3.11.91 \(\int \frac {(a+b x)^{10} (A+B x)}{(d+e x)^3} \, dx\) [1091]
Optimal. Leaf size=445 \[ \frac {15 b^2 (b d-a e)^7 (11 b B d-8 A b e-3 a B e) x}{e^{11}}+\frac {(b d-a e)^{10} (B d-A e)}{2 e^{12} (d+e x)^2}-\frac {(b d-a e)^9 (11 b B d-10 A b e-a B e)}{e^{12} (d+e x)}-\frac {15 b^3 (b d-a e)^6 (11 b B d-7 A b e-4 a B e) (d+e x)^2}{e^{12}}+\frac {14 b^4 (b d-a e)^5 (11 b B d-6 A b e-5 a B e) (d+e x)^3}{e^{12}}-\frac {21 b^5 (b d-a e)^4 (11 b B d-5 A b e-6 a B e) (d+e x)^4}{2 e^{12}}+\frac {6 b^6 (b d-a e)^3 (11 b B d-4 A b e-7 a B e) (d+e x)^5}{e^{12}}-\frac {5 b^7 (b d-a e)^2 (11 b B d-3 A b e-8 a B e) (d+e x)^6}{2 e^{12}}+\frac {5 b^8 (b d-a e) (11 b B d-2 A b e-9 a B e) (d+e x)^7}{7 e^{12}}-\frac {b^9 (11 b B d-A b e-10 a B e) (d+e x)^8}{8 e^{12}}+\frac {b^{10} B (d+e x)^9}{9 e^{12}}-\frac {5 b (b d-a e)^8 (11 b B d-9 A b e-2 a B e) \log (d+e x)}{e^{12}} \]
[Out]
15*b^2*(-a*e+b*d)^7*(-8*A*b*e-3*B*a*e+11*B*b*d)*x/e^11+1/2*(-a*e+b*d)^10*(-A*e+B*d)/e^12/(e*x+d)^2-(-a*e+b*d)^
9*(-10*A*b*e-B*a*e+11*B*b*d)/e^12/(e*x+d)-15*b^3*(-a*e+b*d)^6*(-7*A*b*e-4*B*a*e+11*B*b*d)*(e*x+d)^2/e^12+14*b^
4*(-a*e+b*d)^5*(-6*A*b*e-5*B*a*e+11*B*b*d)*(e*x+d)^3/e^12-21/2*b^5*(-a*e+b*d)^4*(-5*A*b*e-6*B*a*e+11*B*b*d)*(e
*x+d)^4/e^12+6*b^6*(-a*e+b*d)^3*(-4*A*b*e-7*B*a*e+11*B*b*d)*(e*x+d)^5/e^12-5/2*b^7*(-a*e+b*d)^2*(-3*A*b*e-8*B*
a*e+11*B*b*d)*(e*x+d)^6/e^12+5/7*b^8*(-a*e+b*d)*(-2*A*b*e-9*B*a*e+11*B*b*d)*(e*x+d)^7/e^12-1/8*b^9*(-A*b*e-10*
B*a*e+11*B*b*d)*(e*x+d)^8/e^12+1/9*b^10*B*(e*x+d)^9/e^12-5*b*(-a*e+b*d)^8*(-9*A*b*e-2*B*a*e+11*B*b*d)*ln(e*x+d
)/e^12
________________________________________________________________________________________
Rubi [A]
time = 0.96, antiderivative size = 445, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78}
\begin {gather*} -\frac {b^9 (d+e x)^8 (-10 a B e-A b e+11 b B d)}{8 e^{12}}+\frac {5 b^8 (d+e x)^7 (b d-a e) (-9 a B e-2 A b e+11 b B d)}{7 e^{12}}-\frac {5 b^7 (d+e x)^6 (b d-a e)^2 (-8 a B e-3 A b e+11 b B d)}{2 e^{12}}+\frac {6 b^6 (d+e x)^5 (b d-a e)^3 (-7 a B e-4 A b e+11 b B d)}{e^{12}}-\frac {21 b^5 (d+e x)^4 (b d-a e)^4 (-6 a B e-5 A b e+11 b B d)}{2 e^{12}}+\frac {14 b^4 (d+e x)^3 (b d-a e)^5 (-5 a B e-6 A b e+11 b B d)}{e^{12}}-\frac {15 b^3 (d+e x)^2 (b d-a e)^6 (-4 a B e-7 A b e+11 b B d)}{e^{12}}+\frac {15 b^2 x (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{e^{11}}-\frac {(b d-a e)^9 (-a B e-10 A b e+11 b B d)}{e^{12} (d+e x)}+\frac {(b d-a e)^{10} (B d-A e)}{2 e^{12} (d+e x)^2}-\frac {5 b (b d-a e)^8 \log (d+e x) (-2 a B e-9 A b e+11 b B d)}{e^{12}}+\frac {b^{10} B (d+e x)^9}{9 e^{12}} \end {gather*}
Antiderivative was successfully verified.
[In]
Int[((a + b*x)^10*(A + B*x))/(d + e*x)^3,x]
[Out]
(15*b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b*e - 3*a*B*e)*x)/e^11 + ((b*d - a*e)^10*(B*d - A*e))/(2*e^12*(d + e*x)^
2) - ((b*d - a*e)^9*(11*b*B*d - 10*A*b*e - a*B*e))/(e^12*(d + e*x)) - (15*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*
e - 4*a*B*e)*(d + e*x)^2)/e^12 + (14*b^4*(b*d - a*e)^5*(11*b*B*d - 6*A*b*e - 5*a*B*e)*(d + e*x)^3)/e^12 - (21*
b^5*(b*d - a*e)^4*(11*b*B*d - 5*A*b*e - 6*a*B*e)*(d + e*x)^4)/(2*e^12) + (6*b^6*(b*d - a*e)^3*(11*b*B*d - 4*A*
b*e - 7*a*B*e)*(d + e*x)^5)/e^12 - (5*b^7*(b*d - a*e)^2*(11*b*B*d - 3*A*b*e - 8*a*B*e)*(d + e*x)^6)/(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)^7)/(7*e^12) - (b^9*(11*b*B*d - A*b*e - 10*a*B*e)*
(d + e*x)^8)/(8*e^12) + (b^10*B*(d + e*x)^9)/(9*e^12) - (5*b*(b*d - a*e)^8*(11*b*B*d - 9*A*b*e - 2*a*B*e)*Log[
d + e*x])/e^12
Rule 78
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 \frac {(a+b x)^{10} (A+B x)}{(d+e x)^3} \, dx &=\int \left (-\frac {15 b^2 (b d-a e)^7 (-11 b B d+8 A b e+3 a B e)}{e^{11}}+\frac {(-b d+a e)^{10} (-B d+A e)}{e^{11} (d+e x)^3}+\frac {(-b d+a e)^9 (-11 b B d+10 A b e+a B e)}{e^{11} (d+e x)^2}+\frac {5 b (b d-a e)^8 (-11 b B d+9 A b e+2 a B e)}{e^{11} (d+e x)}+\frac {30 b^3 (b d-a e)^6 (-11 b B d+7 A b e+4 a B e) (d+e x)}{e^{11}}-\frac {42 b^4 (b d-a e)^5 (-11 b B d+6 A b e+5 a B e) (d+e x)^2}{e^{11}}+\frac {42 b^5 (b d-a e)^4 (-11 b B d+5 A b e+6 a B e) (d+e x)^3}{e^{11}}-\frac {30 b^6 (b d-a e)^3 (-11 b B d+4 A b e+7 a B e) (d+e x)^4}{e^{11}}+\frac {15 b^7 (b d-a e)^2 (-11 b B d+3 A b e+8 a B e) (d+e x)^5}{e^{11}}-\frac {5 b^8 (b d-a e) (-11 b B d+2 A b e+9 a B e) (d+e x)^6}{e^{11}}+\frac {b^9 (-11 b B d+A b e+10 a B e) (d+e x)^7}{e^{11}}+\frac {b^{10} B (d+e x)^8}{e^{11}}\right ) \, dx\\ &=\frac {15 b^2 (b d-a e)^7 (11 b B d-8 A b e-3 a B e) x}{e^{11}}+\frac {(b d-a e)^{10} (B d-A e)}{2 e^{12} (d+e x)^2}-\frac {(b d-a e)^9 (11 b B d-10 A b e-a B e)}{e^{12} (d+e x)}-\frac {15 b^3 (b d-a e)^6 (11 b B d-7 A b e-4 a B e) (d+e x)^2}{e^{12}}+\frac {14 b^4 (b d-a e)^5 (11 b B d-6 A b e-5 a B e) (d+e x)^3}{e^{12}}-\frac {21 b^5 (b d-a e)^4 (11 b B d-5 A b e-6 a B e) (d+e x)^4}{2 e^{12}}+\frac {6 b^6 (b d-a e)^3 (11 b B d-4 A b e-7 a B e) (d+e x)^5}{e^{12}}-\frac {5 b^7 (b d-a e)^2 (11 b B d-3 A b e-8 a B e) (d+e x)^6}{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)^7}{7 e^{12}}-\frac {b^9 (11 b B d-A b e-10 a B e) (d+e x)^8}{8 e^{12}}+\frac {b^{10} B (d+e x)^9}{9 e^{12}}-\frac {5 b (b d-a e)^8 (11 b B d-9 A b e-2 a B e) \log (d+e x)}{e^{12}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(1480\) vs. \(2(445)=890\).
time = 0.51, size = 1480, normalized size = 3.33 \begin {gather*} \frac {-252 a^{10} e^{10} (A e+B (d+2 e x))-2520 a^9 b e^9 (A e (d+2 e x)-B d (3 d+4 e x))+11340 a^8 b^2 e^8 \left (A d e (3 d+4 e x)+B \left (-5 d^3-4 d^2 e x+4 d e^2 x^2+2 e^3 x^3\right )\right )+30240 a^7 b^3 e^7 \left (A e \left (-5 d^3-4 d^2 e x+4 d e^2 x^2+2 e^3 x^3\right )+B \left (7 d^4+2 d^3 e x-11 d^2 e^2 x^2-4 d e^3 x^3+e^4 x^4\right )\right )+17640 a^6 b^4 e^6 \left (3 A e \left (7 d^4+2 d^3 e x-11 d^2 e^2 x^2-4 d e^3 x^3+e^4 x^4\right )+B \left (-27 d^5+6 d^4 e x+63 d^3 e^2 x^2+20 d^2 e^3 x^3-5 d e^4 x^4+2 e^5 x^5\right )\right )+10584 a^5 b^5 e^5 \left (2 A e \left (-27 d^5+6 d^4 e x+63 d^3 e^2 x^2+20 d^2 e^3 x^3-5 d e^4 x^4+2 e^5 x^5\right )+3 B \left (22 d^6-16 d^5 e x-68 d^4 e^2 x^2-20 d^3 e^3 x^3+5 d^2 e^4 x^4-2 d e^5 x^5+e^6 x^6\right )\right )+5292 a^4 b^6 e^4 \left (5 A e \left (22 d^6-16 d^5 e x-68 d^4 e^2 x^2-20 d^3 e^3 x^3+5 d^2 e^4 x^4-2 d e^5 x^5+e^6 x^6\right )+B \left (-130 d^7+160 d^6 e x+500 d^5 e^2 x^2+140 d^4 e^3 x^3-35 d^3 e^4 x^4+14 d^2 e^5 x^5-7 d e^6 x^6+4 e^7 x^7\right )\right )+1008 a^3 b^7 e^3 \left (3 A e \left (-130 d^7+160 d^6 e x+500 d^5 e^2 x^2+140 d^4 e^3 x^3-35 d^3 e^4 x^4+14 d^2 e^5 x^5-7 d e^6 x^6+4 e^7 x^7\right )+2 B \left (225 d^8-390 d^7 e x-1035 d^6 e^2 x^2-280 d^5 e^3 x^3+70 d^4 e^4 x^4-28 d^3 e^5 x^5+14 d^2 e^6 x^6-8 d e^7 x^7+5 e^8 x^8\right )\right )+108 a^2 b^8 e^2 \left (7 A e \left (225 d^8-390 d^7 e x-1035 d^6 e^2 x^2-280 d^5 e^3 x^3+70 d^4 e^4 x^4-28 d^3 e^5 x^5+14 d^2 e^6 x^6-8 d e^7 x^7+5 e^8 x^8\right )-3 B \left (595 d^9-1330 d^8 e x-3185 d^7 e^2 x^2-840 d^6 e^3 x^3+210 d^5 e^4 x^4-84 d^4 e^5 x^5+42 d^3 e^6 x^6-24 d^2 e^7 x^7+15 d e^8 x^8-10 e^9 x^9\right )\right )+18 a b^9 e \left (4 A e \left (-595 d^9+1330 d^8 e x+3185 d^7 e^2 x^2+840 d^6 e^3 x^3-210 d^5 e^4 x^4+84 d^4 e^5 x^5-42 d^3 e^6 x^6+24 d^2 e^7 x^7-15 d e^8 x^8+10 e^9 x^9\right )+5 B \left (532 d^{10}-1456 d^9 e x-3248 d^8 e^2 x^2-840 d^7 e^3 x^3+210 d^6 e^4 x^4-84 d^5 e^5 x^5+42 d^4 e^6 x^6-24 d^3 e^7 x^7+15 d^2 e^8 x^8-10 d e^9 x^9+7 e^{10} x^{10}\right )\right )+b^{10} \left (9 A e \left (532 d^{10}-1456 d^9 e x-3248 d^8 e^2 x^2-840 d^7 e^3 x^3+210 d^6 e^4 x^4-84 d^5 e^5 x^5+42 d^4 e^6 x^6-24 d^3 e^7 x^7+15 d^2 e^8 x^8-10 d e^9 x^9+7 e^{10} x^{10}\right )+B \left (-5292 d^{11}+17136 d^{10} e x+36288 d^9 e^2 x^2+9240 d^8 e^3 x^3-2310 d^7 e^4 x^4+924 d^6 e^5 x^5-462 d^5 e^6 x^6+264 d^4 e^7 x^7-165 d^3 e^8 x^8+110 d^2 e^9 x^9-77 d e^{10} x^{10}+56 e^{11} x^{11}\right )\right )-2520 b (b d-a e)^8 (11 b B d-9 A b e-2 a B e) (d+e x)^2 \log (d+e x)}{504 e^{12} (d+e x)^2} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[((a + b*x)^10*(A + B*x))/(d + e*x)^3,x]
[Out]
(-252*a^10*e^10*(A*e + B*(d + 2*e*x)) - 2520*a^9*b*e^9*(A*e*(d + 2*e*x) - B*d*(3*d + 4*e*x)) + 11340*a^8*b^2*e
^8*(A*d*e*(3*d + 4*e*x) + B*(-5*d^3 - 4*d^2*e*x + 4*d*e^2*x^2 + 2*e^3*x^3)) + 30240*a^7*b^3*e^7*(A*e*(-5*d^3 -
4*d^2*e*x + 4*d*e^2*x^2 + 2*e^3*x^3) + B*(7*d^4 + 2*d^3*e*x - 11*d^2*e^2*x^2 - 4*d*e^3*x^3 + e^4*x^4)) + 1764
0*a^6*b^4*e^6*(3*A*e*(7*d^4 + 2*d^3*e*x - 11*d^2*e^2*x^2 - 4*d*e^3*x^3 + e^4*x^4) + B*(-27*d^5 + 6*d^4*e*x + 6
3*d^3*e^2*x^2 + 20*d^2*e^3*x^3 - 5*d*e^4*x^4 + 2*e^5*x^5)) + 10584*a^5*b^5*e^5*(2*A*e*(-27*d^5 + 6*d^4*e*x + 6
3*d^3*e^2*x^2 + 20*d^2*e^3*x^3 - 5*d*e^4*x^4 + 2*e^5*x^5) + 3*B*(22*d^6 - 16*d^5*e*x - 68*d^4*e^2*x^2 - 20*d^3
*e^3*x^3 + 5*d^2*e^4*x^4 - 2*d*e^5*x^5 + e^6*x^6)) + 5292*a^4*b^6*e^4*(5*A*e*(22*d^6 - 16*d^5*e*x - 68*d^4*e^2
*x^2 - 20*d^3*e^3*x^3 + 5*d^2*e^4*x^4 - 2*d*e^5*x^5 + e^6*x^6) + B*(-130*d^7 + 160*d^6*e*x + 500*d^5*e^2*x^2 +
140*d^4*e^3*x^3 - 35*d^3*e^4*x^4 + 14*d^2*e^5*x^5 - 7*d*e^6*x^6 + 4*e^7*x^7)) + 1008*a^3*b^7*e^3*(3*A*e*(-130
*d^7 + 160*d^6*e*x + 500*d^5*e^2*x^2 + 140*d^4*e^3*x^3 - 35*d^3*e^4*x^4 + 14*d^2*e^5*x^5 - 7*d*e^6*x^6 + 4*e^7
*x^7) + 2*B*(225*d^8 - 390*d^7*e*x - 1035*d^6*e^2*x^2 - 280*d^5*e^3*x^3 + 70*d^4*e^4*x^4 - 28*d^3*e^5*x^5 + 14
*d^2*e^6*x^6 - 8*d*e^7*x^7 + 5*e^8*x^8)) + 108*a^2*b^8*e^2*(7*A*e*(225*d^8 - 390*d^7*e*x - 1035*d^6*e^2*x^2 -
280*d^5*e^3*x^3 + 70*d^4*e^4*x^4 - 28*d^3*e^5*x^5 + 14*d^2*e^6*x^6 - 8*d*e^7*x^7 + 5*e^8*x^8) - 3*B*(595*d^9 -
1330*d^8*e*x - 3185*d^7*e^2*x^2 - 840*d^6*e^3*x^3 + 210*d^5*e^4*x^4 - 84*d^4*e^5*x^5 + 42*d^3*e^6*x^6 - 24*d^
2*e^7*x^7 + 15*d*e^8*x^8 - 10*e^9*x^9)) + 18*a*b^9*e*(4*A*e*(-595*d^9 + 1330*d^8*e*x + 3185*d^7*e^2*x^2 + 840*
d^6*e^3*x^3 - 210*d^5*e^4*x^4 + 84*d^4*e^5*x^5 - 42*d^3*e^6*x^6 + 24*d^2*e^7*x^7 - 15*d*e^8*x^8 + 10*e^9*x^9)
+ 5*B*(532*d^10 - 1456*d^9*e*x - 3248*d^8*e^2*x^2 - 840*d^7*e^3*x^3 + 210*d^6*e^4*x^4 - 84*d^5*e^5*x^5 + 42*d^
4*e^6*x^6 - 24*d^3*e^7*x^7 + 15*d^2*e^8*x^8 - 10*d*e^9*x^9 + 7*e^10*x^10)) + b^10*(9*A*e*(532*d^10 - 1456*d^9*
e*x - 3248*d^8*e^2*x^2 - 840*d^7*e^3*x^3 + 210*d^6*e^4*x^4 - 84*d^5*e^5*x^5 + 42*d^4*e^6*x^6 - 24*d^3*e^7*x^7
+ 15*d^2*e^8*x^8 - 10*d*e^9*x^9 + 7*e^10*x^10) + B*(-5292*d^11 + 17136*d^10*e*x + 36288*d^9*e^2*x^2 + 9240*d^8
*e^3*x^3 - 2310*d^7*e^4*x^4 + 924*d^6*e^5*x^5 - 462*d^5*e^6*x^6 + 264*d^4*e^7*x^7 - 165*d^3*e^8*x^8 + 110*d^2*
e^9*x^9 - 77*d*e^10*x^10 + 56*e^11*x^11)) - 2520*b*(b*d - a*e)^8*(11*b*B*d - 9*A*b*e - 2*a*B*e)*(d + e*x)^2*Lo
g[d + e*x])/(504*e^12*(d + e*x)^2)
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(2116\) vs.
\(2(433)=866\).
time = 0.10, size = 2117, normalized size = 4.76
| | |
| method |
result |
size |
| | |
| norman |
\(\text {Expression too large to display}\) |
\(1902\) |
| default |
\(\text {Expression too large to display}\) |
\(2117\) |
| risch |
\(\text {Expression too large to display}\) |
\(2236\) |
| | |
|
|
|
|
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((b*x+a)^10*(B*x+A)/(e*x+d)^3,x,method=_RETURNVERBOSE)
[Out]
b^2/e^11*(-252*B*a^5*b^3*d*e^7*x^3+420*B*a^4*b^4*d^2*e^6*x^3-400*B*a^3*b^5*d^3*e^5*x^3+225*B*a^2*b^6*d^4*e^4*x
^3-70*B*a*b^7*d^5*e^3*x^3-378*A*a^5*b^3*d*e^7*x^2+630*A*a^4*b^4*d^2*e^6*x^2-600*A*a^3*b^5*d^3*e^5*x^2+675/2*A*
a^2*b^6*d^4*e^4*x^2-105*A*a*b^7*d^5*e^3*x^2-315*B*a^6*b^2*d*e^7*x^2+756*B*a^5*b^3*d^2*e^6*x^2-1050*B*a^4*b^4*d
^3*e^5*x^2+900*B*a^3*b^5*d^4*e^4*x^2-945/2*B*a^2*b^6*d^5*e^3*x^2+140*B*a*b^7*d^6*e^2*x^2-630*A*a^6*b^2*d*e^7*x
+1512*A*a^5*b^3*d^2*e^6*x-2100*A*a^4*b^4*d^3*e^5*x+1800*A*a^3*b^5*d^4*e^4*x-945*A*a^2*b^6*d^5*e^3*x+280*A*a*b^
7*d^6*e^2*x-360*B*a^7*b*d*e^7*x+1260*B*a^6*b^2*d^2*e^6*x-2520*B*a^5*b^3*d^3*e^5*x+3150*B*a^4*b^4*d^4*e^4*x-252
0*B*a^3*b^5*d^5*e^3*x+1260*B*a^2*b^6*d^6*e^2*x-360*B*a*b^7*d^7*e*x-45/2*B*a^2*b^6*d*e^7*x^6+10*B*a*b^7*d^2*e^6
*x^6-27*A*a^2*b^6*d*e^7*x^5+12*A*a*b^7*d^2*e^6*x^5+45*B*a^8*e^8*x+45*B*b^8*d^8*x+1/9*b^8*B*x^9*e^8+1/8*A*b^8*e
^8*x^8+A*b^8*d^2*e^6*x^6-18*B*b^8*d^7*e*x^2+120*A*a^7*b*e^8*x-36*A*b^8*d^7*e*x-30/7*B*a*b^7*d*e^7*x^7-5*A*a*b^
7*d*e^7*x^6-72*B*a^3*b^5*d*e^7*x^5+54*B*a^2*b^6*d^2*e^6*x^5-20*B*a*b^7*d^3*e^5*x^5-90*A*a^3*b^5*d*e^7*x^4+135/
2*A*a^2*b^6*d^2*e^6*x^4-25*A*a*b^7*d^3*e^5*x^4-315/2*B*a^4*b^4*d*e^7*x^4+180*B*a^3*b^5*d^2*e^6*x^4-225/2*B*a^2
*b^6*d^3*e^5*x^4+75/2*B*a*b^7*d^4*e^4*x^4-210*A*a^4*b^4*d*e^7*x^3+240*A*a^3*b^5*d^2*e^6*x^3-150*A*a^2*b^6*d^3*
e^5*x^3+50*A*a*b^7*d^4*e^4*x^3+5/4*B*a*b^7*e^8*x^8-3/8*B*b^8*d*e^7*x^8+10/7*A*a*b^7*e^8*x^7-3/7*A*b^8*d*e^7*x^
7+45/7*B*a^2*b^6*e^8*x^7+6/7*B*b^8*d^2*e^6*x^7+15/2*A*a^2*b^6*e^8*x^6+20*B*a^3*b^5*e^8*x^6-5/3*B*b^8*d^3*e^5*x
^6+24*A*a^3*b^5*e^8*x^5-2*A*b^8*d^3*e^5*x^5+42*B*a^4*b^4*e^8*x^5+3*B*b^8*d^4*e^4*x^5+105/2*A*a^4*b^4*e^8*x^4+1
5/4*A*b^8*d^4*e^4*x^4+63*B*a^5*b^3*e^8*x^4-21/4*B*b^8*d^5*e^3*x^4+84*A*a^5*b^3*e^8*x^3-7*A*b^8*d^5*e^3*x^3+70*
B*a^6*b^2*e^8*x^3+28/3*B*b^8*d^6*e^2*x^3+105*A*a^6*b^2*e^8*x^2+14*A*b^8*d^6*e^2*x^2+60*B*a^7*b*e^8*x^2)-1/2*(A
*a^10*e^11-10*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+210*A*a^6*b^4*d^4*e^7-252*A*a^5*b^5*d^
5*e^6+210*A*a^4*b^6*d^6*e^5-120*A*a^3*b^7*d^7*e^4+45*A*a^2*b^8*d^8*e^3-10*A*a*b^9*d^9*e^2+A*b^10*d^10*e-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+120*B*a^7*b^3*d^4*e^7-210*B*a^6*b^4*d^5*e^6+252*B*a^5*b^5*d^6*
e^5-210*B*a^4*b^6*d^7*e^4+120*B*a^3*b^7*d^8*e^3-45*B*a^2*b^8*d^9*e^2+10*B*a*b^9*d^10*e-B*b^10*d^11)/e^12/(e*x+
d)^2-1/e^12*(10*A*a^9*b*e^10-90*A*a^8*b^2*d*e^9+360*A*a^7*b^3*d^2*e^8-840*A*a^6*b^4*d^3*e^7+1260*A*a^5*b^5*d^4
*e^6-1260*A*a^4*b^6*d^5*e^5+840*A*a^3*b^7*d^6*e^4-360*A*a^2*b^8*d^7*e^3+90*A*a*b^9*d^8*e^2-10*A*b^10*d^9*e+B*a
^10*e^10-20*B*a^9*b*d*e^9+135*B*a^8*b^2*d^2*e^8-480*B*a^7*b^3*d^3*e^7+1050*B*a^6*b^4*d^4*e^6-1512*B*a^5*b^5*d^
5*e^5+1470*B*a^4*b^6*d^6*e^4-960*B*a^3*b^7*d^7*e^3+405*B*a^2*b^8*d^8*e^2-100*B*a*b^9*d^9*e+11*B*b^10*d^10)/(e*
x+d)+5*b/e^12*(9*A*a^8*b*e^9-72*A*a^7*b^2*d*e^8+252*A*a^6*b^3*d^2*e^7-504*A*a^5*b^4*d^3*e^6+630*A*a^4*b^5*d^4*
e^5-504*A*a^3*b^6*d^5*e^4+252*A*a^2*b^7*d^6*e^3-72*A*a*b^8*d^7*e^2+9*A*b^9*d^8*e+2*B*a^9*e^9-27*B*a^8*b*d*e^8+
144*B*a^7*b^2*d^2*e^7-420*B*a^6*b^3*d^3*e^6+756*B*a^5*b^4*d^4*e^5-882*B*a^4*b^5*d^5*e^4+672*B*a^3*b^6*d^6*e^3-
324*B*a^2*b^7*d^7*e^2+90*B*a*b^8*d^8*e-11*B*b^9*d^9)*ln(e*x+d)
________________________________________________________________________________________
Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 1859 vs.
\(2 (463) = 926\).
time = 0.36, size = 1859, normalized size = 4.18 \begin {gather*} \text {Too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((b*x+a)^10*(B*x+A)/(e*x+d)^3,x, algorithm="maxima")
[Out]
-5*(11*B*b^10*d^9 - 2*B*a^9*b*e^9 - 9*A*a^8*b^2*e^9 - 9*(10*B*a*b^9*e + A*b^10*e)*d^8 + 36*(9*B*a^2*b^8*e^2 +
2*A*a*b^9*e^2)*d^7 - 84*(8*B*a^3*b^7*e^3 + 3*A*a^2*b^8*e^3)*d^6 + 126*(7*B*a^4*b^6*e^4 + 4*A*a^3*b^7*e^4)*d^5
- 126*(6*B*a^5*b^5*e^5 + 5*A*a^4*b^6*e^5)*d^4 + 84*(5*B*a^6*b^4*e^6 + 6*A*a^5*b^5*e^6)*d^3 - 36*(4*B*a^7*b^3*e
^7 + 7*A*a^6*b^4*e^7)*d^2 + 9*(3*B*a^8*b^2*e^8 + 8*A*a^7*b^3*e^8)*d)*e^(-12)*log(x*e + d) + 1/504*(56*B*b^10*x
^9*e^8 - 63*(3*B*b^10*d*e^7 - 10*B*a*b^9*e^8 - A*b^10*e^8)*x^8 + 72*(6*B*b^10*d^2*e^6 + 45*B*a^2*b^8*e^8 + 10*
A*a*b^9*e^8 - 3*(10*B*a*b^9*e^7 + A*b^10*e^7)*d)*x^7 - 84*(10*B*b^10*d^3*e^5 - 120*B*a^3*b^7*e^8 - 45*A*a^2*b^
8*e^8 - 6*(10*B*a*b^9*e^6 + A*b^10*e^6)*d^2 + 15*(9*B*a^2*b^8*e^7 + 2*A*a*b^9*e^7)*d)*x^6 + 504*(3*B*b^10*d^4*
e^4 + 42*B*a^4*b^6*e^8 + 24*A*a^3*b^7*e^8 - 2*(10*B*a*b^9*e^5 + A*b^10*e^5)*d^3 + 6*(9*B*a^2*b^8*e^6 + 2*A*a*b
^9*e^6)*d^2 - 9*(8*B*a^3*b^7*e^7 + 3*A*a^2*b^8*e^7)*d)*x^5 - 126*(21*B*b^10*d^5*e^3 - 252*B*a^5*b^5*e^8 - 210*
A*a^4*b^6*e^8 - 15*(10*B*a*b^9*e^4 + A*b^10*e^4)*d^4 + 50*(9*B*a^2*b^8*e^5 + 2*A*a*b^9*e^5)*d^3 - 90*(8*B*a^3*
b^7*e^6 + 3*A*a^2*b^8*e^6)*d^2 + 90*(7*B*a^4*b^6*e^7 + 4*A*a^3*b^7*e^7)*d)*x^4 + 168*(28*B*b^10*d^6*e^2 + 210*
B*a^6*b^4*e^8 + 252*A*a^5*b^5*e^8 - 21*(10*B*a*b^9*e^3 + A*b^10*e^3)*d^5 + 75*(9*B*a^2*b^8*e^4 + 2*A*a*b^9*e^4
)*d^4 - 150*(8*B*a^3*b^7*e^5 + 3*A*a^2*b^8*e^5)*d^3 + 180*(7*B*a^4*b^6*e^6 + 4*A*a^3*b^7*e^6)*d^2 - 126*(6*B*a
^5*b^5*e^7 + 5*A*a^4*b^6*e^7)*d)*x^3 - 252*(36*B*b^10*d^7*e - 120*B*a^7*b^3*e^8 - 210*A*a^6*b^4*e^8 - 28*(10*B
*a*b^9*e^2 + A*b^10*e^2)*d^6 + 105*(9*B*a^2*b^8*e^3 + 2*A*a*b^9*e^3)*d^5 - 225*(8*B*a^3*b^7*e^4 + 3*A*a^2*b^8*
e^4)*d^4 + 300*(7*B*a^4*b^6*e^5 + 4*A*a^3*b^7*e^5)*d^3 - 252*(6*B*a^5*b^5*e^6 + 5*A*a^4*b^6*e^6)*d^2 + 126*(5*
B*a^6*b^4*e^7 + 6*A*a^5*b^5*e^7)*d)*x^2 + 504*(45*B*b^10*d^8 + 45*B*a^8*b^2*e^8 + 120*A*a^7*b^3*e^8 - 36*(10*B
*a*b^9*e + A*b^10*e)*d^7 + 140*(9*B*a^2*b^8*e^2 + 2*A*a*b^9*e^2)*d^6 - 315*(8*B*a^3*b^7*e^3 + 3*A*a^2*b^8*e^3)
*d^5 + 450*(7*B*a^4*b^6*e^4 + 4*A*a^3*b^7*e^4)*d^4 - 420*(6*B*a^5*b^5*e^5 + 5*A*a^4*b^6*e^5)*d^3 + 252*(5*B*a^
6*b^4*e^6 + 6*A*a^5*b^5*e^6)*d^2 - 90*(4*B*a^7*b^3*e^7 + 7*A*a^6*b^4*e^7)*d)*x)*e^(-11) - 1/2*(21*B*b^10*d^11
+ A*a^10*e^11 - 19*(10*B*a*b^9*e + A*b^10*e)*d^10 + 85*(9*B*a^2*b^8*e^2 + 2*A*a*b^9*e^2)*d^9 - 225*(8*B*a^3*b^
7*e^3 + 3*A*a^2*b^8*e^3)*d^8 + 390*(7*B*a^4*b^6*e^4 + 4*A*a^3*b^7*e^4)*d^7 - 462*(6*B*a^5*b^5*e^5 + 5*A*a^4*b^
6*e^5)*d^6 + 378*(5*B*a^6*b^4*e^6 + 6*A*a^5*b^5*e^6)*d^5 - 210*(4*B*a^7*b^3*e^7 + 7*A*a^6*b^4*e^7)*d^4 + 75*(3
*B*a^8*b^2*e^8 + 8*A*a^7*b^3*e^8)*d^3 - 15*(2*B*a^9*b*e^9 + 9*A*a^8*b^2*e^9)*d^2 + (B*a^10*e^10 + 10*A*a^9*b*e
^10)*d + 2*(11*B*b^10*d^10*e + B*a^10*e^11 + 10*A*a^9*b*e^11 - 10*(10*B*a*b^9*e^2 + A*b^10*e^2)*d^9 + 45*(9*B*
a^2*b^8*e^3 + 2*A*a*b^9*e^3)*d^8 - 120*(8*B*a^3*b^7*e^4 + 3*A*a^2*b^8*e^4)*d^7 + 210*(7*B*a^4*b^6*e^5 + 4*A*a^
3*b^7*e^5)*d^6 - 252*(6*B*a^5*b^5*e^6 + 5*A*a^4*b^6*e^6)*d^5 + 210*(5*B*a^6*b^4*e^7 + 6*A*a^5*b^5*e^7)*d^4 - 1
20*(4*B*a^7*b^3*e^8 + 7*A*a^6*b^4*e^8)*d^3 + 45*(3*B*a^8*b^2*e^9 + 8*A*a^7*b^3*e^9)*d^2 - 10*(2*B*a^9*b*e^10 +
9*A*a^8*b^2*e^10)*d)*x)/(x^2*e^14 + 2*d*x*e^13 + d^2*e^12)
________________________________________________________________________________________
Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 2483 vs.
\(2 (463) = 926\).
time = 1.03, size = 2483, normalized size = 5.58 \begin {gather*} \text {Too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((b*x+a)^10*(B*x+A)/(e*x+d)^3,x, algorithm="fricas")
[Out]
-1/504*(5292*B*b^10*d^11 - (56*B*b^10*x^11 - 252*A*a^10 + 63*(10*B*a*b^9 + A*b^10)*x^10 + 360*(9*B*a^2*b^8 + 2
*A*a*b^9)*x^9 + 1260*(8*B*a^3*b^7 + 3*A*a^2*b^8)*x^8 + 3024*(7*B*a^4*b^6 + 4*A*a^3*b^7)*x^7 + 5292*(6*B*a^5*b^
5 + 5*A*a^4*b^6)*x^6 + 7056*(5*B*a^6*b^4 + 6*A*a^5*b^5)*x^5 + 7560*(4*B*a^7*b^3 + 7*A*a^6*b^4)*x^4 + 7560*(3*B
*a^8*b^2 + 8*A*a^7*b^3)*x^3 - 504*(B*a^10 + 10*A*a^9*b)*x)*e^11 + (77*B*b^10*d*x^10 + 90*(10*B*a*b^9 + A*b^10)
*d*x^9 + 540*(9*B*a^2*b^8 + 2*A*a*b^9)*d*x^8 + 2016*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*x^7 + 5292*(7*B*a^4*b^6 + 4*
A*a^3*b^7)*d*x^6 + 10584*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*x^5 + 17640*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*x^4 + 30240*(
4*B*a^7*b^3 + 7*A*a^6*b^4)*d*x^3 - 15120*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*x^2 - 5040*(2*B*a^9*b + 9*A*a^8*b^2)*d*
x + 252*(B*a^10 + 10*A*a^9*b)*d)*e^10 - (110*B*b^10*d^2*x^9 + 135*(10*B*a*b^9 + A*b^10)*d^2*x^8 + 864*(9*B*a^2
*b^8 + 2*A*a*b^9)*d^2*x^7 + 3528*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*x^6 + 10584*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*x
^5 + 26460*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*x^4 + 70560*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*x^3 - 83160*(4*B*a^7*b^
3 + 7*A*a^6*b^4)*d^2*x^2 - 15120*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*x + 3780*(2*B*a^9*b + 9*A*a^8*b^2)*d^2)*e^9 +
3*(55*B*b^10*d^3*x^8 + 72*(10*B*a*b^9 + A*b^10)*d^3*x^7 + 504*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*x^6 + 2352*(8*B*a
^3*b^7 + 3*A*a^2*b^8)*d^3*x^5 + 8820*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*x^4 + 35280*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d
^3*x^3 - 74088*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*x^2 - 5040*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*x + 6300*(3*B*a^8*b^
2 + 8*A*a^7*b^3)*d^3)*e^8 - 6*(44*B*b^10*d^4*x^7 + 63*(10*B*a*b^9 + A*b^10)*d^4*x^6 + 504*(9*B*a^2*b^8 + 2*A*a
*b^9)*d^4*x^5 + 2940*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*x^4 + 17640*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*x^3 - 59976*(
6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*x^2 + 3528*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*x + 8820*(4*B*a^7*b^3 + 7*A*a^6*b^4)
*d^4)*e^7 + 42*(11*B*b^10*d^5*x^6 + 18*(10*B*a*b^9 + A*b^10)*d^5*x^5 + 180*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*x^4 +
1680*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*x^3 - 9000*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*x^2 + 2016*(6*B*a^5*b^5 + 5*A
*a^4*b^6)*d^5*x + 2268*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5)*e^6 - 42*(22*B*b^10*d^6*x^5 + 45*(10*B*a*b^9 + A*b^10)
*d^6*x^4 + 720*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*x^3 - 6210*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*x^2 + 2880*(7*B*a^4*b^
6 + 4*A*a^3*b^7)*d^6*x + 2772*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6)*e^5 + 210*(11*B*b^10*d^7*x^4 + 36*(10*B*a*b^9 +
A*b^10)*d^7*x^3 - 546*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*x^2 + 468*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*x + 468*(7*B*a^
4*b^6 + 4*A*a^3*b^7)*d^7)*e^4 - 84*(110*B*b^10*d^8*x^3 - 348*(10*B*a*b^9 + A*b^10)*d^8*x^2 + 570*(9*B*a^2*b^8
+ 2*A*a*b^9)*d^8*x + 675*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8)*e^3 - 252*(144*B*b^10*d^9*x^2 - 52*(10*B*a*b^9 + A*b
^10)*d^9*x - 85*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9)*e^2 - 252*(68*B*b^10*d^10*x + 19*(10*B*a*b^9 + A*b^10)*d^10)*e
+ 2520*(11*B*b^10*d^11 - (2*B*a^9*b + 9*A*a^8*b^2)*x^2*e^11 + (9*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*x^2 - 2*(2*B*a^
9*b + 9*A*a^8*b^2)*d*x)*e^10 - (36*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*x^2 - 18*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*x
+ (2*B*a^9*b + 9*A*a^8*b^2)*d^2)*e^9 + 3*(28*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*x^2 - 24*(4*B*a^7*b^3 + 7*A*a^6*b
^4)*d^3*x + 3*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3)*e^8 - 6*(21*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*x^2 - 28*(5*B*a^6*b
^4 + 6*A*a^5*b^5)*d^4*x + 6*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4)*e^7 + 42*(3*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*x^2 -
6*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*x + 2*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5)*e^6 - 42*(2*(8*B*a^3*b^7 + 3*A*a^2*b
^8)*d^6*x^2 - 6*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*x + 3*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6)*e^5 + 6*(6*(9*B*a^2*b^8
+ 2*A*a*b^9)*d^7*x^2 - 28*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*x + 21*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7)*e^4 - 3*(3*
(10*B*a*b^9 + A*b^10)*d^8*x^2 - 24*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*x + 28*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8)*e^3 +
(11*B*b^10*d^9*x^2 - 18*(10*B*a*b^9 + A*b^10)*d^9*x + 36*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9)*e^2 + (22*B*b^10*d^10
*x - 9*(10*B*a*b^9 + A*b^10)*d^10)*e)*log(x*e + d))/(x^2*e^14 + 2*d*x*e^13 + d^2*e^12)
________________________________________________________________________________________
Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 2004 vs.
\(2 (462) = 924\).
time = 165.35, size = 2004, normalized size = 4.50 \begin {gather*} \frac {B b^{10} x^{9}}{9 e^{3}} + \frac {5 b \left (a e - b d\right )^{8} \cdot \left (9 A b e + 2 B a e - 11 B b d\right ) \log {\left (d + e x \right )}}{e^{12}} + x^{8} \left (\frac {A b^{10}}{8 e^{3}} + \frac {5 B a b^{9}}{4 e^{3}} - \frac {3 B b^{10} d}{8 e^{4}}\right ) + x^{7} \cdot \left (\frac {10 A a b^{9}}{7 e^{3}} - \frac {3 A b^{10} d}{7 e^{4}} + \frac {45 B a^{2} b^{8}}{7 e^{3}} - \frac {30 B a b^{9} d}{7 e^{4}} + \frac {6 B b^{10} d^{2}}{7 e^{5}}\right ) + x^{6} \cdot \left (\frac {15 A a^{2} b^{8}}{2 e^{3}} - \frac {5 A a b^{9} d}{e^{4}} + \frac {A b^{10} d^{2}}{e^{5}} + \frac {20 B a^{3} b^{7}}{e^{3}} - \frac {45 B a^{2} b^{8} d}{2 e^{4}} + \frac {10 B a b^{9} d^{2}}{e^{5}} - \frac {5 B b^{10} d^{3}}{3 e^{6}}\right ) + x^{5} \cdot \left (\frac {24 A a^{3} b^{7}}{e^{3}} - \frac {27 A a^{2} b^{8} d}{e^{4}} + \frac {12 A a b^{9} d^{2}}{e^{5}} - \frac {2 A b^{10} d^{3}}{e^{6}} + \frac {42 B a^{4} b^{6}}{e^{3}} - \frac {72 B a^{3} b^{7} d}{e^{4}} + \frac {54 B a^{2} b^{8} d^{2}}{e^{5}} - \frac {20 B a b^{9} d^{3}}{e^{6}} + \frac {3 B b^{10} d^{4}}{e^{7}}\right ) + x^{4} \cdot \left (\frac {105 A a^{4} b^{6}}{2 e^{3}} - \frac {90 A a^{3} b^{7} d}{e^{4}} + \frac {135 A a^{2} b^{8} d^{2}}{2 e^{5}} - \frac {25 A a b^{9} d^{3}}{e^{6}} + \frac {15 A b^{10} d^{4}}{4 e^{7}} + \frac {63 B a^{5} b^{5}}{e^{3}} - \frac {315 B a^{4} b^{6} d}{2 e^{4}} + \frac {180 B a^{3} b^{7} d^{2}}{e^{5}} - \frac {225 B a^{2} b^{8} d^{3}}{2 e^{6}} + \frac {75 B a b^{9} d^{4}}{2 e^{7}} - \frac {21 B b^{10} d^{5}}{4 e^{8}}\right ) + x^{3} \cdot \left (\frac {84 A a^{5} b^{5}}{e^{3}} - \frac {210 A a^{4} b^{6} d}{e^{4}} + \frac {240 A a^{3} b^{7} d^{2}}{e^{5}} - \frac {150 A a^{2} b^{8} d^{3}}{e^{6}} + \frac {50 A a b^{9} d^{4}}{e^{7}} - \frac {7 A b^{10} d^{5}}{e^{8}} + \frac {70 B a^{6} b^{4}}{e^{3}} - \frac {252 B a^{5} b^{5} d}{e^{4}} + \frac {420 B a^{4} b^{6} d^{2}}{e^{5}} - \frac {400 B a^{3} b^{7} d^{3}}{e^{6}} + \frac {225 B a^{2} b^{8} d^{4}}{e^{7}} - \frac {70 B a b^{9} d^{5}}{e^{8}} + \frac {28 B b^{10} d^{6}}{3 e^{9}}\right ) + x^{2} \cdot \left (\frac {105 A a^{6} b^{4}}{e^{3}} - \frac {378 A a^{5} b^{5} d}{e^{4}} + \frac {630 A a^{4} b^{6} d^{2}}{e^{5}} - \frac {600 A a^{3} b^{7} d^{3}}{e^{6}} + \frac {675 A a^{2} b^{8} d^{4}}{2 e^{7}} - \frac {105 A a b^{9} d^{5}}{e^{8}} + \frac {14 A b^{10} d^{6}}{e^{9}} + \frac {60 B a^{7} b^{3}}{e^{3}} - \frac {315 B a^{6} b^{4} d}{e^{4}} + \frac {756 B a^{5} b^{5} d^{2}}{e^{5}} - \frac {1050 B a^{4} b^{6} d^{3}}{e^{6}} + \frac {900 B a^{3} b^{7} d^{4}}{e^{7}} - \frac {945 B a^{2} b^{8} d^{5}}{2 e^{8}} + \frac {140 B a b^{9} d^{6}}{e^{9}} - \frac {18 B b^{10} d^{7}}{e^{10}}\right ) + x \left (\frac {120 A a^{7} b^{3}}{e^{3}} - \frac {630 A a^{6} b^{4} d}{e^{4}} + \frac {1512 A a^{5} b^{5} d^{2}}{e^{5}} - \frac {2100 A a^{4} b^{6} d^{3}}{e^{6}} + \frac {1800 A a^{3} b^{7} d^{4}}{e^{7}} - \frac {945 A a^{2} b^{8} d^{5}}{e^{8}} + \frac {280 A a b^{9} d^{6}}{e^{9}} - \frac {36 A b^{10} d^{7}}{e^{10}} + \frac {45 B a^{8} b^{2}}{e^{3}} - \frac {360 B a^{7} b^{3} d}{e^{4}} + \frac {1260 B a^{6} b^{4} d^{2}}{e^{5}} - \frac {2520 B a^{5} b^{5} d^{3}}{e^{6}} + \frac {3150 B a^{4} b^{6} d^{4}}{e^{7}} - \frac {2520 B a^{3} b^{7} d^{5}}{e^{8}} + \frac {1260 B a^{2} b^{8} d^{6}}{e^{9}} - \frac {360 B a b^{9} d^{7}}{e^{10}} + \frac {45 B b^{10} d^{8}}{e^{11}}\right ) + \frac {- A a^{10} e^{11} - 10 A a^{9} b d e^{10} + 135 A a^{8} b^{2} d^{2} e^{9} - 600 A a^{7} b^{3} d^{3} e^{8} + 1470 A a^{6} b^{4} d^{4} e^{7} - 2268 A a^{5} b^{5} d^{5} e^{6} + 2310 A a^{4} b^{6} d^{6} e^{5} - 1560 A a^{3} b^{7} d^{7} e^{4} + 675 A a^{2} b^{8} d^{8} e^{3} - 170 A a b^{9} d^{9} e^{2} + 19 A b^{10} d^{10} e - B a^{10} d e^{10} + 30 B a^{9} b d^{2} e^{9} - 225 B a^{8} b^{2} d^{3} e^{8} + 840 B a^{7} b^{3} d^{4} e^{7} - 1890 B a^{6} b^{4} d^{5} e^{6} + 2772 B a^{5} b^{5} d^{6} e^{5} - 2730 B a^{4} b^{6} d^{7} e^{4} + 1800 B a^{3} b^{7} d^{8} e^{3} - 765 B a^{2} b^{8} d^{9} e^{2} + 190 B a b^{9} d^{10} e - 21 B b^{10} d^{11} + x \left (- 20 A a^{9} b e^{11} + 180 A a^{8} b^{2} d e^{10} - 720 A a^{7} b^{3} d^{2} e^{9} + 1680 A a^{6} b^{4} d^{3} e^{8} - 2520 A a^{5} b^{5} d^{4} e^{7} + 2520 A a^{4} b^{6} d^{5} e^{6} - 1680 A a^{3} b^{7} d^{6} e^{5} + 720 A a^{2} b^{8} d^{7} e^{4} - 180 A a b^{9} d^{8} e^{3} + 20 A b^{10} d^{9} e^{2} - 2 B a^{10} e^{11} + 40 B a^{9} b d e^{10} - 270 B a^{8} b^{2} d^{2} e^{9} + 960 B a^{7} b^{3} d^{3} e^{8} - 2100 B a^{6} b^{4} d^{4} e^{7} + 3024 B a^{5} b^{5} d^{5} e^{6} - 2940 B a^{4} b^{6} d^{6} e^{5} + 1920 B a^{3} b^{7} d^{7} e^{4} - 810 B a^{2} b^{8} d^{8} e^{3} + 200 B a b^{9} d^{9} e^{2} - 22 B b^{10} d^{10} e\right )}{2 d^{2} e^{12} + 4 d e^{13} x + 2 e^{14} x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((b*x+a)**10*(B*x+A)/(e*x+d)**3,x)
[Out]
B*b**10*x**9/(9*e**3) + 5*b*(a*e - b*d)**8*(9*A*b*e + 2*B*a*e - 11*B*b*d)*log(d + e*x)/e**12 + x**8*(A*b**10/(
8*e**3) + 5*B*a*b**9/(4*e**3) - 3*B*b**10*d/(8*e**4)) + x**7*(10*A*a*b**9/(7*e**3) - 3*A*b**10*d/(7*e**4) + 45
*B*a**2*b**8/(7*e**3) - 30*B*a*b**9*d/(7*e**4) + 6*B*b**10*d**2/(7*e**5)) + x**6*(15*A*a**2*b**8/(2*e**3) - 5*
A*a*b**9*d/e**4 + A*b**10*d**2/e**5 + 20*B*a**3*b**7/e**3 - 45*B*a**2*b**8*d/(2*e**4) + 10*B*a*b**9*d**2/e**5
- 5*B*b**10*d**3/(3*e**6)) + x**5*(24*A*a**3*b**7/e**3 - 27*A*a**2*b**8*d/e**4 + 12*A*a*b**9*d**2/e**5 - 2*A*b
**10*d**3/e**6 + 42*B*a**4*b**6/e**3 - 72*B*a**3*b**7*d/e**4 + 54*B*a**2*b**8*d**2/e**5 - 20*B*a*b**9*d**3/e**
6 + 3*B*b**10*d**4/e**7) + x**4*(105*A*a**4*b**6/(2*e**3) - 90*A*a**3*b**7*d/e**4 + 135*A*a**2*b**8*d**2/(2*e*
*5) - 25*A*a*b**9*d**3/e**6 + 15*A*b**10*d**4/(4*e**7) + 63*B*a**5*b**5/e**3 - 315*B*a**4*b**6*d/(2*e**4) + 18
0*B*a**3*b**7*d**2/e**5 - 225*B*a**2*b**8*d**3/(2*e**6) + 75*B*a*b**9*d**4/(2*e**7) - 21*B*b**10*d**5/(4*e**8)
) + x**3*(84*A*a**5*b**5/e**3 - 210*A*a**4*b**6*d/e**4 + 240*A*a**3*b**7*d**2/e**5 - 150*A*a**2*b**8*d**3/e**6
+ 50*A*a*b**9*d**4/e**7 - 7*A*b**10*d**5/e**8 + 70*B*a**6*b**4/e**3 - 252*B*a**5*b**5*d/e**4 + 420*B*a**4*b**
6*d**2/e**5 - 400*B*a**3*b**7*d**3/e**6 + 225*B*a**2*b**8*d**4/e**7 - 70*B*a*b**9*d**5/e**8 + 28*B*b**10*d**6/
(3*e**9)) + x**2*(105*A*a**6*b**4/e**3 - 378*A*a**5*b**5*d/e**4 + 630*A*a**4*b**6*d**2/e**5 - 600*A*a**3*b**7*
d**3/e**6 + 675*A*a**2*b**8*d**4/(2*e**7) - 105*A*a*b**9*d**5/e**8 + 14*A*b**10*d**6/e**9 + 60*B*a**7*b**3/e**
3 - 315*B*a**6*b**4*d/e**4 + 756*B*a**5*b**5*d**2/e**5 - 1050*B*a**4*b**6*d**3/e**6 + 900*B*a**3*b**7*d**4/e**
7 - 945*B*a**2*b**8*d**5/(2*e**8) + 140*B*a*b**9*d**6/e**9 - 18*B*b**10*d**7/e**10) + x*(120*A*a**7*b**3/e**3
- 630*A*a**6*b**4*d/e**4 + 1512*A*a**5*b**5*d**2/e**5 - 2100*A*a**4*b**6*d**3/e**6 + 1800*A*a**3*b**7*d**4/e**
7 - 945*A*a**2*b**8*d**5/e**8 + 280*A*a*b**9*d**6/e**9 - 36*A*b**10*d**7/e**10 + 45*B*a**8*b**2/e**3 - 360*B*a
**7*b**3*d/e**4 + 1260*B*a**6*b**4*d**2/e**5 - 2520*B*a**5*b**5*d**3/e**6 + 3150*B*a**4*b**6*d**4/e**7 - 2520*
B*a**3*b**7*d**5/e**8 + 1260*B*a**2*b**8*d**6/e**9 - 360*B*a*b**9*d**7/e**10 + 45*B*b**10*d**8/e**11) + (-A*a*
*10*e**11 - 10*A*a**9*b*d*e**10 + 135*A*a**8*b**2*d**2*e**9 - 600*A*a**7*b**3*d**3*e**8 + 1470*A*a**6*b**4*d**
4*e**7 - 2268*A*a**5*b**5*d**5*e**6 + 2310*A*a**4*b**6*d**6*e**5 - 1560*A*a**3*b**7*d**7*e**4 + 675*A*a**2*b**
8*d**8*e**3 - 170*A*a*b**9*d**9*e**2 + 19*A*b**10*d**10*e - B*a**10*d*e**10 + 30*B*a**9*b*d**2*e**9 - 225*B*a*
*8*b**2*d**3*e**8 + 840*B*a**7*b**3*d**4*e**7 - 1890*B*a**6*b**4*d**5*e**6 + 2772*B*a**5*b**5*d**6*e**5 - 2730
*B*a**4*b**6*d**7*e**4 + 1800*B*a**3*b**7*d**8*e**3 - 765*B*a**2*b**8*d**9*e**2 + 190*B*a*b**9*d**10*e - 21*B*
b**10*d**11 + x*(-20*A*a**9*b*e**11 + 180*A*a**8*b**2*d*e**10 - 720*A*a**7*b**3*d**2*e**9 + 1680*A*a**6*b**4*d
**3*e**8 - 2520*A*a**5*b**5*d**4*e**7 + 2520*A*a**4*b**6*d**5*e**6 - 1680*A*a**3*b**7*d**6*e**5 + 720*A*a**2*b
**8*d**7*e**4 - 180*A*a*b**9*d**8*e**3 + 20*A*b**10*d**9*e**2 - 2*B*a**10*e**11 + 40*B*a**9*b*d*e**10 - 270*B*
a**8*b**2*d**2*e**9 + 960*B*a**7*b**3*d**3*e**8 - 2100*B*a**6*b**4*d**4*e**7 + 3024*B*a**5*b**5*d**5*e**6 - 29
40*B*a**4*b**6*d**6*e**5 + 1920*B*a**3*b**7*d**7*e**4 - 810*B*a**2*b**8*d**8*e**3 + 200*B*a*b**9*d**9*e**2 - 2
2*B*b**10*d**10*e))/(2*d**2*e**12 + 4*d*e**13*x + 2*e**14*x**2)
________________________________________________________________________________________
Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 2002 vs.
\(2 (463) = 926\).
time = 0.78, size = 2002, normalized size = 4.50 \begin {gather*} \text {Too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((b*x+a)^10*(B*x+A)/(e*x+d)^3,x, algorithm="giac")
[Out]
-5*(11*B*b^10*d^9 - 90*B*a*b^9*d^8*e - 9*A*b^10*d^8*e + 324*B*a^2*b^8*d^7*e^2 + 72*A*a*b^9*d^7*e^2 - 672*B*a^3
*b^7*d^6*e^3 - 252*A*a^2*b^8*d^6*e^3 + 882*B*a^4*b^6*d^5*e^4 + 504*A*a^3*b^7*d^5*e^4 - 756*B*a^5*b^5*d^4*e^5 -
630*A*a^4*b^6*d^4*e^5 + 420*B*a^6*b^4*d^3*e^6 + 504*A*a^5*b^5*d^3*e^6 - 144*B*a^7*b^3*d^2*e^7 - 252*A*a^6*b^4
*d^2*e^7 + 27*B*a^8*b^2*d*e^8 + 72*A*a^7*b^3*d*e^8 - 2*B*a^9*b*e^9 - 9*A*a^8*b^2*e^9)*e^(-12)*log(abs(x*e + d)
) + 1/504*(56*B*b^10*x^9*e^24 - 189*B*b^10*d*x^8*e^23 + 432*B*b^10*d^2*x^7*e^22 - 840*B*b^10*d^3*x^6*e^21 + 15
12*B*b^10*d^4*x^5*e^20 - 2646*B*b^10*d^5*x^4*e^19 + 4704*B*b^10*d^6*x^3*e^18 - 9072*B*b^10*d^7*x^2*e^17 + 2268
0*B*b^10*d^8*x*e^16 + 630*B*a*b^9*x^8*e^24 + 63*A*b^10*x^8*e^24 - 2160*B*a*b^9*d*x^7*e^23 - 216*A*b^10*d*x^7*e
^23 + 5040*B*a*b^9*d^2*x^6*e^22 + 504*A*b^10*d^2*x^6*e^22 - 10080*B*a*b^9*d^3*x^5*e^21 - 1008*A*b^10*d^3*x^5*e
^21 + 18900*B*a*b^9*d^4*x^4*e^20 + 1890*A*b^10*d^4*x^4*e^20 - 35280*B*a*b^9*d^5*x^3*e^19 - 3528*A*b^10*d^5*x^3
*e^19 + 70560*B*a*b^9*d^6*x^2*e^18 + 7056*A*b^10*d^6*x^2*e^18 - 181440*B*a*b^9*d^7*x*e^17 - 18144*A*b^10*d^7*x
*e^17 + 3240*B*a^2*b^8*x^7*e^24 + 720*A*a*b^9*x^7*e^24 - 11340*B*a^2*b^8*d*x^6*e^23 - 2520*A*a*b^9*d*x^6*e^23
+ 27216*B*a^2*b^8*d^2*x^5*e^22 + 6048*A*a*b^9*d^2*x^5*e^22 - 56700*B*a^2*b^8*d^3*x^4*e^21 - 12600*A*a*b^9*d^3*
x^4*e^21 + 113400*B*a^2*b^8*d^4*x^3*e^20 + 25200*A*a*b^9*d^4*x^3*e^20 - 238140*B*a^2*b^8*d^5*x^2*e^19 - 52920*
A*a*b^9*d^5*x^2*e^19 + 635040*B*a^2*b^8*d^6*x*e^18 + 141120*A*a*b^9*d^6*x*e^18 + 10080*B*a^3*b^7*x^6*e^24 + 37
80*A*a^2*b^8*x^6*e^24 - 36288*B*a^3*b^7*d*x^5*e^23 - 13608*A*a^2*b^8*d*x^5*e^23 + 90720*B*a^3*b^7*d^2*x^4*e^22
+ 34020*A*a^2*b^8*d^2*x^4*e^22 - 201600*B*a^3*b^7*d^3*x^3*e^21 - 75600*A*a^2*b^8*d^3*x^3*e^21 + 453600*B*a^3*
b^7*d^4*x^2*e^20 + 170100*A*a^2*b^8*d^4*x^2*e^20 - 1270080*B*a^3*b^7*d^5*x*e^19 - 476280*A*a^2*b^8*d^5*x*e^19
+ 21168*B*a^4*b^6*x^5*e^24 + 12096*A*a^3*b^7*x^5*e^24 - 79380*B*a^4*b^6*d*x^4*e^23 - 45360*A*a^3*b^7*d*x^4*e^2
3 + 211680*B*a^4*b^6*d^2*x^3*e^22 + 120960*A*a^3*b^7*d^2*x^3*e^22 - 529200*B*a^4*b^6*d^3*x^2*e^21 - 302400*A*a
^3*b^7*d^3*x^2*e^21 + 1587600*B*a^4*b^6*d^4*x*e^20 + 907200*A*a^3*b^7*d^4*x*e^20 + 31752*B*a^5*b^5*x^4*e^24 +
26460*A*a^4*b^6*x^4*e^24 - 127008*B*a^5*b^5*d*x^3*e^23 - 105840*A*a^4*b^6*d*x^3*e^23 + 381024*B*a^5*b^5*d^2*x^
2*e^22 + 317520*A*a^4*b^6*d^2*x^2*e^22 - 1270080*B*a^5*b^5*d^3*x*e^21 - 1058400*A*a^4*b^6*d^3*x*e^21 + 35280*B
*a^6*b^4*x^3*e^24 + 42336*A*a^5*b^5*x^3*e^24 - 158760*B*a^6*b^4*d*x^2*e^23 - 190512*A*a^5*b^5*d*x^2*e^23 + 635
040*B*a^6*b^4*d^2*x*e^22 + 762048*A*a^5*b^5*d^2*x*e^22 + 30240*B*a^7*b^3*x^2*e^24 + 52920*A*a^6*b^4*x^2*e^24 -
181440*B*a^7*b^3*d*x*e^23 - 317520*A*a^6*b^4*d*x*e^23 + 22680*B*a^8*b^2*x*e^24 + 60480*A*a^7*b^3*x*e^24)*e^(-
27) - 1/2*(21*B*b^10*d^11 - 190*B*a*b^9*d^10*e - 19*A*b^10*d^10*e + 765*B*a^2*b^8*d^9*e^2 + 170*A*a*b^9*d^9*e^
2 - 1800*B*a^3*b^7*d^8*e^3 - 675*A*a^2*b^8*d^8*e^3 + 2730*B*a^4*b^6*d^7*e^4 + 1560*A*a^3*b^7*d^7*e^4 - 2772*B*
a^5*b^5*d^6*e^5 - 2310*A*a^4*b^6*d^6*e^5 + 1890*B*a^6*b^4*d^5*e^6 + 2268*A*a^5*b^5*d^5*e^6 - 840*B*a^7*b^3*d^4
*e^7 - 1470*A*a^6*b^4*d^4*e^7 + 225*B*a^8*b^2*d^3*e^8 + 600*A*a^7*b^3*d^3*e^8 - 30*B*a^9*b*d^2*e^9 - 135*A*a^8
*b^2*d^2*e^9 + B*a^10*d*e^10 + 10*A*a^9*b*d*e^10 + A*a^10*e^11 + 2*(11*B*b^10*d^10*e - 100*B*a*b^9*d^9*e^2 - 1
0*A*b^10*d^9*e^2 + 405*B*a^2*b^8*d^8*e^3 + 90*A*a*b^9*d^8*e^3 - 960*B*a^3*b^7*d^7*e^4 - 360*A*a^2*b^8*d^7*e^4
+ 1470*B*a^4*b^6*d^6*e^5 + 840*A*a^3*b^7*d^6*e^5 - 1512*B*a^5*b^5*d^5*e^6 - 1260*A*a^4*b^6*d^5*e^6 + 1050*B*a^
6*b^4*d^4*e^7 + 1260*A*a^5*b^5*d^4*e^7 - 480*B*a^7*b^3*d^3*e^8 - 840*A*a^6*b^4*d^3*e^8 + 135*B*a^8*b^2*d^2*e^9
+ 360*A*a^7*b^3*d^2*e^9 - 20*B*a^9*b*d*e^10 - 90*A*a^8*b^2*d*e^10 + B*a^10*e^11 + 10*A*a^9*b*e^11)*x)*e^(-12)
/(x*e + d)^2
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Mupad [B]
time = 1.52, size = 2500, normalized size = 5.62 \begin {gather*} \text {Too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((A + B*x)*(a + b*x)^10)/(d + e*x)^3,x)
[Out]
x^5*((3*d*((3*d^2*((A*b^10 + 10*B*a*b^9)/e^3 - (3*B*b^10*d)/e^4))/e^2 - (3*d*((3*d*((A*b^10 + 10*B*a*b^9)/e^3
- (3*B*b^10*d)/e^4))/e - (5*a*b^8*(2*A*b + 9*B*a))/e^3 + (3*B*b^10*d^2)/e^5))/e - (15*a^2*b^7*(3*A*b + 8*B*a))
/e^3 + (B*b^10*d^3)/e^6))/(5*e) - (d^3*((A*b^10 + 10*B*a*b^9)/e^3 - (3*B*b^10*d)/e^4))/(5*e^3) + (3*d^2*((3*d*
((A*b^10 + 10*B*a*b^9)/e^3 - (3*B*b^10*d)/e^4))/e - (5*a*b^8*(2*A*b + 9*B*a))/e^3 + (3*B*b^10*d^2)/e^5))/(5*e^
2) + (6*a^3*b^6*(4*A*b + 7*B*a))/e^3) + x*((3*d*((3*d*((d^3*((3*d^2*((A*b^10 + 10*B*a*b^9)/e^3 - (3*B*b^10*d)/
e^4))/e^2 - (3*d*((3*d*((A*b^10 + 10*B*a*b^9)/e^3 - (3*B*b^10*d)/e^4))/e - (5*a*b^8*(2*A*b + 9*B*a))/e^3 + (3*
B*b^10*d^2)/e^5))/e - (15*a^2*b^7*(3*A*b + 8*B*a))/e^3 + (B*b^10*d^3)/e^6))/e^3 - (3*d*((3*d^2*((3*d^2*((A*b^1
0 + 10*B*a*b^9)/e^3 - (3*B*b^10*d)/e^4))/e^2 - (3*d*((3*d*((A*b^10 + 10*B*a*b^9)/e^3 - (3*B*b^10*d)/e^4))/e -
(5*a*b^8*(2*A*b + 9*B*a))/e^3 + (3*B*b^10*d^2)/e^5))/e - (15*a^2*b^7*(3*A*b + 8*B*a))/e^3 + (B*b^10*d^3)/e^6))
/e^2 - (3*d*((3*d*((3*d^2*((A*b^10 + 10*B*a*b^9)/e^3 - (3*B*b^10*d)/e^4))/e^2 - (3*d*((3*d*((A*b^10 + 10*B*a*b
^9)/e^3 - (3*B*b^10*d)/e^4))/e - (5*a*b^8*(2*A*b + 9*B*a))/e^3 + (3*B*b^10*d^2)/e^5))/e - (15*a^2*b^7*(3*A*b +
8*B*a))/e^3 + (B*b^10*d^3)/e^6))/e - (d^3*((A*b^10 + 10*B*a*b^9)/e^3 - (3*B*b^10*d)/e^4))/e^3 + (3*d^2*((3*d*
((A*b^10 + 10*B*a*b^9)/e^3 - (3*B*b^10*d)/e^4))/e - (5*a*b^8*(2*A*b + 9*B*a))/e^3 + (3*B*b^10*d^2)/e^5))/e^2 +
(30*a^3*b^6*(4*A*b + 7*B*a))/e^3))/e + (d^3*((3*d*((A*b^10 + 10*B*a*b^9)/e^3 - (3*B*b^10*d)/e^4))/e - (5*a*b^
8*(2*A*b + 9*B*a))/e^3 + (3*B*b^10*d^2)/e^5))/e^3 + (42*a^4*b^5*(5*A*b + 6*B*a))/e^3))/e - (3*d^2*((3*d*((3*d^
2*((A*b^10 + 10*B*a*b^9)/e^3 - (3*B*b^10*d)/e^4))/e^2 - (3*d*((3*d*((A*b^10 + 10*B*a*b^9)/e^3 - (3*B*b^10*d)/e
^4))/e - (5*a*b^8*(2*A*b + 9*B*a))/e^3 + (3*B*b^10*d^2)/e^5))/e - (15*a^2*b^7*(3*A*b + 8*B*a))/e^3 + (B*b^10*d
^3)/e^6))/e - (d^3*((A*b^10 + 10*B*a*b^9)/e^3 - (3*B*b^10*d)/e^4))/e^3 + (3*d^2*((3*d*((A*b^10 + 10*B*a*b^9)/e
^3 - (3*B*b^10*d)/e^4))/e - (5*a*b^8*(2*A*b + 9*B*a))/e^3 + (3*B*b^10*d^2)/e^5))/e^2 + (30*a^3*b^6*(4*A*b + 7*
B*a))/e^3))/e^2 + (42*a^5*b^4*(6*A*b + 5*B*a))/e^3))/e + (d^3*((3*d*((3*d^2*((A*b^10 + 10*B*a*b^9)/e^3 - (3*B*
b^10*d)/e^4))/e^2 - (3*d*((3*d*((A*b^10 + 10*B*a*b^9)/e^3 - (3*B*b^10*d)/e^4))/e - (5*a*b^8*(2*A*b + 9*B*a))/e
^3 + (3*B*b^10*d^2)/e^5))/e - (15*a^2*b^7*(3*A*b + 8*B*a))/e^3 + (B*b^10*d^3)/e^6))/e - (d^3*((A*b^10 + 10*B*a
*b^9)/e^3 - (3*B*b^10*d)/e^4))/e^3 + (3*d^2*((3*d*((A*b^10 + 10*B*a*b^9)/e^3 - (3*B*b^10*d)/e^4))/e - (5*a*b^8
*(2*A*b + 9*B*a))/e^3 + (3*B*b^10*d^2)/e^5))/e^2 + (30*a^3*b^6*(4*A*b + 7*B*a))/e^3))/e^3 + (3*d^2*((3*d^2*((3
*d^2*((A*b^10 + 10*B*a*b^9)/e^3 - (3*B*b^10*d)/e^4))/e^2 - (3*d*((3*d*((A*b^10 + 10*B*a*b^9)/e^3 - (3*B*b^10*d
)/e^4))/e - (5*a*b^8*(2*A*b + 9*B*a))/e^3 + (3*B*b^10*d^2)/e^5))/e - (15*a^2*b^7*(3*A*b + 8*B*a))/e^3 + (B*b^1
0*d^3)/e^6))/e^2 - (3*d*((3*d*((3*d^2*((A*b^10 + 10*B*a*b^9)/e^3 - (3*B*b^10*d)/e^4))/e^2 - (3*d*((3*d*((A*b^1
0 + 10*B*a*b^9)/e^3 - (3*B*b^10*d)/e^4))/e - (5*a*b^8*(2*A*b + 9*B*a))/e^3 + (3*B*b^10*d^2)/e^5))/e - (15*a^2*
b^7*(3*A*b + 8*B*a))/e^3 + (B*b^10*d^3)/e^6))/e - (d^3*((A*b^10 + 10*B*a*b^9)/e^3 - (3*B*b^10*d)/e^4))/e^3 + (
3*d^2*((3*d*((A*b^10 + 10*B*a*b^9)/e^3 - (3*B*b^10*d)/e^4))/e - (5*a*b^8*(2*A*b + 9*B*a))/e^3 + (3*B*b^10*d^2)
/e^5))/e^2 + (30*a^3*b^6*(4*A*b + 7*B*a))/e^3))/e + (d^3*((3*d*((A*b^10 + 10*B*a*b^9)/e^3 - (3*B*b^10*d)/e^4))
/e - (5*a*b^8*(2*A*b + 9*B*a))/e^3 + (3*B*b^10*d^2)/e^5))/e^3 + (42*a^4*b^5*(5*A*b + 6*B*a))/e^3))/e^2 - (30*a
^6*b^3*(7*A*b + 4*B*a))/e^3))/e - (3*d^2*((d^3*((3*d^2*((A*b^10 + 10*B*a*b^9)/e^3 - (3*B*b^10*d)/e^4))/e^2 - (
3*d*((3*d*((A*b^10 + 10*B*a*b^9)/e^3 - (3*B*b^10*d)/e^4))/e - (5*a*b^8*(2*A*b + 9*B*a))/e^3 + (3*B*b^10*d^2)/e
^5))/e - (15*a^2*b^7*(3*A*b + 8*B*a))/e^3 + (B*b^10*d^3)/e^6))/e^3 - (3*d*((3*d^2*((3*d^2*((A*b^10 + 10*B*a*b^
9)/e^3 - (3*B*b^10*d)/e^4))/e^2 - (3*d*((3*d*((A*b^10 + 10*B*a*b^9)/e^3 - (3*B*b^10*d)/e^4))/e - (5*a*b^8*(2*A
*b + 9*B*a))/e^3 + (3*B*b^10*d^2)/e^5))/e - (15*a^2*b^7*(3*A*b + 8*B*a))/e^3 + (B*b^10*d^3)/e^6))/e^2 - (3*d*(
(3*d*((3*d^2*((A*b^10 + 10*B*a*b^9)/e^3 - (3*B*b^10*d)/e^4))/e^2 - (3*d*((3*d*((A*b^10 + 10*B*a*b^9)/e^3 - (3*
B*b^10*d)/e^4))/e - (5*a*b^8*(2*A*b + 9*B*a))/e^3 + (3*B*b^10*d^2)/e^5))/e - (15*a^2*b^7*(3*A*b + 8*B*a))/e^3
+ (B*b^10*d^3)/e^6))/e - (d^3*((A*b^10 + 10*B*a*b^9)/e^3 - (3*B*b^10*d)/e^4))/e^3 + (3*d^2*((3*d*((A*b^10 + 10
*B*a*b^9)/e^3 - (3*B*b^10*d)/e^4))/e - (5*a*b^8*(2*A*b + 9*B*a))/e^3 + (3*B*b^10*d^2)/e^5))/e^2 + (30*a^3*b^6*
(4*A*b + 7*B*a))/e^3))/e + (d^3*((3*d*((A*b^10 + 10*B*a*b^9)/e^3 - (3*B*b^10*d)/e^4))/e - (5*a*b^8*(2*A*b + 9*
B*a))/e^3 + (3*B*b^10*d^2)/e^5))/e^3 + (42*a^4*b^5*(5*A*b + 6*B*a))/e^3))/e - (3*d^2*((3*d*((3*d^2*((A*b^10 +
10*B*a*b^9)/e^3 - (3*B*b^10*d)/e^4))/e^2 - (3*d*((3*d*((A*b^10 + 10*B*a*b^9)/e^3 - (3*B*b^10*d)/e^4))/e - (5*a
*b^8*(2*A*b + 9*B*a))/e^3 + (3*B*b^10*d^2)/e^5))/e - (15*a^2*b^7*(3*A*b + 8*B*a))/e^3 + (B*b^10*d^3)/e^6))/e -
(d^3*((A*b^10 + 10*B*a*b^9)/e^3 - (3*B*b^10*d)...
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