Integrand size = 20, antiderivative size = 290 \[ \int (a+b x)^{10} (A+B x) (d+e x)^6 \, dx=\frac {(A b-a B) (b d-a e)^6 (a+b x)^{11}}{11 b^8}+\frac {(b d-a e)^5 (b B d+6 A b e-7 a B e) (a+b x)^{12}}{12 b^8}+\frac {3 e (b d-a e)^4 (2 b B d+5 A b e-7 a B e) (a+b x)^{13}}{13 b^8}+\frac {5 e^2 (b d-a e)^3 (3 b B d+4 A b e-7 a B e) (a+b x)^{14}}{14 b^8}+\frac {e^3 (b d-a e)^2 (4 b B d+3 A b e-7 a B e) (a+b x)^{15}}{3 b^8}+\frac {3 e^4 (b d-a e) (5 b B d+2 A b e-7 a B e) (a+b x)^{16}}{16 b^8}+\frac {e^5 (6 b B d+A b e-7 a B e) (a+b x)^{17}}{17 b^8}+\frac {B e^6 (a+b x)^{18}}{18 b^8} \]
1/11*(A*b-B*a)*(-a*e+b*d)^6*(b*x+a)^11/b^8+1/12*(-a*e+b*d)^5*(6*A*b*e-7*B* a*e+B*b*d)*(b*x+a)^12/b^8+3/13*e*(-a*e+b*d)^4*(5*A*b*e-7*B*a*e+2*B*b*d)*(b *x+a)^13/b^8+5/14*e^2*(-a*e+b*d)^3*(4*A*b*e-7*B*a*e+3*B*b*d)*(b*x+a)^14/b^ 8+1/3*e^3*(-a*e+b*d)^2*(3*A*b*e-7*B*a*e+4*B*b*d)*(b*x+a)^15/b^8+3/16*e^4*( -a*e+b*d)*(2*A*b*e-7*B*a*e+5*B*b*d)*(b*x+a)^16/b^8+1/17*e^5*(A*b*e-7*B*a*e +6*B*b*d)*(b*x+a)^17/b^8+1/18*B*e^6*(b*x+a)^18/b^8
Leaf count is larger than twice the leaf count of optimal. \(1788\) vs. \(2(290)=580\).
Time = 0.45 (sec) , antiderivative size = 1788, normalized size of antiderivative = 6.17 \[ \int (a+b x)^{10} (A+B x) (d+e x)^6 \, dx =\text {Too large to display} \]
a^10*A*d^6*x + (a^9*d^5*(10*A*b*d + a*B*d + 6*a*A*e)*x^2)/2 + (a^8*d^4*(2* a*B*d*(5*b*d + 3*a*e) + 15*A*(3*b^2*d^2 + 4*a*b*d*e + a^2*e^2))*x^3)/3 + ( 5*a^7*d^3*(3*a*B*d*(3*b^2*d^2 + 4*a*b*d*e + a^2*e^2) + A*(24*b^3*d^3 + 54* a*b^2*d^2*e + 30*a^2*b*d*e^2 + 4*a^3*e^3))*x^4)/4 + a^6*d^2*(2*a*B*d*(12*b ^3*d^3 + 27*a*b^2*d^2*e + 15*a^2*b*d*e^2 + 2*a^3*e^3) + A*(42*b^4*d^4 + 14 4*a*b^3*d^3*e + 135*a^2*b^2*d^2*e^2 + 40*a^3*b*d*e^3 + 3*a^4*e^4))*x^5 + ( a^5*d*(5*a*B*d*(42*b^4*d^4 + 144*a*b^3*d^3*e + 135*a^2*b^2*d^2*e^2 + 40*a^ 3*b*d*e^3 + 3*a^4*e^4) + 6*A*(42*b^5*d^5 + 210*a*b^4*d^4*e + 300*a^2*b^3*d ^3*e^2 + 150*a^3*b^2*d^2*e^3 + 25*a^4*b*d*e^4 + a^5*e^5))*x^6)/6 + (a^4*(6 *a*B*d*(42*b^5*d^5 + 210*a*b^4*d^4*e + 300*a^2*b^3*d^3*e^2 + 150*a^3*b^2*d ^2*e^3 + 25*a^4*b*d*e^4 + a^5*e^5) + A*(210*b^6*d^6 + 1512*a*b^5*d^5*e + 3 150*a^2*b^4*d^4*e^2 + 2400*a^3*b^3*d^3*e^3 + 675*a^4*b^2*d^2*e^4 + 60*a^5* b*d*e^5 + a^6*e^6))*x^7)/7 + (a^3*(10*A*b*(12*b^6*d^6 + 126*a*b^5*d^5*e + 378*a^2*b^4*d^4*e^2 + 420*a^3*b^3*d^3*e^3 + 180*a^4*b^2*d^2*e^4 + 27*a^5*b *d*e^5 + a^6*e^6) + a*B*(210*b^6*d^6 + 1512*a*b^5*d^5*e + 3150*a^2*b^4*d^4 *e^2 + 2400*a^3*b^3*d^3*e^3 + 675*a^4*b^2*d^2*e^4 + 60*a^5*b*d*e^5 + a^6*e ^6))*x^8)/8 + (5*a^2*b*(9*A*b*(b^6*d^6 + 16*a*b^5*d^5*e + 70*a^2*b^4*d^4*e ^2 + 112*a^3*b^3*d^3*e^3 + 70*a^4*b^2*d^2*e^4 + 16*a^5*b*d*e^5 + a^6*e^6) + 2*a*B*(12*b^6*d^6 + 126*a*b^5*d^5*e + 378*a^2*b^4*d^4*e^2 + 420*a^3*b^3* d^3*e^3 + 180*a^4*b^2*d^2*e^4 + 27*a^5*b*d*e^5 + a^6*e^6))*x^9)/9 + (a*...
Time = 1.60 (sec) , antiderivative size = 290, 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.
\(\displaystyle \int (a+b x)^{10} (A+B x) (d+e x)^6 \, dx\) |
\(\Big \downarrow \) 86 |
\(\displaystyle \int \left (\frac {e^5 (a+b x)^{16} (-7 a B e+A b e+6 b B d)}{b^7}+\frac {3 e^4 (a+b x)^{15} (b d-a e) (-7 a B e+2 A b e+5 b B d)}{b^7}+\frac {5 e^3 (a+b x)^{14} (b d-a e)^2 (-7 a B e+3 A b e+4 b B d)}{b^7}+\frac {5 e^2 (a+b x)^{13} (b d-a e)^3 (-7 a B e+4 A b e+3 b B d)}{b^7}+\frac {3 e (a+b x)^{12} (b d-a e)^4 (-7 a B e+5 A b e+2 b B d)}{b^7}+\frac {(a+b x)^{11} (b d-a e)^5 (-7 a B e+6 A b e+b B d)}{b^7}+\frac {(a+b x)^{10} (A b-a B) (b d-a e)^6}{b^7}+\frac {B e^6 (a+b x)^{17}}{b^7}\right )dx\) |
\(\Big \downarrow \) 2009 |
\(\displaystyle \frac {e^5 (a+b x)^{17} (-7 a B e+A b e+6 b B d)}{17 b^8}+\frac {3 e^4 (a+b x)^{16} (b d-a e) (-7 a B e+2 A b e+5 b B d)}{16 b^8}+\frac {e^3 (a+b x)^{15} (b d-a e)^2 (-7 a B e+3 A b e+4 b B d)}{3 b^8}+\frac {5 e^2 (a+b x)^{14} (b d-a e)^3 (-7 a B e+4 A b e+3 b B d)}{14 b^8}+\frac {3 e (a+b x)^{13} (b d-a e)^4 (-7 a B e+5 A b e+2 b B d)}{13 b^8}+\frac {(a+b x)^{12} (b d-a e)^5 (-7 a B e+6 A b e+b B d)}{12 b^8}+\frac {(a+b x)^{11} (A b-a B) (b d-a e)^6}{11 b^8}+\frac {B e^6 (a+b x)^{18}}{18 b^8}\) |
((A*b - a*B)*(b*d - a*e)^6*(a + b*x)^11)/(11*b^8) + ((b*d - a*e)^5*(b*B*d + 6*A*b*e - 7*a*B*e)*(a + b*x)^12)/(12*b^8) + (3*e*(b*d - a*e)^4*(2*b*B*d + 5*A*b*e - 7*a*B*e)*(a + b*x)^13)/(13*b^8) + (5*e^2*(b*d - a*e)^3*(3*b*B* d + 4*A*b*e - 7*a*B*e)*(a + b*x)^14)/(14*b^8) + (e^3*(b*d - a*e)^2*(4*b*B* d + 3*A*b*e - 7*a*B*e)*(a + b*x)^15)/(3*b^8) + (3*e^4*(b*d - a*e)*(5*b*B*d + 2*A*b*e - 7*a*B*e)*(a + b*x)^16)/(16*b^8) + (e^5*(6*b*B*d + A*b*e - 7*a *B*e)*(a + b*x)^17)/(17*b^8) + (B*e^6*(a + b*x)^18)/(18*b^8)
3.11.82.3.1 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. \(1904\) vs. \(2(274)=548\).
Time = 2.04 (sec) , antiderivative size = 1905, normalized size of antiderivative = 6.57
method | result | size |
default | \(\text {Expression too large to display}\) | \(1905\) |
norman | \(\text {Expression too large to display}\) | \(2032\) |
gosper | \(\text {Expression too large to display}\) | \(2408\) |
risch | \(\text {Expression too large to display}\) | \(2408\) |
parallelrisch | \(\text {Expression too large to display}\) | \(2408\) |
1/18*b^10*B*e^6*x^18+1/17*((A*b^10+10*B*a*b^9)*e^6+6*b^10*B*d*e^5)*x^17+1/ 16*((10*A*a*b^9+45*B*a^2*b^8)*e^6+6*(A*b^10+10*B*a*b^9)*d*e^5+15*b^10*B*d^ 2*e^4)*x^16+1/15*((45*A*a^2*b^8+120*B*a^3*b^7)*e^6+6*(10*A*a*b^9+45*B*a^2* b^8)*d*e^5+15*(A*b^10+10*B*a*b^9)*d^2*e^4+20*b^10*B*d^3*e^3)*x^15+1/14*((1 20*A*a^3*b^7+210*B*a^4*b^6)*e^6+6*(45*A*a^2*b^8+120*B*a^3*b^7)*d*e^5+15*(1 0*A*a*b^9+45*B*a^2*b^8)*d^2*e^4+20*(A*b^10+10*B*a*b^9)*d^3*e^3+15*b^10*B*d ^4*e^2)*x^14+1/13*((210*A*a^4*b^6+252*B*a^5*b^5)*e^6+6*(120*A*a^3*b^7+210* B*a^4*b^6)*d*e^5+15*(45*A*a^2*b^8+120*B*a^3*b^7)*d^2*e^4+20*(10*A*a*b^9+45 *B*a^2*b^8)*d^3*e^3+15*(A*b^10+10*B*a*b^9)*d^4*e^2+6*b^10*B*d^5*e)*x^13+1/ 12*((252*A*a^5*b^5+210*B*a^6*b^4)*e^6+6*(210*A*a^4*b^6+252*B*a^5*b^5)*d*e^ 5+15*(120*A*a^3*b^7+210*B*a^4*b^6)*d^2*e^4+20*(45*A*a^2*b^8+120*B*a^3*b^7) *d^3*e^3+15*(10*A*a*b^9+45*B*a^2*b^8)*d^4*e^2+6*(A*b^10+10*B*a*b^9)*d^5*e+ b^10*B*d^6)*x^12+1/11*((210*A*a^6*b^4+120*B*a^7*b^3)*e^6+6*(252*A*a^5*b^5+ 210*B*a^6*b^4)*d*e^5+15*(210*A*a^4*b^6+252*B*a^5*b^5)*d^2*e^4+20*(120*A*a^ 3*b^7+210*B*a^4*b^6)*d^3*e^3+15*(45*A*a^2*b^8+120*B*a^3*b^7)*d^4*e^2+6*(10 *A*a*b^9+45*B*a^2*b^8)*d^5*e+(A*b^10+10*B*a*b^9)*d^6)*x^11+1/10*((120*A*a^ 7*b^3+45*B*a^8*b^2)*e^6+6*(210*A*a^6*b^4+120*B*a^7*b^3)*d*e^5+15*(252*A*a^ 5*b^5+210*B*a^6*b^4)*d^2*e^4+20*(210*A*a^4*b^6+252*B*a^5*b^5)*d^3*e^3+15*( 120*A*a^3*b^7+210*B*a^4*b^6)*d^4*e^2+6*(45*A*a^2*b^8+120*B*a^3*b^7)*d^5*e+ (10*A*a*b^9+45*B*a^2*b^8)*d^6)*x^10+1/9*((45*A*a^8*b^2+10*B*a^9*b)*e^6+...
Leaf count of result is larger than twice the leaf count of optimal. 1917 vs. \(2 (274) = 548\).
Time = 0.23 (sec) , antiderivative size = 1917, normalized size of antiderivative = 6.61 \[ \int (a+b x)^{10} (A+B x) (d+e x)^6 \, dx=\text {Too large to display} \]
1/18*B*b^10*e^6*x^18 + A*a^10*d^6*x + 1/17*(6*B*b^10*d*e^5 + (10*B*a*b^9 + A*b^10)*e^6)*x^17 + 1/16*(15*B*b^10*d^2*e^4 + 6*(10*B*a*b^9 + A*b^10)*d*e ^5 + 5*(9*B*a^2*b^8 + 2*A*a*b^9)*e^6)*x^16 + 1/3*(4*B*b^10*d^3*e^3 + 3*(10 *B*a*b^9 + A*b^10)*d^2*e^4 + 6*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^5 + 3*(8*B*a^ 3*b^7 + 3*A*a^2*b^8)*e^6)*x^15 + 5/14*(3*B*b^10*d^4*e^2 + 4*(10*B*a*b^9 + A*b^10)*d^3*e^3 + 15*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^4 + 18*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^5 + 6*(7*B*a^4*b^6 + 4*A*a^3*b^7)*e^6)*x^14 + 1/13*(6*B* b^10*d^5*e + 15*(10*B*a*b^9 + A*b^10)*d^4*e^2 + 100*(9*B*a^2*b^8 + 2*A*a*b ^9)*d^3*e^3 + 225*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^4 + 180*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^5 + 42*(6*B*a^5*b^5 + 5*A*a^4*b^6)*e^6)*x^13 + 1/12*(B*b ^10*d^6 + 6*(10*B*a*b^9 + A*b^10)*d^5*e + 75*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4 *e^2 + 300*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^3 + 450*(7*B*a^4*b^6 + 4*A*a^ 3*b^7)*d^2*e^4 + 252*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^5 + 42*(5*B*a^6*b^4 + 6*A*a^5*b^5)*e^6)*x^12 + 1/11*((10*B*a*b^9 + A*b^10)*d^6 + 30*(9*B*a^2*b^ 8 + 2*A*a*b^9)*d^5*e + 225*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^2 + 600*(7*B* a^4*b^6 + 4*A*a^3*b^7)*d^3*e^3 + 630*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^4 + 252*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*e^5 + 30*(4*B*a^7*b^3 + 7*A*a^6*b^4)*e^ 6)*x^11 + 1/2*((9*B*a^2*b^8 + 2*A*a*b^9)*d^6 + 18*(8*B*a^3*b^7 + 3*A*a^2*b ^8)*d^5*e + 90*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^2 + 168*(6*B*a^5*b^5 + 5* A*a^4*b^6)*d^3*e^3 + 126*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^4 + 36*(4*B*...
Leaf count of result is larger than twice the leaf count of optimal. 2424 vs. \(2 (296) = 592\).
Time = 0.14 (sec) , antiderivative size = 2424, normalized size of antiderivative = 8.36 \[ \int (a+b x)^{10} (A+B x) (d+e x)^6 \, dx=\text {Too large to display} \]
A*a**10*d**6*x + B*b**10*e**6*x**18/18 + x**17*(A*b**10*e**6/17 + 10*B*a*b **9*e**6/17 + 6*B*b**10*d*e**5/17) + x**16*(5*A*a*b**9*e**6/8 + 3*A*b**10* d*e**5/8 + 45*B*a**2*b**8*e**6/16 + 15*B*a*b**9*d*e**5/4 + 15*B*b**10*d**2 *e**4/16) + x**15*(3*A*a**2*b**8*e**6 + 4*A*a*b**9*d*e**5 + A*b**10*d**2*e **4 + 8*B*a**3*b**7*e**6 + 18*B*a**2*b**8*d*e**5 + 10*B*a*b**9*d**2*e**4 + 4*B*b**10*d**3*e**3/3) + x**14*(60*A*a**3*b**7*e**6/7 + 135*A*a**2*b**8*d *e**5/7 + 75*A*a*b**9*d**2*e**4/7 + 10*A*b**10*d**3*e**3/7 + 15*B*a**4*b** 6*e**6 + 360*B*a**3*b**7*d*e**5/7 + 675*B*a**2*b**8*d**2*e**4/14 + 100*B*a *b**9*d**3*e**3/7 + 15*B*b**10*d**4*e**2/14) + x**13*(210*A*a**4*b**6*e**6 /13 + 720*A*a**3*b**7*d*e**5/13 + 675*A*a**2*b**8*d**2*e**4/13 + 200*A*a*b **9*d**3*e**3/13 + 15*A*b**10*d**4*e**2/13 + 252*B*a**5*b**5*e**6/13 + 126 0*B*a**4*b**6*d*e**5/13 + 1800*B*a**3*b**7*d**2*e**4/13 + 900*B*a**2*b**8* d**3*e**3/13 + 150*B*a*b**9*d**4*e**2/13 + 6*B*b**10*d**5*e/13) + x**12*(2 1*A*a**5*b**5*e**6 + 105*A*a**4*b**6*d*e**5 + 150*A*a**3*b**7*d**2*e**4 + 75*A*a**2*b**8*d**3*e**3 + 25*A*a*b**9*d**4*e**2/2 + A*b**10*d**5*e/2 + 35 *B*a**6*b**4*e**6/2 + 126*B*a**5*b**5*d*e**5 + 525*B*a**4*b**6*d**2*e**4/2 + 200*B*a**3*b**7*d**3*e**3 + 225*B*a**2*b**8*d**4*e**2/4 + 5*B*a*b**9*d* *5*e + B*b**10*d**6/12) + x**11*(210*A*a**6*b**4*e**6/11 + 1512*A*a**5*b** 5*d*e**5/11 + 3150*A*a**4*b**6*d**2*e**4/11 + 2400*A*a**3*b**7*d**3*e**3/1 1 + 675*A*a**2*b**8*d**4*e**2/11 + 60*A*a*b**9*d**5*e/11 + A*b**10*d**6...
Leaf count of result is larger than twice the leaf count of optimal. 1917 vs. \(2 (274) = 548\).
Time = 0.22 (sec) , antiderivative size = 1917, normalized size of antiderivative = 6.61 \[ \int (a+b x)^{10} (A+B x) (d+e x)^6 \, dx=\text {Too large to display} \]
1/18*B*b^10*e^6*x^18 + A*a^10*d^6*x + 1/17*(6*B*b^10*d*e^5 + (10*B*a*b^9 + A*b^10)*e^6)*x^17 + 1/16*(15*B*b^10*d^2*e^4 + 6*(10*B*a*b^9 + A*b^10)*d*e ^5 + 5*(9*B*a^2*b^8 + 2*A*a*b^9)*e^6)*x^16 + 1/3*(4*B*b^10*d^3*e^3 + 3*(10 *B*a*b^9 + A*b^10)*d^2*e^4 + 6*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^5 + 3*(8*B*a^ 3*b^7 + 3*A*a^2*b^8)*e^6)*x^15 + 5/14*(3*B*b^10*d^4*e^2 + 4*(10*B*a*b^9 + A*b^10)*d^3*e^3 + 15*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^4 + 18*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^5 + 6*(7*B*a^4*b^6 + 4*A*a^3*b^7)*e^6)*x^14 + 1/13*(6*B* b^10*d^5*e + 15*(10*B*a*b^9 + A*b^10)*d^4*e^2 + 100*(9*B*a^2*b^8 + 2*A*a*b ^9)*d^3*e^3 + 225*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^4 + 180*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^5 + 42*(6*B*a^5*b^5 + 5*A*a^4*b^6)*e^6)*x^13 + 1/12*(B*b ^10*d^6 + 6*(10*B*a*b^9 + A*b^10)*d^5*e + 75*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4 *e^2 + 300*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^3 + 450*(7*B*a^4*b^6 + 4*A*a^ 3*b^7)*d^2*e^4 + 252*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^5 + 42*(5*B*a^6*b^4 + 6*A*a^5*b^5)*e^6)*x^12 + 1/11*((10*B*a*b^9 + A*b^10)*d^6 + 30*(9*B*a^2*b^ 8 + 2*A*a*b^9)*d^5*e + 225*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^2 + 600*(7*B* a^4*b^6 + 4*A*a^3*b^7)*d^3*e^3 + 630*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^4 + 252*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*e^5 + 30*(4*B*a^7*b^3 + 7*A*a^6*b^4)*e^ 6)*x^11 + 1/2*((9*B*a^2*b^8 + 2*A*a*b^9)*d^6 + 18*(8*B*a^3*b^7 + 3*A*a^2*b ^8)*d^5*e + 90*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^2 + 168*(6*B*a^5*b^5 + 5* A*a^4*b^6)*d^3*e^3 + 126*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^4 + 36*(4*B*...
Leaf count of result is larger than twice the leaf count of optimal. 2407 vs. \(2 (274) = 548\).
Time = 0.29 (sec) , antiderivative size = 2407, normalized size of antiderivative = 8.30 \[ \int (a+b x)^{10} (A+B x) (d+e x)^6 \, dx=\text {Too large to display} \]
1/18*B*b^10*e^6*x^18 + 6/17*B*b^10*d*e^5*x^17 + 10/17*B*a*b^9*e^6*x^17 + 1 /17*A*b^10*e^6*x^17 + 15/16*B*b^10*d^2*e^4*x^16 + 15/4*B*a*b^9*d*e^5*x^16 + 3/8*A*b^10*d*e^5*x^16 + 45/16*B*a^2*b^8*e^6*x^16 + 5/8*A*a*b^9*e^6*x^16 + 4/3*B*b^10*d^3*e^3*x^15 + 10*B*a*b^9*d^2*e^4*x^15 + A*b^10*d^2*e^4*x^15 + 18*B*a^2*b^8*d*e^5*x^15 + 4*A*a*b^9*d*e^5*x^15 + 8*B*a^3*b^7*e^6*x^15 + 3*A*a^2*b^8*e^6*x^15 + 15/14*B*b^10*d^4*e^2*x^14 + 100/7*B*a*b^9*d^3*e^3*x ^14 + 10/7*A*b^10*d^3*e^3*x^14 + 675/14*B*a^2*b^8*d^2*e^4*x^14 + 75/7*A*a* b^9*d^2*e^4*x^14 + 360/7*B*a^3*b^7*d*e^5*x^14 + 135/7*A*a^2*b^8*d*e^5*x^14 + 15*B*a^4*b^6*e^6*x^14 + 60/7*A*a^3*b^7*e^6*x^14 + 6/13*B*b^10*d^5*e*x^1 3 + 150/13*B*a*b^9*d^4*e^2*x^13 + 15/13*A*b^10*d^4*e^2*x^13 + 900/13*B*a^2 *b^8*d^3*e^3*x^13 + 200/13*A*a*b^9*d^3*e^3*x^13 + 1800/13*B*a^3*b^7*d^2*e^ 4*x^13 + 675/13*A*a^2*b^8*d^2*e^4*x^13 + 1260/13*B*a^4*b^6*d*e^5*x^13 + 72 0/13*A*a^3*b^7*d*e^5*x^13 + 252/13*B*a^5*b^5*e^6*x^13 + 210/13*A*a^4*b^6*e ^6*x^13 + 1/12*B*b^10*d^6*x^12 + 5*B*a*b^9*d^5*e*x^12 + 1/2*A*b^10*d^5*e*x ^12 + 225/4*B*a^2*b^8*d^4*e^2*x^12 + 25/2*A*a*b^9*d^4*e^2*x^12 + 200*B*a^3 *b^7*d^3*e^3*x^12 + 75*A*a^2*b^8*d^3*e^3*x^12 + 525/2*B*a^4*b^6*d^2*e^4*x^ 12 + 150*A*a^3*b^7*d^2*e^4*x^12 + 126*B*a^5*b^5*d*e^5*x^12 + 105*A*a^4*b^6 *d*e^5*x^12 + 35/2*B*a^6*b^4*e^6*x^12 + 21*A*a^5*b^5*e^6*x^12 + 10/11*B*a* b^9*d^6*x^11 + 1/11*A*b^10*d^6*x^11 + 270/11*B*a^2*b^8*d^5*e*x^11 + 60/11* A*a*b^9*d^5*e*x^11 + 1800/11*B*a^3*b^7*d^4*e^2*x^11 + 675/11*A*a^2*b^8*...
Time = 2.30 (sec) , antiderivative size = 2001, normalized size of antiderivative = 6.90 \[ \int (a+b x)^{10} (A+B x) (d+e x)^6 \, dx=\text {Too large to display} \]
x^6*(A*a^10*d*e^5 + 42*A*a^5*b^5*d^6 + 35*B*a^6*b^4*d^6 + (5*B*a^10*d^2*e^ 4)/2 + 210*A*a^6*b^4*d^5*e + 25*A*a^9*b*d^2*e^4 + 120*B*a^7*b^3*d^5*e + (1 00*B*a^9*b*d^3*e^3)/3 + 300*A*a^7*b^3*d^4*e^2 + 150*A*a^8*b^2*d^3*e^3 + (2 25*B*a^8*b^2*d^4*e^2)/2) + x^13*((6*B*b^10*d^5*e)/13 + (210*A*a^4*b^6*e^6) /13 + (252*B*a^5*b^5*e^6)/13 + (15*A*b^10*d^4*e^2)/13 + (200*A*a*b^9*d^3*e ^3)/13 + (720*A*a^3*b^7*d*e^5)/13 + (150*B*a*b^9*d^4*e^2)/13 + (1260*B*a^4 *b^6*d*e^5)/13 + (675*A*a^2*b^8*d^2*e^4)/13 + (900*B*a^2*b^8*d^3*e^3)/13 + (1800*B*a^3*b^7*d^2*e^4)/13) + x^5*(42*A*a^6*b^4*d^6 + 24*B*a^7*b^3*d^6 + 3*A*a^10*d^2*e^4 + 4*B*a^10*d^3*e^3 + 144*A*a^7*b^3*d^5*e + 40*A*a^9*b*d^ 3*e^3 + 54*B*a^8*b^2*d^5*e + 30*B*a^9*b*d^4*e^2 + 135*A*a^8*b^2*d^4*e^2) + x^14*((60*A*a^3*b^7*e^6)/7 + 15*B*a^4*b^6*e^6 + (10*A*b^10*d^3*e^3)/7 + ( 15*B*b^10*d^4*e^2)/14 + (75*A*a*b^9*d^2*e^4)/7 + (135*A*a^2*b^8*d*e^5)/7 + (100*B*a*b^9*d^3*e^3)/7 + (360*B*a^3*b^7*d*e^5)/7 + (675*B*a^2*b^8*d^2*e^ 4)/14) + x^7*((A*a^10*e^6)/7 + (6*B*a^10*d*e^5)/7 + 30*A*a^4*b^6*d^6 + 36* B*a^5*b^5*d^6 + 216*A*a^5*b^5*d^5*e + 180*B*a^6*b^4*d^5*e + (150*B*a^9*b*d ^2*e^4)/7 + 450*A*a^6*b^4*d^4*e^2 + (2400*A*a^7*b^3*d^3*e^3)/7 + (675*A*a^ 8*b^2*d^2*e^4)/7 + (1800*B*a^7*b^3*d^4*e^2)/7 + (900*B*a^8*b^2*d^3*e^3)/7 + (60*A*a^9*b*d*e^5)/7) + x^12*((B*b^10*d^6)/12 + (A*b^10*d^5*e)/2 + 21*A* a^5*b^5*e^6 + (35*B*a^6*b^4*e^6)/2 + (25*A*a*b^9*d^4*e^2)/2 + 105*A*a^4*b^ 6*d*e^5 + 126*B*a^5*b^5*d*e^5 + 75*A*a^2*b^8*d^3*e^3 + 150*A*a^3*b^7*d^...