\(\int (a+b x)^4 (A+B x) (d+e x)^m \, dx\) [3180]

Optimal result

Integrand size = 20, antiderivative size = 234 \[ \int (a+b x)^4 (A+B x) (d+e x)^m \, dx=-\frac {(b d-a e)^4 (B d-A e) (d+e x)^{1+m}}{e^6 (1+m)}+\frac {(b d-a e)^3 (5 b B d-4 A b e-a B e) (d+e x)^{2+m}}{e^6 (2+m)}-\frac {2 b (b d-a e)^2 (5 b B d-3 A b e-2 a B e) (d+e x)^{3+m}}{e^6 (3+m)}+\frac {2 b^2 (b d-a e) (5 b B d-2 A b e-3 a B e) (d+e x)^{4+m}}{e^6 (4+m)}-\frac {b^3 (5 b B d-A b e-4 a B e) (d+e x)^{5+m}}{e^6 (5+m)}+\frac {b^4 B (d+e x)^{6+m}}{e^6 (6+m)} \]

[Out]

-(-a*e+b*d)^4*(-A*e+B*d)*(e*x+d)^(1+m)/e^6/(1+m)+(-a*e+b*d)^3*(-4*A*b*e-B*a*e+5*B*b*d)*(e*x+d)^(2+m)/e^6/(2+m)
-2*b*(-a*e+b*d)^2*(-3*A*b*e-2*B*a*e+5*B*b*d)*(e*x+d)^(3+m)/e^6/(3+m)+2*b^2*(-a*e+b*d)*(-2*A*b*e-3*B*a*e+5*B*b*
d)*(e*x+d)^(4+m)/e^6/(4+m)-b^3*(-A*b*e-4*B*a*e+5*B*b*d)*(e*x+d)^(5+m)/e^6/(5+m)+b^4*B*(e*x+d)^(6+m)/e^6/(6+m)

Rubi [A] (verified)

Time = 0.13 (sec) , antiderivative size = 234, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78} \[ \int (a+b x)^4 (A+B x) (d+e x)^m \, dx=-\frac {b^3 (d+e x)^{m+5} (-4 a B e-A b e+5 b B d)}{e^6 (m+5)}+\frac {2 b^2 (b d-a e) (d+e x)^{m+4} (-3 a B e-2 A b e+5 b B d)}{e^6 (m+4)}-\frac {(b d-a e)^4 (B d-A e) (d+e x)^{m+1}}{e^6 (m+1)}+\frac {(b d-a e)^3 (d+e x)^{m+2} (-a B e-4 A b e+5 b B d)}{e^6 (m+2)}-\frac {2 b (b d-a e)^2 (d+e x)^{m+3} (-2 a B e-3 A b e+5 b B d)}{e^6 (m+3)}+\frac {b^4 B (d+e x)^{m+6}}{e^6 (m+6)} \]

[In]

Int[(a + b*x)^4*(A + B*x)*(d + e*x)^m,x]

[Out]

-(((b*d - a*e)^4*(B*d - A*e)*(d + e*x)^(1 + m))/(e^6*(1 + m))) + ((b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e)*(d
+ e*x)^(2 + m))/(e^6*(2 + m)) - (2*b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e)*(d + e*x)^(3 + m))/(e^6*(3 +
m)) + (2*b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e)*(d + e*x)^(4 + m))/(e^6*(4 + m)) - (b^3*(5*b*B*d - A*b
*e - 4*a*B*e)*(d + e*x)^(5 + m))/(e^6*(5 + m)) + (b^4*B*(d + e*x)^(6 + m))/(e^6*(6 + m))

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*} \text {integral}& = \int \left (\frac {(-b d+a e)^4 (-B d+A e) (d+e x)^m}{e^5}+\frac {(-b d+a e)^3 (-5 b B d+4 A b e+a B e) (d+e x)^{1+m}}{e^5}+\frac {2 b (b d-a e)^2 (-5 b B d+3 A b e+2 a B e) (d+e x)^{2+m}}{e^5}-\frac {2 b^2 (b d-a e) (-5 b B d+2 A b e+3 a B e) (d+e x)^{3+m}}{e^5}+\frac {b^3 (-5 b B d+A b e+4 a B e) (d+e x)^{4+m}}{e^5}+\frac {b^4 B (d+e x)^{5+m}}{e^5}\right ) \, dx \\ & = -\frac {(b d-a e)^4 (B d-A e) (d+e x)^{1+m}}{e^6 (1+m)}+\frac {(b d-a e)^3 (5 b B d-4 A b e-a B e) (d+e x)^{2+m}}{e^6 (2+m)}-\frac {2 b (b d-a e)^2 (5 b B d-3 A b e-2 a B e) (d+e x)^{3+m}}{e^6 (3+m)}+\frac {2 b^2 (b d-a e) (5 b B d-2 A b e-3 a B e) (d+e x)^{4+m}}{e^6 (4+m)}-\frac {b^3 (5 b B d-A b e-4 a B e) (d+e x)^{5+m}}{e^6 (5+m)}+\frac {b^4 B (d+e x)^{6+m}}{e^6 (6+m)} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.26 (sec) , antiderivative size = 208, normalized size of antiderivative = 0.89 \[ \int (a+b x)^4 (A+B x) (d+e x)^m \, dx=\frac {(d+e x)^{1+m} \left (-\frac {(b d-a e)^4 (B d-A e)}{1+m}+\frac {(b d-a e)^3 (5 b B d-4 A b e-a B e) (d+e x)}{2+m}-\frac {2 b (b d-a e)^2 (5 b B d-3 A b e-2 a B e) (d+e x)^2}{3+m}+\frac {2 b^2 (b d-a e) (5 b B d-2 A b e-3 a B e) (d+e x)^3}{4+m}-\frac {b^3 (5 b B d-A b e-4 a B e) (d+e x)^4}{5+m}+\frac {b^4 B (d+e x)^5}{6+m}\right )}{e^6} \]

[In]

Integrate[(a + b*x)^4*(A + B*x)*(d + e*x)^m,x]

[Out]

((d + e*x)^(1 + m)*(-(((b*d - a*e)^4*(B*d - A*e))/(1 + m)) + ((b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e)*(d + e
*x))/(2 + m) - (2*b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e)*(d + e*x)^2)/(3 + m) + (2*b^2*(b*d - a*e)*(5*b
*B*d - 2*A*b*e - 3*a*B*e)*(d + e*x)^3)/(4 + m) - (b^3*(5*b*B*d - A*b*e - 4*a*B*e)*(d + e*x)^4)/(5 + m) + (b^4*
B*(d + e*x)^5)/(6 + m)))/e^6

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(1957\) vs. \(2(234)=468\).

Time = 1.60 (sec) , antiderivative size = 1958, normalized size of antiderivative = 8.37

method	result	size
norman	\(\text {Expression too large to display}\)	\(1958\)
gosper	\(\text {Expression too large to display}\)	\(2355\)
risch	\(\text {Expression too large to display}\)	\(3035\)
parallelrisch	\(\text {Expression too large to display}\)	\(4523\)

[In]

int((b*x+a)^4*(B*x+A)*(e*x+d)^m,x,method=_RETURNVERBOSE)

[Out]

B*b^4/(6+m)*x^6*exp(m*ln(e*x+d))+d*(A*a^4*e^5*m^5+20*A*a^4*e^5*m^4-4*A*a^3*b*d*e^4*m^4-B*a^4*d*e^4*m^4+155*A*a
^4*e^5*m^3-72*A*a^3*b*d*e^4*m^3+12*A*a^2*b^2*d^2*e^3*m^3-18*B*a^4*d*e^4*m^3+8*B*a^3*b*d^2*e^3*m^3+580*A*a^4*e^
5*m^2-476*A*a^3*b*d*e^4*m^2+180*A*a^2*b^2*d^2*e^3*m^2-24*A*a*b^3*d^3*e^2*m^2-119*B*a^4*d*e^4*m^2+120*B*a^3*b*d
^2*e^3*m^2-36*B*a^2*b^2*d^3*e^2*m^2+1044*A*a^4*e^5*m-1368*A*a^3*b*d*e^4*m+888*A*a^2*b^2*d^2*e^3*m-264*A*a*b^3*
d^3*e^2*m+24*A*b^4*d^4*e*m-342*B*a^4*d*e^4*m+592*B*a^3*b*d^2*e^3*m-396*B*a^2*b^2*d^3*e^2*m+96*B*a*b^3*d^4*e*m+
720*A*a^4*e^5-1440*A*a^3*b*d*e^4+1440*A*a^2*b^2*d^2*e^3-720*A*a*b^3*d^3*e^2+144*A*b^4*d^4*e-360*B*a^4*d*e^4+96
0*B*a^3*b*d^2*e^3-1080*B*a^2*b^2*d^3*e^2+576*B*a*b^3*d^4*e-120*B*b^4*d^5)/e^6/(m^6+21*m^5+175*m^4+735*m^3+1624
*m^2+1764*m+720)*exp(m*ln(e*x+d))+(4*A*a^3*b*e^4*m^4+6*A*a^2*b^2*d*e^3*m^4+B*a^4*e^4*m^4+4*B*a^3*b*d*e^3*m^4+7
2*A*a^3*b*e^4*m^3+90*A*a^2*b^2*d*e^3*m^3-12*A*a*b^3*d^2*e^2*m^3+18*B*a^4*e^4*m^3+60*B*a^3*b*d*e^3*m^3-18*B*a^2
*b^2*d^2*e^2*m^3+476*A*a^3*b*e^4*m^2+444*A*a^2*b^2*d*e^3*m^2-132*A*a*b^3*d^2*e^2*m^2+12*A*b^4*d^3*e*m^2+119*B*
a^4*e^4*m^2+296*B*a^3*b*d*e^3*m^2-198*B*a^2*b^2*d^2*e^2*m^2+48*B*a*b^3*d^3*e*m^2+1368*A*a^3*b*e^4*m+720*A*a^2*
b^2*d*e^3*m-360*A*a*b^3*d^2*e^2*m+72*A*b^4*d^3*e*m+342*B*a^4*e^4*m+480*B*a^3*b*d*e^3*m-540*B*a^2*b^2*d^2*e^2*m
+288*B*a*b^3*d^3*e*m-60*B*b^4*d^4*m+1440*A*a^3*b*e^4+360*B*a^4*e^4)/e^4/(m^5+20*m^4+155*m^3+580*m^2+1044*m+720
)*x^2*exp(m*ln(e*x+d))+(A*a^4*e^5*m^5+4*A*a^3*b*d*e^4*m^5+B*a^4*d*e^4*m^5+20*A*a^4*e^5*m^4+72*A*a^3*b*d*e^4*m^
4-12*A*a^2*b^2*d^2*e^3*m^4+18*B*a^4*d*e^4*m^4-8*B*a^3*b*d^2*e^3*m^4+155*A*a^4*e^5*m^3+476*A*a^3*b*d*e^4*m^3-18
0*A*a^2*b^2*d^2*e^3*m^3+24*A*a*b^3*d^3*e^2*m^3+119*B*a^4*d*e^4*m^3-120*B*a^3*b*d^2*e^3*m^3+36*B*a^2*b^2*d^3*e^
2*m^3+580*A*a^4*e^5*m^2+1368*A*a^3*b*d*e^4*m^2-888*A*a^2*b^2*d^2*e^3*m^2+264*A*a*b^3*d^3*e^2*m^2-24*A*b^4*d^4*
e*m^2+342*B*a^4*d*e^4*m^2-592*B*a^3*b*d^2*e^3*m^2+396*B*a^2*b^2*d^3*e^2*m^2-96*B*a*b^3*d^4*e*m^2+1044*A*a^4*e^
5*m+1440*A*a^3*b*d*e^4*m-1440*A*a^2*b^2*d^2*e^3*m+720*A*a*b^3*d^3*e^2*m-144*A*b^4*d^4*e*m+360*B*a^4*d*e^4*m-96
0*B*a^3*b*d^2*e^3*m+1080*B*a^2*b^2*d^3*e^2*m-576*B*a*b^3*d^4*e*m+120*B*b^4*d^5*m+720*A*a^4*e^5)/e^5/(m^6+21*m^
5+175*m^4+735*m^3+1624*m^2+1764*m+720)*x*exp(m*ln(e*x+d))+(A*b*e*m+4*B*a*e*m+B*b*d*m+6*A*b*e+24*B*a*e)*b^3/e/(
m^2+11*m+30)*x^5*exp(m*ln(e*x+d))+(4*A*a*b*e^2*m^2+A*b^2*d*e*m^2+6*B*a^2*e^2*m^2+4*B*a*b*d*e*m^2+44*A*a*b*e^2*
m+6*A*b^2*d*e*m+66*B*a^2*e^2*m+24*B*a*b*d*e*m-5*B*b^2*d^2*m+120*A*a*b*e^2+180*B*a^2*e^2)*b^2/e^2/(m^3+15*m^2+7
4*m+120)*x^4*exp(m*ln(e*x+d))+2*(3*A*a^2*b*e^3*m^3+2*A*a*b^2*d*e^2*m^3+2*B*a^3*e^3*m^3+3*B*a^2*b*d*e^2*m^3+45*
A*a^2*b*e^3*m^2+22*A*a*b^2*d*e^2*m^2-2*A*b^3*d^2*e*m^2+30*B*a^3*e^3*m^2+33*B*a^2*b*d*e^2*m^2-8*B*a*b^2*d^2*e*m
^2+222*A*a^2*b*e^3*m+60*A*a*b^2*d*e^2*m-12*A*b^3*d^2*e*m+148*B*a^3*e^3*m+90*B*a^2*b*d*e^2*m-48*B*a*b^2*d^2*e*m
+10*B*b^3*d^3*m+360*A*a^2*b*e^3+240*B*a^3*e^3)*b/e^3/(m^4+18*m^3+119*m^2+342*m+360)*x^3*exp(m*ln(e*x+d))

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 2274 vs. \(2 (234) = 468\).

Time = 0.30 (sec) , antiderivative size = 2274, normalized size of antiderivative = 9.72 \[ \int (a+b x)^4 (A+B x) (d+e x)^m \, dx=\text {Too large to display} \]

[In]

integrate((b*x+a)^4*(B*x+A)*(e*x+d)^m,x, algorithm="fricas")

[Out]

(A*a^4*d*e^5*m^5 - 120*B*b^4*d^6 + 720*A*a^4*d*e^5 + 144*(4*B*a*b^3 + A*b^4)*d^5*e - 360*(3*B*a^2*b^2 + 2*A*a*
b^3)*d^4*e^2 + 480*(2*B*a^3*b + 3*A*a^2*b^2)*d^3*e^3 - 360*(B*a^4 + 4*A*a^3*b)*d^2*e^4 + (B*b^4*e^6*m^5 + 15*B
*b^4*e^6*m^4 + 85*B*b^4*e^6*m^3 + 225*B*b^4*e^6*m^2 + 274*B*b^4*e^6*m + 120*B*b^4*e^6)*x^6 + (144*(4*B*a*b^3 +
A*b^4)*e^6 + (B*b^4*d*e^5 + (4*B*a*b^3 + A*b^4)*e^6)*m^5 + 2*(5*B*b^4*d*e^5 + 8*(4*B*a*b^3 + A*b^4)*e^6)*m^4
+ 5*(7*B*b^4*d*e^5 + 19*(4*B*a*b^3 + A*b^4)*e^6)*m^3 + 10*(5*B*b^4*d*e^5 + 26*(4*B*a*b^3 + A*b^4)*e^6)*m^2 + 1
2*(2*B*b^4*d*e^5 + 27*(4*B*a*b^3 + A*b^4)*e^6)*m)*x^5 + (20*A*a^4*d*e^5 - (B*a^4 + 4*A*a^3*b)*d^2*e^4)*m^4 + (
360*(3*B*a^2*b^2 + 2*A*a*b^3)*e^6 + ((4*B*a*b^3 + A*b^4)*d*e^5 + 2*(3*B*a^2*b^2 + 2*A*a*b^3)*e^6)*m^5 - (5*B*b
^4*d^2*e^4 - 12*(4*B*a*b^3 + A*b^4)*d*e^5 - 34*(3*B*a^2*b^2 + 2*A*a*b^3)*e^6)*m^4 - (30*B*b^4*d^2*e^4 - 47*(4*
B*a*b^3 + A*b^4)*d*e^5 - 214*(3*B*a^2*b^2 + 2*A*a*b^3)*e^6)*m^3 - (55*B*b^4*d^2*e^4 - 72*(4*B*a*b^3 + A*b^4)*d
*e^5 - 614*(3*B*a^2*b^2 + 2*A*a*b^3)*e^6)*m^2 - 6*(5*B*b^4*d^2*e^4 - 6*(4*B*a*b^3 + A*b^4)*d*e^5 - 132*(3*B*a^
2*b^2 + 2*A*a*b^3)*e^6)*m)*x^4 + (155*A*a^4*d*e^5 + 4*(2*B*a^3*b + 3*A*a^2*b^2)*d^3*e^3 - 18*(B*a^4 + 4*A*a^3*
b)*d^2*e^4)*m^3 + 2*(240*(2*B*a^3*b + 3*A*a^2*b^2)*e^6 + ((3*B*a^2*b^2 + 2*A*a*b^3)*d*e^5 + (2*B*a^3*b + 3*A*a
^2*b^2)*e^6)*m^5 - 2*((4*B*a*b^3 + A*b^4)*d^2*e^4 - 7*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^5 - 9*(2*B*a^3*b + 3*A*a^2
*b^2)*e^6)*m^4 + (10*B*b^4*d^3*e^3 - 18*(4*B*a*b^3 + A*b^4)*d^2*e^4 + 65*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^5 + 121
*(2*B*a^3*b + 3*A*a^2*b^2)*e^6)*m^3 + 2*(15*B*b^4*d^3*e^3 - 20*(4*B*a*b^3 + A*b^4)*d^2*e^4 + 56*(3*B*a^2*b^2 +
2*A*a*b^3)*d*e^5 + 186*(2*B*a^3*b + 3*A*a^2*b^2)*e^6)*m^2 + 4*(5*B*b^4*d^3*e^3 - 6*(4*B*a*b^3 + A*b^4)*d^2*e^
4 + 15*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^5 + 127*(2*B*a^3*b + 3*A*a^2*b^2)*e^6)*m)*x^3 + (580*A*a^4*d*e^5 - 12*(3*
B*a^2*b^2 + 2*A*a*b^3)*d^4*e^2 + 60*(2*B*a^3*b + 3*A*a^2*b^2)*d^3*e^3 - 119*(B*a^4 + 4*A*a^3*b)*d^2*e^4)*m^2 +
(360*(B*a^4 + 4*A*a^3*b)*e^6 + (2*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^5 + (B*a^4 + 4*A*a^3*b)*e^6)*m^5 - (6*(3*B*a^
2*b^2 + 2*A*a*b^3)*d^2*e^4 - 32*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^5 - 19*(B*a^4 + 4*A*a^3*b)*e^6)*m^4 + (12*(4*B*a
*b^3 + A*b^4)*d^3*e^3 - 72*(3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^4 + 178*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^5 + 137*(B*a^
4 + 4*A*a^3*b)*e^6)*m^3 - (60*B*b^4*d^4*e^2 - 84*(4*B*a*b^3 + A*b^4)*d^3*e^3 + 246*(3*B*a^2*b^2 + 2*A*a*b^3)*d
^2*e^4 - 388*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^5 - 461*(B*a^4 + 4*A*a^3*b)*e^6)*m^2 - 6*(10*B*b^4*d^4*e^2 - 12*(4*
B*a*b^3 + A*b^4)*d^3*e^3 + 30*(3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^4 - 40*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^5 - 117*(B*
a^4 + 4*A*a^3*b)*e^6)*m)*x^2 + 2*(522*A*a^4*d*e^5 + 12*(4*B*a*b^3 + A*b^4)*d^5*e - 66*(3*B*a^2*b^2 + 2*A*a*b^3
)*d^4*e^2 + 148*(2*B*a^3*b + 3*A*a^2*b^2)*d^3*e^3 - 171*(B*a^4 + 4*A*a^3*b)*d^2*e^4)*m + (720*A*a^4*e^6 + (A*a
^4*e^6 + (B*a^4 + 4*A*a^3*b)*d*e^5)*m^5 + 2*(10*A*a^4*e^6 - 2*(2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^4 + 9*(B*a^4 + 4
*A*a^3*b)*d*e^5)*m^4 + (155*A*a^4*e^6 + 12*(3*B*a^2*b^2 + 2*A*a*b^3)*d^3*e^3 - 60*(2*B*a^3*b + 3*A*a^2*b^2)*d^
2*e^4 + 119*(B*a^4 + 4*A*a^3*b)*d*e^5)*m^3 + 2*(290*A*a^4*e^6 - 12*(4*B*a*b^3 + A*b^4)*d^4*e^2 + 66*(3*B*a^2*b
^2 + 2*A*a*b^3)*d^3*e^3 - 148*(2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^4 + 171*(B*a^4 + 4*A*a^3*b)*d*e^5)*m^2 + 12*(10*
B*b^4*d^5*e + 87*A*a^4*e^6 - 12*(4*B*a*b^3 + A*b^4)*d^4*e^2 + 30*(3*B*a^2*b^2 + 2*A*a*b^3)*d^3*e^3 - 40*(2*B*a
^3*b + 3*A*a^2*b^2)*d^2*e^4 + 30*(B*a^4 + 4*A*a^3*b)*d*e^5)*m)*x)*(e*x + d)^m/(e^6*m^6 + 21*e^6*m^5 + 175*e^6*
m^4 + 735*e^6*m^3 + 1624*e^6*m^2 + 1764*e^6*m + 720*e^6)

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 28048 vs. \(2 (224) = 448\).

Time = 5.41 (sec) , antiderivative size = 28048, normalized size of antiderivative = 119.86 \[ \int (a+b x)^4 (A+B x) (d+e x)^m \, dx=\text {Too large to display} \]

[In]

integrate((b*x+a)**4*(B*x+A)*(e*x+d)**m,x)

[Out]

Piecewise((d**m*(A*a**4*x + 2*A*a**3*b*x**2 + 2*A*a**2*b**2*x**3 + A*a*b**3*x**4 + A*b**4*x**5/5 + B*a**4*x**2
/2 + 4*B*a**3*b*x**3/3 + 3*B*a**2*b**2*x**4/2 + 4*B*a*b**3*x**5/5 + B*b**4*x**6/6), Eq(e, 0)), (-12*A*a**4*e**
5/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5
) - 12*A*a**3*b*d*e**4/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10
*x**4 + 60*e**11*x**5) - 60*A*a**3*b*e**5*x/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e*
*9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 12*A*a**2*b**2*d**2*e**3/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d
**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 60*A*a**2*b**2*d*e**4*x/(60*d**5*e**6
+ 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 120*A*a**2*
b**2*e**5*x**2/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 +
60*e**11*x**5) - 12*A*a*b**3*d**3*e**2/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x*
*3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 60*A*a*b**3*d**2*e**3*x/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e*
*8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 120*A*a*b**3*d*e**4*x**2/(60*d**5*e**6 + 30
0*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 120*A*a*b**3*e**
5*x**3/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11
*x**5) - 12*A*b**4*d**4*e/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e*
*10*x**4 + 60*e**11*x**5) - 60*A*b**4*d**3*e**2*x/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d
**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 120*A*b**4*d**2*e**3*x**2/(60*d**5*e**6 + 300*d**4*e**7*x
+ 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 120*A*b**4*d*e**4*x**3/(60*d**
5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 60*A*
b**4*e**5*x**4/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 +
60*e**11*x**5) - 3*B*a**4*d*e**4/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 3
00*d*e**10*x**4 + 60*e**11*x**5) - 15*B*a**4*e**5*x/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600
*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 8*B*a**3*b*d**2*e**3/(60*d**5*e**6 + 300*d**4*e**7*x + 6
00*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 40*B*a**3*b*d*e**4*x/(60*d**5*e**
6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 80*B*a**3*
b*e**5*x**2/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*
e**11*x**5) - 18*B*a**2*b**2*d**3*e**2/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x*
*3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 90*B*a**2*b**2*d**2*e**3*x/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3
*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 180*B*a**2*b**2*d*e**4*x**2/(60*d**5*e**
6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 180*B*a**2
*b**2*e**5*x**3/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 +
60*e**11*x**5) - 48*B*a*b**3*d**4*e/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3
+ 300*d*e**10*x**4 + 60*e**11*x**5) - 240*B*a*b**3*d**3*e**2*x/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**
8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 480*B*a*b**3*d**2*e**3*x**2/(60*d**5*e**6 +
300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 480*B*a*b**3*d
*e**4*x**3/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e
**11*x**5) - 240*B*a*b**3*e**5*x**4/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3
+ 300*d*e**10*x**4 + 60*e**11*x**5) + 60*B*b**4*d**5*log(d/e + x)/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e
**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) + 137*B*b**4*d**5/(60*d**5*e**6 + 300*d**4*e
**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) + 300*B*b**4*d**4*e*x*log(
d/e + x)/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**
11*x**5) + 625*B*b**4*d**4*e*x/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300
*d*e**10*x**4 + 60*e**11*x**5) + 600*B*b**4*d**3*e**2*x**2*log(d/e + x)/(60*d**5*e**6 + 300*d**4*e**7*x + 600*
d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) + 1100*B*b**4*d**3*e**2*x**2/(60*d**5*
e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) + 600*B*b
**4*d**2*e**3*x**3*log(d/e + x)/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 30
0*d*e**10*x**4 + 60*e**11*x**5) + 900*B*b**4*d**2*e**3*x**3/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x*
*2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) + 300*B*b**4*d*e**4*x**4*log(d/e + x)/(60*d**5*e**
6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) + 300*B*b**4
*d*e**4*x**4/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60
*e**11*x**5) + 60*B*b**4*e**5*x**5*log(d/e + x)/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**
2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5), Eq(m, -6)), (-3*A*a**4*e**5/(12*d**4*e**6 + 48*d**3*e**7*x +
72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 4*A*a**3*b*d*e**4/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d*
*2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 16*A*a**3*b*e**5*x/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e
**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 6*A*a**2*b**2*d**2*e**3/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*
e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 24*A*a**2*b**2*d*e**4*x/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2
*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 36*A*a**2*b**2*e**5*x**2/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d*
*2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 12*A*a*b**3*d**3*e**2/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**
2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 48*A*a*b**3*d**2*e**3*x/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d*
*2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 72*A*a*b**3*d*e**4*x**2/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d
**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 48*A*a*b**3*e**5*x**3/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d*
*2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) + 12*A*b**4*d**4*e*log(d/e + x)/(12*d**4*e**6 + 48*d**3*e**7*x
+ 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) + 25*A*b**4*d**4*e/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d
**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) + 48*A*b**4*d**3*e**2*x*log(d/e + x)/(12*d**4*e**6 + 48*d**3*e
**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) + 88*A*b**4*d**3*e**2*x/(12*d**4*e**6 + 48*d**3*e*
*7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) + 72*A*b**4*d**2*e**3*x**2*log(d/e + x)/(12*d**4*e*
*6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) + 108*A*b**4*d**2*e**3*x**2/(12*d**4
*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) + 48*A*b**4*d*e**4*x**3*log(d/e +
x)/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) + 48*A*b**4*d*e**4*x*
*3/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) + 12*A*b**4*e**5*x**4*
log(d/e + x)/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - B*a**4*d*e
**4/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 4*B*a**4*e**5*x/(12
*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 4*B*a**3*b*d**2*e**3/(12*d
**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 16*B*a**3*b*d*e**4*x/(12*d**
4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 24*B*a**3*b*e**5*x**2/(12*d**4
*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 18*B*a**2*b**2*d**3*e**2/(12*d*
*4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 72*B*a**2*b**2*d**2*e**3*x/(1
2*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 108*B*a**2*b**2*d*e**4*x*
*2/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 72*B*a**2*b**2*e**5*
x**3/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) + 48*B*a*b**3*d**4*e
*log(d/e + x)/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) + 100*B*a*b
**3*d**4*e/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) + 192*B*a*b**3
*d**3*e**2*x*log(d/e + x)/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4)
+ 352*B*a*b**3*d**3*e**2*x/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**
4) + 288*B*a*b**3*d**2*e**3*x**2*log(d/e + x)/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x
**3 + 12*e**10*x**4) + 432*B*a*b**3*d**2*e**3*x**2/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e
**9*x**3 + 12*e**10*x**4) + 192*B*a*b**3*d*e**4*x**3*log(d/e + x)/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**
8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) + 192*B*a*b**3*d*e**4*x**3/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e
**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) + 48*B*a*b**3*e**5*x**4*log(d/e + x)/(12*d**4*e**6 + 48*d**3*e**7*x
+ 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 60*B*b**4*d**5*log(d/e + x)/(12*d**4*e**6 + 48*d**3*e
**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 125*B*b**4*d**5/(12*d**4*e**6 + 48*d**3*e**7*x +
72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 240*B*b**4*d**4*e*x*log(d/e + x)/(12*d**4*e**6 + 48*d**
3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 440*B*b**4*d**4*e*x/(12*d**4*e**6 + 48*d**3*e
**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 360*B*b**4*d**3*e**2*x**2*log(d/e + x)/(12*d**4*
e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 540*B*b**4*d**3*e**2*x**2/(12*d*
*4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 240*B*b**4*d**2*e**3*x**3*log
(d/e + x)/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 240*B*b**4*d*
*2*e**3*x**3/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 60*B*b**4*
d*e**4*x**4*log(d/e + x)/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4)
+ 12*B*b**4*e**5*x**5/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4), Eq
(m, -5)), (-2*A*a**4*e**5/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 4*A*a**3*b*d*e**4/(6
*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 12*A*a**3*b*e**5*x/(6*d**3*e**6 + 18*d**2*e**7*x
+ 18*d*e**8*x**2 + 6*e**9*x**3) - 12*A*a**2*b**2*d**2*e**3/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6
*e**9*x**3) - 36*A*a**2*b**2*d*e**4*x/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 36*A*a**
2*b**2*e**5*x**2/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 24*A*a*b**3*d**3*e**2*log(d/e
+ x)/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 44*A*a*b**3*d**3*e**2/(6*d**3*e**6 + 18*
d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 72*A*a*b**3*d**2*e**3*x*log(d/e + x)/(6*d**3*e**6 + 18*d**2*e**7
*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 108*A*a*b**3*d**2*e**3*x/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 +
6*e**9*x**3) + 72*A*a*b**3*d*e**4*x**2*log(d/e + x)/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x
**3) + 72*A*a*b**3*d*e**4*x**2/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 24*A*a*b**3*e**
5*x**3*log(d/e + x)/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 24*A*b**4*d**4*e*log(d/e +
x)/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 44*A*b**4*d**4*e/(6*d**3*e**6 + 18*d**2*e*
*7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 72*A*b**4*d**3*e**2*x*log(d/e + x)/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d
*e**8*x**2 + 6*e**9*x**3) - 108*A*b**4*d**3*e**2*x/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**
3) - 72*A*b**4*d**2*e**3*x**2*log(d/e + x)/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 72*
A*b**4*d**2*e**3*x**2/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 24*A*b**4*d*e**4*x**3*lo
g(d/e + x)/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 6*A*b**4*e**5*x**4/(6*d**3*e**6 + 1
8*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - B*a**4*d*e**4/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 +
6*e**9*x**3) - 3*B*a**4*e**5*x/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 8*B*a**3*b*d**
2*e**3/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 24*B*a**3*b*d*e**4*x/(6*d**3*e**6 + 18*
d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 24*B*a**3*b*e**5*x**2/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*
x**2 + 6*e**9*x**3) + 36*B*a**2*b**2*d**3*e**2*log(d/e + x)/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6
*e**9*x**3) + 66*B*a**2*b**2*d**3*e**2/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 108*B*a
**2*b**2*d**2*e**3*x*log(d/e + x)/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 162*B*a**2*b
**2*d**2*e**3*x/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 108*B*a**2*b**2*d*e**4*x**2*lo
g(d/e + x)/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 108*B*a**2*b**2*d*e**4*x**2/(6*d**3
*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 36*B*a**2*b**2*e**5*x**3*log(d/e + x)/(6*d**3*e**6 +
18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 96*B*a*b**3*d**4*e*log(d/e + x)/(6*d**3*e**6 + 18*d**2*e**7*x
+ 18*d*e**8*x**2 + 6*e**9*x**3) - 176*B*a*b**3*d**4*e/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9
*x**3) - 288*B*a*b**3*d**3*e**2*x*log(d/e + x)/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) -
432*B*a*b**3*d**3*e**2*x/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 288*B*a*b**3*d**2*e*
*3*x**2*log(d/e + x)/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 288*B*a*b**3*d**2*e**3*x*
*2/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 96*B*a*b**3*d*e**4*x**3*log(d/e + x)/(6*d**
3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 24*B*a*b**3*e**5*x**4/(6*d**3*e**6 + 18*d**2*e**7*x
+ 18*d*e**8*x**2 + 6*e**9*x**3) + 60*B*b**4*d**5*log(d/e + x)/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 +
6*e**9*x**3) + 110*B*b**4*d**5/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 180*B*b**4*d**
4*e*x*log(d/e + x)/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 270*B*b**4*d**4*e*x/(6*d**3
*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 180*B*b**4*d**3*e**2*x**2*log(d/e + x)/(6*d**3*e**6 +
18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 180*B*b**4*d**3*e**2*x**2/(6*d**3*e**6 + 18*d**2*e**7*x + 18
*d*e**8*x**2 + 6*e**9*x**3) + 60*B*b**4*d**2*e**3*x**3*log(d/e + x)/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*
x**2 + 6*e**9*x**3) - 15*B*b**4*d*e**4*x**4/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 3*
B*b**4*e**5*x**5/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3), Eq(m, -4)), (-3*A*a**4*e**5/(6
*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 12*A*a**3*b*d*e**4/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 24*A*
a**3*b*e**5*x/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 36*A*a**2*b**2*d**2*e**3*log(d/e + x)/(6*d**2*e**6 +
12*d*e**7*x + 6*e**8*x**2) + 54*A*a**2*b**2*d**2*e**3/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 72*A*a**2*b
**2*d*e**4*x*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 72*A*a**2*b**2*d*e**4*x/(6*d**2*e**6 + 1
2*d*e**7*x + 6*e**8*x**2) + 36*A*a**2*b**2*e**5*x**2*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) -
72*A*a*b**3*d**3*e**2*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 108*A*a*b**3*d**3*e**2/(6*d**2*
e**6 + 12*d*e**7*x + 6*e**8*x**2) - 144*A*a*b**3*d**2*e**3*x*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*
x**2) - 144*A*a*b**3*d**2*e**3*x/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 72*A*a*b**3*d*e**4*x**2*log(d/e +
x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 24*A*a*b**3*e**5*x**3/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2
) + 36*A*b**4*d**4*e*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 54*A*b**4*d**4*e/(6*d**2*e**6 +
12*d*e**7*x + 6*e**8*x**2) + 72*A*b**4*d**3*e**2*x*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 72
*A*b**4*d**3*e**2*x/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 36*A*b**4*d**2*e**3*x**2*log(d/e + x)/(6*d**2*
e**6 + 12*d*e**7*x + 6*e**8*x**2) - 12*A*b**4*d*e**4*x**3/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 3*A*b**4
*e**5*x**4/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 3*B*a**4*d*e**4/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**
2) - 6*B*a**4*e**5*x/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 24*B*a**3*b*d**2*e**3*log(d/e + x)/(6*d**2*e*
*6 + 12*d*e**7*x + 6*e**8*x**2) + 36*B*a**3*b*d**2*e**3/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 48*B*a**3*
b*d*e**4*x*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 48*B*a**3*b*d*e**4*x/(6*d**2*e**6 + 12*d*e
**7*x + 6*e**8*x**2) + 24*B*a**3*b*e**5*x**2*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 108*B*a*
*2*b**2*d**3*e**2*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 162*B*a**2*b**2*d**3*e**2/(6*d**2*e
**6 + 12*d*e**7*x + 6*e**8*x**2) - 216*B*a**2*b**2*d**2*e**3*x*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**
8*x**2) - 216*B*a**2*b**2*d**2*e**3*x/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 108*B*a**2*b**2*d*e**4*x**2*
log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 36*B*a**2*b**2*e**5*x**3/(6*d**2*e**6 + 12*d*e**7*x +
6*e**8*x**2) + 144*B*a*b**3*d**4*e*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 216*B*a*b**3*d**4
*e/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 288*B*a*b**3*d**3*e**2*x*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*
x + 6*e**8*x**2) + 288*B*a*b**3*d**3*e**2*x/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 144*B*a*b**3*d**2*e**3
*x**2*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 48*B*a*b**3*d*e**4*x**3/(6*d**2*e**6 + 12*d*e**
7*x + 6*e**8*x**2) + 12*B*a*b**3*e**5*x**4/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 60*B*b**4*d**5*log(d/e
+ x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 90*B*b**4*d**5/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 12
0*B*b**4*d**4*e*x*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 120*B*b**4*d**4*e*x/(6*d**2*e**6 +
12*d*e**7*x + 6*e**8*x**2) - 60*B*b**4*d**3*e**2*x**2*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) +
20*B*b**4*d**2*e**3*x**3/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 5*B*b**4*d*e**4*x**4/(6*d**2*e**6 + 12*d
*e**7*x + 6*e**8*x**2) + 2*B*b**4*e**5*x**5/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2), Eq(m, -3)), (-12*A*a**4
*e**5/(12*d*e**6 + 12*e**7*x) + 48*A*a**3*b*d*e**4*log(d/e + x)/(12*d*e**6 + 12*e**7*x) + 48*A*a**3*b*d*e**4/(
12*d*e**6 + 12*e**7*x) + 48*A*a**3*b*e**5*x*log(d/e + x)/(12*d*e**6 + 12*e**7*x) - 144*A*a**2*b**2*d**2*e**3*l
og(d/e + x)/(12*d*e**6 + 12*e**7*x) - 144*A*a**2*b**2*d**2*e**3/(12*d*e**6 + 12*e**7*x) - 144*A*a**2*b**2*d*e*
*4*x*log(d/e + x)/(12*d*e**6 + 12*e**7*x) + 72*A*a**2*b**2*e**5*x**2/(12*d*e**6 + 12*e**7*x) + 144*A*a*b**3*d*
*3*e**2*log(d/e + x)/(12*d*e**6 + 12*e**7*x) + 144*A*a*b**3*d**3*e**2/(12*d*e**6 + 12*e**7*x) + 144*A*a*b**3*d
**2*e**3*x*log(d/e + x)/(12*d*e**6 + 12*e**7*x) - 72*A*a*b**3*d*e**4*x**2/(12*d*e**6 + 12*e**7*x) + 24*A*a*b**
3*e**5*x**3/(12*d*e**6 + 12*e**7*x) - 48*A*b**4*d**4*e*log(d/e + x)/(12*d*e**6 + 12*e**7*x) - 48*A*b**4*d**4*e
/(12*d*e**6 + 12*e**7*x) - 48*A*b**4*d**3*e**2*x*log(d/e + x)/(12*d*e**6 + 12*e**7*x) + 24*A*b**4*d**2*e**3*x*
*2/(12*d*e**6 + 12*e**7*x) - 8*A*b**4*d*e**4*x**3/(12*d*e**6 + 12*e**7*x) + 4*A*b**4*e**5*x**4/(12*d*e**6 + 12
*e**7*x) + 12*B*a**4*d*e**4*log(d/e + x)/(12*d*e**6 + 12*e**7*x) + 12*B*a**4*d*e**4/(12*d*e**6 + 12*e**7*x) +
12*B*a**4*e**5*x*log(d/e + x)/(12*d*e**6 + 12*e**7*x) - 96*B*a**3*b*d**2*e**3*log(d/e + x)/(12*d*e**6 + 12*e**
7*x) - 96*B*a**3*b*d**2*e**3/(12*d*e**6 + 12*e**7*x) - 96*B*a**3*b*d*e**4*x*log(d/e + x)/(12*d*e**6 + 12*e**7*
x) + 48*B*a**3*b*e**5*x**2/(12*d*e**6 + 12*e**7*x) + 216*B*a**2*b**2*d**3*e**2*log(d/e + x)/(12*d*e**6 + 12*e*
*7*x) + 216*B*a**2*b**2*d**3*e**2/(12*d*e**6 + 12*e**7*x) + 216*B*a**2*b**2*d**2*e**3*x*log(d/e + x)/(12*d*e**
6 + 12*e**7*x) - 108*B*a**2*b**2*d*e**4*x**2/(12*d*e**6 + 12*e**7*x) + 36*B*a**2*b**2*e**5*x**3/(12*d*e**6 + 1
2*e**7*x) - 192*B*a*b**3*d**4*e*log(d/e + x)/(12*d*e**6 + 12*e**7*x) - 192*B*a*b**3*d**4*e/(12*d*e**6 + 12*e**
7*x) - 192*B*a*b**3*d**3*e**2*x*log(d/e + x)/(12*d*e**6 + 12*e**7*x) + 96*B*a*b**3*d**2*e**3*x**2/(12*d*e**6 +
12*e**7*x) - 32*B*a*b**3*d*e**4*x**3/(12*d*e**6 + 12*e**7*x) + 16*B*a*b**3*e**5*x**4/(12*d*e**6 + 12*e**7*x)
+ 60*B*b**4*d**5*log(d/e + x)/(12*d*e**6 + 12*e**7*x) + 60*B*b**4*d**5/(12*d*e**6 + 12*e**7*x) + 60*B*b**4*d**
4*e*x*log(d/e + x)/(12*d*e**6 + 12*e**7*x) - 30*B*b**4*d**3*e**2*x**2/(12*d*e**6 + 12*e**7*x) + 10*B*b**4*d**2
*e**3*x**3/(12*d*e**6 + 12*e**7*x) - 5*B*b**4*d*e**4*x**4/(12*d*e**6 + 12*e**7*x) + 3*B*b**4*e**5*x**5/(12*d*e
**6 + 12*e**7*x), Eq(m, -2)), (A*a**4*log(d/e + x)/e - 4*A*a**3*b*d*log(d/e + x)/e**2 + 4*A*a**3*b*x/e + 6*A*a
**2*b**2*d**2*log(d/e + x)/e**3 - 6*A*a**2*b**2*d*x/e**2 + 3*A*a**2*b**2*x**2/e - 4*A*a*b**3*d**3*log(d/e + x)
/e**4 + 4*A*a*b**3*d**2*x/e**3 - 2*A*a*b**3*d*x**2/e**2 + 4*A*a*b**3*x**3/(3*e) + A*b**4*d**4*log(d/e + x)/e**
5 - A*b**4*d**3*x/e**4 + A*b**4*d**2*x**2/(2*e**3) - A*b**4*d*x**3/(3*e**2) + A*b**4*x**4/(4*e) - B*a**4*d*log
(d/e + x)/e**2 + B*a**4*x/e + 4*B*a**3*b*d**2*log(d/e + x)/e**3 - 4*B*a**3*b*d*x/e**2 + 2*B*a**3*b*x**2/e - 6*
B*a**2*b**2*d**3*log(d/e + x)/e**4 + 6*B*a**2*b**2*d**2*x/e**3 - 3*B*a**2*b**2*d*x**2/e**2 + 2*B*a**2*b**2*x**
3/e + 4*B*a*b**3*d**4*log(d/e + x)/e**5 - 4*B*a*b**3*d**3*x/e**4 + 2*B*a*b**3*d**2*x**2/e**3 - 4*B*a*b**3*d*x*
*3/(3*e**2) + B*a*b**3*x**4/e - B*b**4*d**5*log(d/e + x)/e**6 + B*b**4*d**4*x/e**5 - B*b**4*d**3*x**2/(2*e**4)
+ B*b**4*d**2*x**3/(3*e**3) - B*b**4*d*x**4/(4*e**2) + B*b**4*x**5/(5*e), Eq(m, -1)), (A*a**4*d*e**5*m**5*(d
+ e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6)
+ 20*A*a**4*d*e**5*m**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m*
*2 + 1764*e**6*m + 720*e**6) + 155*A*a**4*d*e**5*m**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 +
735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 580*A*a**4*d*e**5*m**2*(d + e*x)**m/(e**6*m**6 + 2
1*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 1044*A*a**4*d*e**5*m*
(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e*
*6) + 720*A*a**4*d*e**5*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**
2 + 1764*e**6*m + 720*e**6) + A*a**4*e**6*m**5*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*
e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 20*A*a**4*e**6*m**4*x*(d + e*x)**m/(e**6*m**6 + 21*e**6
*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 155*A*a**4*e**6*m**3*x*(d +
e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6)
+ 580*A*a**4*e**6*m**2*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m*
*2 + 1764*e**6*m + 720*e**6) + 1044*A*a**4*e**6*m*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 7
35*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 720*A*a**4*e**6*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*
m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 4*A*a**3*b*d**2*e**4*m**4*(d
+ e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6
) - 72*A*a**3*b*d**2*e**4*m**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e
**6*m**2 + 1764*e**6*m + 720*e**6) - 476*A*a**3*b*d**2*e**4*m**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*
e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 1368*A*a**3*b*d**2*e**4*m*(d + e*x)**m/
(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 1440*A*
a**3*b*d**2*e**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 176
4*e**6*m + 720*e**6) + 4*A*a**3*b*d*e**5*m**5*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e
**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 72*A*a**3*b*d*e**5*m**4*x*(d + e*x)**m/(e**6*m**6 + 21*e
**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 476*A*a**3*b*d*e**5*m**3
*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720
*e**6) + 1368*A*a**3*b*d*e**5*m**2*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 +
1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 1440*A*a**3*b*d*e**5*m*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 1
75*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 4*A*a**3*b*e**6*m**5*x**2*(d + e*x)*
*m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 76*A
*a**3*b*e**6*m**4*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2
+ 1764*e**6*m + 720*e**6) + 548*A*a**3*b*e**6*m**3*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**
4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 1844*A*a**3*b*e**6*m**2*x**2*(d + e*x)**m/(e**6
*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 2808*A*a**3*
b*e**6*m*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e
**6*m + 720*e**6) + 1440*A*a**3*b*e**6*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*
m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 12*A*a**2*b**2*d**3*e**3*m**3*(d + e*x)**m/(e**6*m**6 + 21*e
**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 180*A*a**2*b**2*d**3*e**
3*m**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m +
720*e**6) + 888*A*a**2*b**2*d**3*e**3*m*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**
3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 1440*A*a**2*b**2*d**3*e**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m*
*5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 12*A*a**2*b**2*d**2*e**4*m**4*
x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*
e**6) - 180*A*a**2*b**2*d**2*e**4*m**3*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**
3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 888*A*a**2*b**2*d**2*e**4*m**2*x*(d + e*x)**m/(e**6*m**6 + 21*e
**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 1440*A*a**2*b**2*d**2*e*
*4*m*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m +
720*e**6) + 6*A*a**2*b**2*d*e**5*m**5*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*
m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 96*A*a**2*b**2*d*e**5*m**4*x**2*(d + e*x)**m/(e**6*m**6 + 21
*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 534*A*a**2*b**2*d*e**5
*m**3*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6
*m + 720*e**6) + 1164*A*a**2*b**2*d*e**5*m**2*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 73
5*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 720*A*a**2*b**2*d*e**5*m*x**2*(d + e*x)**m/(e**6*m**6
+ 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 6*A*a**2*b**2*e**
6*m**5*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**
6*m + 720*e**6) + 108*A*a**2*b**2*e**6*m**4*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*
e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 726*A*a**2*b**2*e**6*m**3*x**3*(d + e*x)**m/(e**6*m**6
+ 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 2232*A*a**2*b**2*e
**6*m**2*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e
**6*m + 720*e**6) + 3048*A*a**2*b**2*e**6*m*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*
e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 1440*A*a**2*b**2*e**6*x**3*(d + e*x)**m/(e**6*m**6 + 21
*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 24*A*a*b**3*d**4*e**2*
m**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 7
20*e**6) - 264*A*a*b**3*d**4*e**2*m*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1
624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 720*A*a*b**3*d**4*e**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*
e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 24*A*a*b**3*d**3*e**3*m**3*x*(d + e*x)*
*m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 264*
A*a*b**3*d**3*e**3*m**2*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m
**2 + 1764*e**6*m + 720*e**6) + 720*A*a*b**3*d**3*e**3*m*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m
**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 12*A*a*b**3*d**2*e**4*m**4*x**2*(d + e*x)**m/
(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 144*A*a
*b**3*d**2*e**4*m**3*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m
**2 + 1764*e**6*m + 720*e**6) - 492*A*a*b**3*d**2*e**4*m**2*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*
e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 360*A*a*b**3*d**2*e**4*m*x**2*(d + e*x)
**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 4*A
*a*b**3*d*e**5*m**5*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m*
*2 + 1764*e**6*m + 720*e**6) + 56*A*a*b**3*d*e**5*m**4*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*
m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 260*A*a*b**3*d*e**5*m**3*x**3*(d + e*x)**m/(
e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 448*A*a*
b**3*d*e**5*m**2*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2
+ 1764*e**6*m + 720*e**6) + 240*A*a*b**3*d*e**5*m*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4
+ 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 4*A*a*b**3*e**6*m**5*x**4*(d + e*x)**m/(e**6*m**6
+ 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 68*A*a*b**3*e**6*
m**4*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*
m + 720*e**6) + 428*A*a*b**3*e**6*m**3*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*
m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 1228*A*a*b**3*e**6*m**2*x**4*(d + e*x)**m/(e**6*m**6 + 21*e*
*6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 1584*A*a*b**3*e**6*m*x**4
*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e
**6) + 720*A*a*b**3*e**6*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e*
*6*m**2 + 1764*e**6*m + 720*e**6) + 24*A*b**4*d**5*e*m*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4
+ 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 144*A*b**4*d**5*e*(d + e*x)**m/(e**6*m**6 + 21*e*
*6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 24*A*b**4*d**4*e**2*m**2*
x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*
e**6) - 144*A*b**4*d**4*e**2*m*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624
*e**6*m**2 + 1764*e**6*m + 720*e**6) + 12*A*b**4*d**3*e**3*m**3*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 +
175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 84*A*b**4*d**3*e**3*m**2*x**2*(d +
e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) +
72*A*b**4*d**3*e**3*m*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6
*m**2 + 1764*e**6*m + 720*e**6) - 4*A*b**4*d**2*e**4*m**4*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e*
*6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 36*A*b**4*d**2*e**4*m**3*x**3*(d + e*x)**
m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 80*A*
b**4*d**2*e**4*m**2*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m*
*2 + 1764*e**6*m + 720*e**6) - 48*A*b**4*d**2*e**4*m*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m*
*4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + A*b**4*d*e**5*m**5*x**4*(d + e*x)**m/(e**6*m**
6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 12*A*b**4*d*e**5
*m**4*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6
*m + 720*e**6) + 47*A*b**4*d*e**5*m**3*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*
m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 72*A*b**4*d*e**5*m**2*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6
*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 36*A*b**4*d*e**5*m*x**4*(d
+ e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6)
+ A*b**4*e**6*m**5*x**5*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m*
*2 + 1764*e**6*m + 720*e**6) + 16*A*b**4*e**6*m**4*x**5*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4
+ 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 95*A*b**4*e**6*m**3*x**5*(d + e*x)**m/(e**6*m**6
+ 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 260*A*b**4*e**6*m
**2*x**5*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m
+ 720*e**6) + 324*A*b**4*e**6*m*x**5*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 +
1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 144*A*b**4*e**6*x**5*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*
e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - B*a**4*d**2*e**4*m**4*(d + e*x)**m/(e**
6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 18*B*a**4*d
**2*e**4*m**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e
**6*m + 720*e**6) - 119*B*a**4*d**2*e**4*m**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**
6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 342*B*a**4*d**2*e**4*m*(d + e*x)**m/(e**6*m**6 + 21*e**6*m
**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 360*B*a**4*d**2*e**4*(d + e*x
)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + B*
a**4*d*e**5*m**5*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1
764*e**6*m + 720*e**6) + 18*B*a**4*d*e**5*m**4*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*
e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 119*B*a**4*d*e**5*m**3*x*(d + e*x)**m/(e**6*m**6 + 21*e
**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 342*B*a**4*d*e**5*m**2*x
*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e
**6) + 360*B*a**4*d*e**5*m*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**
6*m**2 + 1764*e**6*m + 720*e**6) + B*a**4*e**6*m**5*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**
4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 19*B*a**4*e**6*m**4*x**2*(d + e*x)**m/(e**6*m**
6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 137*B*a**4*e**6*
m**3*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*
m + 720*e**6) + 461*B*a**4*e**6*m**2*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m*
*3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 702*B*a**4*e**6*m*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5
+ 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 360*B*a**4*e**6*x**2*(d + e*x)**m
/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 8*B*a*
*3*b*d**3*e**3*m**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 +
1764*e**6*m + 720*e**6) + 120*B*a**3*b*d**3*e**3*m**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 +
735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 592*B*a**3*b*d**3*e**3*m*(d + e*x)**m/(e**6*m**6 +
21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 960*B*a**3*b*d**3*e
**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 72
0*e**6) - 8*B*a**3*b*d**2*e**4*m**4*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 +
1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 120*B*a**3*b*d**2*e**4*m**3*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m*
*5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 592*B*a**3*b*d**2*e**4*m**2*x*
(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e*
*6) - 960*B*a**3*b*d**2*e**4*m*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624
*e**6*m**2 + 1764*e**6*m + 720*e**6) + 4*B*a**3*b*d*e**5*m**5*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 17
5*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 64*B*a**3*b*d*e**5*m**4*x**2*(d + e*x
)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 35
6*B*a**3*b*d*e**5*m**3*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6
*m**2 + 1764*e**6*m + 720*e**6) + 776*B*a**3*b*d*e**5*m**2*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e
**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 480*B*a**3*b*d*e**5*m*x**2*(d + e*x)**m/
(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 4*B*a**
3*b*e**6*m**5*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1
764*e**6*m + 720*e**6) + 72*B*a**3*b*e**6*m**4*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 7
35*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 484*B*a**3*b*e**6*m**3*x**3*(d + e*x)**m/(e**6*m**6
+ 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 1488*B*a**3*b*e**6
*m**2*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6
*m + 720*e**6) + 2032*B*a**3*b*e**6*m*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m
**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 960*B*a**3*b*e**6*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5
+ 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 36*B*a**2*b**2*d**4*e**2*m**2*(d
+ e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6
) - 396*B*a**2*b**2*d**4*e**2*m*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*
e**6*m**2 + 1764*e**6*m + 720*e**6) - 1080*B*a**2*b**2*d**4*e**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*
e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 36*B*a**2*b**2*d**3*e**3*m**3*x*(d + e*
x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 3
96*B*a**2*b**2*d**3*e**3*m**2*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*
e**6*m**2 + 1764*e**6*m + 720*e**6) + 1080*B*a**2*b**2*d**3*e**3*m*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 +
175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 18*B*a**2*b**2*d**2*e**4*m**4*x**2*
(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e*
*6) - 216*B*a**2*b**2*d**2*e**4*m**3*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m*
*3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 738*B*a**2*b**2*d**2*e**4*m**2*x**2*(d + e*x)**m/(e**6*m**6 +
21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 540*B*a**2*b**2*d**2
*e**4*m*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e*
*6*m + 720*e**6) + 6*B*a**2*b**2*d*e**5*m**5*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735
*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 84*B*a**2*b**2*d*e**5*m**4*x**3*(d + e*x)**m/(e**6*m**
6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 390*B*a**2*b**2*
d*e**5*m**3*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 176
4*e**6*m + 720*e**6) + 672*B*a**2*b**2*d*e**5*m**2*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4
+ 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 360*B*a**2*b**2*d*e**5*m*x**3*(d + e*x)**m/(e**6
*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 6*B*a**2*b**
2*e**6*m**5*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 176
4*e**6*m + 720*e**6) + 102*B*a**2*b**2*e**6*m**4*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 +
735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 642*B*a**2*b**2*e**6*m**3*x**4*(d + e*x)**m/(e**6*
m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 1842*B*a**2*b
**2*e**6*m**2*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1
764*e**6*m + 720*e**6) + 2376*B*a**2*b**2*e**6*m*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 +
735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 1080*B*a**2*b**2*e**6*x**4*(d + e*x)**m/(e**6*m**6
+ 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 96*B*a*b**3*d**5*
e*m*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 72
0*e**6) + 576*B*a*b**3*d**5*e*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e*
*6*m**2 + 1764*e**6*m + 720*e**6) - 96*B*a*b**3*d**4*e**2*m**2*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*
e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 576*B*a*b**3*d**4*e**2*m*x*(d + e*x)**m
/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 48*B*a
*b**3*d**3*e**3*m**3*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m
**2 + 1764*e**6*m + 720*e**6) + 336*B*a*b**3*d**3*e**3*m**2*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*
e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 288*B*a*b**3*d**3*e**3*m*x**2*(d + e*x)
**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 16*
B*a*b**3*d**2*e**4*m**4*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**
6*m**2 + 1764*e**6*m + 720*e**6) - 144*B*a*b**3*d**2*e**4*m**3*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 1
75*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 320*B*a*b**3*d**2*e**4*m**2*x**3*(d
+ e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6)
- 192*B*a*b**3*d**2*e**4*m*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624
*e**6*m**2 + 1764*e**6*m + 720*e**6) + 4*B*a*b**3*d*e**5*m**5*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 17
5*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 48*B*a*b**3*d*e**5*m**4*x**4*(d + e*x
)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 18
8*B*a*b**3*d*e**5*m**3*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6
*m**2 + 1764*e**6*m + 720*e**6) + 288*B*a*b**3*d*e**5*m**2*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e
**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 144*B*a*b**3*d*e**5*m*x**4*(d + e*x)**m/
(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 4*B*a*b
**3*e**6*m**5*x**5*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1
764*e**6*m + 720*e**6) + 64*B*a*b**3*e**6*m**4*x**5*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 7
35*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 380*B*a*b**3*e**6*m**3*x**5*(d + e*x)**m/(e**6*m**6
+ 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 1040*B*a*b**3*e**6
*m**2*x**5*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6
*m + 720*e**6) + 1296*B*a*b**3*e**6*m*x**5*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m
**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 576*B*a*b**3*e**6*x**5*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5
+ 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 120*B*b**4*d**6*(d + e*x)**m/(e*
*6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 120*B*b**4
*d**5*e*m*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**
6*m + 720*e**6) - 60*B*b**4*d**4*e**2*m**2*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e
**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 60*B*b**4*d**4*e**2*m*x**2*(d + e*x)**m/(e**6*m**6 + 21*
e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 20*B*b**4*d**3*e**3*m**
3*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m +
720*e**6) + 60*B*b**4*d**3*e**3*m**2*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m
**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 40*B*b**4*d**3*e**3*m*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*
m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 5*B*b**4*d**2*e**4*m**4*x**4
*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e
**6) - 30*B*b**4*d**2*e**4*m**3*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 +
1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 55*B*b**4*d**2*e**4*m**2*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**
5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 30*B*b**4*d**2*e**4*m*x**4*(d +
e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6)
+ B*b**4*d*e**5*m**5*x**5*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m
**2 + 1764*e**6*m + 720*e**6) + 10*B*b**4*d*e**5*m**4*x**5*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m
**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 35*B*b**4*d*e**5*m**3*x**5*(d + e*x)**m/(e**6
*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 50*B*b**4*d*
e**5*m**2*x**5*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*
e**6*m + 720*e**6) + 24*B*b**4*d*e**5*m*x**5*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6
*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + B*b**4*e**6*m**5*x**6*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**
5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 15*B*b**4*e**6*m**4*x**6*(d + e
*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) +
85*B*b**4*e**6*m**3*x**6*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m*
*2 + 1764*e**6*m + 720*e**6) + 225*B*b**4*e**6*m**2*x**6*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**
4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 274*B*b**4*e**6*m*x**6*(d + e*x)**m/(e**6*m**6
+ 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 120*B*b**4*e**6*x*
*6*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720
*e**6), True))

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 957 vs. \(2 (234) = 468\).

Time = 0.23 (sec) , antiderivative size = 957, normalized size of antiderivative = 4.09 \[ \int (a+b x)^4 (A+B x) (d+e x)^m \, dx=\text {Too large to display} \]

[In]

integrate((b*x+a)^4*(B*x+A)*(e*x+d)^m,x, algorithm="maxima")

[Out]

(e^2*(m + 1)*x^2 + d*e*m*x - d^2)*(e*x + d)^m*B*a^4/((m^2 + 3*m + 2)*e^2) + 4*(e^2*(m + 1)*x^2 + d*e*m*x - d^2
)*(e*x + d)^m*A*a^3*b/((m^2 + 3*m + 2)*e^2) + (e*x + d)^(m + 1)*A*a^4/(e*(m + 1)) + 4*((m^2 + 3*m + 2)*e^3*x^3
+ (m^2 + m)*d*e^2*x^2 - 2*d^2*e*m*x + 2*d^3)*(e*x + d)^m*B*a^3*b/((m^3 + 6*m^2 + 11*m + 6)*e^3) + 6*((m^2 + 3
*m + 2)*e^3*x^3 + (m^2 + m)*d*e^2*x^2 - 2*d^2*e*m*x + 2*d^3)*(e*x + d)^m*A*a^2*b^2/((m^3 + 6*m^2 + 11*m + 6)*e
^3) + 6*((m^3 + 6*m^2 + 11*m + 6)*e^4*x^4 + (m^3 + 3*m^2 + 2*m)*d*e^3*x^3 - 3*(m^2 + m)*d^2*e^2*x^2 + 6*d^3*e*
m*x - 6*d^4)*(e*x + d)^m*B*a^2*b^2/((m^4 + 10*m^3 + 35*m^2 + 50*m + 24)*e^4) + 4*((m^3 + 6*m^2 + 11*m + 6)*e^4
*x^4 + (m^3 + 3*m^2 + 2*m)*d*e^3*x^3 - 3*(m^2 + m)*d^2*e^2*x^2 + 6*d^3*e*m*x - 6*d^4)*(e*x + d)^m*A*a*b^3/((m^
4 + 10*m^3 + 35*m^2 + 50*m + 24)*e^4) + 4*((m^4 + 10*m^3 + 35*m^2 + 50*m + 24)*e^5*x^5 + (m^4 + 6*m^3 + 11*m^2
+ 6*m)*d*e^4*x^4 - 4*(m^3 + 3*m^2 + 2*m)*d^2*e^3*x^3 + 12*(m^2 + m)*d^3*e^2*x^2 - 24*d^4*e*m*x + 24*d^5)*(e*x
+ d)^m*B*a*b^3/((m^5 + 15*m^4 + 85*m^3 + 225*m^2 + 274*m + 120)*e^5) + ((m^4 + 10*m^3 + 35*m^2 + 50*m + 24)*e
^5*x^5 + (m^4 + 6*m^3 + 11*m^2 + 6*m)*d*e^4*x^4 - 4*(m^3 + 3*m^2 + 2*m)*d^2*e^3*x^3 + 12*(m^2 + m)*d^3*e^2*x^2
- 24*d^4*e*m*x + 24*d^5)*(e*x + d)^m*A*b^4/((m^5 + 15*m^4 + 85*m^3 + 225*m^2 + 274*m + 120)*e^5) + ((m^5 + 15
*m^4 + 85*m^3 + 225*m^2 + 274*m + 120)*e^6*x^6 + (m^5 + 10*m^4 + 35*m^3 + 50*m^2 + 24*m)*d*e^5*x^5 - 5*(m^4 +
6*m^3 + 11*m^2 + 6*m)*d^2*e^4*x^4 + 20*(m^3 + 3*m^2 + 2*m)*d^3*e^3*x^3 - 60*(m^2 + m)*d^4*e^2*x^2 + 120*d^5*e*
m*x - 120*d^6)*(e*x + d)^m*B*b^4/((m^6 + 21*m^5 + 175*m^4 + 735*m^3 + 1624*m^2 + 1764*m + 720)*e^6)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 4377 vs. \(2 (234) = 468\).

Time = 0.35 (sec) , antiderivative size = 4377, normalized size of antiderivative = 18.71 \[ \int (a+b x)^4 (A+B x) (d+e x)^m \, dx=\text {Too large to display} \]

[In]

integrate((b*x+a)^4*(B*x+A)*(e*x+d)^m,x, algorithm="giac")

[Out]

((e*x + d)^m*B*b^4*e^6*m^5*x^6 + (e*x + d)^m*B*b^4*d*e^5*m^5*x^5 + 4*(e*x + d)^m*B*a*b^3*e^6*m^5*x^5 + (e*x +
d)^m*A*b^4*e^6*m^5*x^5 + 15*(e*x + d)^m*B*b^4*e^6*m^4*x^6 + 4*(e*x + d)^m*B*a*b^3*d*e^5*m^5*x^4 + (e*x + d)^m*
A*b^4*d*e^5*m^5*x^4 + 6*(e*x + d)^m*B*a^2*b^2*e^6*m^5*x^4 + 4*(e*x + d)^m*A*a*b^3*e^6*m^5*x^4 + 10*(e*x + d)^m
*B*b^4*d*e^5*m^4*x^5 + 64*(e*x + d)^m*B*a*b^3*e^6*m^4*x^5 + 16*(e*x + d)^m*A*b^4*e^6*m^4*x^5 + 85*(e*x + d)^m*
B*b^4*e^6*m^3*x^6 + 6*(e*x + d)^m*B*a^2*b^2*d*e^5*m^5*x^3 + 4*(e*x + d)^m*A*a*b^3*d*e^5*m^5*x^3 + 4*(e*x + d)^
m*B*a^3*b*e^6*m^5*x^3 + 6*(e*x + d)^m*A*a^2*b^2*e^6*m^5*x^3 - 5*(e*x + d)^m*B*b^4*d^2*e^4*m^4*x^4 + 48*(e*x +
d)^m*B*a*b^3*d*e^5*m^4*x^4 + 12*(e*x + d)^m*A*b^4*d*e^5*m^4*x^4 + 102*(e*x + d)^m*B*a^2*b^2*e^6*m^4*x^4 + 68*(
e*x + d)^m*A*a*b^3*e^6*m^4*x^4 + 35*(e*x + d)^m*B*b^4*d*e^5*m^3*x^5 + 380*(e*x + d)^m*B*a*b^3*e^6*m^3*x^5 + 95
*(e*x + d)^m*A*b^4*e^6*m^3*x^5 + 225*(e*x + d)^m*B*b^4*e^6*m^2*x^6 + 4*(e*x + d)^m*B*a^3*b*d*e^5*m^5*x^2 + 6*(
e*x + d)^m*A*a^2*b^2*d*e^5*m^5*x^2 + (e*x + d)^m*B*a^4*e^6*m^5*x^2 + 4*(e*x + d)^m*A*a^3*b*e^6*m^5*x^2 - 16*(e
*x + d)^m*B*a*b^3*d^2*e^4*m^4*x^3 - 4*(e*x + d)^m*A*b^4*d^2*e^4*m^4*x^3 + 84*(e*x + d)^m*B*a^2*b^2*d*e^5*m^4*x
^3 + 56*(e*x + d)^m*A*a*b^3*d*e^5*m^4*x^3 + 72*(e*x + d)^m*B*a^3*b*e^6*m^4*x^3 + 108*(e*x + d)^m*A*a^2*b^2*e^6
*m^4*x^3 - 30*(e*x + d)^m*B*b^4*d^2*e^4*m^3*x^4 + 188*(e*x + d)^m*B*a*b^3*d*e^5*m^3*x^4 + 47*(e*x + d)^m*A*b^4
*d*e^5*m^3*x^4 + 642*(e*x + d)^m*B*a^2*b^2*e^6*m^3*x^4 + 428*(e*x + d)^m*A*a*b^3*e^6*m^3*x^4 + 50*(e*x + d)^m*
B*b^4*d*e^5*m^2*x^5 + 1040*(e*x + d)^m*B*a*b^3*e^6*m^2*x^5 + 260*(e*x + d)^m*A*b^4*e^6*m^2*x^5 + 274*(e*x + d)
^m*B*b^4*e^6*m*x^6 + (e*x + d)^m*B*a^4*d*e^5*m^5*x + 4*(e*x + d)^m*A*a^3*b*d*e^5*m^5*x + (e*x + d)^m*A*a^4*e^6
*m^5*x - 18*(e*x + d)^m*B*a^2*b^2*d^2*e^4*m^4*x^2 - 12*(e*x + d)^m*A*a*b^3*d^2*e^4*m^4*x^2 + 64*(e*x + d)^m*B*
a^3*b*d*e^5*m^4*x^2 + 96*(e*x + d)^m*A*a^2*b^2*d*e^5*m^4*x^2 + 19*(e*x + d)^m*B*a^4*e^6*m^4*x^2 + 76*(e*x + d)
^m*A*a^3*b*e^6*m^4*x^2 + 20*(e*x + d)^m*B*b^4*d^3*e^3*m^3*x^3 - 144*(e*x + d)^m*B*a*b^3*d^2*e^4*m^3*x^3 - 36*(
e*x + d)^m*A*b^4*d^2*e^4*m^3*x^3 + 390*(e*x + d)^m*B*a^2*b^2*d*e^5*m^3*x^3 + 260*(e*x + d)^m*A*a*b^3*d*e^5*m^3
*x^3 + 484*(e*x + d)^m*B*a^3*b*e^6*m^3*x^3 + 726*(e*x + d)^m*A*a^2*b^2*e^6*m^3*x^3 - 55*(e*x + d)^m*B*b^4*d^2*
e^4*m^2*x^4 + 288*(e*x + d)^m*B*a*b^3*d*e^5*m^2*x^4 + 72*(e*x + d)^m*A*b^4*d*e^5*m^2*x^4 + 1842*(e*x + d)^m*B*
a^2*b^2*e^6*m^2*x^4 + 1228*(e*x + d)^m*A*a*b^3*e^6*m^2*x^4 + 24*(e*x + d)^m*B*b^4*d*e^5*m*x^5 + 1296*(e*x + d)
^m*B*a*b^3*e^6*m*x^5 + 324*(e*x + d)^m*A*b^4*e^6*m*x^5 + 120*(e*x + d)^m*B*b^4*e^6*x^6 + (e*x + d)^m*A*a^4*d*e
^5*m^5 - 8*(e*x + d)^m*B*a^3*b*d^2*e^4*m^4*x - 12*(e*x + d)^m*A*a^2*b^2*d^2*e^4*m^4*x + 18*(e*x + d)^m*B*a^4*d
*e^5*m^4*x + 72*(e*x + d)^m*A*a^3*b*d*e^5*m^4*x + 20*(e*x + d)^m*A*a^4*e^6*m^4*x + 48*(e*x + d)^m*B*a*b^3*d^3*
e^3*m^3*x^2 + 12*(e*x + d)^m*A*b^4*d^3*e^3*m^3*x^2 - 216*(e*x + d)^m*B*a^2*b^2*d^2*e^4*m^3*x^2 - 144*(e*x + d)
^m*A*a*b^3*d^2*e^4*m^3*x^2 + 356*(e*x + d)^m*B*a^3*b*d*e^5*m^3*x^2 + 534*(e*x + d)^m*A*a^2*b^2*d*e^5*m^3*x^2 +
137*(e*x + d)^m*B*a^4*e^6*m^3*x^2 + 548*(e*x + d)^m*A*a^3*b*e^6*m^3*x^2 + 60*(e*x + d)^m*B*b^4*d^3*e^3*m^2*x^
3 - 320*(e*x + d)^m*B*a*b^3*d^2*e^4*m^2*x^3 - 80*(e*x + d)^m*A*b^4*d^2*e^4*m^2*x^3 + 672*(e*x + d)^m*B*a^2*b^2
*d*e^5*m^2*x^3 + 448*(e*x + d)^m*A*a*b^3*d*e^5*m^2*x^3 + 1488*(e*x + d)^m*B*a^3*b*e^6*m^2*x^3 + 2232*(e*x + d)
^m*A*a^2*b^2*e^6*m^2*x^3 - 30*(e*x + d)^m*B*b^4*d^2*e^4*m*x^4 + 144*(e*x + d)^m*B*a*b^3*d*e^5*m*x^4 + 36*(e*x
+ d)^m*A*b^4*d*e^5*m*x^4 + 2376*(e*x + d)^m*B*a^2*b^2*e^6*m*x^4 + 1584*(e*x + d)^m*A*a*b^3*e^6*m*x^4 + 576*(e*
x + d)^m*B*a*b^3*e^6*x^5 + 144*(e*x + d)^m*A*b^4*e^6*x^5 - (e*x + d)^m*B*a^4*d^2*e^4*m^4 - 4*(e*x + d)^m*A*a^3
*b*d^2*e^4*m^4 + 20*(e*x + d)^m*A*a^4*d*e^5*m^4 + 36*(e*x + d)^m*B*a^2*b^2*d^3*e^3*m^3*x + 24*(e*x + d)^m*A*a*
b^3*d^3*e^3*m^3*x - 120*(e*x + d)^m*B*a^3*b*d^2*e^4*m^3*x - 180*(e*x + d)^m*A*a^2*b^2*d^2*e^4*m^3*x + 119*(e*x
+ d)^m*B*a^4*d*e^5*m^3*x + 476*(e*x + d)^m*A*a^3*b*d*e^5*m^3*x + 155*(e*x + d)^m*A*a^4*e^6*m^3*x - 60*(e*x +
d)^m*B*b^4*d^4*e^2*m^2*x^2 + 336*(e*x + d)^m*B*a*b^3*d^3*e^3*m^2*x^2 + 84*(e*x + d)^m*A*b^4*d^3*e^3*m^2*x^2 -
738*(e*x + d)^m*B*a^2*b^2*d^2*e^4*m^2*x^2 - 492*(e*x + d)^m*A*a*b^3*d^2*e^4*m^2*x^2 + 776*(e*x + d)^m*B*a^3*b*
d*e^5*m^2*x^2 + 1164*(e*x + d)^m*A*a^2*b^2*d*e^5*m^2*x^2 + 461*(e*x + d)^m*B*a^4*e^6*m^2*x^2 + 1844*(e*x + d)^
m*A*a^3*b*e^6*m^2*x^2 + 40*(e*x + d)^m*B*b^4*d^3*e^3*m*x^3 - 192*(e*x + d)^m*B*a*b^3*d^2*e^4*m*x^3 - 48*(e*x +
d)^m*A*b^4*d^2*e^4*m*x^3 + 360*(e*x + d)^m*B*a^2*b^2*d*e^5*m*x^3 + 240*(e*x + d)^m*A*a*b^3*d*e^5*m*x^3 + 2032
*(e*x + d)^m*B*a^3*b*e^6*m*x^3 + 3048*(e*x + d)^m*A*a^2*b^2*e^6*m*x^3 + 1080*(e*x + d)^m*B*a^2*b^2*e^6*x^4 + 7
20*(e*x + d)^m*A*a*b^3*e^6*x^4 + 8*(e*x + d)^m*B*a^3*b*d^3*e^3*m^3 + 12*(e*x + d)^m*A*a^2*b^2*d^3*e^3*m^3 - 18
*(e*x + d)^m*B*a^4*d^2*e^4*m^3 - 72*(e*x + d)^m*A*a^3*b*d^2*e^4*m^3 + 155*(e*x + d)^m*A*a^4*d*e^5*m^3 - 96*(e*
x + d)^m*B*a*b^3*d^4*e^2*m^2*x - 24*(e*x + d)^m*A*b^4*d^4*e^2*m^2*x + 396*(e*x + d)^m*B*a^2*b^2*d^3*e^3*m^2*x
+ 264*(e*x + d)^m*A*a*b^3*d^3*e^3*m^2*x - 592*(e*x + d)^m*B*a^3*b*d^2*e^4*m^2*x - 888*(e*x + d)^m*A*a^2*b^2*d^
2*e^4*m^2*x + 342*(e*x + d)^m*B*a^4*d*e^5*m^2*x + 1368*(e*x + d)^m*A*a^3*b*d*e^5*m^2*x + 580*(e*x + d)^m*A*a^4
*e^6*m^2*x - 60*(e*x + d)^m*B*b^4*d^4*e^2*m*x^2 + 288*(e*x + d)^m*B*a*b^3*d^3*e^3*m*x^2 + 72*(e*x + d)^m*A*b^4
*d^3*e^3*m*x^2 - 540*(e*x + d)^m*B*a^2*b^2*d^2*e^4*m*x^2 - 360*(e*x + d)^m*A*a*b^3*d^2*e^4*m*x^2 + 480*(e*x +
d)^m*B*a^3*b*d*e^5*m*x^2 + 720*(e*x + d)^m*A*a^2*b^2*d*e^5*m*x^2 + 702*(e*x + d)^m*B*a^4*e^6*m*x^2 + 2808*(e*x
+ d)^m*A*a^3*b*e^6*m*x^2 + 960*(e*x + d)^m*B*a^3*b*e^6*x^3 + 1440*(e*x + d)^m*A*a^2*b^2*e^6*x^3 - 36*(e*x + d
)^m*B*a^2*b^2*d^4*e^2*m^2 - 24*(e*x + d)^m*A*a*b^3*d^4*e^2*m^2 + 120*(e*x + d)^m*B*a^3*b*d^3*e^3*m^2 + 180*(e*
x + d)^m*A*a^2*b^2*d^3*e^3*m^2 - 119*(e*x + d)^m*B*a^4*d^2*e^4*m^2 - 476*(e*x + d)^m*A*a^3*b*d^2*e^4*m^2 + 580
*(e*x + d)^m*A*a^4*d*e^5*m^2 + 120*(e*x + d)^m*B*b^4*d^5*e*m*x - 576*(e*x + d)^m*B*a*b^3*d^4*e^2*m*x - 144*(e*
x + d)^m*A*b^4*d^4*e^2*m*x + 1080*(e*x + d)^m*B*a^2*b^2*d^3*e^3*m*x + 720*(e*x + d)^m*A*a*b^3*d^3*e^3*m*x - 96
0*(e*x + d)^m*B*a^3*b*d^2*e^4*m*x - 1440*(e*x + d)^m*A*a^2*b^2*d^2*e^4*m*x + 360*(e*x + d)^m*B*a^4*d*e^5*m*x +
1440*(e*x + d)^m*A*a^3*b*d*e^5*m*x + 1044*(e*x + d)^m*A*a^4*e^6*m*x + 360*(e*x + d)^m*B*a^4*e^6*x^2 + 1440*(e
*x + d)^m*A*a^3*b*e^6*x^2 + 96*(e*x + d)^m*B*a*b^3*d^5*e*m + 24*(e*x + d)^m*A*b^4*d^5*e*m - 396*(e*x + d)^m*B*
a^2*b^2*d^4*e^2*m - 264*(e*x + d)^m*A*a*b^3*d^4*e^2*m + 592*(e*x + d)^m*B*a^3*b*d^3*e^3*m + 888*(e*x + d)^m*A*
a^2*b^2*d^3*e^3*m - 342*(e*x + d)^m*B*a^4*d^2*e^4*m - 1368*(e*x + d)^m*A*a^3*b*d^2*e^4*m + 1044*(e*x + d)^m*A*
a^4*d*e^5*m + 720*(e*x + d)^m*A*a^4*e^6*x - 120*(e*x + d)^m*B*b^4*d^6 + 576*(e*x + d)^m*B*a*b^3*d^5*e + 144*(e
*x + d)^m*A*b^4*d^5*e - 1080*(e*x + d)^m*B*a^2*b^2*d^4*e^2 - 720*(e*x + d)^m*A*a*b^3*d^4*e^2 + 960*(e*x + d)^m
*B*a^3*b*d^3*e^3 + 1440*(e*x + d)^m*A*a^2*b^2*d^3*e^3 - 360*(e*x + d)^m*B*a^4*d^2*e^4 - 1440*(e*x + d)^m*A*a^3
*b*d^2*e^4 + 720*(e*x + d)^m*A*a^4*d*e^5)/(e^6*m^6 + 21*e^6*m^5 + 175*e^6*m^4 + 735*e^6*m^3 + 1624*e^6*m^2 + 1
764*e^6*m + 720*e^6)

Mupad [B] (verification not implemented)

Time = 3.99 (sec) , antiderivative size = 2117, normalized size of antiderivative = 9.05 \[ \int (a+b x)^4 (A+B x) (d+e x)^m \, dx=\text {Too large to display} \]

[In]

int((A + B*x)*(a + b*x)^4*(d + e*x)^m,x)

[Out]

((d + e*x)^m*(720*A*a^4*d*e^5 - 120*B*b^4*d^6 + 144*A*b^4*d^5*e - 360*B*a^4*d^2*e^4 - 720*A*a*b^3*d^4*e^2 - 14
40*A*a^3*b*d^2*e^4 + 960*B*a^3*b*d^3*e^3 + 580*A*a^4*d*e^5*m^2 + 155*A*a^4*d*e^5*m^3 + 20*A*a^4*d*e^5*m^4 + A*
a^4*d*e^5*m^5 - 342*B*a^4*d^2*e^4*m + 1440*A*a^2*b^2*d^3*e^3 - 1080*B*a^2*b^2*d^4*e^2 - 119*B*a^4*d^2*e^4*m^2
- 18*B*a^4*d^2*e^4*m^3 - B*a^4*d^2*e^4*m^4 + 576*B*a*b^3*d^5*e + 1044*A*a^4*d*e^5*m + 24*A*b^4*d^5*e*m + 888*A
*a^2*b^2*d^3*e^3*m - 24*A*a*b^3*d^4*e^2*m^2 - 476*A*a^3*b*d^2*e^4*m^2 - 72*A*a^3*b*d^2*e^4*m^3 - 4*A*a^3*b*d^2
*e^4*m^4 - 396*B*a^2*b^2*d^4*e^2*m + 120*B*a^3*b*d^3*e^3*m^2 + 8*B*a^3*b*d^3*e^3*m^3 + 96*B*a*b^3*d^5*e*m + 18
0*A*a^2*b^2*d^3*e^3*m^2 + 12*A*a^2*b^2*d^3*e^3*m^3 - 36*B*a^2*b^2*d^4*e^2*m^2 - 264*A*a*b^3*d^4*e^2*m - 1368*A
*a^3*b*d^2*e^4*m + 592*B*a^3*b*d^3*e^3*m))/(e^6*(1764*m + 1624*m^2 + 735*m^3 + 175*m^4 + 21*m^5 + m^6 + 720))
+ (x*(d + e*x)^m*(720*A*a^4*e^6 + 1044*A*a^4*e^6*m + 580*A*a^4*e^6*m^2 + 155*A*a^4*e^6*m^3 + 20*A*a^4*e^6*m^4
+ A*a^4*e^6*m^5 - 144*A*b^4*d^4*e^2*m + 342*B*a^4*d*e^5*m^2 + 119*B*a^4*d*e^5*m^3 + 18*B*a^4*d*e^5*m^4 + B*a^4
*d*e^5*m^5 - 24*A*b^4*d^4*e^2*m^2 + 360*B*a^4*d*e^5*m + 120*B*b^4*d^5*e*m - 1440*A*a^2*b^2*d^2*e^4*m + 264*A*a
*b^3*d^3*e^3*m^2 + 24*A*a*b^3*d^3*e^3*m^3 + 1080*B*a^2*b^2*d^3*e^3*m - 96*B*a*b^3*d^4*e^2*m^2 - 592*B*a^3*b*d^
2*e^4*m^2 - 120*B*a^3*b*d^2*e^4*m^3 - 8*B*a^3*b*d^2*e^4*m^4 + 1440*A*a^3*b*d*e^5*m - 888*A*a^2*b^2*d^2*e^4*m^2
- 180*A*a^2*b^2*d^2*e^4*m^3 - 12*A*a^2*b^2*d^2*e^4*m^4 + 396*B*a^2*b^2*d^3*e^3*m^2 + 36*B*a^2*b^2*d^3*e^3*m^3
+ 720*A*a*b^3*d^3*e^3*m + 1368*A*a^3*b*d*e^5*m^2 + 476*A*a^3*b*d*e^5*m^3 + 72*A*a^3*b*d*e^5*m^4 + 4*A*a^3*b*d
*e^5*m^5 - 576*B*a*b^3*d^4*e^2*m - 960*B*a^3*b*d^2*e^4*m))/(e^6*(1764*m + 1624*m^2 + 735*m^3 + 175*m^4 + 21*m^
5 + m^6 + 720)) + (x^2*(m + 1)*(d + e*x)^m*(360*B*a^4*e^4 + 1440*A*a^3*b*e^4 + 342*B*a^4*e^4*m - 60*B*b^4*d^4*
m + 119*B*a^4*e^4*m^2 + 18*B*a^4*e^4*m^3 + B*a^4*e^4*m^4 + 476*A*a^3*b*e^4*m^2 + 72*A*a^3*b*e^4*m^3 + 4*A*a^3*
b*e^4*m^4 + 12*A*b^4*d^3*e*m^2 + 1368*A*a^3*b*e^4*m + 72*A*b^4*d^3*e*m - 132*A*a*b^3*d^2*e^2*m^2 + 444*A*a^2*b
^2*d*e^3*m^2 - 12*A*a*b^3*d^2*e^2*m^3 + 90*A*a^2*b^2*d*e^3*m^3 + 6*A*a^2*b^2*d*e^3*m^4 - 540*B*a^2*b^2*d^2*e^2
*m + 288*B*a*b^3*d^3*e*m + 480*B*a^3*b*d*e^3*m - 198*B*a^2*b^2*d^2*e^2*m^2 - 18*B*a^2*b^2*d^2*e^2*m^3 - 360*A*
a*b^3*d^2*e^2*m + 720*A*a^2*b^2*d*e^3*m + 48*B*a*b^3*d^3*e*m^2 + 296*B*a^3*b*d*e^3*m^2 + 60*B*a^3*b*d*e^3*m^3
+ 4*B*a^3*b*d*e^3*m^4))/(e^4*(1764*m + 1624*m^2 + 735*m^3 + 175*m^4 + 21*m^5 + m^6 + 720)) + (B*b^4*x^6*(d + e
*x)^m*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120))/(1764*m + 1624*m^2 + 735*m^3 + 175*m^4 + 21*m^5 + m^6 +
720) + (b^2*x^4*(d + e*x)^m*(11*m + 6*m^2 + m^3 + 6)*(180*B*a^2*e^2 + 120*A*a*b*e^2 + 66*B*a^2*e^2*m - 5*B*b^
2*d^2*m + 6*B*a^2*e^2*m^2 + 44*A*a*b*e^2*m + 6*A*b^2*d*e*m + 4*A*a*b*e^2*m^2 + A*b^2*d*e*m^2 + 24*B*a*b*d*e*m
+ 4*B*a*b*d*e*m^2))/(e^2*(1764*m + 1624*m^2 + 735*m^3 + 175*m^4 + 21*m^5 + m^6 + 720)) + (b^3*x^5*(d + e*x)^m*
(50*m + 35*m^2 + 10*m^3 + m^4 + 24)*(6*A*b*e + 24*B*a*e + A*b*e*m + 4*B*a*e*m + B*b*d*m))/(e*(1764*m + 1624*m^
2 + 735*m^3 + 175*m^4 + 21*m^5 + m^6 + 720)) + (2*b*x^3*(d + e*x)^m*(3*m + m^2 + 2)*(240*B*a^3*e^3 + 360*A*a^2
*b*e^3 + 148*B*a^3*e^3*m + 10*B*b^3*d^3*m + 30*B*a^3*e^3*m^2 + 2*B*a^3*e^3*m^3 + 45*A*a^2*b*e^3*m^2 + 3*A*a^2*
b*e^3*m^3 - 2*A*b^3*d^2*e*m^2 + 222*A*a^2*b*e^3*m - 12*A*b^3*d^2*e*m + 60*A*a*b^2*d*e^2*m - 48*B*a*b^2*d^2*e*m
+ 90*B*a^2*b*d*e^2*m + 22*A*a*b^2*d*e^2*m^2 + 2*A*a*b^2*d*e^2*m^3 - 8*B*a*b^2*d^2*e*m^2 + 33*B*a^2*b*d*e^2*m^
2 + 3*B*a^2*b*d*e^2*m^3))/(e^3*(1764*m + 1624*m^2 + 735*m^3 + 175*m^4 + 21*m^5 + m^6 + 720))