3.11.98 \(\int \frac {(a+b x)^{10} (A+B x)}{(d+e x)^{10}} \, dx\) [1098]
Optimal. Leaf size=441 \[ -\frac {b^9 (10 b B d-A b e-10 a B e) x}{e^{11}}+\frac {b^{10} B x^2}{2 e^{10}}+\frac {(b d-a e)^{10} (B d-A e)}{9 e^{12} (d+e x)^9}-\frac {(b d-a e)^9 (11 b B d-10 A b e-a B e)}{8 e^{12} (d+e x)^8}+\frac {5 b (b d-a e)^8 (11 b B d-9 A b e-2 a B e)}{7 e^{12} (d+e x)^7}-\frac {5 b^2 (b d-a e)^7 (11 b B d-8 A b e-3 a B e)}{2 e^{12} (d+e x)^6}+\frac {6 b^3 (b d-a e)^6 (11 b B d-7 A b e-4 a B e)}{e^{12} (d+e x)^5}-\frac {21 b^4 (b d-a e)^5 (11 b B d-6 A b e-5 a B e)}{2 e^{12} (d+e x)^4}+\frac {14 b^5 (b d-a e)^4 (11 b B d-5 A b e-6 a B e)}{e^{12} (d+e x)^3}-\frac {15 b^6 (b d-a e)^3 (11 b B d-4 A b e-7 a B e)}{e^{12} (d+e x)^2}+\frac {15 b^7 (b d-a e)^2 (11 b B d-3 A b e-8 a B e)}{e^{12} (d+e x)}+\frac {5 b^8 (b d-a e) (11 b B d-2 A b e-9 a B e) \log (d+e x)}{e^{12}} \]
[Out]
-b^9*(-A*b*e-10*B*a*e+10*B*b*d)*x/e^11+1/2*b^10*B*x^2/e^10+1/9*(-a*e+b*d)^10*(-A*e+B*d)/e^12/(e*x+d)^9-1/8*(-a
*e+b*d)^9*(-10*A*b*e-B*a*e+11*B*b*d)/e^12/(e*x+d)^8+5/7*b*(-a*e+b*d)^8*(-9*A*b*e-2*B*a*e+11*B*b*d)/e^12/(e*x+d
)^7-5/2*b^2*(-a*e+b*d)^7*(-8*A*b*e-3*B*a*e+11*B*b*d)/e^12/(e*x+d)^6+6*b^3*(-a*e+b*d)^6*(-7*A*b*e-4*B*a*e+11*B*
b*d)/e^12/(e*x+d)^5-21/2*b^4*(-a*e+b*d)^5*(-6*A*b*e-5*B*a*e+11*B*b*d)/e^12/(e*x+d)^4+14*b^5*(-a*e+b*d)^4*(-5*A
*b*e-6*B*a*e+11*B*b*d)/e^12/(e*x+d)^3-15*b^6*(-a*e+b*d)^3*(-4*A*b*e-7*B*a*e+11*B*b*d)/e^12/(e*x+d)^2+15*b^7*(-
a*e+b*d)^2*(-3*A*b*e-8*B*a*e+11*B*b*d)/e^12/(e*x+d)+5*b^8*(-a*e+b*d)*(-2*A*b*e-9*B*a*e+11*B*b*d)*ln(e*x+d)/e^1
2
________________________________________________________________________________________
Rubi [A]
time = 0.58, antiderivative size = 441, 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 x (-10 a B e-A b e+10 b B d)}{e^{11}}+\frac {5 b^8 (b d-a e) \log (d+e x) (-9 a B e-2 A b e+11 b B d)}{e^{12}}+\frac {15 b^7 (b d-a e)^2 (-8 a B e-3 A b e+11 b B d)}{e^{12} (d+e x)}-\frac {15 b^6 (b d-a e)^3 (-7 a B e-4 A b e+11 b B d)}{e^{12} (d+e x)^2}+\frac {14 b^5 (b d-a e)^4 (-6 a B e-5 A b e+11 b B d)}{e^{12} (d+e x)^3}-\frac {21 b^4 (b d-a e)^5 (-5 a B e-6 A b e+11 b B d)}{2 e^{12} (d+e x)^4}+\frac {6 b^3 (b d-a e)^6 (-4 a B e-7 A b e+11 b B d)}{e^{12} (d+e x)^5}-\frac {5 b^2 (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{2 e^{12} (d+e x)^6}+\frac {5 b (b d-a e)^8 (-2 a B e-9 A b e+11 b B d)}{7 e^{12} (d+e x)^7}-\frac {(b d-a e)^9 (-a B e-10 A b e+11 b B d)}{8 e^{12} (d+e x)^8}+\frac {(b d-a e)^{10} (B d-A e)}{9 e^{12} (d+e x)^9}+\frac {b^{10} B x^2}{2 e^{10}} \end {gather*}
Antiderivative was successfully verified.
[In]
Int[((a + b*x)^10*(A + B*x))/(d + e*x)^10,x]
[Out]
-((b^9*(10*b*B*d - A*b*e - 10*a*B*e)*x)/e^11) + (b^10*B*x^2)/(2*e^10) + ((b*d - a*e)^10*(B*d - A*e))/(9*e^12*(
d + e*x)^9) - ((b*d - a*e)^9*(11*b*B*d - 10*A*b*e - a*B*e))/(8*e^12*(d + e*x)^8) + (5*b*(b*d - a*e)^8*(11*b*B*
d - 9*A*b*e - 2*a*B*e))/(7*e^12*(d + e*x)^7) - (5*b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b*e - 3*a*B*e))/(2*e^12*(d
+ e*x)^6) + (6*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*e - 4*a*B*e))/(e^12*(d + e*x)^5) - (21*b^4*(b*d - a*e)^5*(
11*b*B*d - 6*A*b*e - 5*a*B*e))/(2*e^12*(d + e*x)^4) + (14*b^5*(b*d - a*e)^4*(11*b*B*d - 5*A*b*e - 6*a*B*e))/(e
^12*(d + e*x)^3) - (15*b^6*(b*d - a*e)^3*(11*b*B*d - 4*A*b*e - 7*a*B*e))/(e^12*(d + e*x)^2) + (15*b^7*(b*d - a
*e)^2*(11*b*B*d - 3*A*b*e - 8*a*B*e))/(e^12*(d + e*x)) + (5*b^8*(b*d - a*e)*(11*b*B*d - 2*A*b*e - 9*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)^{10}} \, dx &=\int \left (\frac {b^9 (-10 b B d+A b e+10 a B e)}{e^{11}}+\frac {b^{10} B x}{e^{10}}+\frac {(-b d+a e)^{10} (-B d+A e)}{e^{11} (d+e x)^{10}}+\frac {(-b d+a e)^9 (-11 b B d+10 A b e+a B e)}{e^{11} (d+e x)^9}+\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)^8}-\frac {15 b^2 (b d-a e)^7 (-11 b B d+8 A b e+3 a B e)}{e^{11} (d+e x)^7}+\frac {30 b^3 (b d-a e)^6 (-11 b B d+7 A b e+4 a B e)}{e^{11} (d+e x)^6}-\frac {42 b^4 (b d-a e)^5 (-11 b B d+6 A b e+5 a B e)}{e^{11} (d+e x)^5}+\frac {42 b^5 (b d-a e)^4 (-11 b B d+5 A b e+6 a B e)}{e^{11} (d+e x)^4}-\frac {30 b^6 (b d-a e)^3 (-11 b B d+4 A b e+7 a B e)}{e^{11} (d+e x)^3}+\frac {15 b^7 (b d-a e)^2 (-11 b B d+3 A b e+8 a B e)}{e^{11} (d+e x)^2}-\frac {5 b^8 (b d-a e) (-11 b B d+2 A b e+9 a B e)}{e^{11} (d+e x)}\right ) \, dx\\ &=-\frac {b^9 (10 b B d-A b e-10 a B e) x}{e^{11}}+\frac {b^{10} B x^2}{2 e^{10}}+\frac {(b d-a e)^{10} (B d-A e)}{9 e^{12} (d+e x)^9}-\frac {(b d-a e)^9 (11 b B d-10 A b e-a B e)}{8 e^{12} (d+e x)^8}+\frac {5 b (b d-a e)^8 (11 b B d-9 A b e-2 a B e)}{7 e^{12} (d+e x)^7}-\frac {5 b^2 (b d-a e)^7 (11 b B d-8 A b e-3 a B e)}{2 e^{12} (d+e x)^6}+\frac {6 b^3 (b d-a e)^6 (11 b B d-7 A b e-4 a B e)}{e^{12} (d+e x)^5}-\frac {21 b^4 (b d-a e)^5 (11 b B d-6 A b e-5 a B e)}{2 e^{12} (d+e x)^4}+\frac {14 b^5 (b d-a e)^4 (11 b B d-5 A b e-6 a B e)}{e^{12} (d+e x)^3}-\frac {15 b^6 (b d-a e)^3 (11 b B d-4 A b e-7 a B e)}{e^{12} (d+e x)^2}+\frac {15 b^7 (b d-a e)^2 (11 b B d-3 A b e-8 a B e)}{e^{12} (d+e x)}+\frac {5 b^8 (b d-a e) (11 b B d-2 A b e-9 a B e) \log (d+e x)}{e^{12}}\\ \end {align*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(1460\) vs. \(2(441)=882\).
time = 0.63, size = 1460, normalized size = 3.31 \begin {gather*} -\frac {7 a^{10} e^{10} (8 A e+B (d+9 e x))+10 a^9 b e^9 \left (7 A e (d+9 e x)+2 B \left (d^2+9 d e x+36 e^2 x^2\right )\right )+45 a^8 b^2 e^8 \left (2 A e \left (d^2+9 d e x+36 e^2 x^2\right )+B \left (d^3+9 d^2 e x+36 d e^2 x^2+84 e^3 x^3\right )\right )+24 a^7 b^3 e^7 \left (5 A e \left (d^3+9 d^2 e x+36 d e^2 x^2+84 e^3 x^3\right )+4 B \left (d^4+9 d^3 e x+36 d^2 e^2 x^2+84 d e^3 x^3+126 e^4 x^4\right )\right )+42 a^6 b^4 e^6 \left (4 A e \left (d^4+9 d^3 e x+36 d^2 e^2 x^2+84 d e^3 x^3+126 e^4 x^4\right )+5 B \left (d^5+9 d^4 e x+36 d^3 e^2 x^2+84 d^2 e^3 x^3+126 d e^4 x^4+126 e^5 x^5\right )\right )+252 a^5 b^5 e^5 \left (A e \left (d^5+9 d^4 e x+36 d^3 e^2 x^2+84 d^2 e^3 x^3+126 d e^4 x^4+126 e^5 x^5\right )+2 B \left (d^6+9 d^5 e x+36 d^4 e^2 x^2+84 d^3 e^3 x^3+126 d^2 e^4 x^4+126 d e^5 x^5+84 e^6 x^6\right )\right )+210 a^4 b^6 e^4 \left (2 A e \left (d^6+9 d^5 e x+36 d^4 e^2 x^2+84 d^3 e^3 x^3+126 d^2 e^4 x^4+126 d e^5 x^5+84 e^6 x^6\right )+7 B \left (d^7+9 d^6 e x+36 d^5 e^2 x^2+84 d^4 e^3 x^3+126 d^3 e^4 x^4+126 d^2 e^5 x^5+84 d e^6 x^6+36 e^7 x^7\right )\right )+840 a^3 b^7 e^3 \left (A e \left (d^7+9 d^6 e x+36 d^5 e^2 x^2+84 d^4 e^3 x^3+126 d^3 e^4 x^4+126 d^2 e^5 x^5+84 d e^6 x^6+36 e^7 x^7\right )+8 B \left (d^8+9 d^7 e x+36 d^6 e^2 x^2+84 d^5 e^3 x^3+126 d^4 e^4 x^4+126 d^3 e^5 x^5+84 d^2 e^6 x^6+36 d e^7 x^7+9 e^8 x^8\right )\right )-9 a^2 b^8 e^2 \left (-280 A e \left (d^8+9 d^7 e x+36 d^6 e^2 x^2+84 d^5 e^3 x^3+126 d^4 e^4 x^4+126 d^3 e^5 x^5+84 d^2 e^6 x^6+36 d e^7 x^7+9 e^8 x^8\right )+B d \left (7129 d^8+61641 d^7 e x+235224 d^6 e^2 x^2+518616 d^5 e^3 x^3+725004 d^4 e^4 x^4+661500 d^3 e^5 x^5+388080 d^2 e^6 x^6+136080 d e^7 x^7+22680 e^8 x^8\right )\right )-2 a b^9 e \left (A d e \left (7129 d^8+61641 d^7 e x+235224 d^6 e^2 x^2+518616 d^5 e^3 x^3+725004 d^4 e^4 x^4+661500 d^3 e^5 x^5+388080 d^2 e^6 x^6+136080 d e^7 x^7+22680 e^8 x^8\right )-10 B \left (4861 d^{10}+41229 d^9 e x+153576 d^8 e^2 x^2+328104 d^7 e^3 x^3+439236 d^6 e^4 x^4+375732 d^5 e^5 x^5+197568 d^4 e^6 x^6+54432 d^3 e^7 x^7+2268 d^2 e^8 x^8-2268 d e^9 x^9-252 e^{10} x^{10}\right )\right )-b^{10} \left (-2 A e \left (4861 d^{10}+41229 d^9 e x+153576 d^8 e^2 x^2+328104 d^7 e^3 x^3+439236 d^6 e^4 x^4+375732 d^5 e^5 x^5+197568 d^4 e^6 x^6+54432 d^3 e^7 x^7+2268 d^2 e^8 x^8-2268 d e^9 x^9-252 e^{10} x^{10}\right )+B \left (42131 d^{11}+351459 d^{10} e x+1281096 d^9 e^2 x^2+2656584 d^8 e^3 x^3+3402756 d^7 e^4 x^4+2704212 d^6 e^5 x^5+1220688 d^5 e^6 x^6+190512 d^4 e^7 x^7-77112 d^3 e^8 x^8-36288 d^2 e^9 x^9-2772 d e^{10} x^{10}+252 e^{11} x^{11}\right )\right )-2520 b^8 (b d-a e) (11 b B d-2 A b e-9 a B e) (d+e x)^9 \log (d+e x)}{504 e^{12} (d+e x)^9} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[((a + b*x)^10*(A + B*x))/(d + e*x)^10,x]
[Out]
-1/504*(7*a^10*e^10*(8*A*e + B*(d + 9*e*x)) + 10*a^9*b*e^9*(7*A*e*(d + 9*e*x) + 2*B*(d^2 + 9*d*e*x + 36*e^2*x^
2)) + 45*a^8*b^2*e^8*(2*A*e*(d^2 + 9*d*e*x + 36*e^2*x^2) + B*(d^3 + 9*d^2*e*x + 36*d*e^2*x^2 + 84*e^3*x^3)) +
24*a^7*b^3*e^7*(5*A*e*(d^3 + 9*d^2*e*x + 36*d*e^2*x^2 + 84*e^3*x^3) + 4*B*(d^4 + 9*d^3*e*x + 36*d^2*e^2*x^2 +
84*d*e^3*x^3 + 126*e^4*x^4)) + 42*a^6*b^4*e^6*(4*A*e*(d^4 + 9*d^3*e*x + 36*d^2*e^2*x^2 + 84*d*e^3*x^3 + 126*e^
4*x^4) + 5*B*(d^5 + 9*d^4*e*x + 36*d^3*e^2*x^2 + 84*d^2*e^3*x^3 + 126*d*e^4*x^4 + 126*e^5*x^5)) + 252*a^5*b^5*
e^5*(A*e*(d^5 + 9*d^4*e*x + 36*d^3*e^2*x^2 + 84*d^2*e^3*x^3 + 126*d*e^4*x^4 + 126*e^5*x^5) + 2*B*(d^6 + 9*d^5*
e*x + 36*d^4*e^2*x^2 + 84*d^3*e^3*x^3 + 126*d^2*e^4*x^4 + 126*d*e^5*x^5 + 84*e^6*x^6)) + 210*a^4*b^6*e^4*(2*A*
e*(d^6 + 9*d^5*e*x + 36*d^4*e^2*x^2 + 84*d^3*e^3*x^3 + 126*d^2*e^4*x^4 + 126*d*e^5*x^5 + 84*e^6*x^6) + 7*B*(d^
7 + 9*d^6*e*x + 36*d^5*e^2*x^2 + 84*d^4*e^3*x^3 + 126*d^3*e^4*x^4 + 126*d^2*e^5*x^5 + 84*d*e^6*x^6 + 36*e^7*x^
7)) + 840*a^3*b^7*e^3*(A*e*(d^7 + 9*d^6*e*x + 36*d^5*e^2*x^2 + 84*d^4*e^3*x^3 + 126*d^3*e^4*x^4 + 126*d^2*e^5*
x^5 + 84*d*e^6*x^6 + 36*e^7*x^7) + 8*B*(d^8 + 9*d^7*e*x + 36*d^6*e^2*x^2 + 84*d^5*e^3*x^3 + 126*d^4*e^4*x^4 +
126*d^3*e^5*x^5 + 84*d^2*e^6*x^6 + 36*d*e^7*x^7 + 9*e^8*x^8)) - 9*a^2*b^8*e^2*(-280*A*e*(d^8 + 9*d^7*e*x + 36*
d^6*e^2*x^2 + 84*d^5*e^3*x^3 + 126*d^4*e^4*x^4 + 126*d^3*e^5*x^5 + 84*d^2*e^6*x^6 + 36*d*e^7*x^7 + 9*e^8*x^8)
+ B*d*(7129*d^8 + 61641*d^7*e*x + 235224*d^6*e^2*x^2 + 518616*d^5*e^3*x^3 + 725004*d^4*e^4*x^4 + 661500*d^3*e^
5*x^5 + 388080*d^2*e^6*x^6 + 136080*d*e^7*x^7 + 22680*e^8*x^8)) - 2*a*b^9*e*(A*d*e*(7129*d^8 + 61641*d^7*e*x +
235224*d^6*e^2*x^2 + 518616*d^5*e^3*x^3 + 725004*d^4*e^4*x^4 + 661500*d^3*e^5*x^5 + 388080*d^2*e^6*x^6 + 1360
80*d*e^7*x^7 + 22680*e^8*x^8) - 10*B*(4861*d^10 + 41229*d^9*e*x + 153576*d^8*e^2*x^2 + 328104*d^7*e^3*x^3 + 43
9236*d^6*e^4*x^4 + 375732*d^5*e^5*x^5 + 197568*d^4*e^6*x^6 + 54432*d^3*e^7*x^7 + 2268*d^2*e^8*x^8 - 2268*d*e^9
*x^9 - 252*e^10*x^10)) - b^10*(-2*A*e*(4861*d^10 + 41229*d^9*e*x + 153576*d^8*e^2*x^2 + 328104*d^7*e^3*x^3 + 4
39236*d^6*e^4*x^4 + 375732*d^5*e^5*x^5 + 197568*d^4*e^6*x^6 + 54432*d^3*e^7*x^7 + 2268*d^2*e^8*x^8 - 2268*d*e^
9*x^9 - 252*e^10*x^10) + B*(42131*d^11 + 351459*d^10*e*x + 1281096*d^9*e^2*x^2 + 2656584*d^8*e^3*x^3 + 3402756
*d^7*e^4*x^4 + 2704212*d^6*e^5*x^5 + 1220688*d^5*e^6*x^6 + 190512*d^4*e^7*x^7 - 77112*d^3*e^8*x^8 - 36288*d^2*
e^9*x^9 - 2772*d*e^10*x^10 + 252*e^11*x^11)) - 2520*b^8*(b*d - a*e)*(11*b*B*d - 2*A*b*e - 9*a*B*e)*(d + e*x)^9
*Log[d + e*x])/(e^12*(d + e*x)^9)
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(1927\) vs.
\(2(429)=858\).
time = 0.08, size = 1928, normalized size = 4.37
| | |
| method |
result |
size |
| | |
| default |
\(\text {Expression too large to display}\) |
\(1928\) |
| norman |
\(\text {Expression too large to display}\) |
\(1933\) |
| risch |
\(\text {Expression too large to display}\) |
\(1942\) |
| | |
|
|
|
|
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((b*x+a)^10*(B*x+A)/(e*x+d)^10,x,method=_RETURNVERBOSE)
[Out]
b^9/e^11*(1/2*B*b*e*x^2+A*b*e*x+10*B*a*e*x-10*B*b*d*x)-15*b^6/e^12*(4*A*a^3*b*e^4-12*A*a^2*b^2*d*e^3+12*A*a*b^
3*d^2*e^2-4*A*b^4*d^3*e+7*B*a^4*e^4-32*B*a^3*b*d*e^3+54*B*a^2*b^2*d^2*e^2-40*B*a*b^3*d^3*e+11*B*b^4*d^4)/(e*x+
d)^2-21/2*b^4/e^12*(6*A*a^5*b*e^6-30*A*a^4*b^2*d*e^5+60*A*a^3*b^3*d^2*e^4-60*A*a^2*b^4*d^3*e^3+30*A*a*b^5*d^4*
e^2-6*A*b^6*d^5*e+5*B*a^6*e^6-36*B*a^5*b*d*e^5+105*B*a^4*b^2*d^2*e^4-160*B*a^3*b^3*d^3*e^3+135*B*a^2*b^4*d^4*e
^2-60*B*a*b^5*d^5*e+11*B*b^6*d^6)/(e*x+d)^4-1/8/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)^8-15*b^7/e^12*(3*A*a^2*b*e^3-6*A*a*b^2*d*e^2+3*A*b^3*d^2*e+8*B*a
^3*e^3-27*B*a^2*b*d*e^2+30*B*a*b^2*d^2*e-11*B*b^3*d^3)/(e*x+d)-1/9*(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)^9-5/7*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)/(e*x+d)^7-5/2*b^2/e^12*(8*A*a^7*b*e^8-56*A*a^6*b^2*d*e^7+168*A*a^5*b^3*d^2*e^6-280*A*a^4*b^4*d^3
*e^5+280*A*a^3*b^5*d^4*e^4-168*A*a^2*b^6*d^5*e^3+56*A*a*b^7*d^6*e^2-8*A*b^8*d^7*e+3*B*a^8*e^8-32*B*a^7*b*d*e^7
+140*B*a^6*b^2*d^2*e^6-336*B*a^5*b^3*d^3*e^5+490*B*a^4*b^4*d^4*e^4-448*B*a^3*b^5*d^5*e^3+252*B*a^2*b^6*d^6*e^2
-80*B*a*b^7*d^7*e+11*B*b^8*d^8)/(e*x+d)^6-6*b^3/e^12*(7*A*a^6*b*e^7-42*A*a^5*b^2*d*e^6+105*A*a^4*b^3*d^2*e^5-1
40*A*a^3*b^4*d^3*e^4+105*A*a^2*b^5*d^4*e^3-42*A*a*b^6*d^5*e^2+7*A*b^7*d^6*e+4*B*a^7*e^7-35*B*a^6*b*d*e^6+126*B
*a^5*b^2*d^2*e^5-245*B*a^4*b^3*d^3*e^4+280*B*a^3*b^4*d^4*e^3-189*B*a^2*b^5*d^5*e^2+70*B*a*b^6*d^6*e-11*B*b^7*d
^7)/(e*x+d)^5-14*b^5/e^12*(5*A*a^4*b*e^5-20*A*a^3*b^2*d*e^4+30*A*a^2*b^3*d^2*e^3-20*A*a*b^4*d^3*e^2+5*A*b^5*d^
4*e+6*B*a^5*e^5-35*B*a^4*b*d*e^4+80*B*a^3*b^2*d^2*e^3-90*B*a^2*b^3*d^3*e^2+50*B*a*b^4*d^4*e-11*B*b^5*d^5)/(e*x
+d)^3+5*b^8/e^12*(2*A*a*b*e^2-2*A*b^2*d*e+9*B*a^2*e^2-20*B*a*b*d*e+11*B*b^2*d^2)*ln(e*x+d)
________________________________________________________________________________________
Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 1931 vs.
\(2 (458) = 916\).
time = 0.54, size = 1931, normalized size = 4.38 \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)^10,x, algorithm="maxima")
[Out]
5*(11*B*b^10*d^2 + 9*B*a^2*b^8*e^2 + 2*A*a*b^9*e^2 - 2*(10*B*a*b^9*e + A*b^10*e)*d)*e^(-12)*log(x*e + d) + 1/2
*(B*b^10*x^2*e - 2*(10*B*b^10*d - 10*B*a*b^9*e - A*b^10*e)*x)*e^(-11) + 1/504*(42131*B*b^10*d^11 - 56*A*a^10*e
^11 - 9722*(10*B*a*b^9*e + A*b^10*e)*d^10 + 7129*(9*B*a^2*b^8*e^2 + 2*A*a*b^9*e^2)*d^9 - 840*(8*B*a^3*b^7*e^3
+ 3*A*a^2*b^8*e^3)*d^8 + 7560*(11*B*b^10*d^3*e^8 - 8*B*a^3*b^7*e^11 - 3*A*a^2*b^8*e^11 - 3*(10*B*a*b^9*e^9 + A
*b^10*e^9)*d^2 + 3*(9*B*a^2*b^8*e^10 + 2*A*a*b^9*e^10)*d)*x^8 - 210*(7*B*a^4*b^6*e^4 + 4*A*a^3*b^7*e^4)*d^7 +
7560*(77*B*b^10*d^4*e^7 - 7*B*a^4*b^6*e^11 - 4*A*a^3*b^7*e^11 - 20*(10*B*a*b^9*e^8 + A*b^10*e^8)*d^3 + 18*(9*B
*a^2*b^8*e^9 + 2*A*a*b^9*e^9)*d^2 - 4*(8*B*a^3*b^7*e^10 + 3*A*a^2*b^8*e^10)*d)*x^7 - 84*(6*B*a^5*b^5*e^5 + 5*A
*a^4*b^6*e^5)*d^6 + 3528*(517*B*b^10*d^5*e^6 - 12*B*a^5*b^5*e^11 - 10*A*a^4*b^6*e^11 - 130*(10*B*a*b^9*e^7 + A
*b^10*e^7)*d^4 + 110*(9*B*a^2*b^8*e^8 + 2*A*a*b^9*e^8)*d^3 - 20*(8*B*a^3*b^7*e^9 + 3*A*a^2*b^8*e^9)*d^2 - 5*(7
*B*a^4*b^6*e^10 + 4*A*a^3*b^7*e^10)*d)*x^6 - 42*(5*B*a^6*b^4*e^6 + 6*A*a^5*b^5*e^6)*d^5 + 5292*(627*B*b^10*d^6
*e^5 - 5*B*a^6*b^4*e^11 - 6*A*a^5*b^5*e^11 - 154*(10*B*a*b^9*e^6 + A*b^10*e^6)*d^5 + 125*(9*B*a^2*b^8*e^7 + 2*
A*a*b^9*e^7)*d^4 - 20*(8*B*a^3*b^7*e^8 + 3*A*a^2*b^8*e^8)*d^3 - 5*(7*B*a^4*b^6*e^9 + 4*A*a^3*b^7*e^9)*d^2 - 2*
(6*B*a^5*b^5*e^10 + 5*A*a^4*b^6*e^10)*d)*x^5 - 24*(4*B*a^7*b^3*e^7 + 7*A*a^6*b^4*e^7)*d^4 + 756*(5049*B*b^10*d
^7*e^4 - 16*B*a^7*b^3*e^11 - 28*A*a^6*b^4*e^11 - 1218*(10*B*a*b^9*e^5 + A*b^10*e^5)*d^6 + 959*(9*B*a^2*b^8*e^6
+ 2*A*a*b^9*e^6)*d^5 - 140*(8*B*a^3*b^7*e^7 + 3*A*a^2*b^8*e^7)*d^4 - 35*(7*B*a^4*b^6*e^8 + 4*A*a^3*b^7*e^8)*d
^3 - 14*(6*B*a^5*b^5*e^9 + 5*A*a^4*b^6*e^9)*d^2 - 7*(5*B*a^6*b^4*e^10 + 6*A*a^5*b^5*e^10)*d)*x^4 - 15*(3*B*a^8
*b^2*e^8 + 8*A*a^7*b^3*e^8)*d^3 + 252*(11253*B*b^10*d^8*e^3 - 15*B*a^8*b^2*e^11 - 40*A*a^7*b^3*e^11 - 2676*(10
*B*a*b^9*e^4 + A*b^10*e^4)*d^7 + 2058*(9*B*a^2*b^8*e^5 + 2*A*a*b^9*e^5)*d^6 - 280*(8*B*a^3*b^7*e^6 + 3*A*a^2*b
^8*e^6)*d^5 - 70*(7*B*a^4*b^6*e^7 + 4*A*a^3*b^7*e^7)*d^4 - 28*(6*B*a^5*b^5*e^8 + 5*A*a^4*b^6*e^8)*d^3 - 14*(5*
B*a^6*b^4*e^9 + 6*A*a^5*b^5*e^9)*d^2 - 8*(4*B*a^7*b^3*e^10 + 7*A*a^6*b^4*e^10)*d)*x^3 - 10*(2*B*a^9*b*e^9 + 9*
A*a^8*b^2*e^9)*d^2 + 36*(36839*B*b^10*d^9*e^2 - 20*B*a^9*b*e^11 - 90*A*a^8*b^2*e^11 - 8658*(10*B*a*b^9*e^3 + A
*b^10*e^3)*d^8 + 6534*(9*B*a^2*b^8*e^4 + 2*A*a*b^9*e^4)*d^7 - 840*(8*B*a^3*b^7*e^5 + 3*A*a^2*b^8*e^5)*d^6 - 21
0*(7*B*a^4*b^6*e^6 + 4*A*a^3*b^7*e^6)*d^5 - 84*(6*B*a^5*b^5*e^7 + 5*A*a^4*b^6*e^7)*d^4 - 42*(5*B*a^6*b^4*e^8 +
6*A*a^5*b^5*e^8)*d^3 - 24*(4*B*a^7*b^3*e^9 + 7*A*a^6*b^4*e^9)*d^2 - 15*(3*B*a^8*b^2*e^10 + 8*A*a^7*b^3*e^10)*
d)*x^2 - 7*(B*a^10*e^10 + 10*A*a^9*b*e^10)*d + 9*(39611*B*b^10*d^10*e - 7*B*a^10*e^11 - 70*A*a^9*b*e^11 - 9218
*(10*B*a*b^9*e^2 + A*b^10*e^2)*d^9 + 6849*(9*B*a^2*b^8*e^3 + 2*A*a*b^9*e^3)*d^8 - 840*(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 - 84*(6*B*a^5*b^5*e^6 + 5*A*a^4*b^6*e^6)*d^5 - 4
2*(5*B*a^6*b^4*e^7 + 6*A*a^5*b^5*e^7)*d^4 - 24*(4*B*a^7*b^3*e^8 + 7*A*a^6*b^4*e^8)*d^3 - 15*(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^9*e^21 + 9*d*x^8*e^20 + 36*d^2*x^7*e^1
9 + 84*d^3*x^6*e^18 + 126*d^4*x^5*e^17 + 126*d^5*x^4*e^16 + 84*d^6*x^3*e^15 + 36*d^7*x^2*e^14 + 9*d^8*x*e^13 +
d^9*e^12)
________________________________________________________________________________________
Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 2430 vs.
\(2 (458) = 916\).
time = 1.04, size = 2430, normalized size = 5.51 \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)^10,x, algorithm="fricas")
[Out]
1/504*(42131*B*b^10*d^11 + (252*B*b^10*x^11 - 56*A*a^10 + 504*(10*B*a*b^9 + A*b^10)*x^10 - 7560*(8*B*a^3*b^7 +
3*A*a^2*b^8)*x^8 - 7560*(7*B*a^4*b^6 + 4*A*a^3*b^7)*x^7 - 7056*(6*B*a^5*b^5 + 5*A*a^4*b^6)*x^6 - 5292*(5*B*a^
6*b^4 + 6*A*a^5*b^5)*x^5 - 3024*(4*B*a^7*b^3 + 7*A*a^6*b^4)*x^4 - 1260*(3*B*a^8*b^2 + 8*A*a^7*b^3)*x^3 - 360*(
2*B*a^9*b + 9*A*a^8*b^2)*x^2 - 63*(B*a^10 + 10*A*a^9*b)*x)*e^11 - (2772*B*b^10*d*x^10 - 4536*(10*B*a*b^9 + A*b
^10)*d*x^9 - 22680*(9*B*a^2*b^8 + 2*A*a*b^9)*d*x^8 + 30240*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*x^7 + 17640*(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 + 5292*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*x^4 +
2016*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*x^3 + 540*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*x^2 + 90*(2*B*a^9*b + 9*A*a^8*b^2)*
d*x + 7*(B*a^10 + 10*A*a^9*b)*d)*e^10 - (36288*B*b^10*d^2*x^9 + 4536*(10*B*a*b^9 + A*b^10)*d^2*x^8 - 136080*(9
*B*a^2*b^8 + 2*A*a*b^9)*d^2*x^7 + 70560*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*x^6 + 26460*(7*B*a^4*b^6 + 4*A*a^3*b^7
)*d^2*x^5 + 10584*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*x^4 + 3528*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*x^3 + 864*(4*B*a^
7*b^3 + 7*A*a^6*b^4)*d^2*x^2 + 135*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*x + 10*(2*B*a^9*b + 9*A*a^8*b^2)*d^2)*e^9 -
3*(25704*B*b^10*d^3*x^8 + 36288*(10*B*a*b^9 + A*b^10)*d^3*x^7 - 129360*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*x^6 + 35
280*(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 + 2352*(6*B*a^5*b^5 + 5*A*a
^4*b^6)*d^3*x^3 + 504*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*x^2 + 72*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*x + 5*(3*B*a^8*
b^2 + 8*A*a^7*b^3)*d^3)*e^8 + 6*(31752*B*b^10*d^4*x^7 - 65856*(10*B*a*b^9 + A*b^10)*d^4*x^6 + 110250*(9*B*a^2*
b^8 + 2*A*a*b^9)*d^4*x^5 - 17640*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*x^4 - 2940*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*x^
3 - 504*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*x^2 - 63*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*x - 4*(4*B*a^7*b^3 + 7*A*a^6*
b^4)*d^4)*e^7 + 42*(29064*B*b^10*d^5*x^6 - 17892*(10*B*a*b^9 + A*b^10)*d^5*x^5 + 17262*(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 - 180*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*x^2 - 18*(6*B*a^5*
b^5 + 5*A*a^4*b^6)*d^5*x - (5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5)*e^6 + 42*(64386*B*b^10*d^6*x^5 - 20916*(10*B*a*b^9
+ A*b^10)*d^6*x^4 + 12348*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*x^3 - 720*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*x^2 - 45*(7
*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*x - 2*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6)*e^5 + 6*(567126*B*b^10*d^7*x^4 - 109368*(
10*B*a*b^9 + A*b^10)*d^7*x^3 + 39204*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*x^2 - 1260*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*
x - 35*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7)*e^4 + 3*(885528*B*b^10*d^8*x^3 - 102384*(10*B*a*b^9 + A*b^10)*d^8*x^2
+ 20547*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*x - 280*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8)*e^3 + (1281096*B*b^10*d^9*x^2 -
82458*(10*B*a*b^9 + A*b^10)*d^9*x + 7129*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9)*e^2 + (351459*B*b^10*d^10*x - 9722*(1
0*B*a*b^9 + A*b^10)*d^10)*e + 2520*(11*B*b^10*d^11 + (9*B*a^2*b^8 + 2*A*a*b^9)*x^9*e^11 - (2*(10*B*a*b^9 + A*b
^10)*d*x^9 - 9*(9*B*a^2*b^8 + 2*A*a*b^9)*d*x^8)*e^10 + (11*B*b^10*d^2*x^9 - 18*(10*B*a*b^9 + A*b^10)*d^2*x^8 +
36*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*x^7)*e^9 + 3*(33*B*b^10*d^3*x^8 - 24*(10*B*a*b^9 + A*b^10)*d^3*x^7 + 28*(9*B
*a^2*b^8 + 2*A*a*b^9)*d^3*x^6)*e^8 + 6*(66*B*b^10*d^4*x^7 - 28*(10*B*a*b^9 + A*b^10)*d^4*x^6 + 21*(9*B*a^2*b^8
+ 2*A*a*b^9)*d^4*x^5)*e^7 + 42*(22*B*b^10*d^5*x^6 - 6*(10*B*a*b^9 + A*b^10)*d^5*x^5 + 3*(9*B*a^2*b^8 + 2*A*a*
b^9)*d^5*x^4)*e^6 + 42*(33*B*b^10*d^6*x^5 - 6*(10*B*a*b^9 + A*b^10)*d^6*x^4 + 2*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*
x^3)*e^5 + 6*(231*B*b^10*d^7*x^4 - 28*(10*B*a*b^9 + A*b^10)*d^7*x^3 + 6*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*x^2)*e^4
+ 3*(308*B*b^10*d^8*x^3 - 24*(10*B*a*b^9 + A*b^10)*d^8*x^2 + 3*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*x)*e^3 + (396*B*
b^10*d^9*x^2 - 18*(10*B*a*b^9 + A*b^10)*d^9*x + (9*B*a^2*b^8 + 2*A*a*b^9)*d^9)*e^2 + (99*B*b^10*d^10*x - 2*(10
*B*a*b^9 + A*b^10)*d^10)*e)*log(x*e + d))/(x^9*e^21 + 9*d*x^8*e^20 + 36*d^2*x^7*e^19 + 84*d^3*x^6*e^18 + 126*d
^4*x^5*e^17 + 126*d^5*x^4*e^16 + 84*d^6*x^3*e^15 + 36*d^7*x^2*e^14 + 9*d^8*x*e^13 + d^9*e^12)
________________________________________________________________________________________
Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((b*x+a)**10*(B*x+A)/(e*x+d)**10,x)
[Out]
Timed out
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 1843 vs.
\(2 (458) = 916\).
time = 1.69, size = 1843, normalized size = 4.18 \begin {gather*} 5 \, {\left (11 \, B b^{10} d^{2} - 20 \, B a b^{9} d e - 2 \, A b^{10} d e + 9 \, B a^{2} b^{8} e^{2} + 2 \, A a b^{9} e^{2}\right )} e^{\left (-12\right )} \log \left ({\left | x e + d \right |}\right ) + \frac {1}{2} \, {\left (B b^{10} x^{2} e^{10} - 20 \, B b^{10} d x e^{9} + 20 \, B a b^{9} x e^{10} + 2 \, A b^{10} x e^{10}\right )} e^{\left (-20\right )} + \frac {{\left (42131 \, B b^{10} d^{11} - 97220 \, B a b^{9} d^{10} e - 9722 \, A b^{10} d^{10} e + 64161 \, B a^{2} b^{8} d^{9} e^{2} + 14258 \, A a b^{9} d^{9} e^{2} - 6720 \, B a^{3} b^{7} d^{8} e^{3} - 2520 \, A a^{2} b^{8} d^{8} e^{3} - 1470 \, B a^{4} b^{6} d^{7} e^{4} - 840 \, A a^{3} b^{7} d^{7} e^{4} - 504 \, B a^{5} b^{5} d^{6} e^{5} - 420 \, A a^{4} b^{6} d^{6} e^{5} - 210 \, B a^{6} b^{4} d^{5} e^{6} - 252 \, A a^{5} b^{5} d^{5} e^{6} - 96 \, B a^{7} b^{3} d^{4} e^{7} - 168 \, 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} - 20 \, B a^{9} b d^{2} e^{9} - 90 \, A a^{8} b^{2} d^{2} e^{9} - 7 \, B a^{10} d e^{10} - 70 \, A a^{9} b d e^{10} - 56 \, A a^{10} e^{11} + 7560 \, {\left (11 \, B b^{10} d^{3} e^{8} - 30 \, B a b^{9} d^{2} e^{9} - 3 \, A b^{10} d^{2} e^{9} + 27 \, B a^{2} b^{8} d e^{10} + 6 \, A a b^{9} d e^{10} - 8 \, B a^{3} b^{7} e^{11} - 3 \, A a^{2} b^{8} e^{11}\right )} x^{8} + 7560 \, {\left (77 \, B b^{10} d^{4} e^{7} - 200 \, B a b^{9} d^{3} e^{8} - 20 \, A b^{10} d^{3} e^{8} + 162 \, B a^{2} b^{8} d^{2} e^{9} + 36 \, A a b^{9} d^{2} e^{9} - 32 \, B a^{3} b^{7} d e^{10} - 12 \, A a^{2} b^{8} d e^{10} - 7 \, B a^{4} b^{6} e^{11} - 4 \, A a^{3} b^{7} e^{11}\right )} x^{7} + 3528 \, {\left (517 \, B b^{10} d^{5} e^{6} - 1300 \, B a b^{9} d^{4} e^{7} - 130 \, A b^{10} d^{4} e^{7} + 990 \, B a^{2} b^{8} d^{3} e^{8} + 220 \, A a b^{9} d^{3} e^{8} - 160 \, B a^{3} b^{7} d^{2} e^{9} - 60 \, A a^{2} b^{8} d^{2} e^{9} - 35 \, B a^{4} b^{6} d e^{10} - 20 \, A a^{3} b^{7} d e^{10} - 12 \, B a^{5} b^{5} e^{11} - 10 \, A a^{4} b^{6} e^{11}\right )} x^{6} + 5292 \, {\left (627 \, B b^{10} d^{6} e^{5} - 1540 \, B a b^{9} d^{5} e^{6} - 154 \, A b^{10} d^{5} e^{6} + 1125 \, B a^{2} b^{8} d^{4} e^{7} + 250 \, 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} - 35 \, B a^{4} b^{6} d^{2} e^{9} - 20 \, A a^{3} b^{7} d^{2} e^{9} - 12 \, B a^{5} b^{5} d e^{10} - 10 \, A a^{4} b^{6} d e^{10} - 5 \, B a^{6} b^{4} e^{11} - 6 \, A a^{5} b^{5} e^{11}\right )} x^{5} + 756 \, {\left (5049 \, B b^{10} d^{7} e^{4} - 12180 \, B a b^{9} d^{6} e^{5} - 1218 \, A b^{10} d^{6} e^{5} + 8631 \, B a^{2} b^{8} d^{5} e^{6} + 1918 \, A a b^{9} d^{5} e^{6} - 1120 \, B a^{3} b^{7} d^{4} e^{7} - 420 \, A a^{2} b^{8} d^{4} e^{7} - 245 \, B a^{4} b^{6} d^{3} e^{8} - 140 \, A a^{3} b^{7} d^{3} e^{8} - 84 \, B a^{5} b^{5} d^{2} e^{9} - 70 \, 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} - 16 \, B a^{7} b^{3} e^{11} - 28 \, A a^{6} b^{4} e^{11}\right )} x^{4} + 252 \, {\left (11253 \, B b^{10} d^{8} e^{3} - 26760 \, B a b^{9} d^{7} e^{4} - 2676 \, A b^{10} d^{7} e^{4} + 18522 \, B a^{2} b^{8} d^{6} e^{5} + 4116 \, A a b^{9} d^{6} e^{5} - 2240 \, B a^{3} b^{7} d^{5} e^{6} - 840 \, A a^{2} b^{8} d^{5} e^{6} - 490 \, B a^{4} b^{6} d^{4} e^{7} - 280 \, A a^{3} b^{7} d^{4} e^{7} - 168 \, B a^{5} b^{5} d^{3} e^{8} - 140 \, A a^{4} b^{6} d^{3} e^{8} - 70 \, B a^{6} b^{4} d^{2} e^{9} - 84 \, A a^{5} b^{5} d^{2} e^{9} - 32 \, B a^{7} b^{3} d e^{10} - 56 \, A a^{6} b^{4} d e^{10} - 15 \, B a^{8} b^{2} e^{11} - 40 \, A a^{7} b^{3} e^{11}\right )} x^{3} + 36 \, {\left (36839 \, B b^{10} d^{9} e^{2} - 86580 \, B a b^{9} d^{8} e^{3} - 8658 \, A b^{10} d^{8} e^{3} + 58806 \, B a^{2} b^{8} d^{7} e^{4} + 13068 \, A a b^{9} d^{7} e^{4} - 6720 \, B a^{3} b^{7} d^{6} e^{5} - 2520 \, A a^{2} b^{8} d^{6} e^{5} - 1470 \, B a^{4} b^{6} d^{5} e^{6} - 840 \, A a^{3} b^{7} d^{5} e^{6} - 504 \, B a^{5} b^{5} d^{4} e^{7} - 420 \, A a^{4} b^{6} d^{4} e^{7} - 210 \, B a^{6} b^{4} d^{3} e^{8} - 252 \, A a^{5} b^{5} d^{3} e^{8} - 96 \, B a^{7} b^{3} d^{2} e^{9} - 168 \, A a^{6} b^{4} d^{2} e^{9} - 45 \, B a^{8} b^{2} d e^{10} - 120 \, A a^{7} b^{3} d e^{10} - 20 \, B a^{9} b e^{11} - 90 \, A a^{8} b^{2} e^{11}\right )} x^{2} + 9 \, {\left (39611 \, B b^{10} d^{10} e - 92180 \, B a b^{9} d^{9} e^{2} - 9218 \, A b^{10} d^{9} e^{2} + 61641 \, B a^{2} b^{8} d^{8} e^{3} + 13698 \, A a b^{9} d^{8} e^{3} - 6720 \, B a^{3} b^{7} d^{7} e^{4} - 2520 \, 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} - 504 \, B a^{5} b^{5} d^{5} e^{6} - 420 \, A a^{4} b^{6} d^{5} e^{6} - 210 \, B a^{6} b^{4} d^{4} e^{7} - 252 \, A a^{5} b^{5} d^{4} e^{7} - 96 \, B a^{7} b^{3} d^{3} e^{8} - 168 \, A a^{6} b^{4} d^{3} e^{8} - 45 \, B a^{8} b^{2} d^{2} e^{9} - 120 \, 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} - 7 \, B a^{10} e^{11} - 70 \, A a^{9} b e^{11}\right )} x\right )} e^{\left (-12\right )}}{504 \, {\left (x e + d\right )}^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((b*x+a)^10*(B*x+A)/(e*x+d)^10,x, algorithm="giac")
[Out]
5*(11*B*b^10*d^2 - 20*B*a*b^9*d*e - 2*A*b^10*d*e + 9*B*a^2*b^8*e^2 + 2*A*a*b^9*e^2)*e^(-12)*log(abs(x*e + d))
+ 1/2*(B*b^10*x^2*e^10 - 20*B*b^10*d*x*e^9 + 20*B*a*b^9*x*e^10 + 2*A*b^10*x*e^10)*e^(-20) + 1/504*(42131*B*b^1
0*d^11 - 97220*B*a*b^9*d^10*e - 9722*A*b^10*d^10*e + 64161*B*a^2*b^8*d^9*e^2 + 14258*A*a*b^9*d^9*e^2 - 6720*B*
a^3*b^7*d^8*e^3 - 2520*A*a^2*b^8*d^8*e^3 - 1470*B*a^4*b^6*d^7*e^4 - 840*A*a^3*b^7*d^7*e^4 - 504*B*a^5*b^5*d^6*
e^5 - 420*A*a^4*b^6*d^6*e^5 - 210*B*a^6*b^4*d^5*e^6 - 252*A*a^5*b^5*d^5*e^6 - 96*B*a^7*b^3*d^4*e^7 - 168*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 - 20*B*a^9*b*d^2*e^9 - 90*A*a^8*b^2*d^2*e^9 - 7*B*
a^10*d*e^10 - 70*A*a^9*b*d*e^10 - 56*A*a^10*e^11 + 7560*(11*B*b^10*d^3*e^8 - 30*B*a*b^9*d^2*e^9 - 3*A*b^10*d^2
*e^9 + 27*B*a^2*b^8*d*e^10 + 6*A*a*b^9*d*e^10 - 8*B*a^3*b^7*e^11 - 3*A*a^2*b^8*e^11)*x^8 + 7560*(77*B*b^10*d^4
*e^7 - 200*B*a*b^9*d^3*e^8 - 20*A*b^10*d^3*e^8 + 162*B*a^2*b^8*d^2*e^9 + 36*A*a*b^9*d^2*e^9 - 32*B*a^3*b^7*d*e
^10 - 12*A*a^2*b^8*d*e^10 - 7*B*a^4*b^6*e^11 - 4*A*a^3*b^7*e^11)*x^7 + 3528*(517*B*b^10*d^5*e^6 - 1300*B*a*b^9
*d^4*e^7 - 130*A*b^10*d^4*e^7 + 990*B*a^2*b^8*d^3*e^8 + 220*A*a*b^9*d^3*e^8 - 160*B*a^3*b^7*d^2*e^9 - 60*A*a^2
*b^8*d^2*e^9 - 35*B*a^4*b^6*d*e^10 - 20*A*a^3*b^7*d*e^10 - 12*B*a^5*b^5*e^11 - 10*A*a^4*b^6*e^11)*x^6 + 5292*(
627*B*b^10*d^6*e^5 - 1540*B*a*b^9*d^5*e^6 - 154*A*b^10*d^5*e^6 + 1125*B*a^2*b^8*d^4*e^7 + 250*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 - 35*B*a^4*b^6*d^2*e^9 - 20*A*a^3*b^7*d^2*e^9 - 12*B*a^5*b^5*d*
e^10 - 10*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 + 756*(5049*B*b^10*d^7*e^4 - 12180*B*a*b
^9*d^6*e^5 - 1218*A*b^10*d^6*e^5 + 8631*B*a^2*b^8*d^5*e^6 + 1918*A*a*b^9*d^5*e^6 - 1120*B*a^3*b^7*d^4*e^7 - 42
0*A*a^2*b^8*d^4*e^7 - 245*B*a^4*b^6*d^3*e^8 - 140*A*a^3*b^7*d^3*e^8 - 84*B*a^5*b^5*d^2*e^9 - 70*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 - 16*B*a^7*b^3*e^11 - 28*A*a^6*b^4*e^11)*x^4 + 252*(11253*B*b^
10*d^8*e^3 - 26760*B*a*b^9*d^7*e^4 - 2676*A*b^10*d^7*e^4 + 18522*B*a^2*b^8*d^6*e^5 + 4116*A*a*b^9*d^6*e^5 - 22
40*B*a^3*b^7*d^5*e^6 - 840*A*a^2*b^8*d^5*e^6 - 490*B*a^4*b^6*d^4*e^7 - 280*A*a^3*b^7*d^4*e^7 - 168*B*a^5*b^5*d
^3*e^8 - 140*A*a^4*b^6*d^3*e^8 - 70*B*a^6*b^4*d^2*e^9 - 84*A*a^5*b^5*d^2*e^9 - 32*B*a^7*b^3*d*e^10 - 56*A*a^6*
b^4*d*e^10 - 15*B*a^8*b^2*e^11 - 40*A*a^7*b^3*e^11)*x^3 + 36*(36839*B*b^10*d^9*e^2 - 86580*B*a*b^9*d^8*e^3 - 8
658*A*b^10*d^8*e^3 + 58806*B*a^2*b^8*d^7*e^4 + 13068*A*a*b^9*d^7*e^4 - 6720*B*a^3*b^7*d^6*e^5 - 2520*A*a^2*b^8
*d^6*e^5 - 1470*B*a^4*b^6*d^5*e^6 - 840*A*a^3*b^7*d^5*e^6 - 504*B*a^5*b^5*d^4*e^7 - 420*A*a^4*b^6*d^4*e^7 - 21
0*B*a^6*b^4*d^3*e^8 - 252*A*a^5*b^5*d^3*e^8 - 96*B*a^7*b^3*d^2*e^9 - 168*A*a^6*b^4*d^2*e^9 - 45*B*a^8*b^2*d*e^
10 - 120*A*a^7*b^3*d*e^10 - 20*B*a^9*b*e^11 - 90*A*a^8*b^2*e^11)*x^2 + 9*(39611*B*b^10*d^10*e - 92180*B*a*b^9*
d^9*e^2 - 9218*A*b^10*d^9*e^2 + 61641*B*a^2*b^8*d^8*e^3 + 13698*A*a*b^9*d^8*e^3 - 6720*B*a^3*b^7*d^7*e^4 - 252
0*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 - 504*B*a^5*b^5*d^5*e^6 - 420*A*a^4*b^6*d
^5*e^6 - 210*B*a^6*b^4*d^4*e^7 - 252*A*a^5*b^5*d^4*e^7 - 96*B*a^7*b^3*d^3*e^8 - 168*A*a^6*b^4*d^3*e^8 - 45*B*a
^8*b^2*d^2*e^9 - 120*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 - 7*B*a^10*e^11 - 70*A*a^9*b*
e^11)*x)*e^(-12)/(x*e + d)^9
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Mupad [B]
time = 1.53, size = 2048, normalized size = 4.64 \begin {gather*} x\,\left (\frac {A\,b^{10}+10\,B\,a\,b^9}{e^{10}}-\frac {10\,B\,b^{10}\,d}{e^{11}}\right )-\frac {x^7\,\left (105\,B\,a^4\,b^6\,e^{10}+480\,B\,a^3\,b^7\,d\,e^9+60\,A\,a^3\,b^7\,e^{10}-2430\,B\,a^2\,b^8\,d^2\,e^8+180\,A\,a^2\,b^8\,d\,e^9+3000\,B\,a\,b^9\,d^3\,e^7-540\,A\,a\,b^9\,d^2\,e^8-1155\,B\,b^{10}\,d^4\,e^6+300\,A\,b^{10}\,d^3\,e^7\right )+x^4\,\left (24\,B\,a^7\,b^3\,e^{10}+\frac {105\,B\,a^6\,b^4\,d\,e^9}{2}+42\,A\,a^6\,b^4\,e^{10}+126\,B\,a^5\,b^5\,d^2\,e^8+63\,A\,a^5\,b^5\,d\,e^9+\frac {735\,B\,a^4\,b^6\,d^3\,e^7}{2}+105\,A\,a^4\,b^6\,d^2\,e^8+1680\,B\,a^3\,b^7\,d^4\,e^6+210\,A\,a^3\,b^7\,d^3\,e^7-\frac {25893\,B\,a^2\,b^8\,d^5\,e^5}{2}+630\,A\,a^2\,b^8\,d^4\,e^6+18270\,B\,a\,b^9\,d^6\,e^4-2877\,A\,a\,b^9\,d^5\,e^5-\frac {15147\,B\,b^{10}\,d^7\,e^3}{2}+1827\,A\,b^{10}\,d^6\,e^4\right )+x^6\,\left (84\,B\,a^5\,b^5\,e^{10}+245\,B\,a^4\,b^6\,d\,e^9+70\,A\,a^4\,b^6\,e^{10}+1120\,B\,a^3\,b^7\,d^2\,e^8+140\,A\,a^3\,b^7\,d\,e^9-6930\,B\,a^2\,b^8\,d^3\,e^7+420\,A\,a^2\,b^8\,d^2\,e^8+9100\,B\,a\,b^9\,d^4\,e^6-1540\,A\,a\,b^9\,d^3\,e^7-3619\,B\,b^{10}\,d^5\,e^5+910\,A\,b^{10}\,d^4\,e^6\right )+x^3\,\left (\frac {15\,B\,a^8\,b^2\,e^{10}}{2}+16\,B\,a^7\,b^3\,d\,e^9+20\,A\,a^7\,b^3\,e^{10}+35\,B\,a^6\,b^4\,d^2\,e^8+28\,A\,a^6\,b^4\,d\,e^9+84\,B\,a^5\,b^5\,d^3\,e^7+42\,A\,a^5\,b^5\,d^2\,e^8+245\,B\,a^4\,b^6\,d^4\,e^6+70\,A\,a^4\,b^6\,d^3\,e^7+1120\,B\,a^3\,b^7\,d^5\,e^5+140\,A\,a^3\,b^7\,d^4\,e^6-9261\,B\,a^2\,b^8\,d^6\,e^4+420\,A\,a^2\,b^8\,d^5\,e^5+13380\,B\,a\,b^9\,d^7\,e^3-2058\,A\,a\,b^9\,d^6\,e^4-\frac {11253\,B\,b^{10}\,d^8\,e^2}{2}+1338\,A\,b^{10}\,d^7\,e^3\right )+\frac {7\,B\,a^{10}\,d\,e^{10}+56\,A\,a^{10}\,e^{11}+20\,B\,a^9\,b\,d^2\,e^9+70\,A\,a^9\,b\,d\,e^{10}+45\,B\,a^8\,b^2\,d^3\,e^8+90\,A\,a^8\,b^2\,d^2\,e^9+96\,B\,a^7\,b^3\,d^4\,e^7+120\,A\,a^7\,b^3\,d^3\,e^8+210\,B\,a^6\,b^4\,d^5\,e^6+168\,A\,a^6\,b^4\,d^4\,e^7+504\,B\,a^5\,b^5\,d^6\,e^5+252\,A\,a^5\,b^5\,d^5\,e^6+1470\,B\,a^4\,b^6\,d^7\,e^4+420\,A\,a^4\,b^6\,d^6\,e^5+6720\,B\,a^3\,b^7\,d^8\,e^3+840\,A\,a^3\,b^7\,d^7\,e^4-64161\,B\,a^2\,b^8\,d^9\,e^2+2520\,A\,a^2\,b^8\,d^8\,e^3+97220\,B\,a\,b^9\,d^{10}\,e-14258\,A\,a\,b^9\,d^9\,e^2-42131\,B\,b^{10}\,d^{11}+9722\,A\,b^{10}\,d^{10}\,e}{504\,e}+x\,\left (\frac {B\,a^{10}\,e^{10}}{8}+\frac {5\,B\,a^9\,b\,d\,e^9}{14}+\frac {5\,A\,a^9\,b\,e^{10}}{4}+\frac {45\,B\,a^8\,b^2\,d^2\,e^8}{56}+\frac {45\,A\,a^8\,b^2\,d\,e^9}{28}+\frac {12\,B\,a^7\,b^3\,d^3\,e^7}{7}+\frac {15\,A\,a^7\,b^3\,d^2\,e^8}{7}+\frac {15\,B\,a^6\,b^4\,d^4\,e^6}{4}+3\,A\,a^6\,b^4\,d^3\,e^7+9\,B\,a^5\,b^5\,d^5\,e^5+\frac {9\,A\,a^5\,b^5\,d^4\,e^6}{2}+\frac {105\,B\,a^4\,b^6\,d^6\,e^4}{4}+\frac {15\,A\,a^4\,b^6\,d^5\,e^5}{2}+120\,B\,a^3\,b^7\,d^7\,e^3+15\,A\,a^3\,b^7\,d^6\,e^4-\frac {61641\,B\,a^2\,b^8\,d^8\,e^2}{56}+45\,A\,a^2\,b^8\,d^7\,e^3+\frac {23045\,B\,a\,b^9\,d^9\,e}{14}-\frac {6849\,A\,a\,b^9\,d^8\,e^2}{28}-\frac {39611\,B\,b^{10}\,d^{10}}{56}+\frac {4609\,A\,b^{10}\,d^9\,e}{28}\right )+x^8\,\left (120\,B\,a^3\,b^7\,e^{10}-405\,B\,a^2\,b^8\,d\,e^9+45\,A\,a^2\,b^8\,e^{10}+450\,B\,a\,b^9\,d^2\,e^8-90\,A\,a\,b^9\,d\,e^9-165\,B\,b^{10}\,d^3\,e^7+45\,A\,b^{10}\,d^2\,e^8\right )+x^5\,\left (\frac {105\,B\,a^6\,b^4\,e^{10}}{2}+126\,B\,a^5\,b^5\,d\,e^9+63\,A\,a^5\,b^5\,e^{10}+\frac {735\,B\,a^4\,b^6\,d^2\,e^8}{2}+105\,A\,a^4\,b^6\,d\,e^9+1680\,B\,a^3\,b^7\,d^3\,e^7+210\,A\,a^3\,b^7\,d^2\,e^8-\frac {23625\,B\,a^2\,b^8\,d^4\,e^6}{2}+630\,A\,a^2\,b^8\,d^3\,e^7+16170\,B\,a\,b^9\,d^5\,e^5-2625\,A\,a\,b^9\,d^4\,e^6-\frac {13167\,B\,b^{10}\,d^6\,e^4}{2}+1617\,A\,b^{10}\,d^5\,e^5\right )+x^2\,\left (\frac {10\,B\,a^9\,b\,e^{10}}{7}+\frac {45\,B\,a^8\,b^2\,d\,e^9}{14}+\frac {45\,A\,a^8\,b^2\,e^{10}}{7}+\frac {48\,B\,a^7\,b^3\,d^2\,e^8}{7}+\frac {60\,A\,a^7\,b^3\,d\,e^9}{7}+15\,B\,a^6\,b^4\,d^3\,e^7+12\,A\,a^6\,b^4\,d^2\,e^8+36\,B\,a^5\,b^5\,d^4\,e^6+18\,A\,a^5\,b^5\,d^3\,e^7+105\,B\,a^4\,b^6\,d^5\,e^5+30\,A\,a^4\,b^6\,d^4\,e^6+480\,B\,a^3\,b^7\,d^6\,e^4+60\,A\,a^3\,b^7\,d^5\,e^5-\frac {29403\,B\,a^2\,b^8\,d^7\,e^3}{7}+180\,A\,a^2\,b^8\,d^6\,e^4+\frac {43290\,B\,a\,b^9\,d^8\,e^2}{7}-\frac {6534\,A\,a\,b^9\,d^7\,e^3}{7}-\frac {36839\,B\,b^{10}\,d^9\,e}{14}+\frac {4329\,A\,b^{10}\,d^8\,e^2}{7}\right )}{d^9\,e^{11}+9\,d^8\,e^{12}\,x+36\,d^7\,e^{13}\,x^2+84\,d^6\,e^{14}\,x^3+126\,d^5\,e^{15}\,x^4+126\,d^4\,e^{16}\,x^5+84\,d^3\,e^{17}\,x^6+36\,d^2\,e^{18}\,x^7+9\,d\,e^{19}\,x^8+e^{20}\,x^9}+\frac {\ln \left (d+e\,x\right )\,\left (45\,B\,a^2\,b^8\,e^2-100\,B\,a\,b^9\,d\,e+10\,A\,a\,b^9\,e^2+55\,B\,b^{10}\,d^2-10\,A\,b^{10}\,d\,e\right )}{e^{12}}+\frac {B\,b^{10}\,x^2}{2\,e^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((A + B*x)*(a + b*x)^10)/(d + e*x)^10,x)
[Out]
x*((A*b^10 + 10*B*a*b^9)/e^10 - (10*B*b^10*d)/e^11) - (x^7*(60*A*a^3*b^7*e^10 + 105*B*a^4*b^6*e^10 + 300*A*b^1
0*d^3*e^7 - 1155*B*b^10*d^4*e^6 - 540*A*a*b^9*d^2*e^8 + 180*A*a^2*b^8*d*e^9 + 3000*B*a*b^9*d^3*e^7 + 480*B*a^3
*b^7*d*e^9 - 2430*B*a^2*b^8*d^2*e^8) + x^4*(42*A*a^6*b^4*e^10 + 24*B*a^7*b^3*e^10 + 1827*A*b^10*d^6*e^4 - (151
47*B*b^10*d^7*e^3)/2 - 2877*A*a*b^9*d^5*e^5 + 63*A*a^5*b^5*d*e^9 + 18270*B*a*b^9*d^6*e^4 + (105*B*a^6*b^4*d*e^
9)/2 + 630*A*a^2*b^8*d^4*e^6 + 210*A*a^3*b^7*d^3*e^7 + 105*A*a^4*b^6*d^2*e^8 - (25893*B*a^2*b^8*d^5*e^5)/2 + 1
680*B*a^3*b^7*d^4*e^6 + (735*B*a^4*b^6*d^3*e^7)/2 + 126*B*a^5*b^5*d^2*e^8) + x^6*(70*A*a^4*b^6*e^10 + 84*B*a^5
*b^5*e^10 + 910*A*b^10*d^4*e^6 - 3619*B*b^10*d^5*e^5 - 1540*A*a*b^9*d^3*e^7 + 140*A*a^3*b^7*d*e^9 + 9100*B*a*b
^9*d^4*e^6 + 245*B*a^4*b^6*d*e^9 + 420*A*a^2*b^8*d^2*e^8 - 6930*B*a^2*b^8*d^3*e^7 + 1120*B*a^3*b^7*d^2*e^8) +
x^3*(20*A*a^7*b^3*e^10 + (15*B*a^8*b^2*e^10)/2 + 1338*A*b^10*d^7*e^3 - (11253*B*b^10*d^8*e^2)/2 - 2058*A*a*b^9
*d^6*e^4 + 28*A*a^6*b^4*d*e^9 + 13380*B*a*b^9*d^7*e^3 + 16*B*a^7*b^3*d*e^9 + 420*A*a^2*b^8*d^5*e^5 + 140*A*a^3
*b^7*d^4*e^6 + 70*A*a^4*b^6*d^3*e^7 + 42*A*a^5*b^5*d^2*e^8 - 9261*B*a^2*b^8*d^6*e^4 + 1120*B*a^3*b^7*d^5*e^5 +
245*B*a^4*b^6*d^4*e^6 + 84*B*a^5*b^5*d^3*e^7 + 35*B*a^6*b^4*d^2*e^8) + (56*A*a^10*e^11 - 42131*B*b^10*d^11 +
9722*A*b^10*d^10*e + 7*B*a^10*d*e^10 - 14258*A*a*b^9*d^9*e^2 + 20*B*a^9*b*d^2*e^9 + 2520*A*a^2*b^8*d^8*e^3 + 8
40*A*a^3*b^7*d^7*e^4 + 420*A*a^4*b^6*d^6*e^5 + 252*A*a^5*b^5*d^5*e^6 + 168*A*a^6*b^4*d^4*e^7 + 120*A*a^7*b^3*d
^3*e^8 + 90*A*a^8*b^2*d^2*e^9 - 64161*B*a^2*b^8*d^9*e^2 + 6720*B*a^3*b^7*d^8*e^3 + 1470*B*a^4*b^6*d^7*e^4 + 50
4*B*a^5*b^5*d^6*e^5 + 210*B*a^6*b^4*d^5*e^6 + 96*B*a^7*b^3*d^4*e^7 + 45*B*a^8*b^2*d^3*e^8 + 70*A*a^9*b*d*e^10
+ 97220*B*a*b^9*d^10*e)/(504*e) + x*((B*a^10*e^10)/8 - (39611*B*b^10*d^10)/56 + (5*A*a^9*b*e^10)/4 + (4609*A*b
^10*d^9*e)/28 - (6849*A*a*b^9*d^8*e^2)/28 + (45*A*a^8*b^2*d*e^9)/28 + 45*A*a^2*b^8*d^7*e^3 + 15*A*a^3*b^7*d^6*
e^4 + (15*A*a^4*b^6*d^5*e^5)/2 + (9*A*a^5*b^5*d^4*e^6)/2 + 3*A*a^6*b^4*d^3*e^7 + (15*A*a^7*b^3*d^2*e^8)/7 - (6
1641*B*a^2*b^8*d^8*e^2)/56 + 120*B*a^3*b^7*d^7*e^3 + (105*B*a^4*b^6*d^6*e^4)/4 + 9*B*a^5*b^5*d^5*e^5 + (15*B*a
^6*b^4*d^4*e^6)/4 + (12*B*a^7*b^3*d^3*e^7)/7 + (45*B*a^8*b^2*d^2*e^8)/56 + (23045*B*a*b^9*d^9*e)/14 + (5*B*a^9
*b*d*e^9)/14) + x^8*(45*A*a^2*b^8*e^10 + 120*B*a^3*b^7*e^10 + 45*A*b^10*d^2*e^8 - 165*B*b^10*d^3*e^7 + 450*B*a
*b^9*d^2*e^8 - 405*B*a^2*b^8*d*e^9 - 90*A*a*b^9*d*e^9) + x^5*(63*A*a^5*b^5*e^10 + (105*B*a^6*b^4*e^10)/2 + 161
7*A*b^10*d^5*e^5 - (13167*B*b^10*d^6*e^4)/2 - 2625*A*a*b^9*d^4*e^6 + 105*A*a^4*b^6*d*e^9 + 16170*B*a*b^9*d^5*e
^5 + 126*B*a^5*b^5*d*e^9 + 630*A*a^2*b^8*d^3*e^7 + 210*A*a^3*b^7*d^2*e^8 - (23625*B*a^2*b^8*d^4*e^6)/2 + 1680*
B*a^3*b^7*d^3*e^7 + (735*B*a^4*b^6*d^2*e^8)/2) + x^2*((10*B*a^9*b*e^10)/7 - (36839*B*b^10*d^9*e)/14 + (45*A*a^
8*b^2*e^10)/7 + (4329*A*b^10*d^8*e^2)/7 - (6534*A*a*b^9*d^7*e^3)/7 + (60*A*a^7*b^3*d*e^9)/7 + (43290*B*a*b^9*d
^8*e^2)/7 + (45*B*a^8*b^2*d*e^9)/14 + 180*A*a^2*b^8*d^6*e^4 + 60*A*a^3*b^7*d^5*e^5 + 30*A*a^4*b^6*d^4*e^6 + 18
*A*a^5*b^5*d^3*e^7 + 12*A*a^6*b^4*d^2*e^8 - (29403*B*a^2*b^8*d^7*e^3)/7 + 480*B*a^3*b^7*d^6*e^4 + 105*B*a^4*b^
6*d^5*e^5 + 36*B*a^5*b^5*d^4*e^6 + 15*B*a^6*b^4*d^3*e^7 + (48*B*a^7*b^3*d^2*e^8)/7))/(d^9*e^11 + e^20*x^9 + 9*
d^8*e^12*x + 9*d*e^19*x^8 + 36*d^7*e^13*x^2 + 84*d^6*e^14*x^3 + 126*d^5*e^15*x^4 + 126*d^4*e^16*x^5 + 84*d^3*e
^17*x^6 + 36*d^2*e^18*x^7) + (log(d + e*x)*(55*B*b^10*d^2 - 10*A*b^10*d*e + 10*A*a*b^9*e^2 + 45*B*a^2*b^8*e^2
- 100*B*a*b^9*d*e))/e^12 + (B*b^10*x^2)/(2*e^10)
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