\(\int (d+e x)^m (a^2+2 a b x+b^2 x^2)^3 \, dx\) [1731]

Optimal result

Integrand size = 26, antiderivative size = 206 \[ \int (d+e x)^m \left (a^2+2 a b x+b^2 x^2\right )^3 \, dx=\frac {(b d-a e)^6 (d+e x)^{1+m}}{e^7 (1+m)}-\frac {6 b (b d-a e)^5 (d+e x)^{2+m}}{e^7 (2+m)}+\frac {15 b^2 (b d-a e)^4 (d+e x)^{3+m}}{e^7 (3+m)}-\frac {20 b^3 (b d-a e)^3 (d+e x)^{4+m}}{e^7 (4+m)}+\frac {15 b^4 (b d-a e)^2 (d+e x)^{5+m}}{e^7 (5+m)}-\frac {6 b^5 (b d-a e) (d+e x)^{6+m}}{e^7 (6+m)}+\frac {b^6 (d+e x)^{7+m}}{e^7 (7+m)} \]

[Out]

(-a*e+b*d)^6*(e*x+d)^(1+m)/e^7/(1+m)-6*b*(-a*e+b*d)^5*(e*x+d)^(2+m)/e^7/(2+m)+15*b^2*(-a*e+b*d)^4*(e*x+d)^(3+m
)/e^7/(3+m)-20*b^3*(-a*e+b*d)^3*(e*x+d)^(4+m)/e^7/(4+m)+15*b^4*(-a*e+b*d)^2*(e*x+d)^(5+m)/e^7/(5+m)-6*b^5*(-a*
e+b*d)*(e*x+d)^(6+m)/e^7/(6+m)+b^6*(e*x+d)^(7+m)/e^7/(7+m)

Rubi [A] (verified)

Time = 0.09 (sec) , antiderivative size = 206, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {27, 45} \[ \int (d+e x)^m \left (a^2+2 a b x+b^2 x^2\right )^3 \, dx=-\frac {6 b^5 (b d-a e) (d+e x)^{m+6}}{e^7 (m+6)}+\frac {15 b^4 (b d-a e)^2 (d+e x)^{m+5}}{e^7 (m+5)}-\frac {20 b^3 (b d-a e)^3 (d+e x)^{m+4}}{e^7 (m+4)}+\frac {15 b^2 (b d-a e)^4 (d+e x)^{m+3}}{e^7 (m+3)}+\frac {(b d-a e)^6 (d+e x)^{m+1}}{e^7 (m+1)}-\frac {6 b (b d-a e)^5 (d+e x)^{m+2}}{e^7 (m+2)}+\frac {b^6 (d+e x)^{m+7}}{e^7 (m+7)} \]

[In]

Int[(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^3,x]

[Out]

((b*d - a*e)^6*(d + e*x)^(1 + m))/(e^7*(1 + m)) - (6*b*(b*d - a*e)^5*(d + e*x)^(2 + m))/(e^7*(2 + m)) + (15*b^
2*(b*d - a*e)^4*(d + e*x)^(3 + m))/(e^7*(3 + m)) - (20*b^3*(b*d - a*e)^3*(d + e*x)^(4 + m))/(e^7*(4 + m)) + (1
5*b^4*(b*d - a*e)^2*(d + e*x)^(5 + m))/(e^7*(5 + m)) - (6*b^5*(b*d - a*e)*(d + e*x)^(6 + m))/(e^7*(6 + m)) + (
b^6*(d + e*x)^(7 + m))/(e^7*(7 + m))

Rule 27

Int[(u_.)*((a_) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> Int[u*Cancel[(b/2 + c*x)^(2*p)/c^p], x] /; Fr
eeQ[{a, b, c}, x] && EqQ[b^2 - 4*a*c, 0] && IntegerQ[p]

Rule 45

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d
*x)^n, x], x] /; FreeQ[{a, b, c, d, n}, x] && NeQ[b*c - a*d, 0] && IGtQ[m, 0] && ( !IntegerQ[n] || (EqQ[c, 0]
&& LeQ[7*m + 4*n + 4, 0]) || LtQ[9*m + 5*(n + 1), 0] || GtQ[m + n + 2, 0])

Rubi steps \begin{align*} \text {integral}& = \int (a+b x)^6 (d+e x)^m \, dx \\ & = \int \left (\frac {(-b d+a e)^6 (d+e x)^m}{e^6}-\frac {6 b (b d-a e)^5 (d+e x)^{1+m}}{e^6}+\frac {15 b^2 (b d-a e)^4 (d+e x)^{2+m}}{e^6}-\frac {20 b^3 (b d-a e)^3 (d+e x)^{3+m}}{e^6}+\frac {15 b^4 (b d-a e)^2 (d+e x)^{4+m}}{e^6}-\frac {6 b^5 (b d-a e) (d+e x)^{5+m}}{e^6}+\frac {b^6 (d+e x)^{6+m}}{e^6}\right ) \, dx \\ & = \frac {(b d-a e)^6 (d+e x)^{1+m}}{e^7 (1+m)}-\frac {6 b (b d-a e)^5 (d+e x)^{2+m}}{e^7 (2+m)}+\frac {15 b^2 (b d-a e)^4 (d+e x)^{3+m}}{e^7 (3+m)}-\frac {20 b^3 (b d-a e)^3 (d+e x)^{4+m}}{e^7 (4+m)}+\frac {15 b^4 (b d-a e)^2 (d+e x)^{5+m}}{e^7 (5+m)}-\frac {6 b^5 (b d-a e) (d+e x)^{6+m}}{e^7 (6+m)}+\frac {b^6 (d+e x)^{7+m}}{e^7 (7+m)} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.18 (sec) , antiderivative size = 175, normalized size of antiderivative = 0.85 \[ \int (d+e x)^m \left (a^2+2 a b x+b^2 x^2\right )^3 \, dx=\frac {(d+e x)^{1+m} \left (\frac {(b d-a e)^6}{1+m}-\frac {6 b (b d-a e)^5 (d+e x)}{2+m}+\frac {15 b^2 (b d-a e)^4 (d+e x)^2}{3+m}-\frac {20 b^3 (b d-a e)^3 (d+e x)^3}{4+m}+\frac {15 b^4 (b d-a e)^2 (d+e x)^4}{5+m}-\frac {6 b^5 (b d-a e) (d+e x)^5}{6+m}+\frac {b^6 (d+e x)^6}{7+m}\right )}{e^7} \]

[In]

Integrate[(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^3,x]

[Out]

((d + e*x)^(1 + m)*((b*d - a*e)^6/(1 + m) - (6*b*(b*d - a*e)^5*(d + e*x))/(2 + m) + (15*b^2*(b*d - a*e)^4*(d +
e*x)^2)/(3 + m) - (20*b^3*(b*d - a*e)^3*(d + e*x)^3)/(4 + m) + (15*b^4*(b*d - a*e)^2*(d + e*x)^4)/(5 + m) - (
6*b^5*(b*d - a*e)*(d + e*x)^5)/(6 + m) + (b^6*(d + e*x)^6)/(7 + m)))/e^7

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(1693\) vs. \(2(206)=412\).

Time = 2.39 (sec) , antiderivative size = 1694, normalized size of antiderivative = 8.22

method	result	size
norman	\(\text {Expression too large to display}\)	\(1694\)
gosper	\(\text {Expression too large to display}\)	\(2157\)
risch	\(\text {Expression too large to display}\)	\(2687\)
parallelrisch	\(\text {Expression too large to display}\)	\(3994\)

[In]

int((e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^3,x,method=_RETURNVERBOSE)

[Out]

b^6/(7+m)*x^7*exp(m*ln(e*x+d))+d*(a^6*e^6*m^6+27*a^6*e^6*m^5-6*a^5*b*d*e^5*m^5+295*a^6*e^6*m^4-150*a^5*b*d*e^5
*m^4+30*a^4*b^2*d^2*e^4*m^4+1665*a^6*e^6*m^3-1470*a^5*b*d*e^5*m^3+660*a^4*b^2*d^2*e^4*m^3-120*a^3*b^3*d^3*e^3*
m^3+5104*a^6*e^6*m^2-7050*a^5*b*d*e^5*m^2+5370*a^4*b^2*d^2*e^4*m^2-2160*a^3*b^3*d^3*e^3*m^2+360*a^2*b^4*d^4*e^
2*m^2+8028*a^6*e^6*m-16524*a^5*b*d*e^5*m+19140*a^4*b^2*d^2*e^4*m-12840*a^3*b^3*d^3*e^3*m+4680*a^2*b^4*d^4*e^2*
m-720*a*b^5*d^5*e*m+5040*a^6*e^6-15120*a^5*b*d*e^5+25200*a^4*b^2*d^2*e^4-25200*a^3*b^3*d^3*e^3+15120*a^2*b^4*d
^4*e^2-5040*a*b^5*d^5*e+720*b^6*d^6)/e^7/(m^7+28*m^6+322*m^5+1960*m^4+6769*m^3+13132*m^2+13068*m+5040)*exp(m*l
n(e*x+d))+(a^6*e^6*m^6+6*a^5*b*d*e^5*m^6+27*a^6*e^6*m^5+150*a^5*b*d*e^5*m^5-30*a^4*b^2*d^2*e^4*m^5+295*a^6*e^6
*m^4+1470*a^5*b*d*e^5*m^4-660*a^4*b^2*d^2*e^4*m^4+120*a^3*b^3*d^3*e^3*m^4+1665*a^6*e^6*m^3+7050*a^5*b*d*e^5*m^
3-5370*a^4*b^2*d^2*e^4*m^3+2160*a^3*b^3*d^3*e^3*m^3-360*a^2*b^4*d^4*e^2*m^3+5104*a^6*e^6*m^2+16524*a^5*b*d*e^5
*m^2-19140*a^4*b^2*d^2*e^4*m^2+12840*a^3*b^3*d^3*e^3*m^2-4680*a^2*b^4*d^4*e^2*m^2+720*a*b^5*d^5*e*m^2+8028*a^6
*e^6*m+15120*a^5*b*d*e^5*m-25200*a^4*b^2*d^2*e^4*m+25200*a^3*b^3*d^3*e^3*m-15120*a^2*b^4*d^4*e^2*m+5040*a*b^5*
d^5*e*m-720*b^6*d^6*m+5040*a^6*e^6)/e^6/(m^7+28*m^6+322*m^5+1960*m^4+6769*m^3+13132*m^2+13068*m+5040)*x*exp(m*
ln(e*x+d))+(6*a*e*m+b*d*m+42*a*e)*b^5/e/(m^2+13*m+42)*x^6*exp(m*ln(e*x+d))+3*(5*a^2*e^2*m^2+2*a*b*d*e*m^2+65*a
^2*e^2*m+14*a*b*d*e*m-2*b^2*d^2*m+210*a^2*e^2)*b^4/e^2/(m^3+18*m^2+107*m+210)*x^5*exp(m*ln(e*x+d))+5*(4*a^3*e^
3*m^3+3*a^2*b*d*e^2*m^3+72*a^3*e^3*m^2+39*a^2*b*d*e^2*m^2-6*a*b^2*d^2*e*m^2+428*a^3*e^3*m+126*a^2*b*d*e^2*m-42
*a*b^2*d^2*e*m+6*b^3*d^3*m+840*a^3*e^3)*b^3/e^3/(m^4+22*m^3+179*m^2+638*m+840)*x^4*exp(m*ln(e*x+d))+5*(3*a^4*e
^4*m^4+4*a^3*b*d*e^3*m^4+66*a^4*e^4*m^3+72*a^3*b*d*e^3*m^3-12*a^2*b^2*d^2*e^2*m^3+537*a^4*e^4*m^2+428*a^3*b*d*
e^3*m^2-156*a^2*b^2*d^2*e^2*m^2+24*a*b^3*d^3*e*m^2+1914*a^4*e^4*m+840*a^3*b*d*e^3*m-504*a^2*b^2*d^2*e^2*m+168*
a*b^3*d^3*e*m-24*b^4*d^4*m+2520*a^4*e^4)*b^2/e^4/(m^5+25*m^4+245*m^3+1175*m^2+2754*m+2520)*x^3*exp(m*ln(e*x+d)
)+3*(2*a^5*e^5*m^5+5*a^4*b*d*e^4*m^5+50*a^5*e^5*m^4+110*a^4*b*d*e^4*m^4-20*a^3*b^2*d^2*e^3*m^4+490*a^5*e^5*m^3
+895*a^4*b*d*e^4*m^3-360*a^3*b^2*d^2*e^3*m^3+60*a^2*b^3*d^3*e^2*m^3+2350*a^5*e^5*m^2+3190*a^4*b*d*e^4*m^2-2140
*a^3*b^2*d^2*e^3*m^2+780*a^2*b^3*d^3*e^2*m^2-120*a*b^4*d^4*e*m^2+5508*a^5*e^5*m+4200*a^4*b*d*e^4*m-4200*a^3*b^
2*d^2*e^3*m+2520*a^2*b^3*d^3*e^2*m-840*a*b^4*d^4*e*m+120*b^5*d^5*m+5040*a^5*e^5)*b/e^5/(m^6+27*m^5+295*m^4+166
5*m^3+5104*m^2+8028*m+5040)*x^2*exp(m*ln(e*x+d))

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 2230 vs. \(2 (206) = 412\).

Time = 0.73 (sec) , antiderivative size = 2230, normalized size of antiderivative = 10.83 \[ \int (d+e x)^m \left (a^2+2 a b x+b^2 x^2\right )^3 \, dx=\text {Too large to display} \]

[In]

integrate((e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm="fricas")

[Out]

(a^6*d*e^6*m^6 + 720*b^6*d^7 - 5040*a*b^5*d^6*e + 15120*a^2*b^4*d^5*e^2 - 25200*a^3*b^3*d^4*e^3 + 25200*a^4*b^
2*d^3*e^4 - 15120*a^5*b*d^2*e^5 + 5040*a^6*d*e^6 + (b^6*e^7*m^6 + 21*b^6*e^7*m^5 + 175*b^6*e^7*m^4 + 735*b^6*e
^7*m^3 + 1624*b^6*e^7*m^2 + 1764*b^6*e^7*m + 720*b^6*e^7)*x^7 + (5040*a*b^5*e^7 + (b^6*d*e^6 + 6*a*b^5*e^7)*m^
6 + 3*(5*b^6*d*e^6 + 44*a*b^5*e^7)*m^5 + 5*(17*b^6*d*e^6 + 228*a*b^5*e^7)*m^4 + 15*(15*b^6*d*e^6 + 328*a*b^5*e
^7)*m^3 + 2*(137*b^6*d*e^6 + 5547*a*b^5*e^7)*m^2 + 12*(10*b^6*d*e^6 + 1019*a*b^5*e^7)*m)*x^6 - 3*(2*a^5*b*d^2*
e^5 - 9*a^6*d*e^6)*m^5 + 3*(5040*a^2*b^4*e^7 + (2*a*b^5*d*e^6 + 5*a^2*b^4*e^7)*m^6 - (2*b^6*d^2*e^5 - 34*a*b^5
*d*e^6 - 115*a^2*b^4*e^7)*m^5 - 5*(4*b^6*d^2*e^5 - 42*a*b^5*d*e^6 - 207*a^2*b^4*e^7)*m^4 - 5*(14*b^6*d^2*e^5 -
118*a*b^5*d*e^6 - 925*a^2*b^4*e^7)*m^3 - 4*(25*b^6*d^2*e^5 - 187*a*b^5*d*e^6 - 2680*a^2*b^4*e^7)*m^2 - 12*(4*
b^6*d^2*e^5 - 28*a*b^5*d*e^6 - 1005*a^2*b^4*e^7)*m)*x^5 + 5*(6*a^4*b^2*d^3*e^4 - 30*a^5*b*d^2*e^5 + 59*a^6*d*e
^6)*m^4 + 5*(5040*a^3*b^3*e^7 + (3*a^2*b^4*d*e^6 + 4*a^3*b^3*e^7)*m^6 - 3*(2*a*b^5*d^2*e^5 - 19*a^2*b^4*d*e^6
- 32*a^3*b^3*e^7)*m^5 + (6*b^6*d^3*e^4 - 78*a*b^5*d^2*e^5 + 393*a^2*b^4*d*e^6 + 904*a^3*b^3*e^7)*m^4 + 3*(12*b
^6*d^3*e^4 - 106*a*b^5*d^2*e^5 + 401*a^2*b^4*d*e^6 + 1408*a^3*b^3*e^7)*m^3 + 2*(33*b^6*d^3*e^4 - 249*a*b^5*d^2
*e^5 + 810*a^2*b^4*d*e^6 + 5090*a^3*b^3*e^7)*m^2 + 36*(b^6*d^3*e^4 - 7*a*b^5*d^2*e^5 + 21*a^2*b^4*d*e^6 + 328*
a^3*b^3*e^7)*m)*x^4 - 15*(8*a^3*b^3*d^4*e^3 - 44*a^4*b^2*d^3*e^4 + 98*a^5*b*d^2*e^5 - 111*a^6*d*e^6)*m^3 + 5*(
5040*a^4*b^2*e^7 + (4*a^3*b^3*d*e^6 + 3*a^4*b^2*e^7)*m^6 - 3*(4*a^2*b^4*d^2*e^5 - 28*a^3*b^3*d*e^6 - 25*a^4*b^
2*e^7)*m^5 + (24*a*b^5*d^3*e^4 - 192*a^2*b^4*d^2*e^5 + 652*a^3*b^3*d*e^6 + 741*a^4*b^2*e^7)*m^4 - 3*(8*b^6*d^4
*e^3 - 80*a*b^5*d^3*e^4 + 332*a^2*b^4*d^2*e^5 - 756*a^3*b^3*d*e^6 - 1219*a^4*b^2*e^7)*m^3 - 8*(9*b^6*d^4*e^3 -
69*a*b^5*d^3*e^4 + 228*a^2*b^4*d^2*e^5 - 422*a^3*b^3*d*e^6 - 1167*a^4*b^2*e^7)*m^2 - 12*(4*b^6*d^4*e^3 - 28*a
*b^5*d^3*e^4 + 84*a^2*b^4*d^2*e^5 - 140*a^3*b^3*d*e^6 - 949*a^4*b^2*e^7)*m)*x^3 + 2*(180*a^2*b^4*d^5*e^2 - 108
0*a^3*b^3*d^4*e^3 + 2685*a^4*b^2*d^3*e^4 - 3525*a^5*b*d^2*e^5 + 2552*a^6*d*e^6)*m^2 + 3*(5040*a^5*b*e^7 + (5*a
^4*b^2*d*e^6 + 2*a^5*b*e^7)*m^6 - (20*a^3*b^3*d^2*e^5 - 115*a^4*b^2*d*e^6 - 52*a^5*b*e^7)*m^5 + 5*(12*a^2*b^4*
d^3*e^4 - 76*a^3*b^3*d^2*e^5 + 201*a^4*b^2*d*e^6 + 108*a^5*b*e^7)*m^4 - 5*(24*a*b^5*d^4*e^3 - 168*a^2*b^4*d^3*
e^4 + 500*a^3*b^3*d^2*e^5 - 817*a^4*b^2*d*e^6 - 568*a^5*b*e^7)*m^3 + 2*(60*b^6*d^5*e^2 - 480*a*b^5*d^4*e^3 + 1
650*a^2*b^4*d^3*e^4 - 3170*a^3*b^3*d^2*e^5 + 3695*a^4*b^2*d*e^6 + 3929*a^5*b*e^7)*m^2 + 12*(10*b^6*d^5*e^2 - 7
0*a*b^5*d^4*e^3 + 210*a^2*b^4*d^3*e^4 - 350*a^3*b^3*d^2*e^5 + 350*a^4*b^2*d*e^6 + 879*a^5*b*e^7)*m)*x^2 - 12*(
60*a*b^5*d^6*e - 390*a^2*b^4*d^5*e^2 + 1070*a^3*b^3*d^4*e^3 - 1595*a^4*b^2*d^3*e^4 + 1377*a^5*b*d^2*e^5 - 669*
a^6*d*e^6)*m + (5040*a^6*e^7 + (6*a^5*b*d*e^6 + a^6*e^7)*m^6 - 3*(10*a^4*b^2*d^2*e^5 - 50*a^5*b*d*e^6 - 9*a^6*
e^7)*m^5 + 5*(24*a^3*b^3*d^3*e^4 - 132*a^4*b^2*d^2*e^5 + 294*a^5*b*d*e^6 + 59*a^6*e^7)*m^4 - 15*(24*a^2*b^4*d^
4*e^3 - 144*a^3*b^3*d^3*e^4 + 358*a^4*b^2*d^2*e^5 - 470*a^5*b*d*e^6 - 111*a^6*e^7)*m^3 + 4*(180*a*b^5*d^5*e^2
- 1170*a^2*b^4*d^4*e^3 + 3210*a^3*b^3*d^3*e^4 - 4785*a^4*b^2*d^2*e^5 + 4131*a^5*b*d*e^6 + 1276*a^6*e^7)*m^2 -
36*(20*b^6*d^6*e - 140*a*b^5*d^5*e^2 + 420*a^2*b^4*d^4*e^3 - 700*a^3*b^3*d^3*e^4 + 700*a^4*b^2*d^2*e^5 - 420*a
^5*b*d*e^6 - 223*a^6*e^7)*m)*x)*(e*x + d)^m/(e^7*m^7 + 28*e^7*m^6 + 322*e^7*m^5 + 1960*e^7*m^4 + 6769*e^7*m^3
+ 13132*e^7*m^2 + 13068*e^7*m + 5040*e^7)

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 28410 vs. \(2 (182) = 364\).

Time = 5.67 (sec) , antiderivative size = 28410, normalized size of antiderivative = 137.91 \[ \int (d+e x)^m \left (a^2+2 a b x+b^2 x^2\right )^3 \, dx=\text {Too large to display} \]

[In]

integrate((e*x+d)**m*(b**2*x**2+2*a*b*x+a**2)**3,x)

[Out]

Piecewise((d**m*(a**6*x + 3*a**5*b*x**2 + 5*a**4*b**2*x**3 + 5*a**3*b**3*x**4 + 3*a**2*b**4*x**5 + a*b**5*x**6
+ b**6*x**7/7), Eq(e, 0)), (-10*a**6*e**6/(60*d**6*e**7 + 360*d**5*e**8*x + 900*d**4*e**9*x**2 + 1200*d**3*e*
*10*x**3 + 900*d**2*e**11*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6) - 12*a**5*b*d*e**5/(60*d**6*e**7 + 360*d**5
*e**8*x + 900*d**4*e**9*x**2 + 1200*d**3*e**10*x**3 + 900*d**2*e**11*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6)
- 72*a**5*b*e**6*x/(60*d**6*e**7 + 360*d**5*e**8*x + 900*d**4*e**9*x**2 + 1200*d**3*e**10*x**3 + 900*d**2*e**1
1*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6) - 15*a**4*b**2*d**2*e**4/(60*d**6*e**7 + 360*d**5*e**8*x + 900*d**4
*e**9*x**2 + 1200*d**3*e**10*x**3 + 900*d**2*e**11*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6) - 90*a**4*b**2*d*e
**5*x/(60*d**6*e**7 + 360*d**5*e**8*x + 900*d**4*e**9*x**2 + 1200*d**3*e**10*x**3 + 900*d**2*e**11*x**4 + 360*
d*e**12*x**5 + 60*e**13*x**6) - 225*a**4*b**2*e**6*x**2/(60*d**6*e**7 + 360*d**5*e**8*x + 900*d**4*e**9*x**2 +
1200*d**3*e**10*x**3 + 900*d**2*e**11*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6) - 20*a**3*b**3*d**3*e**3/(60*d
**6*e**7 + 360*d**5*e**8*x + 900*d**4*e**9*x**2 + 1200*d**3*e**10*x**3 + 900*d**2*e**11*x**4 + 360*d*e**12*x**
5 + 60*e**13*x**6) - 120*a**3*b**3*d**2*e**4*x/(60*d**6*e**7 + 360*d**5*e**8*x + 900*d**4*e**9*x**2 + 1200*d**
3*e**10*x**3 + 900*d**2*e**11*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6) - 300*a**3*b**3*d*e**5*x**2/(60*d**6*e*
*7 + 360*d**5*e**8*x + 900*d**4*e**9*x**2 + 1200*d**3*e**10*x**3 + 900*d**2*e**11*x**4 + 360*d*e**12*x**5 + 60
*e**13*x**6) - 400*a**3*b**3*e**6*x**3/(60*d**6*e**7 + 360*d**5*e**8*x + 900*d**4*e**9*x**2 + 1200*d**3*e**10*
x**3 + 900*d**2*e**11*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6) - 30*a**2*b**4*d**4*e**2/(60*d**6*e**7 + 360*d*
*5*e**8*x + 900*d**4*e**9*x**2 + 1200*d**3*e**10*x**3 + 900*d**2*e**11*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6
) - 180*a**2*b**4*d**3*e**3*x/(60*d**6*e**7 + 360*d**5*e**8*x + 900*d**4*e**9*x**2 + 1200*d**3*e**10*x**3 + 90
0*d**2*e**11*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6) - 450*a**2*b**4*d**2*e**4*x**2/(60*d**6*e**7 + 360*d**5*
e**8*x + 900*d**4*e**9*x**2 + 1200*d**3*e**10*x**3 + 900*d**2*e**11*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6) -
600*a**2*b**4*d*e**5*x**3/(60*d**6*e**7 + 360*d**5*e**8*x + 900*d**4*e**9*x**2 + 1200*d**3*e**10*x**3 + 900*d
**2*e**11*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6) - 450*a**2*b**4*e**6*x**4/(60*d**6*e**7 + 360*d**5*e**8*x +
900*d**4*e**9*x**2 + 1200*d**3*e**10*x**3 + 900*d**2*e**11*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6) - 60*a*b*
*5*d**5*e/(60*d**6*e**7 + 360*d**5*e**8*x + 900*d**4*e**9*x**2 + 1200*d**3*e**10*x**3 + 900*d**2*e**11*x**4 +
360*d*e**12*x**5 + 60*e**13*x**6) - 360*a*b**5*d**4*e**2*x/(60*d**6*e**7 + 360*d**5*e**8*x + 900*d**4*e**9*x**
2 + 1200*d**3*e**10*x**3 + 900*d**2*e**11*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6) - 900*a*b**5*d**3*e**3*x**2
/(60*d**6*e**7 + 360*d**5*e**8*x + 900*d**4*e**9*x**2 + 1200*d**3*e**10*x**3 + 900*d**2*e**11*x**4 + 360*d*e**
12*x**5 + 60*e**13*x**6) - 1200*a*b**5*d**2*e**4*x**3/(60*d**6*e**7 + 360*d**5*e**8*x + 900*d**4*e**9*x**2 + 1
200*d**3*e**10*x**3 + 900*d**2*e**11*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6) - 900*a*b**5*d*e**5*x**4/(60*d**
6*e**7 + 360*d**5*e**8*x + 900*d**4*e**9*x**2 + 1200*d**3*e**10*x**3 + 900*d**2*e**11*x**4 + 360*d*e**12*x**5
+ 60*e**13*x**6) - 360*a*b**5*e**6*x**5/(60*d**6*e**7 + 360*d**5*e**8*x + 900*d**4*e**9*x**2 + 1200*d**3*e**10
*x**3 + 900*d**2*e**11*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6) + 60*b**6*d**6*log(d/e + x)/(60*d**6*e**7 + 36
0*d**5*e**8*x + 900*d**4*e**9*x**2 + 1200*d**3*e**10*x**3 + 900*d**2*e**11*x**4 + 360*d*e**12*x**5 + 60*e**13*
x**6) + 147*b**6*d**6/(60*d**6*e**7 + 360*d**5*e**8*x + 900*d**4*e**9*x**2 + 1200*d**3*e**10*x**3 + 900*d**2*e
**11*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6) + 360*b**6*d**5*e*x*log(d/e + x)/(60*d**6*e**7 + 360*d**5*e**8*x
+ 900*d**4*e**9*x**2 + 1200*d**3*e**10*x**3 + 900*d**2*e**11*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6) + 822*b
**6*d**5*e*x/(60*d**6*e**7 + 360*d**5*e**8*x + 900*d**4*e**9*x**2 + 1200*d**3*e**10*x**3 + 900*d**2*e**11*x**4
+ 360*d*e**12*x**5 + 60*e**13*x**6) + 900*b**6*d**4*e**2*x**2*log(d/e + x)/(60*d**6*e**7 + 360*d**5*e**8*x +
900*d**4*e**9*x**2 + 1200*d**3*e**10*x**3 + 900*d**2*e**11*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6) + 1875*b**
6*d**4*e**2*x**2/(60*d**6*e**7 + 360*d**5*e**8*x + 900*d**4*e**9*x**2 + 1200*d**3*e**10*x**3 + 900*d**2*e**11*
x**4 + 360*d*e**12*x**5 + 60*e**13*x**6) + 1200*b**6*d**3*e**3*x**3*log(d/e + x)/(60*d**6*e**7 + 360*d**5*e**8
*x + 900*d**4*e**9*x**2 + 1200*d**3*e**10*x**3 + 900*d**2*e**11*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6) + 220
0*b**6*d**3*e**3*x**3/(60*d**6*e**7 + 360*d**5*e**8*x + 900*d**4*e**9*x**2 + 1200*d**3*e**10*x**3 + 900*d**2*e
**11*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6) + 900*b**6*d**2*e**4*x**4*log(d/e + x)/(60*d**6*e**7 + 360*d**5*
e**8*x + 900*d**4*e**9*x**2 + 1200*d**3*e**10*x**3 + 900*d**2*e**11*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6) +
1350*b**6*d**2*e**4*x**4/(60*d**6*e**7 + 360*d**5*e**8*x + 900*d**4*e**9*x**2 + 1200*d**3*e**10*x**3 + 900*d*
*2*e**11*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6) + 360*b**6*d*e**5*x**5*log(d/e + x)/(60*d**6*e**7 + 360*d**5
*e**8*x + 900*d**4*e**9*x**2 + 1200*d**3*e**10*x**3 + 900*d**2*e**11*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6)
+ 360*b**6*d*e**5*x**5/(60*d**6*e**7 + 360*d**5*e**8*x + 900*d**4*e**9*x**2 + 1200*d**3*e**10*x**3 + 900*d**2*
e**11*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6) + 60*b**6*e**6*x**6*log(d/e + x)/(60*d**6*e**7 + 360*d**5*e**8*
x + 900*d**4*e**9*x**2 + 1200*d**3*e**10*x**3 + 900*d**2*e**11*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6), Eq(m,
-7)), (-2*a**6*e**6/(10*d**5*e**7 + 50*d**4*e**8*x + 100*d**3*e**9*x**2 + 100*d**2*e**10*x**3 + 50*d*e**11*x*
*4 + 10*e**12*x**5) - 3*a**5*b*d*e**5/(10*d**5*e**7 + 50*d**4*e**8*x + 100*d**3*e**9*x**2 + 100*d**2*e**10*x**
3 + 50*d*e**11*x**4 + 10*e**12*x**5) - 15*a**5*b*e**6*x/(10*d**5*e**7 + 50*d**4*e**8*x + 100*d**3*e**9*x**2 +
100*d**2*e**10*x**3 + 50*d*e**11*x**4 + 10*e**12*x**5) - 5*a**4*b**2*d**2*e**4/(10*d**5*e**7 + 50*d**4*e**8*x
+ 100*d**3*e**9*x**2 + 100*d**2*e**10*x**3 + 50*d*e**11*x**4 + 10*e**12*x**5) - 25*a**4*b**2*d*e**5*x/(10*d**5
*e**7 + 50*d**4*e**8*x + 100*d**3*e**9*x**2 + 100*d**2*e**10*x**3 + 50*d*e**11*x**4 + 10*e**12*x**5) - 50*a**4
*b**2*e**6*x**2/(10*d**5*e**7 + 50*d**4*e**8*x + 100*d**3*e**9*x**2 + 100*d**2*e**10*x**3 + 50*d*e**11*x**4 +
10*e**12*x**5) - 10*a**3*b**3*d**3*e**3/(10*d**5*e**7 + 50*d**4*e**8*x + 100*d**3*e**9*x**2 + 100*d**2*e**10*x
**3 + 50*d*e**11*x**4 + 10*e**12*x**5) - 50*a**3*b**3*d**2*e**4*x/(10*d**5*e**7 + 50*d**4*e**8*x + 100*d**3*e*
*9*x**2 + 100*d**2*e**10*x**3 + 50*d*e**11*x**4 + 10*e**12*x**5) - 100*a**3*b**3*d*e**5*x**2/(10*d**5*e**7 + 5
0*d**4*e**8*x + 100*d**3*e**9*x**2 + 100*d**2*e**10*x**3 + 50*d*e**11*x**4 + 10*e**12*x**5) - 100*a**3*b**3*e*
*6*x**3/(10*d**5*e**7 + 50*d**4*e**8*x + 100*d**3*e**9*x**2 + 100*d**2*e**10*x**3 + 50*d*e**11*x**4 + 10*e**12
*x**5) - 30*a**2*b**4*d**4*e**2/(10*d**5*e**7 + 50*d**4*e**8*x + 100*d**3*e**9*x**2 + 100*d**2*e**10*x**3 + 50
*d*e**11*x**4 + 10*e**12*x**5) - 150*a**2*b**4*d**3*e**3*x/(10*d**5*e**7 + 50*d**4*e**8*x + 100*d**3*e**9*x**2
+ 100*d**2*e**10*x**3 + 50*d*e**11*x**4 + 10*e**12*x**5) - 300*a**2*b**4*d**2*e**4*x**2/(10*d**5*e**7 + 50*d*
*4*e**8*x + 100*d**3*e**9*x**2 + 100*d**2*e**10*x**3 + 50*d*e**11*x**4 + 10*e**12*x**5) - 300*a**2*b**4*d*e**5
*x**3/(10*d**5*e**7 + 50*d**4*e**8*x + 100*d**3*e**9*x**2 + 100*d**2*e**10*x**3 + 50*d*e**11*x**4 + 10*e**12*x
**5) - 150*a**2*b**4*e**6*x**4/(10*d**5*e**7 + 50*d**4*e**8*x + 100*d**3*e**9*x**2 + 100*d**2*e**10*x**3 + 50*
d*e**11*x**4 + 10*e**12*x**5) + 60*a*b**5*d**5*e*log(d/e + x)/(10*d**5*e**7 + 50*d**4*e**8*x + 100*d**3*e**9*x
**2 + 100*d**2*e**10*x**3 + 50*d*e**11*x**4 + 10*e**12*x**5) + 137*a*b**5*d**5*e/(10*d**5*e**7 + 50*d**4*e**8*
x + 100*d**3*e**9*x**2 + 100*d**2*e**10*x**3 + 50*d*e**11*x**4 + 10*e**12*x**5) + 300*a*b**5*d**4*e**2*x*log(d
/e + x)/(10*d**5*e**7 + 50*d**4*e**8*x + 100*d**3*e**9*x**2 + 100*d**2*e**10*x**3 + 50*d*e**11*x**4 + 10*e**12
*x**5) + 625*a*b**5*d**4*e**2*x/(10*d**5*e**7 + 50*d**4*e**8*x + 100*d**3*e**9*x**2 + 100*d**2*e**10*x**3 + 50
*d*e**11*x**4 + 10*e**12*x**5) + 600*a*b**5*d**3*e**3*x**2*log(d/e + x)/(10*d**5*e**7 + 50*d**4*e**8*x + 100*d
**3*e**9*x**2 + 100*d**2*e**10*x**3 + 50*d*e**11*x**4 + 10*e**12*x**5) + 1100*a*b**5*d**3*e**3*x**2/(10*d**5*e
**7 + 50*d**4*e**8*x + 100*d**3*e**9*x**2 + 100*d**2*e**10*x**3 + 50*d*e**11*x**4 + 10*e**12*x**5) + 600*a*b**
5*d**2*e**4*x**3*log(d/e + x)/(10*d**5*e**7 + 50*d**4*e**8*x + 100*d**3*e**9*x**2 + 100*d**2*e**10*x**3 + 50*d
*e**11*x**4 + 10*e**12*x**5) + 900*a*b**5*d**2*e**4*x**3/(10*d**5*e**7 + 50*d**4*e**8*x + 100*d**3*e**9*x**2 +
100*d**2*e**10*x**3 + 50*d*e**11*x**4 + 10*e**12*x**5) + 300*a*b**5*d*e**5*x**4*log(d/e + x)/(10*d**5*e**7 +
50*d**4*e**8*x + 100*d**3*e**9*x**2 + 100*d**2*e**10*x**3 + 50*d*e**11*x**4 + 10*e**12*x**5) + 300*a*b**5*d*e*
*5*x**4/(10*d**5*e**7 + 50*d**4*e**8*x + 100*d**3*e**9*x**2 + 100*d**2*e**10*x**3 + 50*d*e**11*x**4 + 10*e**12
*x**5) + 60*a*b**5*e**6*x**5*log(d/e + x)/(10*d**5*e**7 + 50*d**4*e**8*x + 100*d**3*e**9*x**2 + 100*d**2*e**10
*x**3 + 50*d*e**11*x**4 + 10*e**12*x**5) - 60*b**6*d**6*log(d/e + x)/(10*d**5*e**7 + 50*d**4*e**8*x + 100*d**3
*e**9*x**2 + 100*d**2*e**10*x**3 + 50*d*e**11*x**4 + 10*e**12*x**5) - 137*b**6*d**6/(10*d**5*e**7 + 50*d**4*e*
*8*x + 100*d**3*e**9*x**2 + 100*d**2*e**10*x**3 + 50*d*e**11*x**4 + 10*e**12*x**5) - 300*b**6*d**5*e*x*log(d/e
+ x)/(10*d**5*e**7 + 50*d**4*e**8*x + 100*d**3*e**9*x**2 + 100*d**2*e**10*x**3 + 50*d*e**11*x**4 + 10*e**12*x
**5) - 625*b**6*d**5*e*x/(10*d**5*e**7 + 50*d**4*e**8*x + 100*d**3*e**9*x**2 + 100*d**2*e**10*x**3 + 50*d*e**1
1*x**4 + 10*e**12*x**5) - 600*b**6*d**4*e**2*x**2*log(d/e + x)/(10*d**5*e**7 + 50*d**4*e**8*x + 100*d**3*e**9*
x**2 + 100*d**2*e**10*x**3 + 50*d*e**11*x**4 + 10*e**12*x**5) - 1100*b**6*d**4*e**2*x**2/(10*d**5*e**7 + 50*d*
*4*e**8*x + 100*d**3*e**9*x**2 + 100*d**2*e**10*x**3 + 50*d*e**11*x**4 + 10*e**12*x**5) - 600*b**6*d**3*e**3*x
**3*log(d/e + x)/(10*d**5*e**7 + 50*d**4*e**8*x + 100*d**3*e**9*x**2 + 100*d**2*e**10*x**3 + 50*d*e**11*x**4 +
10*e**12*x**5) - 900*b**6*d**3*e**3*x**3/(10*d**5*e**7 + 50*d**4*e**8*x + 100*d**3*e**9*x**2 + 100*d**2*e**10
*x**3 + 50*d*e**11*x**4 + 10*e**12*x**5) - 300*b**6*d**2*e**4*x**4*log(d/e + x)/(10*d**5*e**7 + 50*d**4*e**8*x
+ 100*d**3*e**9*x**2 + 100*d**2*e**10*x**3 + 50*d*e**11*x**4 + 10*e**12*x**5) - 300*b**6*d**2*e**4*x**4/(10*d
**5*e**7 + 50*d**4*e**8*x + 100*d**3*e**9*x**2 + 100*d**2*e**10*x**3 + 50*d*e**11*x**4 + 10*e**12*x**5) - 60*b
**6*d*e**5*x**5*log(d/e + x)/(10*d**5*e**7 + 50*d**4*e**8*x + 100*d**3*e**9*x**2 + 100*d**2*e**10*x**3 + 50*d*
e**11*x**4 + 10*e**12*x**5) + 10*b**6*e**6*x**6/(10*d**5*e**7 + 50*d**4*e**8*x + 100*d**3*e**9*x**2 + 100*d**2
*e**10*x**3 + 50*d*e**11*x**4 + 10*e**12*x**5), Eq(m, -6)), (-a**6*e**6/(4*d**4*e**7 + 16*d**3*e**8*x + 24*d**
2*e**9*x**2 + 16*d*e**10*x**3 + 4*e**11*x**4) - 2*a**5*b*d*e**5/(4*d**4*e**7 + 16*d**3*e**8*x + 24*d**2*e**9*x
**2 + 16*d*e**10*x**3 + 4*e**11*x**4) - 8*a**5*b*e**6*x/(4*d**4*e**7 + 16*d**3*e**8*x + 24*d**2*e**9*x**2 + 16
*d*e**10*x**3 + 4*e**11*x**4) - 5*a**4*b**2*d**2*e**4/(4*d**4*e**7 + 16*d**3*e**8*x + 24*d**2*e**9*x**2 + 16*d
*e**10*x**3 + 4*e**11*x**4) - 20*a**4*b**2*d*e**5*x/(4*d**4*e**7 + 16*d**3*e**8*x + 24*d**2*e**9*x**2 + 16*d*e
**10*x**3 + 4*e**11*x**4) - 30*a**4*b**2*e**6*x**2/(4*d**4*e**7 + 16*d**3*e**8*x + 24*d**2*e**9*x**2 + 16*d*e*
*10*x**3 + 4*e**11*x**4) - 20*a**3*b**3*d**3*e**3/(4*d**4*e**7 + 16*d**3*e**8*x + 24*d**2*e**9*x**2 + 16*d*e**
10*x**3 + 4*e**11*x**4) - 80*a**3*b**3*d**2*e**4*x/(4*d**4*e**7 + 16*d**3*e**8*x + 24*d**2*e**9*x**2 + 16*d*e*
*10*x**3 + 4*e**11*x**4) - 120*a**3*b**3*d*e**5*x**2/(4*d**4*e**7 + 16*d**3*e**8*x + 24*d**2*e**9*x**2 + 16*d*
e**10*x**3 + 4*e**11*x**4) - 80*a**3*b**3*e**6*x**3/(4*d**4*e**7 + 16*d**3*e**8*x + 24*d**2*e**9*x**2 + 16*d*e
**10*x**3 + 4*e**11*x**4) + 60*a**2*b**4*d**4*e**2*log(d/e + x)/(4*d**4*e**7 + 16*d**3*e**8*x + 24*d**2*e**9*x
**2 + 16*d*e**10*x**3 + 4*e**11*x**4) + 125*a**2*b**4*d**4*e**2/(4*d**4*e**7 + 16*d**3*e**8*x + 24*d**2*e**9*x
**2 + 16*d*e**10*x**3 + 4*e**11*x**4) + 240*a**2*b**4*d**3*e**3*x*log(d/e + x)/(4*d**4*e**7 + 16*d**3*e**8*x +
24*d**2*e**9*x**2 + 16*d*e**10*x**3 + 4*e**11*x**4) + 440*a**2*b**4*d**3*e**3*x/(4*d**4*e**7 + 16*d**3*e**8*x
+ 24*d**2*e**9*x**2 + 16*d*e**10*x**3 + 4*e**11*x**4) + 360*a**2*b**4*d**2*e**4*x**2*log(d/e + x)/(4*d**4*e**
7 + 16*d**3*e**8*x + 24*d**2*e**9*x**2 + 16*d*e**10*x**3 + 4*e**11*x**4) + 540*a**2*b**4*d**2*e**4*x**2/(4*d**
4*e**7 + 16*d**3*e**8*x + 24*d**2*e**9*x**2 + 16*d*e**10*x**3 + 4*e**11*x**4) + 240*a**2*b**4*d*e**5*x**3*log(
d/e + x)/(4*d**4*e**7 + 16*d**3*e**8*x + 24*d**2*e**9*x**2 + 16*d*e**10*x**3 + 4*e**11*x**4) + 240*a**2*b**4*d
*e**5*x**3/(4*d**4*e**7 + 16*d**3*e**8*x + 24*d**2*e**9*x**2 + 16*d*e**10*x**3 + 4*e**11*x**4) + 60*a**2*b**4*
e**6*x**4*log(d/e + x)/(4*d**4*e**7 + 16*d**3*e**8*x + 24*d**2*e**9*x**2 + 16*d*e**10*x**3 + 4*e**11*x**4) - 1
20*a*b**5*d**5*e*log(d/e + x)/(4*d**4*e**7 + 16*d**3*e**8*x + 24*d**2*e**9*x**2 + 16*d*e**10*x**3 + 4*e**11*x*
*4) - 250*a*b**5*d**5*e/(4*d**4*e**7 + 16*d**3*e**8*x + 24*d**2*e**9*x**2 + 16*d*e**10*x**3 + 4*e**11*x**4) -
480*a*b**5*d**4*e**2*x*log(d/e + x)/(4*d**4*e**7 + 16*d**3*e**8*x + 24*d**2*e**9*x**2 + 16*d*e**10*x**3 + 4*e*
*11*x**4) - 880*a*b**5*d**4*e**2*x/(4*d**4*e**7 + 16*d**3*e**8*x + 24*d**2*e**9*x**2 + 16*d*e**10*x**3 + 4*e**
11*x**4) - 720*a*b**5*d**3*e**3*x**2*log(d/e + x)/(4*d**4*e**7 + 16*d**3*e**8*x + 24*d**2*e**9*x**2 + 16*d*e**
10*x**3 + 4*e**11*x**4) - 1080*a*b**5*d**3*e**3*x**2/(4*d**4*e**7 + 16*d**3*e**8*x + 24*d**2*e**9*x**2 + 16*d*
e**10*x**3 + 4*e**11*x**4) - 480*a*b**5*d**2*e**4*x**3*log(d/e + x)/(4*d**4*e**7 + 16*d**3*e**8*x + 24*d**2*e*
*9*x**2 + 16*d*e**10*x**3 + 4*e**11*x**4) - 480*a*b**5*d**2*e**4*x**3/(4*d**4*e**7 + 16*d**3*e**8*x + 24*d**2*
e**9*x**2 + 16*d*e**10*x**3 + 4*e**11*x**4) - 120*a*b**5*d*e**5*x**4*log(d/e + x)/(4*d**4*e**7 + 16*d**3*e**8*
x + 24*d**2*e**9*x**2 + 16*d*e**10*x**3 + 4*e**11*x**4) + 24*a*b**5*e**6*x**5/(4*d**4*e**7 + 16*d**3*e**8*x +
24*d**2*e**9*x**2 + 16*d*e**10*x**3 + 4*e**11*x**4) + 60*b**6*d**6*log(d/e + x)/(4*d**4*e**7 + 16*d**3*e**8*x
+ 24*d**2*e**9*x**2 + 16*d*e**10*x**3 + 4*e**11*x**4) + 125*b**6*d**6/(4*d**4*e**7 + 16*d**3*e**8*x + 24*d**2*
e**9*x**2 + 16*d*e**10*x**3 + 4*e**11*x**4) + 240*b**6*d**5*e*x*log(d/e + x)/(4*d**4*e**7 + 16*d**3*e**8*x + 2
4*d**2*e**9*x**2 + 16*d*e**10*x**3 + 4*e**11*x**4) + 440*b**6*d**5*e*x/(4*d**4*e**7 + 16*d**3*e**8*x + 24*d**2
*e**9*x**2 + 16*d*e**10*x**3 + 4*e**11*x**4) + 360*b**6*d**4*e**2*x**2*log(d/e + x)/(4*d**4*e**7 + 16*d**3*e**
8*x + 24*d**2*e**9*x**2 + 16*d*e**10*x**3 + 4*e**11*x**4) + 540*b**6*d**4*e**2*x**2/(4*d**4*e**7 + 16*d**3*e**
8*x + 24*d**2*e**9*x**2 + 16*d*e**10*x**3 + 4*e**11*x**4) + 240*b**6*d**3*e**3*x**3*log(d/e + x)/(4*d**4*e**7
+ 16*d**3*e**8*x + 24*d**2*e**9*x**2 + 16*d*e**10*x**3 + 4*e**11*x**4) + 240*b**6*d**3*e**3*x**3/(4*d**4*e**7
+ 16*d**3*e**8*x + 24*d**2*e**9*x**2 + 16*d*e**10*x**3 + 4*e**11*x**4) + 60*b**6*d**2*e**4*x**4*log(d/e + x)/(
4*d**4*e**7 + 16*d**3*e**8*x + 24*d**2*e**9*x**2 + 16*d*e**10*x**3 + 4*e**11*x**4) - 12*b**6*d*e**5*x**5/(4*d*
*4*e**7 + 16*d**3*e**8*x + 24*d**2*e**9*x**2 + 16*d*e**10*x**3 + 4*e**11*x**4) + 2*b**6*e**6*x**6/(4*d**4*e**7
+ 16*d**3*e**8*x + 24*d**2*e**9*x**2 + 16*d*e**10*x**3 + 4*e**11*x**4), Eq(m, -5)), (-a**6*e**6/(3*d**3*e**7
+ 9*d**2*e**8*x + 9*d*e**9*x**2 + 3*e**10*x**3) - 3*a**5*b*d*e**5/(3*d**3*e**7 + 9*d**2*e**8*x + 9*d*e**9*x**2
+ 3*e**10*x**3) - 9*a**5*b*e**6*x/(3*d**3*e**7 + 9*d**2*e**8*x + 9*d*e**9*x**2 + 3*e**10*x**3) - 15*a**4*b**2
*d**2*e**4/(3*d**3*e**7 + 9*d**2*e**8*x + 9*d*e**9*x**2 + 3*e**10*x**3) - 45*a**4*b**2*d*e**5*x/(3*d**3*e**7 +
9*d**2*e**8*x + 9*d*e**9*x**2 + 3*e**10*x**3) - 45*a**4*b**2*e**6*x**2/(3*d**3*e**7 + 9*d**2*e**8*x + 9*d*e**
9*x**2 + 3*e**10*x**3) + 60*a**3*b**3*d**3*e**3*log(d/e + x)/(3*d**3*e**7 + 9*d**2*e**8*x + 9*d*e**9*x**2 + 3*
e**10*x**3) + 110*a**3*b**3*d**3*e**3/(3*d**3*e**7 + 9*d**2*e**8*x + 9*d*e**9*x**2 + 3*e**10*x**3) + 180*a**3*
b**3*d**2*e**4*x*log(d/e + x)/(3*d**3*e**7 + 9*d**2*e**8*x + 9*d*e**9*x**2 + 3*e**10*x**3) + 270*a**3*b**3*d**
2*e**4*x/(3*d**3*e**7 + 9*d**2*e**8*x + 9*d*e**9*x**2 + 3*e**10*x**3) + 180*a**3*b**3*d*e**5*x**2*log(d/e + x)
/(3*d**3*e**7 + 9*d**2*e**8*x + 9*d*e**9*x**2 + 3*e**10*x**3) + 180*a**3*b**3*d*e**5*x**2/(3*d**3*e**7 + 9*d**
2*e**8*x + 9*d*e**9*x**2 + 3*e**10*x**3) + 60*a**3*b**3*e**6*x**3*log(d/e + x)/(3*d**3*e**7 + 9*d**2*e**8*x +
9*d*e**9*x**2 + 3*e**10*x**3) - 180*a**2*b**4*d**4*e**2*log(d/e + x)/(3*d**3*e**7 + 9*d**2*e**8*x + 9*d*e**9*x
**2 + 3*e**10*x**3) - 330*a**2*b**4*d**4*e**2/(3*d**3*e**7 + 9*d**2*e**8*x + 9*d*e**9*x**2 + 3*e**10*x**3) - 5
40*a**2*b**4*d**3*e**3*x*log(d/e + x)/(3*d**3*e**7 + 9*d**2*e**8*x + 9*d*e**9*x**2 + 3*e**10*x**3) - 810*a**2*
b**4*d**3*e**3*x/(3*d**3*e**7 + 9*d**2*e**8*x + 9*d*e**9*x**2 + 3*e**10*x**3) - 540*a**2*b**4*d**2*e**4*x**2*l
og(d/e + x)/(3*d**3*e**7 + 9*d**2*e**8*x + 9*d*e**9*x**2 + 3*e**10*x**3) - 540*a**2*b**4*d**2*e**4*x**2/(3*d**
3*e**7 + 9*d**2*e**8*x + 9*d*e**9*x**2 + 3*e**10*x**3) - 180*a**2*b**4*d*e**5*x**3*log(d/e + x)/(3*d**3*e**7 +
9*d**2*e**8*x + 9*d*e**9*x**2 + 3*e**10*x**3) + 45*a**2*b**4*e**6*x**4/(3*d**3*e**7 + 9*d**2*e**8*x + 9*d*e**
9*x**2 + 3*e**10*x**3) + 180*a*b**5*d**5*e*log(d/e + x)/(3*d**3*e**7 + 9*d**2*e**8*x + 9*d*e**9*x**2 + 3*e**10
*x**3) + 330*a*b**5*d**5*e/(3*d**3*e**7 + 9*d**2*e**8*x + 9*d*e**9*x**2 + 3*e**10*x**3) + 540*a*b**5*d**4*e**2
*x*log(d/e + x)/(3*d**3*e**7 + 9*d**2*e**8*x + 9*d*e**9*x**2 + 3*e**10*x**3) + 810*a*b**5*d**4*e**2*x/(3*d**3*
e**7 + 9*d**2*e**8*x + 9*d*e**9*x**2 + 3*e**10*x**3) + 540*a*b**5*d**3*e**3*x**2*log(d/e + x)/(3*d**3*e**7 + 9
*d**2*e**8*x + 9*d*e**9*x**2 + 3*e**10*x**3) + 540*a*b**5*d**3*e**3*x**2/(3*d**3*e**7 + 9*d**2*e**8*x + 9*d*e*
*9*x**2 + 3*e**10*x**3) + 180*a*b**5*d**2*e**4*x**3*log(d/e + x)/(3*d**3*e**7 + 9*d**2*e**8*x + 9*d*e**9*x**2
+ 3*e**10*x**3) - 45*a*b**5*d*e**5*x**4/(3*d**3*e**7 + 9*d**2*e**8*x + 9*d*e**9*x**2 + 3*e**10*x**3) + 9*a*b**
5*e**6*x**5/(3*d**3*e**7 + 9*d**2*e**8*x + 9*d*e**9*x**2 + 3*e**10*x**3) - 60*b**6*d**6*log(d/e + x)/(3*d**3*e
**7 + 9*d**2*e**8*x + 9*d*e**9*x**2 + 3*e**10*x**3) - 110*b**6*d**6/(3*d**3*e**7 + 9*d**2*e**8*x + 9*d*e**9*x*
*2 + 3*e**10*x**3) - 180*b**6*d**5*e*x*log(d/e + x)/(3*d**3*e**7 + 9*d**2*e**8*x + 9*d*e**9*x**2 + 3*e**10*x**
3) - 270*b**6*d**5*e*x/(3*d**3*e**7 + 9*d**2*e**8*x + 9*d*e**9*x**2 + 3*e**10*x**3) - 180*b**6*d**4*e**2*x**2*
log(d/e + x)/(3*d**3*e**7 + 9*d**2*e**8*x + 9*d*e**9*x**2 + 3*e**10*x**3) - 180*b**6*d**4*e**2*x**2/(3*d**3*e*
*7 + 9*d**2*e**8*x + 9*d*e**9*x**2 + 3*e**10*x**3) - 60*b**6*d**3*e**3*x**3*log(d/e + x)/(3*d**3*e**7 + 9*d**2
*e**8*x + 9*d*e**9*x**2 + 3*e**10*x**3) + 15*b**6*d**2*e**4*x**4/(3*d**3*e**7 + 9*d**2*e**8*x + 9*d*e**9*x**2
+ 3*e**10*x**3) - 3*b**6*d*e**5*x**5/(3*d**3*e**7 + 9*d**2*e**8*x + 9*d*e**9*x**2 + 3*e**10*x**3) + b**6*e**6*
x**6/(3*d**3*e**7 + 9*d**2*e**8*x + 9*d*e**9*x**2 + 3*e**10*x**3), Eq(m, -4)), (-2*a**6*e**6/(4*d**2*e**7 + 8*
d*e**8*x + 4*e**9*x**2) - 12*a**5*b*d*e**5/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) - 24*a**5*b*e**6*x/(4*d**2
*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 60*a**4*b**2*d**2*e**4*log(d/e + x)/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**
2) + 90*a**4*b**2*d**2*e**4/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 120*a**4*b**2*d*e**5*x*log(d/e + x)/(4*
d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 120*a**4*b**2*d*e**5*x/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 60*a
**4*b**2*e**6*x**2*log(d/e + x)/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) - 240*a**3*b**3*d**3*e**3*log(d/e + x
)/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) - 360*a**3*b**3*d**3*e**3/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2)
- 480*a**3*b**3*d**2*e**4*x*log(d/e + x)/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) - 480*a**3*b**3*d**2*e**4*x/
(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) - 240*a**3*b**3*d*e**5*x**2*log(d/e + x)/(4*d**2*e**7 + 8*d*e**8*x +
4*e**9*x**2) + 80*a**3*b**3*e**6*x**3/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 360*a**2*b**4*d**4*e**2*log(d
/e + x)/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 540*a**2*b**4*d**4*e**2/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*
x**2) + 720*a**2*b**4*d**3*e**3*x*log(d/e + x)/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 720*a**2*b**4*d**3*e
**3*x/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 360*a**2*b**4*d**2*e**4*x**2*log(d/e + x)/(4*d**2*e**7 + 8*d*
e**8*x + 4*e**9*x**2) - 120*a**2*b**4*d*e**5*x**3/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 30*a**2*b**4*e**6
*x**4/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) - 240*a*b**5*d**5*e*log(d/e + x)/(4*d**2*e**7 + 8*d*e**8*x + 4*
e**9*x**2) - 360*a*b**5*d**5*e/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) - 480*a*b**5*d**4*e**2*x*log(d/e + x)/
(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) - 480*a*b**5*d**4*e**2*x/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) - 2
40*a*b**5*d**3*e**3*x**2*log(d/e + x)/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 80*a*b**5*d**2*e**4*x**3/(4*d
**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) - 20*a*b**5*d*e**5*x**4/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 8*a*b*
*5*e**6*x**5/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 60*b**6*d**6*log(d/e + x)/(4*d**2*e**7 + 8*d*e**8*x +
4*e**9*x**2) + 90*b**6*d**6/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 120*b**6*d**5*e*x*log(d/e + x)/(4*d**2*
e**7 + 8*d*e**8*x + 4*e**9*x**2) + 120*b**6*d**5*e*x/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 60*b**6*d**4*e
**2*x**2*log(d/e + x)/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) - 20*b**6*d**3*e**3*x**3/(4*d**2*e**7 + 8*d*e**
8*x + 4*e**9*x**2) + 5*b**6*d**2*e**4*x**4/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) - 2*b**6*d*e**5*x**5/(4*d*
*2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + b**6*e**6*x**6/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2), Eq(m, -3)), (-1
0*a**6*e**6/(10*d*e**7 + 10*e**8*x) + 60*a**5*b*d*e**5*log(d/e + x)/(10*d*e**7 + 10*e**8*x) + 60*a**5*b*d*e**5
/(10*d*e**7 + 10*e**8*x) + 60*a**5*b*e**6*x*log(d/e + x)/(10*d*e**7 + 10*e**8*x) - 300*a**4*b**2*d**2*e**4*log
(d/e + x)/(10*d*e**7 + 10*e**8*x) - 300*a**4*b**2*d**2*e**4/(10*d*e**7 + 10*e**8*x) - 300*a**4*b**2*d*e**5*x*l
og(d/e + x)/(10*d*e**7 + 10*e**8*x) + 150*a**4*b**2*e**6*x**2/(10*d*e**7 + 10*e**8*x) + 600*a**3*b**3*d**3*e**
3*log(d/e + x)/(10*d*e**7 + 10*e**8*x) + 600*a**3*b**3*d**3*e**3/(10*d*e**7 + 10*e**8*x) + 600*a**3*b**3*d**2*
e**4*x*log(d/e + x)/(10*d*e**7 + 10*e**8*x) - 300*a**3*b**3*d*e**5*x**2/(10*d*e**7 + 10*e**8*x) + 100*a**3*b**
3*e**6*x**3/(10*d*e**7 + 10*e**8*x) - 600*a**2*b**4*d**4*e**2*log(d/e + x)/(10*d*e**7 + 10*e**8*x) - 600*a**2*
b**4*d**4*e**2/(10*d*e**7 + 10*e**8*x) - 600*a**2*b**4*d**3*e**3*x*log(d/e + x)/(10*d*e**7 + 10*e**8*x) + 300*
a**2*b**4*d**2*e**4*x**2/(10*d*e**7 + 10*e**8*x) - 100*a**2*b**4*d*e**5*x**3/(10*d*e**7 + 10*e**8*x) + 50*a**2
*b**4*e**6*x**4/(10*d*e**7 + 10*e**8*x) + 300*a*b**5*d**5*e*log(d/e + x)/(10*d*e**7 + 10*e**8*x) + 300*a*b**5*
d**5*e/(10*d*e**7 + 10*e**8*x) + 300*a*b**5*d**4*e**2*x*log(d/e + x)/(10*d*e**7 + 10*e**8*x) - 150*a*b**5*d**3
*e**3*x**2/(10*d*e**7 + 10*e**8*x) + 50*a*b**5*d**2*e**4*x**3/(10*d*e**7 + 10*e**8*x) - 25*a*b**5*d*e**5*x**4/
(10*d*e**7 + 10*e**8*x) + 15*a*b**5*e**6*x**5/(10*d*e**7 + 10*e**8*x) - 60*b**6*d**6*log(d/e + x)/(10*d*e**7 +
10*e**8*x) - 60*b**6*d**6/(10*d*e**7 + 10*e**8*x) - 60*b**6*d**5*e*x*log(d/e + x)/(10*d*e**7 + 10*e**8*x) + 3
0*b**6*d**4*e**2*x**2/(10*d*e**7 + 10*e**8*x) - 10*b**6*d**3*e**3*x**3/(10*d*e**7 + 10*e**8*x) + 5*b**6*d**2*e
**4*x**4/(10*d*e**7 + 10*e**8*x) - 3*b**6*d*e**5*x**5/(10*d*e**7 + 10*e**8*x) + 2*b**6*e**6*x**6/(10*d*e**7 +
10*e**8*x), Eq(m, -2)), (a**6*log(d/e + x)/e - 6*a**5*b*d*log(d/e + x)/e**2 + 6*a**5*b*x/e + 15*a**4*b**2*d**2
*log(d/e + x)/e**3 - 15*a**4*b**2*d*x/e**2 + 15*a**4*b**2*x**2/(2*e) - 20*a**3*b**3*d**3*log(d/e + x)/e**4 + 2
0*a**3*b**3*d**2*x/e**3 - 10*a**3*b**3*d*x**2/e**2 + 20*a**3*b**3*x**3/(3*e) + 15*a**2*b**4*d**4*log(d/e + x)/
e**5 - 15*a**2*b**4*d**3*x/e**4 + 15*a**2*b**4*d**2*x**2/(2*e**3) - 5*a**2*b**4*d*x**3/e**2 + 15*a**2*b**4*x**
4/(4*e) - 6*a*b**5*d**5*log(d/e + x)/e**6 + 6*a*b**5*d**4*x/e**5 - 3*a*b**5*d**3*x**2/e**4 + 2*a*b**5*d**2*x**
3/e**3 - 3*a*b**5*d*x**4/(2*e**2) + 6*a*b**5*x**5/(5*e) + b**6*d**6*log(d/e + x)/e**7 - b**6*d**5*x/e**6 + b**
6*d**4*x**2/(2*e**5) - b**6*d**3*x**3/(3*e**4) + b**6*d**2*x**4/(4*e**3) - b**6*d*x**5/(5*e**2) + b**6*x**6/(6
*e), Eq(m, -1)), (a**6*d*e**6*m**6*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6
769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 27*a**6*d*e**6*m**5*(d + e*x)**m/(e**7*m**7 + 28
*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 2
95*a**6*d*e**6*m**4*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 +
13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 1665*a**6*d*e**6*m**3*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 +
322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 5104*a**6*d*e*
*6*m**2*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*
m**2 + 13068*e**7*m + 5040*e**7) + 8028*a**6*d*e**6*m*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 +
1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 5040*a**6*d*e**6*(d + e*x)**m
/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m
+ 5040*e**7) + a**6*e**7*m**6*x*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769
*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 27*a**6*e**7*m**5*x*(d + e*x)**m/(e**7*m**7 + 28*e*
*7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 295*
a**6*e**7*m**4*x*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13
132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 1665*a**6*e**7*m**3*x*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322
*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 5104*a**6*e**7*m*
*2*x*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**
2 + 13068*e**7*m + 5040*e**7) + 8028*a**6*e**7*m*x*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 19
60*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 5040*a**6*e**7*x*(d + e*x)**m/(e
**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5
040*e**7) - 6*a**5*b*d**2*e**5*m**5*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 +
6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 150*a**5*b*d**2*e**5*m**4*(d + e*x)**m/(e**7*m*
*7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e*
*7) - 1470*a**5*b*d**2*e**5*m**3*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 676
9*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 7050*a**5*b*d**2*e**5*m**2*(d + e*x)**m/(e**7*m**7
+ 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7
) - 16524*a**5*b*d**2*e**5*m*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e*
*7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 15120*a**5*b*d**2*e**5*(d + e*x)**m/(e**7*m**7 + 28*e*
*7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 6*a*
*5*b*d*e**6*m**6*x*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 +
13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 150*a**5*b*d*e**6*m**5*x*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6
+ 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 1470*a**5*b*
d*e**6*m**4*x*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132
*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 7050*a**5*b*d*e**6*m**3*x*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 32
2*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 16524*a**5*b*d*e
**6*m**2*x*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e*
*7*m**2 + 13068*e**7*m + 5040*e**7) + 15120*a**5*b*d*e**6*m*x*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**
7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 6*a**5*b*e**7*m**6*x*
*2*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2
+ 13068*e**7*m + 5040*e**7) + 156*a**5*b*e**7*m**5*x**2*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5
+ 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 1620*a**5*b*e**7*m**4*x**2*
(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 1
3068*e**7*m + 5040*e**7) + 8520*a**5*b*e**7*m**3*x**2*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 +
1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 23574*a**5*b*e**7*m**2*x**2*(
d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13
068*e**7*m + 5040*e**7) + 31644*a**5*b*e**7*m*x**2*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 19
60*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 15120*a**5*b*e**7*x**2*(d + e*x)
**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7
*m + 5040*e**7) + 30*a**4*b**2*d**3*e**4*m**4*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e*
*7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 660*a**4*b**2*d**3*e**4*m**3*(d + e*x
)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**
7*m + 5040*e**7) + 5370*a**4*b**2*d**3*e**4*m**2*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960
*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 19140*a**4*b**2*d**3*e**4*m*(d + e
*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e
**7*m + 5040*e**7) + 25200*a**4*b**2*d**3*e**4*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e
**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 30*a**4*b**2*d**2*e**5*m**5*x*(d + e
*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e
**7*m + 5040*e**7) - 660*a**4*b**2*d**2*e**5*m**4*x*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1
960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 5370*a**4*b**2*d**2*e**5*m**3*x
*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 +
13068*e**7*m + 5040*e**7) - 19140*a**4*b**2*d**2*e**5*m**2*x*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7
*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 25200*a**4*b**2*d**2*e
**5*m*x*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*
m**2 + 13068*e**7*m + 5040*e**7) + 15*a**4*b**2*d*e**6*m**6*x**2*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*
e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 345*a**4*b**2*d*e*
*6*m**5*x**2*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*
e**7*m**2 + 13068*e**7*m + 5040*e**7) + 3015*a**4*b**2*d*e**6*m**4*x**2*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6
+ 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 12255*a**4*
b**2*d*e**6*m**3*x**2*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3
+ 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 22170*a**4*b**2*d*e**6*m**2*x**2*(d + e*x)**m/(e**7*m**7 + 28
*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 1
2600*a**4*b**2*d*e**6*m*x**2*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e*
*7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 15*a**4*b**2*e**7*m**6*x**3*(d + e*x)**m/(e**7*m**7 +
28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) +
375*a**4*b**2*e**7*m**5*x**3*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e
**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 3705*a**4*b**2*e**7*m**4*x**3*(d + e*x)**m/(e**7*m**7
+ 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7
) + 18285*a**4*b**2*e**7*m**3*x**3*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6
769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 46680*a**4*b**2*e**7*m**2*x**3*(d + e*x)**m/(e**
7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 504
0*e**7) + 56940*a**4*b**2*e**7*m*x**3*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4
+ 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 25200*a**4*b**2*e**7*x**3*(d + e*x)**m/(e**7*
m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*
e**7) - 120*a**3*b**3*d**4*e**3*m**3*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 +
6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 2160*a**3*b**3*d**4*e**3*m**2*(d + e*x)**m/(e*
*7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 50
40*e**7) - 12840*a**3*b**3*d**4*e**3*m*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4
+ 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 25200*a**3*b**3*d**4*e**3*(d + e*x)**m/(e**7
*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040
*e**7) + 120*a**3*b**3*d**3*e**4*m**4*x*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**
4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 2160*a**3*b**3*d**3*e**4*m**3*x*(d + e*x)**
m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m
+ 5040*e**7) + 12840*a**3*b**3*d**3*e**4*m**2*x*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960
*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 25200*a**3*b**3*d**3*e**4*m*x*(d +
e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068
*e**7*m + 5040*e**7) - 60*a**3*b**3*d**2*e**5*m**5*x**2*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5
+ 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 1140*a**3*b**3*d**2*e**5*m*
*4*x**2*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*
m**2 + 13068*e**7*m + 5040*e**7) - 7500*a**3*b**3*d**2*e**5*m**3*x**2*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 +
322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 19020*a**3*b*
*3*d**2*e**5*m**2*x**2*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**
3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 12600*a**3*b**3*d**2*e**5*m*x**2*(d + e*x)**m/(e**7*m**7 + 2
8*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) +
20*a**3*b**3*d*e**6*m**6*x**3*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e
**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 420*a**3*b**3*d*e**6*m**5*x**3*(d + e*x)**m/(e**7*m**
7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**
7) + 3260*a**3*b**3*d*e**6*m**4*x**3*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 +
6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 11340*a**3*b**3*d*e**6*m**3*x**3*(d + e*x)**m/
(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m +
5040*e**7) + 16880*a**3*b**3*d*e**6*m**2*x**3*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e
**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 8400*a**3*b**3*d*e**6*m*x**3*(d + e*
x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e*
*7*m + 5040*e**7) + 20*a**3*b**3*e**7*m**6*x**4*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*
e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 480*a**3*b**3*e**7*m**5*x**4*(d + e
*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e
**7*m + 5040*e**7) + 4520*a**3*b**3*e**7*m**4*x**4*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 19
60*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 21120*a**3*b**3*e**7*m**3*x**4*(
d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13
068*e**7*m + 5040*e**7) + 50900*a**3*b**3*e**7*m**2*x**4*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**
5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 59040*a**3*b**3*e**7*m*x**
4*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 +
13068*e**7*m + 5040*e**7) + 25200*a**3*b**3*e**7*x**4*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5
+ 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 360*a**2*b**4*d**5*e**2*m**2
*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 +
13068*e**7*m + 5040*e**7) + 4680*a**2*b**4*d**5*e**2*m*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5
+ 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 15120*a**2*b**4*d**5*e**2*(d
+ e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 130
68*e**7*m + 5040*e**7) - 360*a**2*b**4*d**4*e**3*m**3*x*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5
+ 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 4680*a**2*b**4*d**4*e**3*m*
*2*x*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**
2 + 13068*e**7*m + 5040*e**7) - 15120*a**2*b**4*d**4*e**3*m*x*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**
7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 180*a**2*b**4*d**3*e*
*4*m**4*x**2*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*
e**7*m**2 + 13068*e**7*m + 5040*e**7) + 2520*a**2*b**4*d**3*e**4*m**3*x**2*(d + e*x)**m/(e**7*m**7 + 28*e**7*m
**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 9900*a**
2*b**4*d**3*e**4*m**2*x**2*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7
*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 7560*a**2*b**4*d**3*e**4*m*x**2*(d + e*x)**m/(e**7*m**7
+ 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7)
- 60*a**2*b**4*d**2*e**5*m**5*x**3*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 +
6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 960*a**2*b**4*d**2*e**5*m**4*x**3*(d + e*x)**m/
(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m +
5040*e**7) - 4980*a**2*b**4*d**2*e**5*m**3*x**3*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960
*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 9120*a**2*b**4*d**2*e**5*m**2*x**3
*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 +
13068*e**7*m + 5040*e**7) - 5040*a**2*b**4*d**2*e**5*m*x**3*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*
m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 15*a**2*b**4*d*e**6*m**
6*x**4*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m
**2 + 13068*e**7*m + 5040*e**7) + 285*a**2*b**4*d*e**6*m**5*x**4*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*
e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 1965*a**2*b**4*d*e
**6*m**4*x**4*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132
*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 6015*a**2*b**4*d*e**6*m**3*x**4*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**
6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 8100*a**2*
b**4*d*e**6*m**2*x**4*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3
+ 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 3780*a**2*b**4*d*e**6*m*x**4*(d + e*x)**m/(e**7*m**7 + 28*e**
7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 15*a*
*2*b**4*e**7*m**6*x**5*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**
3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 345*a**2*b**4*e**7*m**5*x**5*(d + e*x)**m/(e**7*m**7 + 28*e*
*7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 3105
*a**2*b**4*e**7*m**4*x**5*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*
m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 13875*a**2*b**4*e**7*m**3*x**5*(d + e*x)**m/(e**7*m**7 +
28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) +
32160*a**2*b**4*e**7*m**2*x**5*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769
*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 36180*a**2*b**4*e**7*m*x**5*(d + e*x)**m/(e**7*m**7
+ 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7
) + 15120*a**2*b**4*e**7*x**5*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e
**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 720*a*b**5*d**6*e*m*(d + e*x)**m/(e**7*m**7 + 28*e**7
*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 5040*a
*b**5*d**6*e*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*
e**7*m**2 + 13068*e**7*m + 5040*e**7) + 720*a*b**5*d**5*e**2*m**2*x*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 3
22*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 5040*a*b**5*d**
5*e**2*m*x*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e*
*7*m**2 + 13068*e**7*m + 5040*e**7) - 360*a*b**5*d**4*e**3*m**3*x**2*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 +
322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 2880*a*b**5*d*
*4*e**3*m**2*x**2*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 1
3132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 2520*a*b**5*d**4*e**3*m*x**2*(d + e*x)**m/(e**7*m**7 + 28*e**7*m*
*6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 120*a*b**
5*d**3*e**4*m**4*x**3*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3
+ 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 1200*a*b**5*d**3*e**4*m**3*x**3*(d + e*x)**m/(e**7*m**7 + 28*
e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 27
60*a*b**5*d**3*e**4*m**2*x**3*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e
**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 1680*a*b**5*d**3*e**4*m*x**3*(d + e*x)**m/(e**7*m**7
+ 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7)
- 30*a*b**5*d**2*e**5*m**5*x**4*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 676
9*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 390*a*b**5*d**2*e**5*m**4*x**4*(d + e*x)**m/(e**7*
m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*
e**7) - 1590*a*b**5*d**2*e**5*m**3*x**4*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**
4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 2490*a*b**5*d**2*e**5*m**2*x**4*(d + e*x)**
m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m
+ 5040*e**7) - 1260*a*b**5*d**2*e**5*m*x**4*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**
7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 6*a*b**5*d*e**6*m**6*x**5*(d + e*x)**m
/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m
+ 5040*e**7) + 102*a*b**5*d*e**6*m**5*x**5*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*
m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 630*a*b**5*d*e**6*m**4*x**5*(d + e*x)**m
/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m
+ 5040*e**7) + 1770*a*b**5*d*e**6*m**3*x**5*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7
*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 2244*a*b**5*d*e**6*m**2*x**5*(d + e*x)*
*m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*
m + 5040*e**7) + 1008*a*b**5*d*e**6*m*x**5*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*
m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 6*a*b**5*e**7*m**6*x**6*(d + e*x)**m/(e*
*7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 50
40*e**7) + 132*a*b**5*e**7*m**5*x**6*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 +
6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 1140*a*b**5*e**7*m**4*x**6*(d + e*x)**m/(e**7*
m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*
e**7) + 4920*a*b**5*e**7*m**3*x**6*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6
769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 11094*a*b**5*e**7*m**2*x**6*(d + e*x)**m/(e**7*m
**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e
**7) + 12228*a*b**5*e**7*m*x**6*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769
*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 5040*a*b**5*e**7*x**6*(d + e*x)**m/(e**7*m**7 + 28*
e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 72
0*b**6*d**7*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e
**7*m**2 + 13068*e**7*m + 5040*e**7) - 720*b**6*d**6*e*m*x*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m
**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 360*b**6*d**5*e**2*m**2*
x**2*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**
2 + 13068*e**7*m + 5040*e**7) + 360*b**6*d**5*e**2*m*x**2*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m*
*5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 120*b**6*d**4*e**3*m**3*x
**3*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2
+ 13068*e**7*m + 5040*e**7) - 360*b**6*d**4*e**3*m**2*x**3*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*
m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 240*b**6*d**4*e**3*m*x*
*3*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2
+ 13068*e**7*m + 5040*e**7) + 30*b**6*d**3*e**4*m**4*x**4*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m*
*5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 180*b**6*d**3*e**4*m**3*x
**4*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2
+ 13068*e**7*m + 5040*e**7) + 330*b**6*d**3*e**4*m**2*x**4*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*
m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 180*b**6*d**3*e**4*m*x*
*4*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2
+ 13068*e**7*m + 5040*e**7) - 6*b**6*d**2*e**5*m**5*x**5*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**
5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 60*b**6*d**2*e**5*m**4*x**
5*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 +
13068*e**7*m + 5040*e**7) - 210*b**6*d**2*e**5*m**3*x**5*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m*
*5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 300*b**6*d**2*e**5*m**2*x
**5*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2
+ 13068*e**7*m + 5040*e**7) - 144*b**6*d**2*e**5*m*x**5*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**
5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + b**6*d*e**6*m**6*x**6*(d +
e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068
*e**7*m + 5040*e**7) + 15*b**6*d*e**6*m**5*x**6*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*
e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 85*b**6*d*e**6*m**4*x**6*(d + e*x)*
*m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*
m + 5040*e**7) + 225*b**6*d*e**6*m**3*x**6*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*
m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 274*b**6*d*e**6*m**2*x**6*(d + e*x)**m/(
e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m +
5040*e**7) + 120*b**6*d*e**6*m*x**6*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 +
6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + b**6*e**7*m**6*x**7*(d + e*x)**m/(e**7*m**7 + 2
8*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) +
21*b**6*e**7*m**5*x**7*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**
3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 175*b**6*e**7*m**4*x**7*(d + e*x)**m/(e**7*m**7 + 28*e**7*m*
*6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 735*b**6*
e**7*m**3*x**7*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 1313
2*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 1624*b**6*e**7*m**2*x**7*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 32
2*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 1764*b**6*e**7*m
*x**7*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m*
*2 + 13068*e**7*m + 5040*e**7) + 720*b**6*e**7*x**7*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 1
960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7), True))

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 818 vs. \(2 (206) = 412\).

Time = 0.23 (sec) , antiderivative size = 818, normalized size of antiderivative = 3.97 \[ \int (d+e x)^m \left (a^2+2 a b x+b^2 x^2\right )^3 \, dx=\frac {6 \, {\left (e^{2} {\left (m + 1\right )} x^{2} + d e m x - d^{2}\right )} {\left (e x + d\right )}^{m} a^{5} b}{{\left (m^{2} + 3 \, m + 2\right )} e^{2}} + \frac {{\left (e x + d\right )}^{m + 1} a^{6}}{e {\left (m + 1\right )}} + \frac {15 \, {\left ({\left (m^{2} + 3 \, m + 2\right )} e^{3} x^{3} + {\left (m^{2} + m\right )} d e^{2} x^{2} - 2 \, d^{2} e m x + 2 \, d^{3}\right )} {\left (e x + d\right )}^{m} a^{4} b^{2}}{{\left (m^{3} + 6 \, m^{2} + 11 \, m + 6\right )} e^{3}} + \frac {20 \, {\left ({\left (m^{3} + 6 \, m^{2} + 11 \, m + 6\right )} e^{4} x^{4} + {\left (m^{3} + 3 \, m^{2} + 2 \, m\right )} d e^{3} x^{3} - 3 \, {\left (m^{2} + m\right )} d^{2} e^{2} x^{2} + 6 \, d^{3} e m x - 6 \, d^{4}\right )} {\left (e x + d\right )}^{m} a^{3} b^{3}}{{\left (m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24\right )} e^{4}} + \frac {15 \, {\left ({\left (m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24\right )} e^{5} x^{5} + {\left (m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right )} d e^{4} x^{4} - 4 \, {\left (m^{3} + 3 \, m^{2} + 2 \, m\right )} d^{2} e^{3} x^{3} + 12 \, {\left (m^{2} + m\right )} d^{3} e^{2} x^{2} - 24 \, d^{4} e m x + 24 \, d^{5}\right )} {\left (e x + d\right )}^{m} a^{2} b^{4}}{{\left (m^{5} + 15 \, m^{4} + 85 \, m^{3} + 225 \, m^{2} + 274 \, m + 120\right )} e^{5}} + \frac {6 \, {\left ({\left (m^{5} + 15 \, m^{4} + 85 \, m^{3} + 225 \, m^{2} + 274 \, m + 120\right )} e^{6} x^{6} + {\left (m^{5} + 10 \, m^{4} + 35 \, m^{3} + 50 \, m^{2} + 24 \, m\right )} d e^{5} x^{5} - 5 \, {\left (m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right )} d^{2} e^{4} x^{4} + 20 \, {\left (m^{3} + 3 \, m^{2} + 2 \, m\right )} d^{3} e^{3} x^{3} - 60 \, {\left (m^{2} + m\right )} d^{4} e^{2} x^{2} + 120 \, d^{5} e m x - 120 \, d^{6}\right )} {\left (e x + d\right )}^{m} a b^{5}}{{\left (m^{6} + 21 \, m^{5} + 175 \, m^{4} + 735 \, m^{3} + 1624 \, m^{2} + 1764 \, m + 720\right )} e^{6}} + \frac {{\left ({\left (m^{6} + 21 \, m^{5} + 175 \, m^{4} + 735 \, m^{3} + 1624 \, m^{2} + 1764 \, m + 720\right )} e^{7} x^{7} + {\left (m^{6} + 15 \, m^{5} + 85 \, m^{4} + 225 \, m^{3} + 274 \, m^{2} + 120 \, m\right )} d e^{6} x^{6} - 6 \, {\left (m^{5} + 10 \, m^{4} + 35 \, m^{3} + 50 \, m^{2} + 24 \, m\right )} d^{2} e^{5} x^{5} + 30 \, {\left (m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right )} d^{3} e^{4} x^{4} - 120 \, {\left (m^{3} + 3 \, m^{2} + 2 \, m\right )} d^{4} e^{3} x^{3} + 360 \, {\left (m^{2} + m\right )} d^{5} e^{2} x^{2} - 720 \, d^{6} e m x + 720 \, d^{7}\right )} {\left (e x + d\right )}^{m} b^{6}}{{\left (m^{7} + 28 \, m^{6} + 322 \, m^{5} + 1960 \, m^{4} + 6769 \, m^{3} + 13132 \, m^{2} + 13068 \, m + 5040\right )} e^{7}} \]

[In]

integrate((e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm="maxima")

[Out]

6*(e^2*(m + 1)*x^2 + d*e*m*x - d^2)*(e*x + d)^m*a^5*b/((m^2 + 3*m + 2)*e^2) + (e*x + d)^(m + 1)*a^6/(e*(m + 1)
) + 15*((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^4*b^2/((m^3 + 6*m^2
+ 11*m + 6)*e^3) + 20*((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^3*b^3/((m^4 + 10*m^3 + 35*m^2 + 50*m + 24)*e^4) + 15*((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 + 1
2*(m^2 + m)*d^3*e^2*x^2 - 24*d^4*e*m*x + 24*d^5)*(e*x + d)^m*a^2*b^4/((m^5 + 15*m^4 + 85*m^3 + 225*m^2 + 274*m
+ 120)*e^5) + 6*((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*a*b^5/((m^6 + 21*m^5 + 175*m^4 + 735*m^3 + 1624*m^2 + 17
64*m + 720)*e^6) + ((m^6 + 21*m^5 + 175*m^4 + 735*m^3 + 1624*m^2 + 1764*m + 720)*e^7*x^7 + (m^6 + 15*m^5 + 85*
m^4 + 225*m^3 + 274*m^2 + 120*m)*d*e^6*x^6 - 6*(m^5 + 10*m^4 + 35*m^3 + 50*m^2 + 24*m)*d^2*e^5*x^5 + 30*(m^4 +
6*m^3 + 11*m^2 + 6*m)*d^3*e^4*x^4 - 120*(m^3 + 3*m^2 + 2*m)*d^4*e^3*x^3 + 360*(m^2 + m)*d^5*e^2*x^2 - 720*d^6
*e*m*x + 720*d^7)*(e*x + d)^m*b^6/((m^7 + 28*m^6 + 322*m^5 + 1960*m^4 + 6769*m^3 + 13132*m^2 + 13068*m + 5040)
*e^7)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 3878 vs. \(2 (206) = 412\).

Time = 0.30 (sec) , antiderivative size = 3878, normalized size of antiderivative = 18.83 \[ \int (d+e x)^m \left (a^2+2 a b x+b^2 x^2\right )^3 \, dx=\text {Too large to display} \]

[In]

integrate((e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm="giac")

[Out]

((e*x + d)^m*b^6*e^7*m^6*x^7 + (e*x + d)^m*b^6*d*e^6*m^6*x^6 + 6*(e*x + d)^m*a*b^5*e^7*m^6*x^6 + 21*(e*x + d)^
m*b^6*e^7*m^5*x^7 + 6*(e*x + d)^m*a*b^5*d*e^6*m^6*x^5 + 15*(e*x + d)^m*a^2*b^4*e^7*m^6*x^5 + 15*(e*x + d)^m*b^
6*d*e^6*m^5*x^6 + 132*(e*x + d)^m*a*b^5*e^7*m^5*x^6 + 175*(e*x + d)^m*b^6*e^7*m^4*x^7 + 15*(e*x + d)^m*a^2*b^4
*d*e^6*m^6*x^4 + 20*(e*x + d)^m*a^3*b^3*e^7*m^6*x^4 - 6*(e*x + d)^m*b^6*d^2*e^5*m^5*x^5 + 102*(e*x + d)^m*a*b^
5*d*e^6*m^5*x^5 + 345*(e*x + d)^m*a^2*b^4*e^7*m^5*x^5 + 85*(e*x + d)^m*b^6*d*e^6*m^4*x^6 + 1140*(e*x + d)^m*a*
b^5*e^7*m^4*x^6 + 735*(e*x + d)^m*b^6*e^7*m^3*x^7 + 20*(e*x + d)^m*a^3*b^3*d*e^6*m^6*x^3 + 15*(e*x + d)^m*a^4*
b^2*e^7*m^6*x^3 - 30*(e*x + d)^m*a*b^5*d^2*e^5*m^5*x^4 + 285*(e*x + d)^m*a^2*b^4*d*e^6*m^5*x^4 + 480*(e*x + d)
^m*a^3*b^3*e^7*m^5*x^4 - 60*(e*x + d)^m*b^6*d^2*e^5*m^4*x^5 + 630*(e*x + d)^m*a*b^5*d*e^6*m^4*x^5 + 3105*(e*x
+ d)^m*a^2*b^4*e^7*m^4*x^5 + 225*(e*x + d)^m*b^6*d*e^6*m^3*x^6 + 4920*(e*x + d)^m*a*b^5*e^7*m^3*x^6 + 1624*(e*
x + d)^m*b^6*e^7*m^2*x^7 + 15*(e*x + d)^m*a^4*b^2*d*e^6*m^6*x^2 + 6*(e*x + d)^m*a^5*b*e^7*m^6*x^2 - 60*(e*x +
d)^m*a^2*b^4*d^2*e^5*m^5*x^3 + 420*(e*x + d)^m*a^3*b^3*d*e^6*m^5*x^3 + 375*(e*x + d)^m*a^4*b^2*e^7*m^5*x^3 + 3
0*(e*x + d)^m*b^6*d^3*e^4*m^4*x^4 - 390*(e*x + d)^m*a*b^5*d^2*e^5*m^4*x^4 + 1965*(e*x + d)^m*a^2*b^4*d*e^6*m^4
*x^4 + 4520*(e*x + d)^m*a^3*b^3*e^7*m^4*x^4 - 210*(e*x + d)^m*b^6*d^2*e^5*m^3*x^5 + 1770*(e*x + d)^m*a*b^5*d*e
^6*m^3*x^5 + 13875*(e*x + d)^m*a^2*b^4*e^7*m^3*x^5 + 274*(e*x + d)^m*b^6*d*e^6*m^2*x^6 + 11094*(e*x + d)^m*a*b
^5*e^7*m^2*x^6 + 1764*(e*x + d)^m*b^6*e^7*m*x^7 + 6*(e*x + d)^m*a^5*b*d*e^6*m^6*x + (e*x + d)^m*a^6*e^7*m^6*x
- 60*(e*x + d)^m*a^3*b^3*d^2*e^5*m^5*x^2 + 345*(e*x + d)^m*a^4*b^2*d*e^6*m^5*x^2 + 156*(e*x + d)^m*a^5*b*e^7*m
^5*x^2 + 120*(e*x + d)^m*a*b^5*d^3*e^4*m^4*x^3 - 960*(e*x + d)^m*a^2*b^4*d^2*e^5*m^4*x^3 + 3260*(e*x + d)^m*a^
3*b^3*d*e^6*m^4*x^3 + 3705*(e*x + d)^m*a^4*b^2*e^7*m^4*x^3 + 180*(e*x + d)^m*b^6*d^3*e^4*m^3*x^4 - 1590*(e*x +
d)^m*a*b^5*d^2*e^5*m^3*x^4 + 6015*(e*x + d)^m*a^2*b^4*d*e^6*m^3*x^4 + 21120*(e*x + d)^m*a^3*b^3*e^7*m^3*x^4 -
300*(e*x + d)^m*b^6*d^2*e^5*m^2*x^5 + 2244*(e*x + d)^m*a*b^5*d*e^6*m^2*x^5 + 32160*(e*x + d)^m*a^2*b^4*e^7*m^
2*x^5 + 120*(e*x + d)^m*b^6*d*e^6*m*x^6 + 12228*(e*x + d)^m*a*b^5*e^7*m*x^6 + 720*(e*x + d)^m*b^6*e^7*x^7 + (e
*x + d)^m*a^6*d*e^6*m^6 - 30*(e*x + d)^m*a^4*b^2*d^2*e^5*m^5*x + 150*(e*x + d)^m*a^5*b*d*e^6*m^5*x + 27*(e*x +
d)^m*a^6*e^7*m^5*x + 180*(e*x + d)^m*a^2*b^4*d^3*e^4*m^4*x^2 - 1140*(e*x + d)^m*a^3*b^3*d^2*e^5*m^4*x^2 + 301
5*(e*x + d)^m*a^4*b^2*d*e^6*m^4*x^2 + 1620*(e*x + d)^m*a^5*b*e^7*m^4*x^2 - 120*(e*x + d)^m*b^6*d^4*e^3*m^3*x^3
+ 1200*(e*x + d)^m*a*b^5*d^3*e^4*m^3*x^3 - 4980*(e*x + d)^m*a^2*b^4*d^2*e^5*m^3*x^3 + 11340*(e*x + d)^m*a^3*b
^3*d*e^6*m^3*x^3 + 18285*(e*x + d)^m*a^4*b^2*e^7*m^3*x^3 + 330*(e*x + d)^m*b^6*d^3*e^4*m^2*x^4 - 2490*(e*x + d
)^m*a*b^5*d^2*e^5*m^2*x^4 + 8100*(e*x + d)^m*a^2*b^4*d*e^6*m^2*x^4 + 50900*(e*x + d)^m*a^3*b^3*e^7*m^2*x^4 - 1
44*(e*x + d)^m*b^6*d^2*e^5*m*x^5 + 1008*(e*x + d)^m*a*b^5*d*e^6*m*x^5 + 36180*(e*x + d)^m*a^2*b^4*e^7*m*x^5 +
5040*(e*x + d)^m*a*b^5*e^7*x^6 - 6*(e*x + d)^m*a^5*b*d^2*e^5*m^5 + 27*(e*x + d)^m*a^6*d*e^6*m^5 + 120*(e*x + d
)^m*a^3*b^3*d^3*e^4*m^4*x - 660*(e*x + d)^m*a^4*b^2*d^2*e^5*m^4*x + 1470*(e*x + d)^m*a^5*b*d*e^6*m^4*x + 295*(
e*x + d)^m*a^6*e^7*m^4*x - 360*(e*x + d)^m*a*b^5*d^4*e^3*m^3*x^2 + 2520*(e*x + d)^m*a^2*b^4*d^3*e^4*m^3*x^2 -
7500*(e*x + d)^m*a^3*b^3*d^2*e^5*m^3*x^2 + 12255*(e*x + d)^m*a^4*b^2*d*e^6*m^3*x^2 + 8520*(e*x + d)^m*a^5*b*e^
7*m^3*x^2 - 360*(e*x + d)^m*b^6*d^4*e^3*m^2*x^3 + 2760*(e*x + d)^m*a*b^5*d^3*e^4*m^2*x^3 - 9120*(e*x + d)^m*a^
2*b^4*d^2*e^5*m^2*x^3 + 16880*(e*x + d)^m*a^3*b^3*d*e^6*m^2*x^3 + 46680*(e*x + d)^m*a^4*b^2*e^7*m^2*x^3 + 180*
(e*x + d)^m*b^6*d^3*e^4*m*x^4 - 1260*(e*x + d)^m*a*b^5*d^2*e^5*m*x^4 + 3780*(e*x + d)^m*a^2*b^4*d*e^6*m*x^4 +
59040*(e*x + d)^m*a^3*b^3*e^7*m*x^4 + 15120*(e*x + d)^m*a^2*b^4*e^7*x^5 + 30*(e*x + d)^m*a^4*b^2*d^3*e^4*m^4 -
150*(e*x + d)^m*a^5*b*d^2*e^5*m^4 + 295*(e*x + d)^m*a^6*d*e^6*m^4 - 360*(e*x + d)^m*a^2*b^4*d^4*e^3*m^3*x + 2
160*(e*x + d)^m*a^3*b^3*d^3*e^4*m^3*x - 5370*(e*x + d)^m*a^4*b^2*d^2*e^5*m^3*x + 7050*(e*x + d)^m*a^5*b*d*e^6*
m^3*x + 1665*(e*x + d)^m*a^6*e^7*m^3*x + 360*(e*x + d)^m*b^6*d^5*e^2*m^2*x^2 - 2880*(e*x + d)^m*a*b^5*d^4*e^3*
m^2*x^2 + 9900*(e*x + d)^m*a^2*b^4*d^3*e^4*m^2*x^2 - 19020*(e*x + d)^m*a^3*b^3*d^2*e^5*m^2*x^2 + 22170*(e*x +
d)^m*a^4*b^2*d*e^6*m^2*x^2 + 23574*(e*x + d)^m*a^5*b*e^7*m^2*x^2 - 240*(e*x + d)^m*b^6*d^4*e^3*m*x^3 + 1680*(e
*x + d)^m*a*b^5*d^3*e^4*m*x^3 - 5040*(e*x + d)^m*a^2*b^4*d^2*e^5*m*x^3 + 8400*(e*x + d)^m*a^3*b^3*d*e^6*m*x^3
+ 56940*(e*x + d)^m*a^4*b^2*e^7*m*x^3 + 25200*(e*x + d)^m*a^3*b^3*e^7*x^4 - 120*(e*x + d)^m*a^3*b^3*d^4*e^3*m^
3 + 660*(e*x + d)^m*a^4*b^2*d^3*e^4*m^3 - 1470*(e*x + d)^m*a^5*b*d^2*e^5*m^3 + 1665*(e*x + d)^m*a^6*d*e^6*m^3
+ 720*(e*x + d)^m*a*b^5*d^5*e^2*m^2*x - 4680*(e*x + d)^m*a^2*b^4*d^4*e^3*m^2*x + 12840*(e*x + d)^m*a^3*b^3*d^3
*e^4*m^2*x - 19140*(e*x + d)^m*a^4*b^2*d^2*e^5*m^2*x + 16524*(e*x + d)^m*a^5*b*d*e^6*m^2*x + 5104*(e*x + d)^m*
a^6*e^7*m^2*x + 360*(e*x + d)^m*b^6*d^5*e^2*m*x^2 - 2520*(e*x + d)^m*a*b^5*d^4*e^3*m*x^2 + 7560*(e*x + d)^m*a^
2*b^4*d^3*e^4*m*x^2 - 12600*(e*x + d)^m*a^3*b^3*d^2*e^5*m*x^2 + 12600*(e*x + d)^m*a^4*b^2*d*e^6*m*x^2 + 31644*
(e*x + d)^m*a^5*b*e^7*m*x^2 + 25200*(e*x + d)^m*a^4*b^2*e^7*x^3 + 360*(e*x + d)^m*a^2*b^4*d^5*e^2*m^2 - 2160*(
e*x + d)^m*a^3*b^3*d^4*e^3*m^2 + 5370*(e*x + d)^m*a^4*b^2*d^3*e^4*m^2 - 7050*(e*x + d)^m*a^5*b*d^2*e^5*m^2 + 5
104*(e*x + d)^m*a^6*d*e^6*m^2 - 720*(e*x + d)^m*b^6*d^6*e*m*x + 5040*(e*x + d)^m*a*b^5*d^5*e^2*m*x - 15120*(e*
x + d)^m*a^2*b^4*d^4*e^3*m*x + 25200*(e*x + d)^m*a^3*b^3*d^3*e^4*m*x - 25200*(e*x + d)^m*a^4*b^2*d^2*e^5*m*x +
15120*(e*x + d)^m*a^5*b*d*e^6*m*x + 8028*(e*x + d)^m*a^6*e^7*m*x + 15120*(e*x + d)^m*a^5*b*e^7*x^2 - 720*(e*x
+ d)^m*a*b^5*d^6*e*m + 4680*(e*x + d)^m*a^2*b^4*d^5*e^2*m - 12840*(e*x + d)^m*a^3*b^3*d^4*e^3*m + 19140*(e*x
+ d)^m*a^4*b^2*d^3*e^4*m - 16524*(e*x + d)^m*a^5*b*d^2*e^5*m + 8028*(e*x + d)^m*a^6*d*e^6*m + 5040*(e*x + d)^m
*a^6*e^7*x + 720*(e*x + d)^m*b^6*d^7 - 5040*(e*x + d)^m*a*b^5*d^6*e + 15120*(e*x + d)^m*a^2*b^4*d^5*e^2 - 2520
0*(e*x + d)^m*a^3*b^3*d^4*e^3 + 25200*(e*x + d)^m*a^4*b^2*d^3*e^4 - 15120*(e*x + d)^m*a^5*b*d^2*e^5 + 5040*(e*
x + d)^m*a^6*d*e^6)/(e^7*m^7 + 28*e^7*m^6 + 322*e^7*m^5 + 1960*e^7*m^4 + 6769*e^7*m^3 + 13132*e^7*m^2 + 13068*
e^7*m + 5040*e^7)

Mupad [B] (verification not implemented)

Time = 10.61 (sec) , antiderivative size = 1898, normalized size of antiderivative = 9.21 \[ \int (d+e x)^m \left (a^2+2 a b x+b^2 x^2\right )^3 \, dx=\text {Too large to display} \]

[In]

int((d + e*x)^m*(a^2 + b^2*x^2 + 2*a*b*x)^3,x)

[Out]

((d + e*x)^m*(720*b^6*d^7 + 5040*a^6*d*e^6 - 15120*a^5*b*d^2*e^5 + 5104*a^6*d*e^6*m^2 + 1665*a^6*d*e^6*m^3 + 2
95*a^6*d*e^6*m^4 + 27*a^6*d*e^6*m^5 + a^6*d*e^6*m^6 + 15120*a^2*b^4*d^5*e^2 - 25200*a^3*b^3*d^4*e^3 + 25200*a^
4*b^2*d^3*e^4 - 5040*a*b^5*d^6*e + 8028*a^6*d*e^6*m - 720*a*b^5*d^6*e*m + 360*a^2*b^4*d^5*e^2*m^2 - 2160*a^3*b
^3*d^4*e^3*m^2 + 5370*a^4*b^2*d^3*e^4*m^2 - 120*a^3*b^3*d^4*e^3*m^3 + 660*a^4*b^2*d^3*e^4*m^3 + 30*a^4*b^2*d^3
*e^4*m^4 - 16524*a^5*b*d^2*e^5*m + 4680*a^2*b^4*d^5*e^2*m - 12840*a^3*b^3*d^4*e^3*m + 19140*a^4*b^2*d^3*e^4*m
- 7050*a^5*b*d^2*e^5*m^2 - 1470*a^5*b*d^2*e^5*m^3 - 150*a^5*b*d^2*e^5*m^4 - 6*a^5*b*d^2*e^5*m^5))/(e^7*(13068*
m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040)) + (x*(d + e*x)^m*(5040*a^6*e^7 + 8028*a^
6*e^7*m + 5104*a^6*e^7*m^2 + 1665*a^6*e^7*m^3 + 295*a^6*e^7*m^4 + 27*a^6*e^7*m^5 + a^6*e^7*m^6 - 720*b^6*d^6*e
*m + 15120*a^5*b*d*e^6*m - 4680*a^2*b^4*d^4*e^3*m^2 + 12840*a^3*b^3*d^3*e^4*m^2 - 19140*a^4*b^2*d^2*e^5*m^2 -
360*a^2*b^4*d^4*e^3*m^3 + 2160*a^3*b^3*d^3*e^4*m^3 - 5370*a^4*b^2*d^2*e^5*m^3 + 120*a^3*b^3*d^3*e^4*m^4 - 660*
a^4*b^2*d^2*e^5*m^4 - 30*a^4*b^2*d^2*e^5*m^5 + 5040*a*b^5*d^5*e^2*m + 16524*a^5*b*d*e^6*m^2 + 7050*a^5*b*d*e^6
*m^3 + 1470*a^5*b*d*e^6*m^4 + 150*a^5*b*d*e^6*m^5 + 6*a^5*b*d*e^6*m^6 - 15120*a^2*b^4*d^4*e^3*m + 25200*a^3*b^
3*d^3*e^4*m - 25200*a^4*b^2*d^2*e^5*m + 720*a*b^5*d^5*e^2*m^2))/(e^7*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^
4 + 322*m^5 + 28*m^6 + m^7 + 5040)) + (b^6*x^7*(d + e*x)^m*(1764*m + 1624*m^2 + 735*m^3 + 175*m^4 + 21*m^5 + m
^6 + 720))/(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040) + (3*b*x^2*(m + 1)*(d +
e*x)^m*(5040*a^5*e^5 + 5508*a^5*e^5*m + 120*b^5*d^5*m + 2350*a^5*e^5*m^2 + 490*a^5*e^5*m^3 + 50*a^5*e^5*m^4 +
2*a^5*e^5*m^5 - 840*a*b^4*d^4*e*m + 4200*a^4*b*d*e^4*m + 780*a^2*b^3*d^3*e^2*m^2 - 2140*a^3*b^2*d^2*e^3*m^2 +
60*a^2*b^3*d^3*e^2*m^3 - 360*a^3*b^2*d^2*e^3*m^3 - 20*a^3*b^2*d^2*e^3*m^4 - 120*a*b^4*d^4*e*m^2 + 3190*a^4*b*
d*e^4*m^2 + 895*a^4*b*d*e^4*m^3 + 110*a^4*b*d*e^4*m^4 + 5*a^4*b*d*e^4*m^5 + 2520*a^2*b^3*d^3*e^2*m - 4200*a^3*
b^2*d^2*e^3*m))/(e^5*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040)) + (3*b^4*x^5
*(d + e*x)^m*(50*m + 35*m^2 + 10*m^3 + m^4 + 24)*(210*a^2*e^2 + 65*a^2*e^2*m - 2*b^2*d^2*m + 5*a^2*e^2*m^2 + 1
4*a*b*d*e*m + 2*a*b*d*e*m^2))/(e^2*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040)
) + (5*b^3*x^4*(d + e*x)^m*(11*m + 6*m^2 + m^3 + 6)*(840*a^3*e^3 + 428*a^3*e^3*m + 6*b^3*d^3*m + 72*a^3*e^3*m^
2 + 4*a^3*e^3*m^3 - 42*a*b^2*d^2*e*m + 126*a^2*b*d*e^2*m - 6*a*b^2*d^2*e*m^2 + 39*a^2*b*d*e^2*m^2 + 3*a^2*b*d*
e^2*m^3))/(e^3*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040)) + (b^5*x^6*(d + e*
x)^m*(42*a*e + 6*a*e*m + b*d*m)*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120))/(e*(13068*m + 13132*m^2 + 676
9*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040)) + (5*b^2*x^3*(d + e*x)^m*(3*m + m^2 + 2)*(2520*a^4*e^4 + 19
14*a^4*e^4*m - 24*b^4*d^4*m + 537*a^4*e^4*m^2 + 66*a^4*e^4*m^3 + 3*a^4*e^4*m^4 + 168*a*b^3*d^3*e*m + 840*a^3*b
*d*e^3*m - 156*a^2*b^2*d^2*e^2*m^2 - 12*a^2*b^2*d^2*e^2*m^3 + 24*a*b^3*d^3*e*m^2 + 428*a^3*b*d*e^3*m^2 + 72*a^
3*b*d*e^3*m^3 + 4*a^3*b*d*e^3*m^4 - 504*a^2*b^2*d^2*e^2*m))/(e^4*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 +
322*m^5 + 28*m^6 + m^7 + 5040))