*d^3*e^4)/11 + (35*B*b^6*d^4*e^3)/11 + (12 6*A*a*b^5*d^2*e^5)/11 + (105*A*a^2*b^4*d*e^6)/11 + (210*B*a*b^5*d^3*e^4)/1 1 + (140*B*a^3*b^3*d*e^6)/11 + (315*B*a^2*b^4*d^2*e^5)/11) + x^3*(2*B*a^5* b*d^7 + (7*B*a^6*d^6*e)/3 + 5*A*a^4*b^2*d^7 + 7*A*a^6*d^5*e^2 + 14*A*a^5*b *d^6*e) + x^8*((A*a^6*e^7)/8 + (B*b^6*d^7)/8 + (7*A*b^6*d^6*e)/8 + (7*B*a^ 6*d*e^6)/8 + (63*A*a*b^5*d^5*e^2)/4 + (63*B*a^5*b*d^2*e^5)/4 + (525*A*a^2* b^4*d^4*e^3)/8 + (175*A*a^3*b^3*d^3*e^4)/2 + (315*A*a^4*b^2*d^2*e^5)/8 + ( 315*B*a^2*b^4*d^5*e^2)/8 + (175*B*a^3*b^3*d^4*e^3)/2 + (525*B*a^4*b^2*d^3* e^4)/8 + (21*A*a^5*b*d*e^6)/4 + (21*B*a*b^5*d^6*e)/4) + x^13*((6*A*a*b^5*e ^7)/13 + (7*A*b^6*d*e^6)/13 + (15*B*a^2*b^4*e^7)/13 + (21*B*b^6*d^2*e^5...