\(\int (d+e x)^m (a+b x+c x^2)^3 \, dx\) [2550]

Optimal result

Integrand size = 20, antiderivative size = 305 \[ \int (d+e x)^m \left (a+b x+c x^2\right )^3 \, dx=\frac {\left (c d^2-b d e+a e^2\right )^3 (d+e x)^{1+m}}{e^7 (1+m)}-\frac {3 (2 c d-b e) \left (c d^2-b d e+a e^2\right )^2 (d+e x)^{2+m}}{e^7 (2+m)}+\frac {3 \left (c d^2-b d e+a e^2\right ) \left (5 c^2 d^2+b^2 e^2-c e (5 b d-a e)\right ) (d+e x)^{3+m}}{e^7 (3+m)}-\frac {(2 c d-b e) \left (10 c^2 d^2+b^2 e^2-2 c e (5 b d-3 a e)\right ) (d+e x)^{4+m}}{e^7 (4+m)}+\frac {3 c \left (5 c^2 d^2+b^2 e^2-c e (5 b d-a e)\right ) (d+e x)^{5+m}}{e^7 (5+m)}-\frac {3 c^2 (2 c d-b e) (d+e x)^{6+m}}{e^7 (6+m)}+\frac {c^3 (d+e x)^{7+m}}{e^7 (7+m)} \]

[Out]

(a*e^2-b*d*e+c*d^2)^3*(e*x+d)^(1+m)/e^7/(1+m)-3*(-b*e+2*c*d)*(a*e^2-b*d*e+c*d^2)^2*(e*x+d)^(2+m)/e^7/(2+m)+3*(
a*e^2-b*d*e+c*d^2)*(5*c^2*d^2+b^2*e^2-c*e*(-a*e+5*b*d))*(e*x+d)^(3+m)/e^7/(3+m)-(-b*e+2*c*d)*(10*c^2*d^2+b^2*e
^2-2*c*e*(-3*a*e+5*b*d))*(e*x+d)^(4+m)/e^7/(4+m)+3*c*(5*c^2*d^2+b^2*e^2-c*e*(-a*e+5*b*d))*(e*x+d)^(5+m)/e^7/(5
+m)-3*c^2*(-b*e+2*c*d)*(e*x+d)^(6+m)/e^7/(6+m)+c^3*(e*x+d)^(7+m)/e^7/(7+m)

Rubi [A] (verified)

Time = 0.14 (sec) , antiderivative size = 305, 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 = {712} \[ \int (d+e x)^m \left (a+b x+c x^2\right )^3 \, dx=\frac {3 (d+e x)^{m+3} \left (a e^2-b d e+c d^2\right ) \left (-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right )}{e^7 (m+3)}-\frac {(2 c d-b e) (d+e x)^{m+4} \left (-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right )}{e^7 (m+4)}+\frac {3 c (d+e x)^{m+5} \left (-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right )}{e^7 (m+5)}+\frac {(d+e x)^{m+1} \left (a e^2-b d e+c d^2\right )^3}{e^7 (m+1)}-\frac {3 (2 c d-b e) (d+e x)^{m+2} \left (a e^2-b d e+c d^2\right )^2}{e^7 (m+2)}-\frac {3 c^2 (2 c d-b e) (d+e x)^{m+6}}{e^7 (m+6)}+\frac {c^3 (d+e x)^{m+7}}{e^7 (m+7)} \]

[In]

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

[Out]

((c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^(1 + m))/(e^7*(1 + m)) - (3*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2*(d +
e*x)^(2 + m))/(e^7*(2 + m)) + (3*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(
3 + m))/(e^7*(3 + m)) - ((2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(d + e*x)^(4 + m))/(e^7*
(4 + m)) + (3*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(5 + m))/(e^7*(5 + m)) - (3*c^2*(2*c*d - b
*e)*(d + e*x)^(6 + m))/(e^7*(6 + m)) + (c^3*(d + e*x)^(7 + m))/(e^7*(7 + m))

Rule 712

Int[((d_.) + (e_.)*(x_))^(m_)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> Int[ExpandIntegrand[(d +
e*x)^m*(a + b*x + c*x^2)^p, x], x] /; FreeQ[{a, b, c, d, e, m}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - b*d*
e + a*e^2, 0] && NeQ[2*c*d - b*e, 0] && IntegerQ[p] && (GtQ[p, 0] || (EqQ[a, 0] && IntegerQ[m]))

Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {\left (c d^2-b d e+a e^2\right )^3 (d+e x)^m}{e^6}+\frac {3 (-2 c d+b e) \left (c d^2-b d e+a e^2\right )^2 (d+e x)^{1+m}}{e^6}+\frac {3 \left (c d^2-b d e+a e^2\right ) \left (5 c^2 d^2-5 b c d e+b^2 e^2+a c e^2\right ) (d+e x)^{2+m}}{e^6}+\frac {(2 c d-b e) \left (-10 c^2 d^2-b^2 e^2+2 c e (5 b d-3 a e)\right ) (d+e x)^{3+m}}{e^6}+\frac {3 c \left (5 c^2 d^2+b^2 e^2-c e (5 b d-a e)\right ) (d+e x)^{4+m}}{e^6}-\frac {3 c^2 (2 c d-b e) (d+e x)^{5+m}}{e^6}+\frac {c^3 (d+e x)^{6+m}}{e^6}\right ) \, dx \\ & = \frac {\left (c d^2-b d e+a e^2\right )^3 (d+e x)^{1+m}}{e^7 (1+m)}-\frac {3 (2 c d-b e) \left (c d^2-b d e+a e^2\right )^2 (d+e x)^{2+m}}{e^7 (2+m)}+\frac {3 \left (c d^2-b d e+a e^2\right ) \left (5 c^2 d^2+b^2 e^2-c e (5 b d-a e)\right ) (d+e x)^{3+m}}{e^7 (3+m)}-\frac {(2 c d-b e) \left (10 c^2 d^2+b^2 e^2-2 c e (5 b d-3 a e)\right ) (d+e x)^{4+m}}{e^7 (4+m)}+\frac {3 c \left (5 c^2 d^2+b^2 e^2-c e (5 b d-a e)\right ) (d+e x)^{5+m}}{e^7 (5+m)}-\frac {3 c^2 (2 c d-b e) (d+e x)^{6+m}}{e^7 (6+m)}+\frac {c^3 (d+e x)^{7+m}}{e^7 (7+m)} \\ \end{align*}

Mathematica [A] (verified)

Time = 1.22 (sec) , antiderivative size = 476, normalized size of antiderivative = 1.56 \[ \int (d+e x)^m \left (a+b x+c x^2\right )^3 \, dx=\frac {(d+e x)^{1+m} \left ((a+x (b+c x))^3+\frac {3 (d+e x) \left (2 (2 c d-b e) \left (c d^2+e (-b d+a e)\right ) (3+m) \left (60 c^2 d^2+b^2 e^2 \left (2+3 m+m^2\right )-4 c e \left (15 b d+a e \left (-13+3 m+m^2\right )\right )\right )-2 (2+m) \left (120 c^4 d^4+b^4 e^4 \left (3+4 m+m^2\right )-2 b^2 c e^3 (1+m) (b d (-3+m)+3 a e (5+m))-8 c^3 d^2 e \left (30 b d+a e \left (-33-2 m+m^2\right )\right )+2 c^2 e^2 \left (4 a b d e \left (-33-2 m+m^2\right )+b^2 d^2 \left (57-2 m+m^2\right )+4 a^2 e^2 \left (24+10 m+m^2\right )\right )\right ) (d+e x)-c e^4 (2+m) (3+m) (4+m) (5+m) (a+x (b+c x))^2 (b e (11+m)+2 c (-5 d+e (6+m) x))-2 e^2 (2+m) (3+m) (a+x (b+c x)) \left (-b^3 e^3 (1+m)+20 c^3 d^2 (-3 d+e (4+m) x)-b c e^2 \left (-2 a e (37+7 m)+b d \left (72+13 m+m^2\right )+b e \left (4+5 m+m^2\right ) x\right )+2 c^2 e \left (5 b d (d (13+m)-2 e (4+m) x)+2 a e \left (d \left (-13+3 m+m^2\right )+e \left (24+10 m+m^2\right ) x\right )\right )\right )\right )}{c e^6 (2+m) (3+m) (4+m) (5+m) (6+m) (7+m)}\right )}{e (1+m)} \]

[In]

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

[Out]

((d + e*x)^(1 + m)*((a + x*(b + c*x))^3 + (3*(d + e*x)*(2*(2*c*d - b*e)*(c*d^2 + e*(-(b*d) + a*e))*(3 + m)*(60
*c^2*d^2 + b^2*e^2*(2 + 3*m + m^2) - 4*c*e*(15*b*d + a*e*(-13 + 3*m + m^2))) - 2*(2 + m)*(120*c^4*d^4 + b^4*e^
4*(3 + 4*m + m^2) - 2*b^2*c*e^3*(1 + m)*(b*d*(-3 + m) + 3*a*e*(5 + m)) - 8*c^3*d^2*e*(30*b*d + a*e*(-33 - 2*m
+ m^2)) + 2*c^2*e^2*(4*a*b*d*e*(-33 - 2*m + m^2) + b^2*d^2*(57 - 2*m + m^2) + 4*a^2*e^2*(24 + 10*m + m^2)))*(d
+ e*x) - c*e^4*(2 + m)*(3 + m)*(4 + m)*(5 + m)*(a + x*(b + c*x))^2*(b*e*(11 + m) + 2*c*(-5*d + e*(6 + m)*x))
- 2*e^2*(2 + m)*(3 + m)*(a + x*(b + c*x))*(-(b^3*e^3*(1 + m)) + 20*c^3*d^2*(-3*d + e*(4 + m)*x) - b*c*e^2*(-2*
a*e*(37 + 7*m) + b*d*(72 + 13*m + m^2) + b*e*(4 + 5*m + m^2)*x) + 2*c^2*e*(5*b*d*(d*(13 + m) - 2*e*(4 + m)*x)
+ 2*a*e*(d*(-13 + 3*m + m^2) + e*(24 + 10*m + m^2)*x)))))/(c*e^6*(2 + m)*(3 + m)*(4 + m)*(5 + m)*(6 + m)*(7 +
m))))/(e*(1 + m))

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(2337\) vs. \(2(305)=610\).

Time = 0.30 (sec) , antiderivative size = 2338, normalized size of antiderivative = 7.67

method	result	size
norman	\(\text {Expression too large to display}\)	\(2338\)
gosper	\(\text {Expression too large to display}\)	\(2927\)
risch	\(\text {Expression too large to display}\)	\(3658\)
parallelrisch	\(\text {Expression too large to display}\)	\(5366\)

[In]

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

[Out]

c^3/(7+m)*x^7*exp(m*ln(e*x+d))+d*(a^3*e^6*m^6+27*a^3*e^6*m^5-3*a^2*b*d*e^5*m^5+295*a^3*e^6*m^4-75*a^2*b*d*e^5*
m^4+6*a^2*c*d^2*e^4*m^4+6*a*b^2*d^2*e^4*m^4+1665*a^3*e^6*m^3-735*a^2*b*d*e^5*m^3+132*a^2*c*d^2*e^4*m^3+132*a*b
^2*d^2*e^4*m^3-36*a*b*c*d^3*e^3*m^3-6*b^3*d^3*e^3*m^3+5104*a^3*e^6*m^2-3525*a^2*b*d*e^5*m^2+1074*a^2*c*d^2*e^4
*m^2+1074*a*b^2*d^2*e^4*m^2-648*a*b*c*d^3*e^3*m^2+72*a*c^2*d^4*e^2*m^2-108*b^3*d^3*e^3*m^2+72*b^2*c*d^4*e^2*m^
2+8028*a^3*e^6*m-8262*a^2*b*d*e^5*m+3828*a^2*c*d^2*e^4*m+3828*a*b^2*d^2*e^4*m-3852*a*b*c*d^3*e^3*m+936*a*c^2*d
^4*e^2*m-642*b^3*d^3*e^3*m+936*b^2*c*d^4*e^2*m-360*b*c^2*d^5*e*m+5040*a^3*e^6-7560*a^2*b*d*e^5+5040*a^2*c*d^2*
e^4+5040*a*b^2*d^2*e^4-7560*a*b*c*d^3*e^3+3024*a*c^2*d^4*e^2-1260*b^3*d^3*e^3+3024*b^2*c*d^4*e^2-2520*b*c^2*d^
5*e+720*c^3*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*ln(e*x+d))+(6*a*b*c*e
^3*m^3+3*a*c^2*d*e^2*m^3+b^3*e^3*m^3+3*b^2*c*d*e^2*m^3+108*a*b*c*e^3*m^2+39*a*c^2*d*e^2*m^2+18*b^3*e^3*m^2+39*
b^2*c*d*e^2*m^2-15*b*c^2*d^2*e*m^2+642*a*b*c*e^3*m+126*a*c^2*d*e^2*m+107*b^3*e^3*m+126*b^2*c*d*e^2*m-105*b*c^2
*d^2*e*m+30*c^3*d^3*m+1260*a*b*c*e^3+210*b^3*e^3)/e^3/(m^4+22*m^3+179*m^2+638*m+840)*x^4*exp(m*ln(e*x+d))+(3*a
^2*c*e^4*m^4+3*a*b^2*e^4*m^4+6*a*b*c*d*e^3*m^4+b^3*d*e^3*m^4+66*a^2*c*e^4*m^3+66*a*b^2*e^4*m^3+108*a*b*c*d*e^3
*m^3-12*a*c^2*d^2*e^2*m^3+18*b^3*d*e^3*m^3-12*b^2*c*d^2*e^2*m^3+537*a^2*c*e^4*m^2+537*a*b^2*e^4*m^2+642*a*b*c*
d*e^3*m^2-156*a*c^2*d^2*e^2*m^2+107*b^3*d*e^3*m^2-156*b^2*c*d^2*e^2*m^2+60*b*c^2*d^3*e*m^2+1914*a^2*c*e^4*m+19
14*a*b^2*e^4*m+1260*a*b*c*d*e^3*m-504*a*c^2*d^2*e^2*m+210*b^3*d*e^3*m-504*b^2*c*d^2*e^2*m+420*b*c^2*d^3*e*m-12
0*c^3*d^4*m+2520*a^2*c*e^4+2520*a*b^2*e^4)/e^4/(m^5+25*m^4+245*m^3+1175*m^2+2754*m+2520)*x^3*exp(m*ln(e*x+d))+
(a^3*e^6*m^6+3*a^2*b*d*e^5*m^6+27*a^3*e^6*m^5+75*a^2*b*d*e^5*m^5-6*a^2*c*d^2*e^4*m^5-6*a*b^2*d^2*e^4*m^5+295*a
^3*e^6*m^4+735*a^2*b*d*e^5*m^4-132*a^2*c*d^2*e^4*m^4-132*a*b^2*d^2*e^4*m^4+36*a*b*c*d^3*e^3*m^4+6*b^3*d^3*e^3*
m^4+1665*a^3*e^6*m^3+3525*a^2*b*d*e^5*m^3-1074*a^2*c*d^2*e^4*m^3-1074*a*b^2*d^2*e^4*m^3+648*a*b*c*d^3*e^3*m^3-
72*a*c^2*d^4*e^2*m^3+108*b^3*d^3*e^3*m^3-72*b^2*c*d^4*e^2*m^3+5104*a^3*e^6*m^2+8262*a^2*b*d*e^5*m^2-3828*a^2*c
*d^2*e^4*m^2-3828*a*b^2*d^2*e^4*m^2+3852*a*b*c*d^3*e^3*m^2-936*a*c^2*d^4*e^2*m^2+642*b^3*d^3*e^3*m^2-936*b^2*c
*d^4*e^2*m^2+360*b*c^2*d^5*e*m^2+8028*a^3*e^6*m+7560*a^2*b*d*e^5*m-5040*a^2*c*d^2*e^4*m-5040*a*b^2*d^2*e^4*m+7
560*a*b*c*d^3*e^3*m-3024*a*c^2*d^4*e^2*m+1260*b^3*d^3*e^3*m-3024*b^2*c*d^4*e^2*m+2520*b*c^2*d^5*e*m-720*c^3*d^
6*m+5040*a^3*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))+(3*b*e*
m+c*d*m+21*b*e)*c^2/e/(m^2+13*m+42)*x^6*exp(m*ln(e*x+d))+3*(a^2*b*e^5*m^5+a^2*c*d*e^4*m^5+a*b^2*d*e^4*m^5+25*a
^2*b*e^5*m^4+22*a^2*c*d*e^4*m^4+22*a*b^2*d*e^4*m^4-6*a*b*c*d^2*e^3*m^4-b^3*d^2*e^3*m^4+245*a^2*b*e^5*m^3+179*a
^2*c*d*e^4*m^3+179*a*b^2*d*e^4*m^3-108*a*b*c*d^2*e^3*m^3+12*a*c^2*d^3*e^2*m^3-18*b^3*d^2*e^3*m^3+12*b^2*c*d^3*
e^2*m^3+1175*a^2*b*e^5*m^2+638*a^2*c*d*e^4*m^2+638*a*b^2*d*e^4*m^2-642*a*b*c*d^2*e^3*m^2+156*a*c^2*d^3*e^2*m^2
-107*b^3*d^2*e^3*m^2+156*b^2*c*d^3*e^2*m^2-60*b*c^2*d^4*e*m^2+2754*a^2*b*e^5*m+840*a^2*c*d*e^4*m+840*a*b^2*d*e
^4*m-1260*a*b*c*d^2*e^3*m+504*a*c^2*d^3*e^2*m-210*b^3*d^2*e^3*m+504*b^2*c*d^3*e^2*m-420*b*c^2*d^4*e*m+120*c^3*
d^5*m+2520*a^2*b*e^5)/e^5/(m^6+27*m^5+295*m^4+1665*m^3+5104*m^2+8028*m+5040)*x^2*exp(m*ln(e*x+d))+3*c*(a*c*e^2
*m^2+b^2*e^2*m^2+b*c*d*e*m^2+13*a*c*e^2*m+13*b^2*e^2*m+7*b*c*d*e*m-2*c^2*d^2*m+42*a*c*e^2+42*b^2*e^2)/e^2/(m^3
+18*m^2+107*m+210)*x^5*exp(m*ln(e*x+d))

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 2550 vs. \(2 (305) = 610\).

Time = 0.32 (sec) , antiderivative size = 2550, normalized size of antiderivative = 8.36 \[ \int (d+e x)^m \left (a+b x+c x^2\right )^3 \, dx=\text {Too large to display} \]

[In]

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

[Out]

(a^3*d*e^6*m^6 + 720*c^3*d^7 - 2520*b*c^2*d^6*e - 7560*a^2*b*d^2*e^5 + 5040*a^3*d*e^6 + 3024*(b^2*c + a*c^2)*d
^5*e^2 - 1260*(b^3 + 6*a*b*c)*d^4*e^3 + 5040*(a*b^2 + a^2*c)*d^3*e^4 + (c^3*e^7*m^6 + 21*c^3*e^7*m^5 + 175*c^3
*e^7*m^4 + 735*c^3*e^7*m^3 + 1624*c^3*e^7*m^2 + 1764*c^3*e^7*m + 720*c^3*e^7)*x^7 + (2520*b*c^2*e^7 + (c^3*d*e
^6 + 3*b*c^2*e^7)*m^6 + 3*(5*c^3*d*e^6 + 22*b*c^2*e^7)*m^5 + 5*(17*c^3*d*e^6 + 114*b*c^2*e^7)*m^4 + 15*(15*c^3
*d*e^6 + 164*b*c^2*e^7)*m^3 + (274*c^3*d*e^6 + 5547*b*c^2*e^7)*m^2 + 6*(20*c^3*d*e^6 + 1019*b*c^2*e^7)*m)*x^6
- 3*(a^2*b*d^2*e^5 - 9*a^3*d*e^6)*m^5 + 3*(1008*(b^2*c + a*c^2)*e^7 + (b*c^2*d*e^6 + (b^2*c + a*c^2)*e^7)*m^6
- (2*c^3*d^2*e^5 - 17*b*c^2*d*e^6 - 23*(b^2*c + a*c^2)*e^7)*m^5 - (20*c^3*d^2*e^5 - 105*b*c^2*d*e^6 - 207*(b^2
*c + a*c^2)*e^7)*m^4 - 5*(14*c^3*d^2*e^5 - 59*b*c^2*d*e^6 - 185*(b^2*c + a*c^2)*e^7)*m^3 - 2*(50*c^3*d^2*e^5 -
187*b*c^2*d*e^6 - 1072*(b^2*c + a*c^2)*e^7)*m^2 - 12*(4*c^3*d^2*e^5 - 14*b*c^2*d*e^6 - 201*(b^2*c + a*c^2)*e^
7)*m)*x^5 - (75*a^2*b*d^2*e^5 - 295*a^3*d*e^6 - 6*(a*b^2 + a^2*c)*d^3*e^4)*m^4 + (1260*(b^3 + 6*a*b*c)*e^7 + (
3*(b^2*c + a*c^2)*d*e^6 + (b^3 + 6*a*b*c)*e^7)*m^6 - 3*(5*b*c^2*d^2*e^5 - 19*(b^2*c + a*c^2)*d*e^6 - 8*(b^3 +
6*a*b*c)*e^7)*m^5 + (30*c^3*d^3*e^4 - 195*b*c^2*d^2*e^5 + 393*(b^2*c + a*c^2)*d*e^6 + 226*(b^3 + 6*a*b*c)*e^7)
*m^4 + 3*(60*c^3*d^3*e^4 - 265*b*c^2*d^2*e^5 + 401*(b^2*c + a*c^2)*d*e^6 + 352*(b^3 + 6*a*b*c)*e^7)*m^3 + 5*(6
6*c^3*d^3*e^4 - 249*b*c^2*d^2*e^5 + 324*(b^2*c + a*c^2)*d*e^6 + 509*(b^3 + 6*a*b*c)*e^7)*m^2 + 18*(10*c^3*d^3*
e^4 - 35*b*c^2*d^2*e^5 + 42*(b^2*c + a*c^2)*d*e^6 + 164*(b^3 + 6*a*b*c)*e^7)*m)*x^4 - 3*(245*a^2*b*d^2*e^5 - 5
55*a^3*d*e^6 + 2*(b^3 + 6*a*b*c)*d^4*e^3 - 44*(a*b^2 + a^2*c)*d^3*e^4)*m^3 + (5040*(a*b^2 + a^2*c)*e^7 + ((b^3
+ 6*a*b*c)*d*e^6 + 3*(a*b^2 + a^2*c)*e^7)*m^6 - 3*(4*(b^2*c + a*c^2)*d^2*e^5 - 7*(b^3 + 6*a*b*c)*d*e^6 - 25*(
a*b^2 + a^2*c)*e^7)*m^5 + (60*b*c^2*d^3*e^4 - 192*(b^2*c + a*c^2)*d^2*e^5 + 163*(b^3 + 6*a*b*c)*d*e^6 + 741*(a
*b^2 + a^2*c)*e^7)*m^4 - 3*(40*c^3*d^4*e^3 - 200*b*c^2*d^3*e^4 + 332*(b^2*c + a*c^2)*d^2*e^5 - 189*(b^3 + 6*a*
b*c)*d*e^6 - 1219*(a*b^2 + a^2*c)*e^7)*m^3 - 4*(90*c^3*d^4*e^3 - 345*b*c^2*d^3*e^4 + 456*(b^2*c + a*c^2)*d^2*e
^5 - 211*(b^3 + 6*a*b*c)*d*e^6 - 2334*(a*b^2 + a^2*c)*e^7)*m^2 - 12*(20*c^3*d^4*e^3 - 70*b*c^2*d^3*e^4 + 84*(b
^2*c + a*c^2)*d^2*e^5 - 35*(b^3 + 6*a*b*c)*d*e^6 - 949*(a*b^2 + a^2*c)*e^7)*m)*x^3 - (3525*a^2*b*d^2*e^5 - 510
4*a^3*d*e^6 - 72*(b^2*c + a*c^2)*d^5*e^2 + 108*(b^3 + 6*a*b*c)*d^4*e^3 - 1074*(a*b^2 + a^2*c)*d^3*e^4)*m^2 + 3
*(2520*a^2*b*e^7 + (a^2*b*e^7 + (a*b^2 + a^2*c)*d*e^6)*m^6 + (26*a^2*b*e^7 - (b^3 + 6*a*b*c)*d^2*e^5 + 23*(a*b
^2 + a^2*c)*d*e^6)*m^5 + (270*a^2*b*e^7 + 12*(b^2*c + a*c^2)*d^3*e^4 - 19*(b^3 + 6*a*b*c)*d^2*e^5 + 201*(a*b^2
+ a^2*c)*d*e^6)*m^4 - (60*b*c^2*d^4*e^3 - 1420*a^2*b*e^7 - 168*(b^2*c + a*c^2)*d^3*e^4 + 125*(b^3 + 6*a*b*c)*
d^2*e^5 - 817*(a*b^2 + a^2*c)*d*e^6)*m^3 + (120*c^3*d^5*e^2 - 480*b*c^2*d^4*e^3 + 3929*a^2*b*e^7 + 660*(b^2*c
+ a*c^2)*d^3*e^4 - 317*(b^3 + 6*a*b*c)*d^2*e^5 + 1478*(a*b^2 + a^2*c)*d*e^6)*m^2 + 6*(20*c^3*d^5*e^2 - 70*b*c^
2*d^4*e^3 + 879*a^2*b*e^7 + 84*(b^2*c + a*c^2)*d^3*e^4 - 35*(b^3 + 6*a*b*c)*d^2*e^5 + 140*(a*b^2 + a^2*c)*d*e^
6)*m)*x^2 - 6*(60*b*c^2*d^6*e + 1377*a^2*b*d^2*e^5 - 1338*a^3*d*e^6 - 156*(b^2*c + a*c^2)*d^5*e^2 + 107*(b^3 +
6*a*b*c)*d^4*e^3 - 638*(a*b^2 + a^2*c)*d^3*e^4)*m + (5040*a^3*e^7 + (3*a^2*b*d*e^6 + a^3*e^7)*m^6 + 3*(25*a^2
*b*d*e^6 + 9*a^3*e^7 - 2*(a*b^2 + a^2*c)*d^2*e^5)*m^5 + (735*a^2*b*d*e^6 + 295*a^3*e^7 + 6*(b^3 + 6*a*b*c)*d^3
*e^4 - 132*(a*b^2 + a^2*c)*d^2*e^5)*m^4 + 3*(1175*a^2*b*d*e^6 + 555*a^3*e^7 - 24*(b^2*c + a*c^2)*d^4*e^3 + 36*
(b^3 + 6*a*b*c)*d^3*e^4 - 358*(a*b^2 + a^2*c)*d^2*e^5)*m^3 + 2*(180*b*c^2*d^5*e^2 + 4131*a^2*b*d*e^6 + 2552*a^
3*e^7 - 468*(b^2*c + a*c^2)*d^4*e^3 + 321*(b^3 + 6*a*b*c)*d^3*e^4 - 1914*(a*b^2 + a^2*c)*d^2*e^5)*m^2 - 36*(20
*c^3*d^6*e - 70*b*c^2*d^5*e^2 - 210*a^2*b*d*e^6 - 223*a^3*e^7 + 84*(b^2*c + a*c^2)*d^4*e^3 - 35*(b^3 + 6*a*b*c
)*d^3*e^4 + 140*(a*b^2 + a^2*c)*d^2*e^5)*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. 40049 vs. \(2 (284) = 568\).

Time = 7.18 (sec) , antiderivative size = 40049, normalized size of antiderivative = 131.31 \[ \int (d+e x)^m \left (a+b x+c x^2\right )^3 \, dx=\text {Too large to display} \]

[In]

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

[Out]

Piecewise((d**m*(a**3*x + 3*a**2*b*x**2/2 + a**2*c*x**3 + a*b**2*x**3 + 3*a*b*c*x**4/2 + 3*a*c**2*x**5/5 + b**
3*x**4/4 + 3*b**2*c*x**5/5 + b*c**2*x**6/2 + c**3*x**7/7), Eq(e, 0)), (-10*a**3*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) -
6*a**2*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) - 36*a**2*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**11*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6) - 3*a**2*c*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) - 18*a**2*c*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) - 45*a**2*c*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)
- 3*a*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) - 18*a*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) - 45*a*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) - 6*a*b*c*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) - 36*a*b*c*d**2*e**4*x/(60*d**6*e**7 + 3
60*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*b*c*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 + 90
0*d**2*e**11*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6) - 120*a*b*c*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) - 6*a*c**2
*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) - 36*a*c**2*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 + 900*d**2*e**11*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6) - 90*a*c**2*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**1
2*x**5 + 60*e**13*x**6) - 120*a*c**2*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) - 90*a*c**2*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) - 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) - 6*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) - 15*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) - 20*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) - 6*b**2*c*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) - 36*b**2*c*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
+ 900*d**2*e**11*x**4 + 360*d*e**12*x**5 + 60*e**13*x**6) - 90*b**2*c*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) -
120*b**2*c*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) - 90*b**2*c*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) - 30*b*c**2*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) - 180*b*c**2*d**4*e**2*x/(60*d**6*e**7 + 360*d**5*e**8*x + 900*d**4*e**9*x**2 + 120
0*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*b*c**2*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) - 600*b*c**2*d**2*e**4*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*b*c**2*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) - 180*b*c**2*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*c**3*d**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) +
147*c**3*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*c**3*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*c**3*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*c**3*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*c**3*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 + 3
60*d*e**12*x**5 + 60*e**13*x**6) + 1200*c**3*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) + 2200*c**3*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*c**3*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*c*
*3*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*c**3*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*c*
*3*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*c**3*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)), (
-4*a**3*e**6/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4 + 2
0*e**12*x**5) - 3*a**2*b*d*e**5/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 1
00*d*e**11*x**4 + 20*e**12*x**5) - 15*a**2*b*e**6*x/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200
*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x**5) - 2*a**2*c*d**2*e**4/(20*d**5*e**7 + 100*d**4*e**8*x + 20
0*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x**5) - 10*a**2*c*d*e**5*x/(20*d**5*e**7
+ 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x**5) - 20*a**2*c*e
**6*x**2/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e*
*12*x**5) - 2*a*b**2*d**2*e**4/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 10
0*d*e**11*x**4 + 20*e**12*x**5) - 10*a*b**2*d*e**5*x/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 20
0*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x**5) - 20*a*b**2*e**6*x**2/(20*d**5*e**7 + 100*d**4*e**8*x +
200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x**5) - 6*a*b*c*d**3*e**3/(20*d**5*e**7
+ 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x**5) - 30*a*b*c*d
**2*e**4*x/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*
e**12*x**5) - 60*a*b*c*d*e**5*x**2/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3
+ 100*d*e**11*x**4 + 20*e**12*x**5) - 60*a*b*c*e**6*x**3/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2
+ 200*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x**5) - 12*a*c**2*d**4*e**2/(20*d**5*e**7 + 100*d**4*e**8*
x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x**5) - 60*a*c**2*d**3*e**3*x/(20*d
**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x**5) - 12
0*a*c**2*d**2*e**4*x**2/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**
11*x**4 + 20*e**12*x**5) - 120*a*c**2*d*e**5*x**3/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d
**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x**5) - 60*a*c**2*e**6*x**4/(20*d**5*e**7 + 100*d**4*e**8*x + 200
*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x**5) - b**3*d**3*e**3/(20*d**5*e**7 + 100
*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x**5) - 5*b**3*d**2*e**4
*x/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x*
*5) - 10*b**3*d*e**5*x**2/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e
**11*x**4 + 20*e**12*x**5) - 10*b**3*e**6*x**3/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2
*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x**5) - 12*b**2*c*d**4*e**2/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d*
*3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x**5) - 60*b**2*c*d**3*e**3*x/(20*d**5*e**7 +
100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x**5) - 120*b**2*c*d
**2*e**4*x**2/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4 +
20*e**12*x**5) - 120*b**2*c*d*e**5*x**3/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*
x**3 + 100*d*e**11*x**4 + 20*e**12*x**5) - 60*b**2*c*e**6*x**4/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9
*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x**5) + 60*b*c**2*d**5*e*log(d/e + x)/(20*d**5*e**7
+ 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x**5) + 137*b*c**2*
d**5*e/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**1
2*x**5) + 300*b*c**2*d**4*e**2*x*log(d/e + x)/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*
e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x**5) + 625*b*c**2*d**4*e**2*x/(20*d**5*e**7 + 100*d**4*e**8*x + 200*
d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x**5) + 600*b*c**2*d**3*e**3*x**2*log(d/e +
x)/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x
**5) + 1100*b*c**2*d**3*e**3*x**2/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 +
100*d*e**11*x**4 + 20*e**12*x**5) + 600*b*c**2*d**2*e**4*x**3*log(d/e + x)/(20*d**5*e**7 + 100*d**4*e**8*x +
200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x**5) + 900*b*c**2*d**2*e**4*x**3/(20*d
**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x**5) + 30
0*b*c**2*d*e**5*x**4*log(d/e + x)/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 +
100*d*e**11*x**4 + 20*e**12*x**5) + 300*b*c**2*d*e**5*x**4/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x*
*2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x**5) + 60*b*c**2*e**6*x**5*log(d/e + x)/(20*d**5*e**7
+ 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x**5) - 120*c**3*d*
*6*log(d/e + x)/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4
+ 20*e**12*x**5) - 274*c**3*d**6/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 +
100*d*e**11*x**4 + 20*e**12*x**5) - 600*c**3*d**5*e*x*log(d/e + x)/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*
e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x**5) - 1250*c**3*d**5*e*x/(20*d**5*e**7 + 100*d
**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x**5) - 1200*c**3*d**4*e**
2*x**2*log(d/e + x)/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x
**4 + 20*e**12*x**5) - 2200*c**3*d**4*e**2*x**2/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**
2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x**5) - 1200*c**3*d**3*e**3*x**3*log(d/e + x)/(20*d**5*e**7 + 100*d
**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x**5) - 1800*c**3*d**3*e**
3*x**3/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**1
2*x**5) - 600*c**3*d**2*e**4*x**4*log(d/e + x)/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2
*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x**5) - 600*c**3*d**2*e**4*x**4/(20*d**5*e**7 + 100*d**4*e**8*x + 20
0*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x**5) - 120*c**3*d*e**5*x**5*log(d/e + x)
/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11*x**4 + 20*e**12*x**5
) + 20*c**3*e**6*x**6/(20*d**5*e**7 + 100*d**4*e**8*x + 200*d**3*e**9*x**2 + 200*d**2*e**10*x**3 + 100*d*e**11
*x**4 + 20*e**12*x**5), Eq(m, -6)), (-a**3*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) - a**2*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) - 4*a**2*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) - a**2*c*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) - 4
*a**2*c*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) - 6*a**2*
c*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) - a*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) - 4*a*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) - 6*a*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) - 6*a*b*c*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) - 24*a*b*c*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) - 36*a*b*c*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) - 24*a*b*c*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) + 12*a*c**2*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) + 25*a*c**2*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) + 48*a*c**2*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) + 88*a*c**2*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) + 72*a*c**2*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) + 108*a*c**2*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) + 48*a*c**2*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) + 48*a*c
**2*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) + 12*a*c**
2*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) -
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) - 4*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) - 6*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) - 4*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) + 12*b**2*c*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) + 25*b**2*c*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) + 48*b**2*c*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) + 88*b**2*c
*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) + 72*b**2*c*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)
+ 108*b**2*c*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) + 48*b**2*c*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) + 48*b**2*c*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) + 12*b**2*c*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) - 60*b*c**2*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) - 125*b*c**2*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) - 240*b*c**2*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) - 440*b*c**2*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) - 360*b*c**2*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) - 540*b*c**2*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) - 240*b*c**2*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) - 240*b*c**2*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) - 60*b*c**2*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) + 12*b*c**2*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*c**3*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*c**3*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*c**3*d**5*e*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*c**3*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*c**3*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*c**3*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*c**3*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*c**3*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*c**3*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*c
**3*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*c**3*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)), (-2*
a**3*e**6/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) - 3*a**2*b*d*e**5/(6*d**3*e**7 + 18*d
**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) - 9*a**2*b*e**6*x/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 +
6*e**10*x**3) - 6*a**2*c*d**2*e**4/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) - 18*a**2*c
*d*e**5*x/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) - 18*a**2*c*e**6*x**2/(6*d**3*e**7 +
18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) - 6*a*b**2*d**2*e**4/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9
*x**2 + 6*e**10*x**3) - 18*a*b**2*d*e**5*x/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) - 18
*a*b**2*e**6*x**2/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) + 36*a*b*c*d**3*e**3*log(d/e
+ x)/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) + 66*a*b*c*d**3*e**3/(6*d**3*e**7 + 18*d**
2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) + 108*a*b*c*d**2*e**4*x*log(d/e + x)/(6*d**3*e**7 + 18*d**2*e**8*x +
18*d*e**9*x**2 + 6*e**10*x**3) + 162*a*b*c*d**2*e**4*x/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**
10*x**3) + 108*a*b*c*d*e**5*x**2*log(d/e + x)/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) +
108*a*b*c*d*e**5*x**2/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) + 36*a*b*c*e**6*x**3*log
(d/e + x)/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) - 72*a*c**2*d**4*e**2*log(d/e + x)/(6
*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) - 132*a*c**2*d**4*e**2/(6*d**3*e**7 + 18*d**2*e**
8*x + 18*d*e**9*x**2 + 6*e**10*x**3) - 216*a*c**2*d**3*e**3*x*log(d/e + x)/(6*d**3*e**7 + 18*d**2*e**8*x + 18*
d*e**9*x**2 + 6*e**10*x**3) - 324*a*c**2*d**3*e**3*x/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*
x**3) - 216*a*c**2*d**2*e**4*x**2*log(d/e + x)/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3)
- 216*a*c**2*d**2*e**4*x**2/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) - 72*a*c**2*d*e**5*
x**3*log(d/e + x)/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) + 18*a*c**2*e**6*x**4/(6*d**3
*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) + 6*b**3*d**3*e**3*log(d/e + x)/(6*d**3*e**7 + 18*d**2
*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) + 11*b**3*d**3*e**3/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 +
6*e**10*x**3) + 18*b**3*d**2*e**4*x*log(d/e + x)/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3
) + 27*b**3*d**2*e**4*x/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) + 18*b**3*d*e**5*x**2*l
og(d/e + x)/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) + 18*b**3*d*e**5*x**2/(6*d**3*e**7
+ 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) + 6*b**3*e**6*x**3*log(d/e + x)/(6*d**3*e**7 + 18*d**2*e**8*
x + 18*d*e**9*x**2 + 6*e**10*x**3) - 72*b**2*c*d**4*e**2*log(d/e + x)/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**
9*x**2 + 6*e**10*x**3) - 132*b**2*c*d**4*e**2/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) -
216*b**2*c*d**3*e**3*x*log(d/e + x)/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) - 324*b**2
*c*d**3*e**3*x/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) - 216*b**2*c*d**2*e**4*x**2*log(
d/e + x)/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) - 216*b**2*c*d**2*e**4*x**2/(6*d**3*e*
*7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) - 72*b**2*c*d*e**5*x**3*log(d/e + x)/(6*d**3*e**7 + 18*d*
*2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) + 18*b**2*c*e**6*x**4/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**
2 + 6*e**10*x**3) + 180*b*c**2*d**5*e*log(d/e + x)/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x*
*3) + 330*b*c**2*d**5*e/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) + 540*b*c**2*d**4*e**2*
x*log(d/e + x)/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) + 810*b*c**2*d**4*e**2*x/(6*d**3
*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) + 540*b*c**2*d**3*e**3*x**2*log(d/e + x)/(6*d**3*e**7
+ 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) + 540*b*c**2*d**3*e**3*x**2/(6*d**3*e**7 + 18*d**2*e**8*x +
18*d*e**9*x**2 + 6*e**10*x**3) + 180*b*c**2*d**2*e**4*x**3*log(d/e + x)/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e
**9*x**2 + 6*e**10*x**3) - 45*b*c**2*d*e**5*x**4/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3
) + 9*b*c**2*e**6*x**5/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) - 120*c**3*d**6*log(d/e
+ x)/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) - 220*c**3*d**6/(6*d**3*e**7 + 18*d**2*e**
8*x + 18*d*e**9*x**2 + 6*e**10*x**3) - 360*c**3*d**5*e*x*log(d/e + x)/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**
9*x**2 + 6*e**10*x**3) - 540*c**3*d**5*e*x/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) - 36
0*c**3*d**4*e**2*x**2*log(d/e + x)/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) - 360*c**3*d
**4*e**2*x**2/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) - 120*c**3*d**3*e**3*x**3*log(d/e
+ x)/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) + 30*c**3*d**2*e**4*x**4/(6*d**3*e**7 + 1
8*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3) - 6*c**3*d*e**5*x**5/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*
x**2 + 6*e**10*x**3) + 2*c**3*e**6*x**6/(6*d**3*e**7 + 18*d**2*e**8*x + 18*d*e**9*x**2 + 6*e**10*x**3), Eq(m,
-4)), (-2*a**3*e**6/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) - 6*a**2*b*d*e**5/(4*d**2*e**7 + 8*d*e**8*x + 4*e
**9*x**2) - 12*a**2*b*e**6*x/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 12*a**2*c*d**2*e**4*log(d/e + x)/(4*d*
*2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 18*a**2*c*d**2*e**4/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 24*a**2*c
*d*e**5*x*log(d/e + x)/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 24*a**2*c*d*e**5*x/(4*d**2*e**7 + 8*d*e**8*x
+ 4*e**9*x**2) + 12*a**2*c*e**6*x**2*log(d/e + x)/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 12*a*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) + 18*a*b**2*d**2*e**4/(4*d**2*e**7 + 8*d*e**8*x + 4*
e**9*x**2) + 24*a*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) + 24*a*b**2*d*e**5*x/(4*
d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 12*a*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) - 72*a*b*c*d**3*e**3*log(d/e + x)/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) - 108*a*b*c*d**3*e**3/(4*d**2*e
**7 + 8*d*e**8*x + 4*e**9*x**2) - 144*a*b*c*d**2*e**4*x*log(d/e + x)/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2)
- 144*a*b*c*d**2*e**4*x/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) - 72*a*b*c*d*e**5*x**2*log(d/e + x)/(4*d**2*e
**7 + 8*d*e**8*x + 4*e**9*x**2) + 24*a*b*c*e**6*x**3/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 72*a*c**2*d**4
*e**2*log(d/e + x)/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 108*a*c**2*d**4*e**2/(4*d**2*e**7 + 8*d*e**8*x +
4*e**9*x**2) + 144*a*c**2*d**3*e**3*x*log(d/e + x)/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 144*a*c**2*d**3
*e**3*x/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 72*a*c**2*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) - 24*a*c**2*d*e**5*x**3/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 6*a*c**2*e**6*x**4/(4*d
**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) - 12*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)
- 18*b**3*d**3*e**3/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) - 24*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) - 24*b**3*d**2*e**4*x/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) - 12*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) + 4*b**3*e**6*x**3/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9
*x**2) + 72*b**2*c*d**4*e**2*log(d/e + x)/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 108*b**2*c*d**4*e**2/(4*d
**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 144*b**2*c*d**3*e**3*x*log(d/e + x)/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*
x**2) + 144*b**2*c*d**3*e**3*x/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 72*b**2*c*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) - 24*b**2*c*d*e**5*x**3/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) +
6*b**2*c*e**6*x**4/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) - 120*b*c**2*d**5*e*log(d/e + x)/(4*d**2*e**7 + 8*
d*e**8*x + 4*e**9*x**2) - 180*b*c**2*d**5*e/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) - 240*b*c**2*d**4*e**2*x*
log(d/e + x)/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) - 240*b*c**2*d**4*e**2*x/(4*d**2*e**7 + 8*d*e**8*x + 4*e
**9*x**2) - 120*b*c**2*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) + 40*b*c**2*d**2*e
**4*x**3/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) - 10*b*c**2*d*e**5*x**4/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x
**2) + 4*b*c**2*e**6*x**5/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 60*c**3*d**6*log(d/e + x)/(4*d**2*e**7 +
8*d*e**8*x + 4*e**9*x**2) + 90*c**3*d**6/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 120*c**3*d**5*e*x*log(d/e
+ x)/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 120*c**3*d**5*e*x/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + 6
0*c**3*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*c**3*d**3*e**3*x**3/(4*d**2*e
**7 + 8*d*e**8*x + 4*e**9*x**2) + 5*c**3*d**2*e**4*x**4/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) - 2*c**3*d*e*
*5*x**5/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2) + c**3*e**6*x**6/(4*d**2*e**7 + 8*d*e**8*x + 4*e**9*x**2), Eq
(m, -3)), (-20*a**3*e**6/(20*d*e**7 + 20*e**8*x) + 60*a**2*b*d*e**5*log(d/e + x)/(20*d*e**7 + 20*e**8*x) + 60*
a**2*b*d*e**5/(20*d*e**7 + 20*e**8*x) + 60*a**2*b*e**6*x*log(d/e + x)/(20*d*e**7 + 20*e**8*x) - 120*a**2*c*d**
2*e**4*log(d/e + x)/(20*d*e**7 + 20*e**8*x) - 120*a**2*c*d**2*e**4/(20*d*e**7 + 20*e**8*x) - 120*a**2*c*d*e**5
*x*log(d/e + x)/(20*d*e**7 + 20*e**8*x) + 60*a**2*c*e**6*x**2/(20*d*e**7 + 20*e**8*x) - 120*a*b**2*d**2*e**4*l
og(d/e + x)/(20*d*e**7 + 20*e**8*x) - 120*a*b**2*d**2*e**4/(20*d*e**7 + 20*e**8*x) - 120*a*b**2*d*e**5*x*log(d
/e + x)/(20*d*e**7 + 20*e**8*x) + 60*a*b**2*e**6*x**2/(20*d*e**7 + 20*e**8*x) + 360*a*b*c*d**3*e**3*log(d/e +
x)/(20*d*e**7 + 20*e**8*x) + 360*a*b*c*d**3*e**3/(20*d*e**7 + 20*e**8*x) + 360*a*b*c*d**2*e**4*x*log(d/e + x)/
(20*d*e**7 + 20*e**8*x) - 180*a*b*c*d*e**5*x**2/(20*d*e**7 + 20*e**8*x) + 60*a*b*c*e**6*x**3/(20*d*e**7 + 20*e
**8*x) - 240*a*c**2*d**4*e**2*log(d/e + x)/(20*d*e**7 + 20*e**8*x) - 240*a*c**2*d**4*e**2/(20*d*e**7 + 20*e**8
*x) - 240*a*c**2*d**3*e**3*x*log(d/e + x)/(20*d*e**7 + 20*e**8*x) + 120*a*c**2*d**2*e**4*x**2/(20*d*e**7 + 20*
e**8*x) - 40*a*c**2*d*e**5*x**3/(20*d*e**7 + 20*e**8*x) + 20*a*c**2*e**6*x**4/(20*d*e**7 + 20*e**8*x) + 60*b**
3*d**3*e**3*log(d/e + x)/(20*d*e**7 + 20*e**8*x) + 60*b**3*d**3*e**3/(20*d*e**7 + 20*e**8*x) + 60*b**3*d**2*e*
*4*x*log(d/e + x)/(20*d*e**7 + 20*e**8*x) - 30*b**3*d*e**5*x**2/(20*d*e**7 + 20*e**8*x) + 10*b**3*e**6*x**3/(2
0*d*e**7 + 20*e**8*x) - 240*b**2*c*d**4*e**2*log(d/e + x)/(20*d*e**7 + 20*e**8*x) - 240*b**2*c*d**4*e**2/(20*d
*e**7 + 20*e**8*x) - 240*b**2*c*d**3*e**3*x*log(d/e + x)/(20*d*e**7 + 20*e**8*x) + 120*b**2*c*d**2*e**4*x**2/(
20*d*e**7 + 20*e**8*x) - 40*b**2*c*d*e**5*x**3/(20*d*e**7 + 20*e**8*x) + 20*b**2*c*e**6*x**4/(20*d*e**7 + 20*e
**8*x) + 300*b*c**2*d**5*e*log(d/e + x)/(20*d*e**7 + 20*e**8*x) + 300*b*c**2*d**5*e/(20*d*e**7 + 20*e**8*x) +
300*b*c**2*d**4*e**2*x*log(d/e + x)/(20*d*e**7 + 20*e**8*x) - 150*b*c**2*d**3*e**3*x**2/(20*d*e**7 + 20*e**8*x
) + 50*b*c**2*d**2*e**4*x**3/(20*d*e**7 + 20*e**8*x) - 25*b*c**2*d*e**5*x**4/(20*d*e**7 + 20*e**8*x) + 15*b*c*
*2*e**6*x**5/(20*d*e**7 + 20*e**8*x) - 120*c**3*d**6*log(d/e + x)/(20*d*e**7 + 20*e**8*x) - 120*c**3*d**6/(20*
d*e**7 + 20*e**8*x) - 120*c**3*d**5*e*x*log(d/e + x)/(20*d*e**7 + 20*e**8*x) + 60*c**3*d**4*e**2*x**2/(20*d*e*
*7 + 20*e**8*x) - 20*c**3*d**3*e**3*x**3/(20*d*e**7 + 20*e**8*x) + 10*c**3*d**2*e**4*x**4/(20*d*e**7 + 20*e**8
*x) - 6*c**3*d*e**5*x**5/(20*d*e**7 + 20*e**8*x) + 4*c**3*e**6*x**6/(20*d*e**7 + 20*e**8*x), Eq(m, -2)), (a**3
*log(d/e + x)/e - 3*a**2*b*d*log(d/e + x)/e**2 + 3*a**2*b*x/e + 3*a**2*c*d**2*log(d/e + x)/e**3 - 3*a**2*c*d*x
/e**2 + 3*a**2*c*x**2/(2*e) + 3*a*b**2*d**2*log(d/e + x)/e**3 - 3*a*b**2*d*x/e**2 + 3*a*b**2*x**2/(2*e) - 6*a*
b*c*d**3*log(d/e + x)/e**4 + 6*a*b*c*d**2*x/e**3 - 3*a*b*c*d*x**2/e**2 + 2*a*b*c*x**3/e + 3*a*c**2*d**4*log(d/
e + x)/e**5 - 3*a*c**2*d**3*x/e**4 + 3*a*c**2*d**2*x**2/(2*e**3) - a*c**2*d*x**3/e**2 + 3*a*c**2*x**4/(4*e) -
b**3*d**3*log(d/e + x)/e**4 + b**3*d**2*x/e**3 - b**3*d*x**2/(2*e**2) + b**3*x**3/(3*e) + 3*b**2*c*d**4*log(d/
e + x)/e**5 - 3*b**2*c*d**3*x/e**4 + 3*b**2*c*d**2*x**2/(2*e**3) - b**2*c*d*x**3/e**2 + 3*b**2*c*x**4/(4*e) -
3*b*c**2*d**5*log(d/e + x)/e**6 + 3*b*c**2*d**4*x/e**5 - 3*b*c**2*d**3*x**2/(2*e**4) + b*c**2*d**2*x**3/e**3 -
3*b*c**2*d*x**4/(4*e**2) + 3*b*c**2*x**5/(5*e) + c**3*d**6*log(d/e + x)/e**7 - c**3*d**5*x/e**6 + c**3*d**4*x
**2/(2*e**5) - c**3*d**3*x**3/(3*e**4) + c**3*d**2*x**4/(4*e**3) - c**3*d*x**5/(5*e**2) + c**3*x**6/(6*e), Eq(
m, -1)), (a**3*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 + 6769*e**7
*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 27*a**3*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) + 295*a**3*
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**3*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**3*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 + 1
3068*e**7*m + 5040*e**7) + 8028*a**3*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**3*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**3*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**3*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**3*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 + 13132*e**7
*m**2 + 13068*e**7*m + 5040*e**7) + 1665*a**3*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**3*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 + 1306
8*e**7*m + 5040*e**7) + 8028*a**3*e**7*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) + 5040*a**3*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 + 5040*e**7
) - 3*a**2*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) - 75*a**2*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) - 735
*a**2*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 + 6769*e**7*m**
3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 3525*a**2*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) - 8262*a
**2*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 + 1
3132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 7560*a**2*b*d**2*e**5*(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) + 3*a**2*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) + 75*a**2*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) + 735*a**2*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 + 1
3068*e**7*m + 5040*e**7) + 3525*a**2*b*d*e**6*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) + 8262*a**2*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) + 7560*a**2*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) + 3*a**2*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) + 78*a**2*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) + 810*a**2*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 + 13068*e**7*m + 5040
*e**7) + 4260*a**2*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) + 11787*a**2*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 + 13068*e**7*m + 5040*
e**7) + 15822*a**2*b*e**7*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 + 676
9*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 7560*a**2*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) + 6
*a**2*c*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) + 132*a**2*c*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) + 1074*a*
*2*c*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) + 3828*a**2*c*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) + 5040*a**2*c*
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) - 6*a**2*c*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) - 132*a**2*c*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 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*
m**2 + 13068*e**7*m + 5040*e**7) - 1074*a**2*c*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) - 3828*a**2*c*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) - 5040*a**2*c*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) + 3*a**2*c*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) + 69*a**2*c*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) + 603*a**2*c*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) + 2451*a**2*c*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) + 4434*a**2*c*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) + 2520*a**2*c*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) + 3*a**2*c*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) + 75*a**2*c*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) + 741*a**2*c*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) + 3657*a**2*c*e**7*m**3*x**3*(d + e*x)**m/(e**7*m**7 + 28*e**7*m**6 + 322*e**7*m**5 + 196
0*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 9336*a**2*c*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 + 5040*e**7) + 11388*a**2*c*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) + 5040*a**2*c*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 + 5
040*e**7) + 6*a*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) + 132*a*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) + 1074*a*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 + 676
9*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 3828*a*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) +
5040*a*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) - 6*a*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) - 132*a*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 + 1960*e**7*m**4 + 6769*e**7*m**3
+ 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 1074*a*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) - 3828*a
*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) - 5040*a*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) + 3*a*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) + 69*a*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) + 603*a*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 + 1
3132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 2451*a*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) + 4434*a*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) + 2520*a*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) + 3*a*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) + 75*a*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) + 741*a*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) + 3657*a*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 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 9336*a*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 + 5040*e**7) + 11388*a*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) + 5040*a*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 + 130
68*e**7*m + 5040*e**7) - 36*a*b*c*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) - 648*a*b*c*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 + 5040*e**7) - 3852*a*b*c*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) - 7560*a*b*c*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) + 36*a*b*c*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) + 648*a*b*c*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)
+ 3852*a*b*c*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) + 7560*a*b*c*d**3*e**4*m*x*(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) -
18*a*b*c*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) - 342*a*b*c*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)
- 2250*a*b*c*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 + 67
69*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 5706*a*b*c*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) - 3780*a*b*c*d**2*e**5*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) + 6*a*b*c*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) + 126*a*b*c*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 + 676
9*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 978*a*b*c*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
) + 3402*a*b*c*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) + 5064*a*b*c*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
) + 2520*a*b*c*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) + 6*a*b*c*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) + 144*
a*b*c*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) + 1356*a*b*c*e**7*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) + 6336*a*b*
c*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 + 13
132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 15270*a*b*c*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) + 17712*a*b*c*
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) + 7560*a*b*c*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) + 72*a*c**2*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) + 936*a*c**2*d**5*e**2*m*(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) + 3024*a*c**2*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 + 13068*e**7
*m + 5040*e**7) - 72*a*c**2*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) - 936*a*c**2*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) - 3024*a*c**2*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) + 36*a*c**2*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) + 504*a*c**2*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) + 1980*a*c**2*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 + 1306
8*e**7*m + 5040*e**7) + 1512*a*c**2*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) - 12*a*c**2*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 + 1
3068*e**7*m + 5040*e**7) - 192*a*c**2*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) - 996*a*c**2*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) - 1824*a*c**2*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) - 1008*a*c**2*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) + 3*a*c**2*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) + 57*a*c**2*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) + 393*a*c**2*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) + 1203*a*c**2*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) + 1620*a*c**2*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) + 756*a*c**2*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) + 3*a*c**2*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) + 69*a*c**2*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 + 1
3068*e**7*m + 5040*e**7) + 621*a*c**2*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) + 2775*a*c**2*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 + 1306
8*e**7*m + 5040*e**7) + 6432*a*c**2*e**7*m**2*x**5*(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) + 7236*a*c**2*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) + 3024*a*c**2*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) - 6*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) - 108*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 + 5040*e**7) - 642*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) - 1260
*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 + 131
32*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 6*b**3*d**3*e**4*m**4*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) + 108*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) + 642*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) + 1260*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) - 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) - 57*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) - 375*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) - 951*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) - 630*b**3*d**2*e**5*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) + 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 + 1306
8*e**7*m + 5040*e**7) + 21*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) + 163*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) + 567*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) + 844*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) + 420*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) + 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)
+ 24*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) + 226*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 + 1960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 1056*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 + 1
3132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 2545*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) + 2952*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) + 1260*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) + 72*b**2*c*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 + 130
68*e**7*m + 5040*e**7) + 936*b**2*c*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) + 3024*b**2*c*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 + 13068*e**7*m +
5040*e**7) - 72*b**2*c*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) - 936*b**2*c*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) - 3024*b**2*c*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) + 36*b**2*c*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) + 504*b**2*c*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) + 1980*b**2*c*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) + 1512*b**2*c*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) - 12*b**2*c*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) - 192*b**2*c*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) - 996*b**2*c*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) - 1824*b**2*c*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) - 1008*b**2*c*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) + 3*b**2*c*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) + 57*b**2*c*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) + 393*b**2*c*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) + 1203*b**2*c*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) + 1620*b**2*c*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) + 756*b**2*c*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) + 3*b**2*c*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) + 69*b**2*c*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) + 621*b**2*c*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) + 2775*b**2*c*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) + 6432*b**2*c*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) + 7236*b**2*c*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) + 3024*b**2*c*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) - 360*b*c**2*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) -
2520*b*c**2*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) + 360*b*c**2*d**5*e**2*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) + 2520*b*c
**2*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 + 1
3132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 180*b*c**2*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) - 1440*b*
c**2*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 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 1260*b*c**2*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) + 60
*b*c**2*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) + 600*b*c**2*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)
+ 1380*b*c**2*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 + 6
769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 840*b*c**2*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) - 15*b*c**2*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 +
6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 195*b*c**2*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 + 5
040*e**7) - 795*b*c**2*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) - 1245*b*c**2*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) - 630*b*c**2*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) + 3*b*c**2*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) + 51*b*c**2*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) + 315*b*c**2*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) + 885*b*c**2*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) + 1122*b*c**2*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) + 504*b*c**2*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) + 3*b*c**2*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 + 504
0*e**7) + 66*b*c**2*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 + 6
769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 570*b*c**2*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) + 2460*b*c**2*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 + 6769
*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 5547*b*c**2*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)
+ 6114*b*c**2*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) + 2520*b*c**2*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) + 720*c**
3*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*c**3*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*c**3*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 + 1
3068*e**7*m + 5040*e**7) + 360*c**3*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*c**3*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 + 13
068*e**7*m + 5040*e**7) - 360*c**3*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*c**3*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 + 130
68*e**7*m + 5040*e**7) + 30*c**3*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*c**3*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 + 13
068*e**7*m + 5040*e**7) + 330*c**3*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*c**3*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 + 130
68*e**7*m + 5040*e**7) - 6*c**3*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 + 1
960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) - 60*c**3*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 + 1306
8*e**7*m + 5040*e**7) - 210*c**3*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*c**3*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 + 13
068*e**7*m + 5040*e**7) - 144*c**3*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 + 1
960*e**7*m**4 + 6769*e**7*m**3 + 13132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + c**3*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*c**3*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*c**3*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 + 5
040*e**7) + 225*c**3*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*c**3*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*c**3*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) + c**3*e**7*m**6*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) + 21*c*
*3*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 + 1
3132*e**7*m**2 + 13068*e**7*m + 5040*e**7) + 175*c**3*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*c**3*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 + 13132*e**
7*m**2 + 13068*e**7*m + 5040*e**7) + 1624*c**3*e**7*m**2*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) + 1764*c**3*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*c**3*e**7*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), True))

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 1132 vs. \(2 (305) = 610\).

Time = 0.24 (sec) , antiderivative size = 1132, normalized size of antiderivative = 3.71 \[ \int (d+e x)^m \left (a+b x+c x^2\right )^3 \, dx=\text {Too large to display} \]

[In]

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

[Out]

3*(e^2*(m + 1)*x^2 + d*e*m*x - d^2)*(e*x + d)^m*a^2*b/((m^2 + 3*m + 2)*e^2) + (e*x + d)^(m + 1)*a^3/(e*(m + 1)
) + 3*((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*b^2/((m^3 + 6*m^2 +
11*m + 6)*e^3) + 3*((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^2*c/((m
^3 + 6*m^2 + 11*m + 6)*e^3) + ((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^3/((m^4 + 10*m^3 + 35*m^2 + 50*m + 24)*e^4) + 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*a*b*c/((m^4 + 10*m^3 + 35*m^2 + 50*m + 24)*e^4) + 3*((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^2*c/((m^5 + 15*m^4 + 85*m^3 + 225*m^2 + 274*m + 120)*e^5) + 3*((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*c^2/((m^5 + 15*m^4 + 85*m^3 + 225*m^2 + 274*m + 120)*e^5
) + 3*((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*c^2/((m^6 + 21*m^5 + 175*m^4 + 735*m^3 + 1624*m^2 + 1764*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 + 72
0*d^7)*(e*x + d)^m*c^3/((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. 5388 vs. \(2 (305) = 610\).

Time = 0.31 (sec) , antiderivative size = 5388, normalized size of antiderivative = 17.67 \[ \int (d+e x)^m \left (a+b x+c x^2\right )^3 \, dx=\text {Too large to display} \]

[In]

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

[Out]

((e*x + d)^m*c^3*e^7*m^6*x^7 + (e*x + d)^m*c^3*d*e^6*m^6*x^6 + 3*(e*x + d)^m*b*c^2*e^7*m^6*x^6 + 21*(e*x + d)^
m*c^3*e^7*m^5*x^7 + 3*(e*x + d)^m*b*c^2*d*e^6*m^6*x^5 + 3*(e*x + d)^m*b^2*c*e^7*m^6*x^5 + 3*(e*x + d)^m*a*c^2*
e^7*m^6*x^5 + 15*(e*x + d)^m*c^3*d*e^6*m^5*x^6 + 66*(e*x + d)^m*b*c^2*e^7*m^5*x^6 + 175*(e*x + d)^m*c^3*e^7*m^
4*x^7 + 3*(e*x + d)^m*b^2*c*d*e^6*m^6*x^4 + 3*(e*x + d)^m*a*c^2*d*e^6*m^6*x^4 + (e*x + d)^m*b^3*e^7*m^6*x^4 +
6*(e*x + d)^m*a*b*c*e^7*m^6*x^4 - 6*(e*x + d)^m*c^3*d^2*e^5*m^5*x^5 + 51*(e*x + d)^m*b*c^2*d*e^6*m^5*x^5 + 69*
(e*x + d)^m*b^2*c*e^7*m^5*x^5 + 69*(e*x + d)^m*a*c^2*e^7*m^5*x^5 + 85*(e*x + d)^m*c^3*d*e^6*m^4*x^6 + 570*(e*x
+ d)^m*b*c^2*e^7*m^4*x^6 + 735*(e*x + d)^m*c^3*e^7*m^3*x^7 + (e*x + d)^m*b^3*d*e^6*m^6*x^3 + 6*(e*x + d)^m*a*
b*c*d*e^6*m^6*x^3 + 3*(e*x + d)^m*a*b^2*e^7*m^6*x^3 + 3*(e*x + d)^m*a^2*c*e^7*m^6*x^3 - 15*(e*x + d)^m*b*c^2*d
^2*e^5*m^5*x^4 + 57*(e*x + d)^m*b^2*c*d*e^6*m^5*x^4 + 57*(e*x + d)^m*a*c^2*d*e^6*m^5*x^4 + 24*(e*x + d)^m*b^3*
e^7*m^5*x^4 + 144*(e*x + d)^m*a*b*c*e^7*m^5*x^4 - 60*(e*x + d)^m*c^3*d^2*e^5*m^4*x^5 + 315*(e*x + d)^m*b*c^2*d
*e^6*m^4*x^5 + 621*(e*x + d)^m*b^2*c*e^7*m^4*x^5 + 621*(e*x + d)^m*a*c^2*e^7*m^4*x^5 + 225*(e*x + d)^m*c^3*d*e
^6*m^3*x^6 + 2460*(e*x + d)^m*b*c^2*e^7*m^3*x^6 + 1624*(e*x + d)^m*c^3*e^7*m^2*x^7 + 3*(e*x + d)^m*a*b^2*d*e^6
*m^6*x^2 + 3*(e*x + d)^m*a^2*c*d*e^6*m^6*x^2 + 3*(e*x + d)^m*a^2*b*e^7*m^6*x^2 - 12*(e*x + d)^m*b^2*c*d^2*e^5*
m^5*x^3 - 12*(e*x + d)^m*a*c^2*d^2*e^5*m^5*x^3 + 21*(e*x + d)^m*b^3*d*e^6*m^5*x^3 + 126*(e*x + d)^m*a*b*c*d*e^
6*m^5*x^3 + 75*(e*x + d)^m*a*b^2*e^7*m^5*x^3 + 75*(e*x + d)^m*a^2*c*e^7*m^5*x^3 + 30*(e*x + d)^m*c^3*d^3*e^4*m
^4*x^4 - 195*(e*x + d)^m*b*c^2*d^2*e^5*m^4*x^4 + 393*(e*x + d)^m*b^2*c*d*e^6*m^4*x^4 + 393*(e*x + d)^m*a*c^2*d
*e^6*m^4*x^4 + 226*(e*x + d)^m*b^3*e^7*m^4*x^4 + 1356*(e*x + d)^m*a*b*c*e^7*m^4*x^4 - 210*(e*x + d)^m*c^3*d^2*
e^5*m^3*x^5 + 885*(e*x + d)^m*b*c^2*d*e^6*m^3*x^5 + 2775*(e*x + d)^m*b^2*c*e^7*m^3*x^5 + 2775*(e*x + d)^m*a*c^
2*e^7*m^3*x^5 + 274*(e*x + d)^m*c^3*d*e^6*m^2*x^6 + 5547*(e*x + d)^m*b*c^2*e^7*m^2*x^6 + 1764*(e*x + d)^m*c^3*
e^7*m*x^7 + 3*(e*x + d)^m*a^2*b*d*e^6*m^6*x + (e*x + d)^m*a^3*e^7*m^6*x - 3*(e*x + d)^m*b^3*d^2*e^5*m^5*x^2 -
18*(e*x + d)^m*a*b*c*d^2*e^5*m^5*x^2 + 69*(e*x + d)^m*a*b^2*d*e^6*m^5*x^2 + 69*(e*x + d)^m*a^2*c*d*e^6*m^5*x^2
+ 78*(e*x + d)^m*a^2*b*e^7*m^5*x^2 + 60*(e*x + d)^m*b*c^2*d^3*e^4*m^4*x^3 - 192*(e*x + d)^m*b^2*c*d^2*e^5*m^4
*x^3 - 192*(e*x + d)^m*a*c^2*d^2*e^5*m^4*x^3 + 163*(e*x + d)^m*b^3*d*e^6*m^4*x^3 + 978*(e*x + d)^m*a*b*c*d*e^6
*m^4*x^3 + 741*(e*x + d)^m*a*b^2*e^7*m^4*x^3 + 741*(e*x + d)^m*a^2*c*e^7*m^4*x^3 + 180*(e*x + d)^m*c^3*d^3*e^4
*m^3*x^4 - 795*(e*x + d)^m*b*c^2*d^2*e^5*m^3*x^4 + 1203*(e*x + d)^m*b^2*c*d*e^6*m^3*x^4 + 1203*(e*x + d)^m*a*c
^2*d*e^6*m^3*x^4 + 1056*(e*x + d)^m*b^3*e^7*m^3*x^4 + 6336*(e*x + d)^m*a*b*c*e^7*m^3*x^4 - 300*(e*x + d)^m*c^3
*d^2*e^5*m^2*x^5 + 1122*(e*x + d)^m*b*c^2*d*e^6*m^2*x^5 + 6432*(e*x + d)^m*b^2*c*e^7*m^2*x^5 + 6432*(e*x + d)^
m*a*c^2*e^7*m^2*x^5 + 120*(e*x + d)^m*c^3*d*e^6*m*x^6 + 6114*(e*x + d)^m*b*c^2*e^7*m*x^6 + 720*(e*x + d)^m*c^3
*e^7*x^7 + (e*x + d)^m*a^3*d*e^6*m^6 - 6*(e*x + d)^m*a*b^2*d^2*e^5*m^5*x - 6*(e*x + d)^m*a^2*c*d^2*e^5*m^5*x +
75*(e*x + d)^m*a^2*b*d*e^6*m^5*x + 27*(e*x + d)^m*a^3*e^7*m^5*x + 36*(e*x + d)^m*b^2*c*d^3*e^4*m^4*x^2 + 36*(
e*x + d)^m*a*c^2*d^3*e^4*m^4*x^2 - 57*(e*x + d)^m*b^3*d^2*e^5*m^4*x^2 - 342*(e*x + d)^m*a*b*c*d^2*e^5*m^4*x^2
+ 603*(e*x + d)^m*a*b^2*d*e^6*m^4*x^2 + 603*(e*x + d)^m*a^2*c*d*e^6*m^4*x^2 + 810*(e*x + d)^m*a^2*b*e^7*m^4*x^
2 - 120*(e*x + d)^m*c^3*d^4*e^3*m^3*x^3 + 600*(e*x + d)^m*b*c^2*d^3*e^4*m^3*x^3 - 996*(e*x + d)^m*b^2*c*d^2*e^
5*m^3*x^3 - 996*(e*x + d)^m*a*c^2*d^2*e^5*m^3*x^3 + 567*(e*x + d)^m*b^3*d*e^6*m^3*x^3 + 3402*(e*x + d)^m*a*b*c
*d*e^6*m^3*x^3 + 3657*(e*x + d)^m*a*b^2*e^7*m^3*x^3 + 3657*(e*x + d)^m*a^2*c*e^7*m^3*x^3 + 330*(e*x + d)^m*c^3
*d^3*e^4*m^2*x^4 - 1245*(e*x + d)^m*b*c^2*d^2*e^5*m^2*x^4 + 1620*(e*x + d)^m*b^2*c*d*e^6*m^2*x^4 + 1620*(e*x +
d)^m*a*c^2*d*e^6*m^2*x^4 + 2545*(e*x + d)^m*b^3*e^7*m^2*x^4 + 15270*(e*x + d)^m*a*b*c*e^7*m^2*x^4 - 144*(e*x
+ d)^m*c^3*d^2*e^5*m*x^5 + 504*(e*x + d)^m*b*c^2*d*e^6*m*x^5 + 7236*(e*x + d)^m*b^2*c*e^7*m*x^5 + 7236*(e*x +
d)^m*a*c^2*e^7*m*x^5 + 2520*(e*x + d)^m*b*c^2*e^7*x^6 - 3*(e*x + d)^m*a^2*b*d^2*e^5*m^5 + 27*(e*x + d)^m*a^3*d
*e^6*m^5 + 6*(e*x + d)^m*b^3*d^3*e^4*m^4*x + 36*(e*x + d)^m*a*b*c*d^3*e^4*m^4*x - 132*(e*x + d)^m*a*b^2*d^2*e^
5*m^4*x - 132*(e*x + d)^m*a^2*c*d^2*e^5*m^4*x + 735*(e*x + d)^m*a^2*b*d*e^6*m^4*x + 295*(e*x + d)^m*a^3*e^7*m^
4*x - 180*(e*x + d)^m*b*c^2*d^4*e^3*m^3*x^2 + 504*(e*x + d)^m*b^2*c*d^3*e^4*m^3*x^2 + 504*(e*x + d)^m*a*c^2*d^
3*e^4*m^3*x^2 - 375*(e*x + d)^m*b^3*d^2*e^5*m^3*x^2 - 2250*(e*x + d)^m*a*b*c*d^2*e^5*m^3*x^2 + 2451*(e*x + d)^
m*a*b^2*d*e^6*m^3*x^2 + 2451*(e*x + d)^m*a^2*c*d*e^6*m^3*x^2 + 4260*(e*x + d)^m*a^2*b*e^7*m^3*x^2 - 360*(e*x +
d)^m*c^3*d^4*e^3*m^2*x^3 + 1380*(e*x + d)^m*b*c^2*d^3*e^4*m^2*x^3 - 1824*(e*x + d)^m*b^2*c*d^2*e^5*m^2*x^3 -
1824*(e*x + d)^m*a*c^2*d^2*e^5*m^2*x^3 + 844*(e*x + d)^m*b^3*d*e^6*m^2*x^3 + 5064*(e*x + d)^m*a*b*c*d*e^6*m^2*
x^3 + 9336*(e*x + d)^m*a*b^2*e^7*m^2*x^3 + 9336*(e*x + d)^m*a^2*c*e^7*m^2*x^3 + 180*(e*x + d)^m*c^3*d^3*e^4*m*
x^4 - 630*(e*x + d)^m*b*c^2*d^2*e^5*m*x^4 + 756*(e*x + d)^m*b^2*c*d*e^6*m*x^4 + 756*(e*x + d)^m*a*c^2*d*e^6*m*
x^4 + 2952*(e*x + d)^m*b^3*e^7*m*x^4 + 17712*(e*x + d)^m*a*b*c*e^7*m*x^4 + 3024*(e*x + d)^m*b^2*c*e^7*x^5 + 30
24*(e*x + d)^m*a*c^2*e^7*x^5 + 6*(e*x + d)^m*a*b^2*d^3*e^4*m^4 + 6*(e*x + d)^m*a^2*c*d^3*e^4*m^4 - 75*(e*x + d
)^m*a^2*b*d^2*e^5*m^4 + 295*(e*x + d)^m*a^3*d*e^6*m^4 - 72*(e*x + d)^m*b^2*c*d^4*e^3*m^3*x - 72*(e*x + d)^m*a*
c^2*d^4*e^3*m^3*x + 108*(e*x + d)^m*b^3*d^3*e^4*m^3*x + 648*(e*x + d)^m*a*b*c*d^3*e^4*m^3*x - 1074*(e*x + d)^m
*a*b^2*d^2*e^5*m^3*x - 1074*(e*x + d)^m*a^2*c*d^2*e^5*m^3*x + 3525*(e*x + d)^m*a^2*b*d*e^6*m^3*x + 1665*(e*x +
d)^m*a^3*e^7*m^3*x + 360*(e*x + d)^m*c^3*d^5*e^2*m^2*x^2 - 1440*(e*x + d)^m*b*c^2*d^4*e^3*m^2*x^2 + 1980*(e*x
+ d)^m*b^2*c*d^3*e^4*m^2*x^2 + 1980*(e*x + d)^m*a*c^2*d^3*e^4*m^2*x^2 - 951*(e*x + d)^m*b^3*d^2*e^5*m^2*x^2 -
5706*(e*x + d)^m*a*b*c*d^2*e^5*m^2*x^2 + 4434*(e*x + d)^m*a*b^2*d*e^6*m^2*x^2 + 4434*(e*x + d)^m*a^2*c*d*e^6*
m^2*x^2 + 11787*(e*x + d)^m*a^2*b*e^7*m^2*x^2 - 240*(e*x + d)^m*c^3*d^4*e^3*m*x^3 + 840*(e*x + d)^m*b*c^2*d^3*
e^4*m*x^3 - 1008*(e*x + d)^m*b^2*c*d^2*e^5*m*x^3 - 1008*(e*x + d)^m*a*c^2*d^2*e^5*m*x^3 + 420*(e*x + d)^m*b^3*
d*e^6*m*x^3 + 2520*(e*x + d)^m*a*b*c*d*e^6*m*x^3 + 11388*(e*x + d)^m*a*b^2*e^7*m*x^3 + 11388*(e*x + d)^m*a^2*c
*e^7*m*x^3 + 1260*(e*x + d)^m*b^3*e^7*x^4 + 7560*(e*x + d)^m*a*b*c*e^7*x^4 - 6*(e*x + d)^m*b^3*d^4*e^3*m^3 - 3
6*(e*x + d)^m*a*b*c*d^4*e^3*m^3 + 132*(e*x + d)^m*a*b^2*d^3*e^4*m^3 + 132*(e*x + d)^m*a^2*c*d^3*e^4*m^3 - 735*
(e*x + d)^m*a^2*b*d^2*e^5*m^3 + 1665*(e*x + d)^m*a^3*d*e^6*m^3 + 360*(e*x + d)^m*b*c^2*d^5*e^2*m^2*x - 936*(e*
x + d)^m*b^2*c*d^4*e^3*m^2*x - 936*(e*x + d)^m*a*c^2*d^4*e^3*m^2*x + 642*(e*x + d)^m*b^3*d^3*e^4*m^2*x + 3852*
(e*x + d)^m*a*b*c*d^3*e^4*m^2*x - 3828*(e*x + d)^m*a*b^2*d^2*e^5*m^2*x - 3828*(e*x + d)^m*a^2*c*d^2*e^5*m^2*x
+ 8262*(e*x + d)^m*a^2*b*d*e^6*m^2*x + 5104*(e*x + d)^m*a^3*e^7*m^2*x + 360*(e*x + d)^m*c^3*d^5*e^2*m*x^2 - 12
60*(e*x + d)^m*b*c^2*d^4*e^3*m*x^2 + 1512*(e*x + d)^m*b^2*c*d^3*e^4*m*x^2 + 1512*(e*x + d)^m*a*c^2*d^3*e^4*m*x
^2 - 630*(e*x + d)^m*b^3*d^2*e^5*m*x^2 - 3780*(e*x + d)^m*a*b*c*d^2*e^5*m*x^2 + 2520*(e*x + d)^m*a*b^2*d*e^6*m
*x^2 + 2520*(e*x + d)^m*a^2*c*d*e^6*m*x^2 + 15822*(e*x + d)^m*a^2*b*e^7*m*x^2 + 5040*(e*x + d)^m*a*b^2*e^7*x^3
+ 5040*(e*x + d)^m*a^2*c*e^7*x^3 + 72*(e*x + d)^m*b^2*c*d^5*e^2*m^2 + 72*(e*x + d)^m*a*c^2*d^5*e^2*m^2 - 108*
(e*x + d)^m*b^3*d^4*e^3*m^2 - 648*(e*x + d)^m*a*b*c*d^4*e^3*m^2 + 1074*(e*x + d)^m*a*b^2*d^3*e^4*m^2 + 1074*(e
*x + d)^m*a^2*c*d^3*e^4*m^2 - 3525*(e*x + d)^m*a^2*b*d^2*e^5*m^2 + 5104*(e*x + d)^m*a^3*d*e^6*m^2 - 720*(e*x +
d)^m*c^3*d^6*e*m*x + 2520*(e*x + d)^m*b*c^2*d^5*e^2*m*x - 3024*(e*x + d)^m*b^2*c*d^4*e^3*m*x - 3024*(e*x + d)
^m*a*c^2*d^4*e^3*m*x + 1260*(e*x + d)^m*b^3*d^3*e^4*m*x + 7560*(e*x + d)^m*a*b*c*d^3*e^4*m*x - 5040*(e*x + d)^
m*a*b^2*d^2*e^5*m*x - 5040*(e*x + d)^m*a^2*c*d^2*e^5*m*x + 7560*(e*x + d)^m*a^2*b*d*e^6*m*x + 8028*(e*x + d)^m
*a^3*e^7*m*x + 7560*(e*x + d)^m*a^2*b*e^7*x^2 - 360*(e*x + d)^m*b*c^2*d^6*e*m + 936*(e*x + d)^m*b^2*c*d^5*e^2*
m + 936*(e*x + d)^m*a*c^2*d^5*e^2*m - 642*(e*x + d)^m*b^3*d^4*e^3*m - 3852*(e*x + d)^m*a*b*c*d^4*e^3*m + 3828*
(e*x + d)^m*a*b^2*d^3*e^4*m + 3828*(e*x + d)^m*a^2*c*d^3*e^4*m - 8262*(e*x + d)^m*a^2*b*d^2*e^5*m + 8028*(e*x
+ d)^m*a^3*d*e^6*m + 5040*(e*x + d)^m*a^3*e^7*x + 720*(e*x + d)^m*c^3*d^7 - 2520*(e*x + d)^m*b*c^2*d^6*e + 302
4*(e*x + d)^m*b^2*c*d^5*e^2 + 3024*(e*x + d)^m*a*c^2*d^5*e^2 - 1260*(e*x + d)^m*b^3*d^4*e^3 - 7560*(e*x + d)^m
*a*b*c*d^4*e^3 + 5040*(e*x + d)^m*a*b^2*d^3*e^4 + 5040*(e*x + d)^m*a^2*c*d^3*e^4 - 7560*(e*x + d)^m*a^2*b*d^2*
e^5 + 5040*(e*x + d)^m*a^3*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 = 11.56 (sec) , antiderivative size = 2542, normalized size of antiderivative = 8.33 \[ \int (d+e x)^m \left (a+b x+c x^2\right )^3 \, dx=\text {Too large to display} \]

[In]

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

[Out]

((d + e*x)^m*(720*c^3*d^7 + 5040*a^3*d*e^6 - 1260*b^3*d^4*e^3 + 5040*a*b^2*d^3*e^4 - 7560*a^2*b*d^2*e^5 + 3024
*a*c^2*d^5*e^2 + 5040*a^2*c*d^3*e^4 + 3024*b^2*c*d^5*e^2 + 5104*a^3*d*e^6*m^2 + 1665*a^3*d*e^6*m^3 + 295*a^3*d
*e^6*m^4 + 27*a^3*d*e^6*m^5 + a^3*d*e^6*m^6 - 642*b^3*d^4*e^3*m - 108*b^3*d^4*e^3*m^2 - 6*b^3*d^4*e^3*m^3 - 25
20*b*c^2*d^6*e + 8028*a^3*d*e^6*m - 7560*a*b*c*d^4*e^3 - 360*b*c^2*d^6*e*m + 3828*a*b^2*d^3*e^4*m - 8262*a^2*b
*d^2*e^5*m + 936*a*c^2*d^5*e^2*m + 3828*a^2*c*d^3*e^4*m + 936*b^2*c*d^5*e^2*m + 1074*a*b^2*d^3*e^4*m^2 - 3525*
a^2*b*d^2*e^5*m^2 + 132*a*b^2*d^3*e^4*m^3 - 735*a^2*b*d^2*e^5*m^3 + 6*a*b^2*d^3*e^4*m^4 - 75*a^2*b*d^2*e^5*m^4
- 3*a^2*b*d^2*e^5*m^5 + 72*a*c^2*d^5*e^2*m^2 + 1074*a^2*c*d^3*e^4*m^2 + 132*a^2*c*d^3*e^4*m^3 + 6*a^2*c*d^3*e
^4*m^4 + 72*b^2*c*d^5*e^2*m^2 - 3852*a*b*c*d^4*e^3*m - 648*a*b*c*d^4*e^3*m^2 - 36*a*b*c*d^4*e^3*m^3))/(e^7*(13
068*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^3*e^7 + 802
8*a^3*e^7*m + 5104*a^3*e^7*m^2 + 1665*a^3*e^7*m^3 + 295*a^3*e^7*m^4 + 27*a^3*e^7*m^5 + a^3*e^7*m^6 + 1260*b^3*
d^3*e^4*m + 642*b^3*d^3*e^4*m^2 + 108*b^3*d^3*e^4*m^3 + 6*b^3*d^3*e^4*m^4 - 720*c^3*d^6*e*m + 7560*a^2*b*d*e^6
*m - 5040*a*b^2*d^2*e^5*m + 8262*a^2*b*d*e^6*m^2 + 3525*a^2*b*d*e^6*m^3 + 735*a^2*b*d*e^6*m^4 + 75*a^2*b*d*e^6
*m^5 + 3*a^2*b*d*e^6*m^6 - 3024*a*c^2*d^4*e^3*m - 5040*a^2*c*d^2*e^5*m + 2520*b*c^2*d^5*e^2*m - 3024*b^2*c*d^4
*e^3*m - 3828*a*b^2*d^2*e^5*m^2 - 1074*a*b^2*d^2*e^5*m^3 - 132*a*b^2*d^2*e^5*m^4 - 6*a*b^2*d^2*e^5*m^5 - 936*a
*c^2*d^4*e^3*m^2 - 3828*a^2*c*d^2*e^5*m^2 - 72*a*c^2*d^4*e^3*m^3 - 1074*a^2*c*d^2*e^5*m^3 - 132*a^2*c*d^2*e^5*
m^4 - 6*a^2*c*d^2*e^5*m^5 + 360*b*c^2*d^5*e^2*m^2 - 936*b^2*c*d^4*e^3*m^2 - 72*b^2*c*d^4*e^3*m^3 + 7560*a*b*c*
d^3*e^4*m + 3852*a*b*c*d^3*e^4*m^2 + 648*a*b*c*d^3*e^4*m^3 + 36*a*b*c*d^3*e^4*m^4))/(e^7*(13068*m + 13132*m^2
+ 6769*m^3 + 1960*m^4 + 322*m^5 + 28*m^6 + m^7 + 5040)) + (c^3*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*x^2*(m + 1)*(d + e*x)^m*(2520*a^2*b*e^5 + 120*c^3*d^5*m + 1175*a^2*b*e^5*m^2 + 245*a^2*b*e^5*m^3 + 25*a^2*b*
e^5*m^4 + a^2*b*e^5*m^5 - 210*b^3*d^2*e^3*m - 107*b^3*d^2*e^3*m^2 - 18*b^3*d^2*e^3*m^3 - b^3*d^2*e^3*m^4 + 275
4*a^2*b*e^5*m + 840*a*b^2*d*e^4*m + 840*a^2*c*d*e^4*m - 420*b*c^2*d^4*e*m + 638*a*b^2*d*e^4*m^2 + 179*a*b^2*d*
e^4*m^3 + 22*a*b^2*d*e^4*m^4 + a*b^2*d*e^4*m^5 + 504*a*c^2*d^3*e^2*m + 638*a^2*c*d*e^4*m^2 + 179*a^2*c*d*e^4*m
^3 + 22*a^2*c*d*e^4*m^4 + a^2*c*d*e^4*m^5 + 504*b^2*c*d^3*e^2*m - 60*b*c^2*d^4*e*m^2 + 156*a*c^2*d^3*e^2*m^2 +
12*a*c^2*d^3*e^2*m^3 + 156*b^2*c*d^3*e^2*m^2 + 12*b^2*c*d^3*e^2*m^3 - 1260*a*b*c*d^2*e^3*m - 642*a*b*c*d^2*e^
3*m^2 - 108*a*b*c*d^2*e^3*m^3 - 6*a*b*c*d^2*e^3*m^4))/(e^5*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^
5 + 28*m^6 + m^7 + 5040)) + (x^4*(d + e*x)^m*(11*m + 6*m^2 + m^3 + 6)*(210*b^3*e^3 + 107*b^3*e^3*m + 30*c^3*d^
3*m + 18*b^3*e^3*m^2 + b^3*e^3*m^3 + 1260*a*b*c*e^3 + 108*a*b*c*e^3*m^2 + 6*a*b*c*e^3*m^3 + 126*a*c^2*d*e^2*m
- 105*b*c^2*d^2*e*m + 126*b^2*c*d*e^2*m + 39*a*c^2*d*e^2*m^2 + 3*a*c^2*d*e^2*m^3 - 15*b*c^2*d^2*e*m^2 + 39*b^2
*c*d*e^2*m^2 + 3*b^2*c*d*e^2*m^3 + 642*a*b*c*e^3*m))/(e^3*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5
+ 28*m^6 + m^7 + 5040)) + (x^3*(d + e*x)^m*(3*m + m^2 + 2)*(2520*a*b^2*e^4 + 2520*a^2*c*e^4 - 120*c^3*d^4*m +
537*a*b^2*e^4*m^2 + 66*a*b^2*e^4*m^3 + 3*a*b^2*e^4*m^4 + 537*a^2*c*e^4*m^2 + 66*a^2*c*e^4*m^3 + 3*a^2*c*e^4*m
^4 + 107*b^3*d*e^3*m^2 + 18*b^3*d*e^3*m^3 + b^3*d*e^3*m^4 + 1914*a*b^2*e^4*m + 1914*a^2*c*e^4*m + 210*b^3*d*e^
3*m + 420*b*c^2*d^3*e*m - 504*a*c^2*d^2*e^2*m - 504*b^2*c*d^2*e^2*m + 60*b*c^2*d^3*e*m^2 - 156*a*c^2*d^2*e^2*m
^2 - 12*a*c^2*d^2*e^2*m^3 - 156*b^2*c*d^2*e^2*m^2 - 12*b^2*c*d^2*e^2*m^3 + 1260*a*b*c*d*e^3*m + 642*a*b*c*d*e^
3*m^2 + 108*a*b*c*d*e^3*m^3 + 6*a*b*c*d*e^3*m^4))/(e^4*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322*m^5 +
28*m^6 + m^7 + 5040)) + (3*c*x^5*(d + e*x)^m*(50*m + 35*m^2 + 10*m^3 + m^4 + 24)*(42*b^2*e^2 + 13*b^2*e^2*m -
2*c^2*d^2*m + b^2*e^2*m^2 + 42*a*c*e^2 + 13*a*c*e^2*m + a*c*e^2*m^2 + 7*b*c*d*e*m + b*c*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)) + (c^2*x^6*(d + e*x)^m*(21*b*e + 3*b*e*m
+ c*d*m)*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120))/(e*(13068*m + 13132*m^2 + 6769*m^3 + 1960*m^4 + 322
*m^5 + 28*m^6 + m^7 + 5040))