Integrand size = 20, antiderivative size = 447 \[ \int \frac {(a+b x)^{10} (A+B x)}{(d+e x)^7} \, dx=\frac {30 b^6 (b d-a e)^3 (11 b B d-4 A b e-7 a B e) x}{e^{11}}+\frac {(b d-a e)^{10} (B d-A e)}{6 e^{12} (d+e x)^6}-\frac {(b d-a e)^9 (11 b B d-10 A b e-a B e)}{5 e^{12} (d+e x)^5}+\frac {5 b (b d-a e)^8 (11 b B d-9 A b e-2 a B e)}{4 e^{12} (d+e x)^4}-\frac {5 b^2 (b d-a e)^7 (11 b B d-8 A b e-3 a B e)}{e^{12} (d+e x)^3}+\frac {15 b^3 (b d-a e)^6 (11 b B d-7 A b e-4 a B e)}{e^{12} (d+e x)^2}-\frac {42 b^4 (b d-a e)^5 (11 b B d-6 A b e-5 a B e)}{e^{12} (d+e x)}-\frac {15 b^7 (b d-a e)^2 (11 b B d-3 A b e-8 a B e) (d+e x)^2}{2 e^{12}}+\frac {5 b^8 (b d-a e) (11 b B d-2 A b e-9 a B e) (d+e x)^3}{3 e^{12}}-\frac {b^9 (11 b B d-A b e-10 a B e) (d+e x)^4}{4 e^{12}}+\frac {b^{10} B (d+e x)^5}{5 e^{12}}-\frac {42 b^5 (b d-a e)^4 (11 b B d-5 A b e-6 a B e) \log (d+e x)}{e^{12}} \]
30*b^6*(-a*e+b*d)^3*(-4*A*b*e-7*B*a*e+11*B*b*d)*x/e^11+1/6*(-a*e+b*d)^10*( -A*e+B*d)/e^12/(e*x+d)^6-1/5*(-a*e+b*d)^9*(-10*A*b*e-B*a*e+11*B*b*d)/e^12/ (e*x+d)^5+5/4*b*(-a*e+b*d)^8*(-9*A*b*e-2*B*a*e+11*B*b*d)/e^12/(e*x+d)^4-5* b^2*(-a*e+b*d)^7*(-8*A*b*e-3*B*a*e+11*B*b*d)/e^12/(e*x+d)^3+15*b^3*(-a*e+b *d)^6*(-7*A*b*e-4*B*a*e+11*B*b*d)/e^12/(e*x+d)^2-42*b^4*(-a*e+b*d)^5*(-6*A *b*e-5*B*a*e+11*B*b*d)/e^12/(e*x+d)-15/2*b^7*(-a*e+b*d)^2*(-3*A*b*e-8*B*a* e+11*B*b*d)*(e*x+d)^2/e^12+5/3*b^8*(-a*e+b*d)*(-2*A*b*e-9*B*a*e+11*B*b*d)* (e*x+d)^3/e^12-1/4*b^9*(-A*b*e-10*B*a*e+11*B*b*d)*(e*x+d)^4/e^12+1/5*b^10* B*(e*x+d)^5/e^12-42*b^5*(-a*e+b*d)^4*(-5*A*b*e-6*B*a*e+11*B*b*d)*ln(e*x+d) /e^12
Time = 0.30 (sec) , antiderivative size = 505, normalized size of antiderivative = 1.13 \[ \int \frac {(a+b x)^{10} (A+B x)}{(d+e x)^7} \, dx=\frac {-60 b^6 e \left (-210 a^4 B e^4-42 b^4 d^3 (5 B d-2 A e)+280 a b^3 d^2 e (3 B d-A e)-315 a^2 b^2 d e^2 (4 B d-A e)-120 a^3 b e^3 (-7 B d+A e)\right ) x+30 b^7 e^2 \left (120 a^3 B e^3+70 a b^2 d e (4 B d-A e)+45 a^2 b e^2 (-7 B d+A e)+28 b^3 d^2 (-3 B d+A e)\right ) x^2-20 b^8 e^3 \left (-45 a^2 B e^2-10 a b e (-7 B d+A e)+7 b^2 d (-4 B d+A e)\right ) x^3+15 b^9 e^4 (-7 b B d+A b e+10 a B e) x^4+12 b^{10} B e^5 x^5+\frac {10 (b d-a e)^{10} (B d-A e)}{(d+e x)^6}-\frac {12 (b d-a e)^9 (11 b B d-10 A b e-a B e)}{(d+e x)^5}+\frac {75 b (b d-a e)^8 (11 b B d-9 A b e-2 a B e)}{(d+e x)^4}-\frac {300 b^2 (b d-a e)^7 (11 b B d-8 A b e-3 a B e)}{(d+e x)^3}+\frac {900 b^3 (b d-a e)^6 (11 b B d-7 A b e-4 a B e)}{(d+e x)^2}-\frac {2520 b^4 (b d-a e)^5 (11 b B d-6 A b e-5 a B e)}{d+e x}-2520 b^5 (b d-a e)^4 (11 b B d-5 A b e-6 a B e) \log (d+e x)}{60 e^{12}} \]
(-60*b^6*e*(-210*a^4*B*e^4 - 42*b^4*d^3*(5*B*d - 2*A*e) + 280*a*b^3*d^2*e* (3*B*d - A*e) - 315*a^2*b^2*d*e^2*(4*B*d - A*e) - 120*a^3*b*e^3*(-7*B*d + A*e))*x + 30*b^7*e^2*(120*a^3*B*e^3 + 70*a*b^2*d*e*(4*B*d - A*e) + 45*a^2* b*e^2*(-7*B*d + A*e) + 28*b^3*d^2*(-3*B*d + A*e))*x^2 - 20*b^8*e^3*(-45*a^ 2*B*e^2 - 10*a*b*e*(-7*B*d + A*e) + 7*b^2*d*(-4*B*d + A*e))*x^3 + 15*b^9*e ^4*(-7*b*B*d + A*b*e + 10*a*B*e)*x^4 + 12*b^10*B*e^5*x^5 + (10*(b*d - a*e) ^10*(B*d - A*e))/(d + e*x)^6 - (12*(b*d - a*e)^9*(11*b*B*d - 10*A*b*e - a* B*e))/(d + e*x)^5 + (75*b*(b*d - a*e)^8*(11*b*B*d - 9*A*b*e - 2*a*B*e))/(d + e*x)^4 - (300*b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b*e - 3*a*B*e))/(d + e* x)^3 + (900*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*e - 4*a*B*e))/(d + e*x)^2 - (2520*b^4*(b*d - a*e)^5*(11*b*B*d - 6*A*b*e - 5*a*B*e))/(d + e*x) - 2520 *b^5*(b*d - a*e)^4*(11*b*B*d - 5*A*b*e - 6*a*B*e)*Log[d + e*x])/(60*e^12)
Time = 1.26 (sec) , antiderivative size = 447, 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.
| \(\displaystyle \int \frac {(a+b x)^{10} (A+B x)}{(d+e x)^7} \, dx\) |
| \(\Big \downarrow \) 86 |
| \(\displaystyle \int \left (\frac {b^9 (d+e x)^3 (10 a B e+A b e-11 b B d)}{e^{11}}-\frac {5 b^8 (d+e x)^2 (b d-a e) (9 a B e+2 A b e-11 b B d)}{e^{11}}+\frac {15 b^7 (d+e x) (b d-a e)^2 (8 a B e+3 A b e-11 b B d)}{e^{11}}-\frac {30 b^6 (b d-a e)^3 (7 a B e+4 A b e-11 b B d)}{e^{11}}+\frac {42 b^5 (b d-a e)^4 (6 a B e+5 A b e-11 b B d)}{e^{11} (d+e x)}-\frac {42 b^4 (b d-a e)^5 (5 a B e+6 A b e-11 b B d)}{e^{11} (d+e x)^2}+\frac {30 b^3 (b d-a e)^6 (4 a B e+7 A b e-11 b B d)}{e^{11} (d+e x)^3}-\frac {15 b^2 (b d-a e)^7 (3 a B e+8 A b e-11 b B d)}{e^{11} (d+e x)^4}+\frac {5 b (b d-a e)^8 (2 a B e+9 A b e-11 b B d)}{e^{11} (d+e x)^5}+\frac {(a e-b d)^9 (a B e+10 A b e-11 b B d)}{e^{11} (d+e x)^6}+\frac {(a e-b d)^{10} (A e-B d)}{e^{11} (d+e x)^7}+\frac {b^{10} B (d+e x)^4}{e^{11}}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\frac {b^9 (d+e x)^4 (-10 a B e-A b e+11 b B d)}{4 e^{12}}+\frac {5 b^8 (d+e x)^3 (b d-a e) (-9 a B e-2 A b e+11 b B d)}{3 e^{12}}-\frac {15 b^7 (d+e x)^2 (b d-a e)^2 (-8 a B e-3 A b e+11 b B d)}{2 e^{12}}+\frac {30 b^6 x (b d-a e)^3 (-7 a B e-4 A b e+11 b B d)}{e^{11}}-\frac {42 b^5 (b d-a e)^4 \log (d+e x) (-6 a B e-5 A b e+11 b B d)}{e^{12}}-\frac {42 b^4 (b d-a e)^5 (-5 a B e-6 A b e+11 b B d)}{e^{12} (d+e x)}+\frac {15 b^3 (b d-a e)^6 (-4 a B e-7 A b e+11 b B d)}{e^{12} (d+e x)^2}-\frac {5 b^2 (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{e^{12} (d+e x)^3}+\frac {5 b (b d-a e)^8 (-2 a B e-9 A b e+11 b B d)}{4 e^{12} (d+e x)^4}-\frac {(b d-a e)^9 (-a B e-10 A b e+11 b B d)}{5 e^{12} (d+e x)^5}+\frac {(b d-a e)^{10} (B d-A e)}{6 e^{12} (d+e x)^6}+\frac {b^{10} B (d+e x)^5}{5 e^{12}}\) |
(30*b^6*(b*d - a*e)^3*(11*b*B*d - 4*A*b*e - 7*a*B*e)*x)/e^11 + ((b*d - a*e )^10*(B*d - A*e))/(6*e^12*(d + e*x)^6) - ((b*d - a*e)^9*(11*b*B*d - 10*A*b *e - a*B*e))/(5*e^12*(d + e*x)^5) + (5*b*(b*d - a*e)^8*(11*b*B*d - 9*A*b*e - 2*a*B*e))/(4*e^12*(d + e*x)^4) - (5*b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b *e - 3*a*B*e))/(e^12*(d + e*x)^3) + (15*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A* b*e - 4*a*B*e))/(e^12*(d + e*x)^2) - (42*b^4*(b*d - a*e)^5*(11*b*B*d - 6*A *b*e - 5*a*B*e))/(e^12*(d + e*x)) - (15*b^7*(b*d - a*e)^2*(11*b*B*d - 3*A* b*e - 8*a*B*e)*(d + e*x)^2)/(2*e^12) + (5*b^8*(b*d - a*e)*(11*b*B*d - 2*A* b*e - 9*a*B*e)*(d + e*x)^3)/(3*e^12) - (b^9*(11*b*B*d - A*b*e - 10*a*B*e)* (d + e*x)^4)/(4*e^12) + (b^10*B*(d + e*x)^5)/(5*e^12) - (42*b^5*(b*d - a*e )^4*(11*b*B*d - 5*A*b*e - 6*a*B*e)*Log[d + e*x])/e^12
3.11.95.3.1 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. \(1920\) vs. \(2(433)=866\).
Time = 2.14 (sec) , antiderivative size = 1921, normalized size of antiderivative = 4.30
| method | result | size |
| norman | \(\text {Expression too large to display}\) | \(1921\) |
| default | \(\text {Expression too large to display}\) | \(1974\) |
| risch | \(\text {Expression too large to display}\) | \(2036\) |
| parallelrisch | \(\text {Expression too large to display}\) | \(3755\) |
(-1/60*(10*A*a^10*e^11+20*A*a^9*b*d*e^10+45*A*a^8*b^2*d^2*e^9+120*A*a^7*b^ 3*d^3*e^8+420*A*a^6*b^4*d^4*e^7+2520*A*a^5*b^5*d^5*e^6-30870*A*a^4*b^6*d^6 *e^5+123480*A*a^3*b^7*d^7*e^4-185220*A*a^2*b^8*d^8*e^3+123480*A*a*b^9*d^9* e^2-30870*A*b^10*d^10*e+2*B*a^10*d*e^10+10*B*a^9*b*d^2*e^9+45*B*a^8*b^2*d^ 3*e^8+240*B*a^7*b^3*d^4*e^7+2100*B*a^6*b^4*d^5*e^6-37044*B*a^5*b^5*d^6*e^5 +216090*B*a^4*b^6*d^7*e^4-493920*B*a^3*b^7*d^8*e^3+555660*B*a^2*b^8*d^9*e^ 2-308700*B*a*b^9*d^10*e+67914*B*b^10*d^11)/e^12-6*(42*A*a^5*b^5*e^6-210*A* a^4*b^6*d*e^5+840*A*a^3*b^7*d^2*e^4-1260*A*a^2*b^8*d^3*e^3+840*A*a*b^9*d^4 *e^2-210*A*b^10*d^5*e+35*B*a^6*b^4*e^6-252*B*a^5*b^5*d*e^5+1470*B*a^4*b^6* d^2*e^4-3360*B*a^3*b^7*d^3*e^3+3780*B*a^2*b^8*d^4*e^2-2100*B*a*b^9*d^5*e+4 62*B*b^10*d^6)/e^7*x^5-15*(7*A*a^6*b^4*e^7+42*A*a^5*b^5*d*e^6-315*A*a^4*b^ 6*d^2*e^5+1260*A*a^3*b^7*d^3*e^4-1890*A*a^2*b^8*d^4*e^3+1260*A*a*b^9*d^5*e ^2-315*A*b^10*d^6*e+4*B*a^7*b^3*e^7+35*B*a^6*b^4*d*e^6-378*B*a^5*b^5*d^2*e ^5+2205*B*a^4*b^6*d^3*e^4-5040*B*a^3*b^7*d^4*e^3+5670*B*a^2*b^8*d^5*e^2-31 50*B*a*b^9*d^6*e+693*B*b^10*d^7)/e^8*x^4-5*(8*A*a^7*b^3*e^8+28*A*a^6*b^4*d *e^7+168*A*a^5*b^5*d^2*e^6-1540*A*a^4*b^6*d^3*e^5+6160*A*a^3*b^7*d^4*e^4-9 240*A*a^2*b^8*d^5*e^3+6160*A*a*b^9*d^6*e^2-1540*A*b^10*d^7*e+3*B*a^8*b^2*e ^8+16*B*a^7*b^3*d*e^7+140*B*a^6*b^4*d^2*e^6-1848*B*a^5*b^5*d^3*e^5+10780*B *a^4*b^6*d^4*e^4-24640*B*a^3*b^7*d^5*e^3+27720*B*a^2*b^8*d^6*e^2-15400*B*a *b^9*d^7*e+3388*B*b^10*d^8)/e^9*x^3-5/4*(9*A*a^8*b^2*e^9+24*A*a^7*b^3*d...
Leaf count of result is larger than twice the leaf count of optimal. 2850 vs. \(2 (433) = 866\).
Time = 0.30 (sec) , antiderivative size = 2850, normalized size of antiderivative = 6.38 \[ \int \frac {(a+b x)^{10} (A+B x)}{(d+e x)^7} \, dx=\text {Too large to display} \]
1/60*(12*B*b^10*e^11*x^11 - 20417*B*b^10*d^11 - 10*A*a^10*e^11 + 10655*(10 *B*a*b^9 + A*b^10)*d^10*e - 25090*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 + 3069 0*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 - 20070*(7*B*a^4*b^6 + 4*A*a^3*b^7)* d^7*e^4 + 6174*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 - 420*(5*B*a^6*b^4 + 6* A*a^5*b^5)*d^5*e^6 - 60*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 - 15*(3*B*a^8* b^2 + 8*A*a^7*b^3)*d^3*e^8 - 5*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 - 2*(B*a^ 10 + 10*A*a^9*b)*d*e^10 - 3*(11*B*b^10*d*e^10 - 5*(10*B*a*b^9 + A*b^10)*e^ 11)*x^10 + 10*(11*B*b^10*d^2*e^9 - 5*(10*B*a*b^9 + A*b^10)*d*e^10 + 10*(9* B*a^2*b^8 + 2*A*a*b^9)*e^11)*x^9 - 45*(11*B*b^10*d^3*e^8 - 5*(10*B*a*b^9 + A*b^10)*d^2*e^9 + 10*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^10 - 10*(8*B*a^3*b^7 + 3*A*a^2*b^8)*e^11)*x^8 + 360*(11*B*b^10*d^4*e^7 - 5*(10*B*a*b^9 + A*b^10) *d^3*e^8 + 10*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9 - 10*(8*B*a^3*b^7 + 3*A*a^ 2*b^8)*d*e^10 + 5*(7*B*a^4*b^6 + 4*A*a^3*b^7)*e^11)*x^7 + (47497*B*b^10*d^ 5*e^6 - 20215*(10*B*a*b^9 + A*b^10)*d^4*e^7 + 36650*(9*B*a^2*b^8 + 2*A*a*b ^9)*d^3*e^8 - 31050*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^9 + 10800*(7*B*a^4*b ^6 + 4*A*a^3*b^7)*d*e^10)*x^6 + 6*(19777*B*b^10*d^6*e^5 - 7615*(10*B*a*b^9 + A*b^10)*d^5*e^6 + 11450*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 - 5850*(8*B*a ^3*b^7 + 3*A*a^2*b^8)*d^3*e^8 - 1800*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9 + 2520*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^10 - 420*(5*B*a^6*b^4 + 6*A*a^5*b^5) *e^11)*x^5 + 15*(5917*B*b^10*d^7*e^4 - 1315*(10*B*a*b^9 + A*b^10)*d^6*e...
Timed out. \[ \int \frac {(a+b x)^{10} (A+B x)}{(d+e x)^7} \, dx=\text {Timed out} \]
Leaf count of result is larger than twice the leaf count of optimal. 1869 vs. \(2 (433) = 866\).
Time = 0.33 (sec) , antiderivative size = 1869, normalized size of antiderivative = 4.18 \[ \int \frac {(a+b x)^{10} (A+B x)}{(d+e x)^7} \, dx=\text {Too large to display} \]
-1/60*(20417*B*b^10*d^11 + 10*A*a^10*e^11 - 10655*(10*B*a*b^9 + A*b^10)*d^ 10*e + 25090*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 - 30690*(8*B*a^3*b^7 + 3*A* a^2*b^8)*d^8*e^3 + 20070*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 - 6174*(6*B*a ^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 + 420*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 + 60*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 + 15*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^ 3*e^8 + 5*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 + 2*(B*a^10 + 10*A*a^9*b)*d*e^ 10 + 2520*(11*B*b^10*d^6*e^5 - 6*(10*B*a*b^9 + A*b^10)*d^5*e^6 + 15*(9*B*a ^2*b^8 + 2*A*a*b^9)*d^4*e^7 - 20*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^8 + 15* (7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9 - 6*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^10 + (5*B*a^6*b^4 + 6*A*a^5*b^5)*e^11)*x^5 + 900*(143*B*b^10*d^7*e^4 - 77*(1 0*B*a*b^9 + A*b^10)*d^6*e^5 + 189*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^6 - 245* (8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^7 + 175*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3* e^8 - 63*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^9 + 7*(5*B*a^6*b^4 + 6*A*a^5*b^ 5)*d*e^10 + (4*B*a^7*b^3 + 7*A*a^6*b^4)*e^11)*x^4 + 300*(803*B*b^10*d^8*e^ 3 - 428*(10*B*a*b^9 + A*b^10)*d^7*e^4 + 1036*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6 *e^5 - 1316*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 + 910*(7*B*a^4*b^6 + 4*A*a ^3*b^7)*d^4*e^7 - 308*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^8 + 28*(5*B*a^6*b^ 4 + 6*A*a^5*b^5)*d^2*e^9 + 4*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*e^10 + (3*B*a^8 *b^2 + 8*A*a^7*b^3)*e^11)*x^3 + 75*(3025*B*b^10*d^9*e^2 - 1599*(10*B*a*b^9 + A*b^10)*d^8*e^3 + 3828*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4 - 4788*(8*B...
Leaf count of result is larger than twice the leaf count of optimal. 2009 vs. \(2 (433) = 866\).
Time = 0.33 (sec) , antiderivative size = 2009, normalized size of antiderivative = 4.49 \[ \int \frac {(a+b x)^{10} (A+B x)}{(d+e x)^7} \, dx=\text {Too large to display} \]
-42*(11*B*b^10*d^5 - 50*B*a*b^9*d^4*e - 5*A*b^10*d^4*e + 90*B*a^2*b^8*d^3* e^2 + 20*A*a*b^9*d^3*e^2 - 80*B*a^3*b^7*d^2*e^3 - 30*A*a^2*b^8*d^2*e^3 + 3 5*B*a^4*b^6*d*e^4 + 20*A*a^3*b^7*d*e^4 - 6*B*a^5*b^5*e^5 - 5*A*a^4*b^6*e^5 )*log(abs(e*x + d))/e^12 - 1/60*(20417*B*b^10*d^11 - 106550*B*a*b^9*d^10*e - 10655*A*b^10*d^10*e + 225810*B*a^2*b^8*d^9*e^2 + 50180*A*a*b^9*d^9*e^2 - 245520*B*a^3*b^7*d^8*e^3 - 92070*A*a^2*b^8*d^8*e^3 + 140490*B*a^4*b^6*d^ 7*e^4 + 80280*A*a^3*b^7*d^7*e^4 - 37044*B*a^5*b^5*d^6*e^5 - 30870*A*a^4*b^ 6*d^6*e^5 + 2100*B*a^6*b^4*d^5*e^6 + 2520*A*a^5*b^5*d^5*e^6 + 240*B*a^7*b^ 3*d^4*e^7 + 420*A*a^6*b^4*d^4*e^7 + 45*B*a^8*b^2*d^3*e^8 + 120*A*a^7*b^3*d ^3*e^8 + 10*B*a^9*b*d^2*e^9 + 45*A*a^8*b^2*d^2*e^9 + 2*B*a^10*d*e^10 + 20* A*a^9*b*d*e^10 + 10*A*a^10*e^11 + 2520*(11*B*b^10*d^6*e^5 - 60*B*a*b^9*d^5 *e^6 - 6*A*b^10*d^5*e^6 + 135*B*a^2*b^8*d^4*e^7 + 30*A*a*b^9*d^4*e^7 - 160 *B*a^3*b^7*d^3*e^8 - 60*A*a^2*b^8*d^3*e^8 + 105*B*a^4*b^6*d^2*e^9 + 60*A*a ^3*b^7*d^2*e^9 - 36*B*a^5*b^5*d*e^10 - 30*A*a^4*b^6*d*e^10 + 5*B*a^6*b^4*e ^11 + 6*A*a^5*b^5*e^11)*x^5 + 900*(143*B*b^10*d^7*e^4 - 770*B*a*b^9*d^6*e^ 5 - 77*A*b^10*d^6*e^5 + 1701*B*a^2*b^8*d^5*e^6 + 378*A*a*b^9*d^5*e^6 - 196 0*B*a^3*b^7*d^4*e^7 - 735*A*a^2*b^8*d^4*e^7 + 1225*B*a^4*b^6*d^3*e^8 + 700 *A*a^3*b^7*d^3*e^8 - 378*B*a^5*b^5*d^2*e^9 - 315*A*a^4*b^6*d^2*e^9 + 35*B* a^6*b^4*d*e^10 + 42*A*a^5*b^5*d*e^10 + 4*B*a^7*b^3*e^11 + 7*A*a^6*b^4*e^11 )*x^4 + 300*(803*B*b^10*d^8*e^3 - 4280*B*a*b^9*d^7*e^4 - 428*A*b^10*d^7...
Time = 1.85 (sec) , antiderivative size = 2252, normalized size of antiderivative = 5.04 \[ \int \frac {(a+b x)^{10} (A+B x)}{(d+e x)^7} \, dx=\text {Too large to display} \]
x*((7*d*((21*d^2*((A*b^10 + 10*B*a*b^9)/e^7 - (7*B*b^10*d)/e^8))/e^2 - (7* d*((7*d*((A*b^10 + 10*B*a*b^9)/e^7 - (7*B*b^10*d)/e^8))/e - (5*a*b^8*(2*A* b + 9*B*a))/e^7 + (21*B*b^10*d^2)/e^9))/e - (15*a^2*b^7*(3*A*b + 8*B*a))/e ^7 + (35*B*b^10*d^3)/e^10))/e - (35*d^3*((A*b^10 + 10*B*a*b^9)/e^7 - (7*B* b^10*d)/e^8))/e^3 + (21*d^2*((7*d*((A*b^10 + 10*B*a*b^9)/e^7 - (7*B*b^10*d )/e^8))/e - (5*a*b^8*(2*A*b + 9*B*a))/e^7 + (21*B*b^10*d^2)/e^9))/e^2 + (3 0*a^3*b^6*(4*A*b + 7*B*a))/e^7 - (35*B*b^10*d^4)/e^11) - x^3*((7*d*((A*b^1 0 + 10*B*a*b^9)/e^7 - (7*B*b^10*d)/e^8))/(3*e) - (5*a*b^8*(2*A*b + 9*B*a)) /(3*e^7) + (7*B*b^10*d^2)/e^9) - x^2*((21*d^2*((A*b^10 + 10*B*a*b^9)/e^7 - (7*B*b^10*d)/e^8))/(2*e^2) - (7*d*((7*d*((A*b^10 + 10*B*a*b^9)/e^7 - (7*B *b^10*d)/e^8))/e - (5*a*b^8*(2*A*b + 9*B*a))/e^7 + (21*B*b^10*d^2)/e^9))/( 2*e) - (15*a^2*b^7*(3*A*b + 8*B*a))/(2*e^7) + (35*B*b^10*d^3)/(2*e^10)) + x^4*((A*b^10 + 10*B*a*b^9)/(4*e^7) - (7*B*b^10*d)/(4*e^8)) - (x^4*(105*A*a ^6*b^4*e^10 + 60*B*a^7*b^3*e^10 - 1155*A*b^10*d^6*e^4 + 2145*B*b^10*d^7*e^ 3 + 5670*A*a*b^9*d^5*e^5 + 630*A*a^5*b^5*d*e^9 - 11550*B*a*b^9*d^6*e^4 + 5 25*B*a^6*b^4*d*e^9 - 11025*A*a^2*b^8*d^4*e^6 + 10500*A*a^3*b^7*d^3*e^7 - 4 725*A*a^4*b^6*d^2*e^8 + 25515*B*a^2*b^8*d^5*e^5 - 29400*B*a^3*b^7*d^4*e^6 + 18375*B*a^4*b^6*d^3*e^7 - 5670*B*a^5*b^5*d^2*e^8) + x^3*(40*A*a^7*b^3*e^ 10 + 15*B*a^8*b^2*e^10 - 2140*A*b^10*d^7*e^3 + 4015*B*b^10*d^8*e^2 + 10360 *A*a*b^9*d^6*e^4 + 140*A*a^6*b^4*d*e^9 - 21400*B*a*b^9*d^7*e^3 + 80*B*a...