\(\int (d+e x)^m (f+g x) (a+b x+c x^2)^2 \, dx\) [926]

Optimal result

Integrand size = 25, antiderivative size = 311 \[ \int (d+e x)^m (f+g x) \left (a+b x+c x^2\right )^2 \, dx=\frac {\left (c d^2-b d e+a e^2\right )^2 (e f-d g) (d+e x)^{1+m}}{e^6 (1+m)}-\frac {\left (c d^2-b d e+a e^2\right ) (c d (4 e f-5 d g)-e (2 b e f-3 b d g+a e g)) (d+e x)^{2+m}}{e^6 (2+m)}+\frac {\left (2 c^2 d^2 (3 e f-5 d g)+b e^2 (b e f-3 b d g+2 a e g)+2 c e (a e (e f-3 d g)-3 b d (e f-2 d g))\right ) (d+e x)^{3+m}}{e^6 (3+m)}+\frac {\left (b^2 e^2 g-2 c^2 d (2 e f-5 d g)+2 c e (b e f-4 b d g+a e g)\right ) (d+e x)^{4+m}}{e^6 (4+m)}+\frac {c (c e f-5 c d g+2 b e g) (d+e x)^{5+m}}{e^6 (5+m)}+\frac {c^2 g (d+e x)^{6+m}}{e^6 (6+m)} \]

[Out]

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

Rubi [A] (verified)

Time = 0.23 (sec) , antiderivative size = 311, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.040, Rules used = {785} \[ \int (d+e x)^m (f+g x) \left (a+b x+c x^2\right )^2 \, dx=\frac {(d+e x)^{m+4} \left (2 c e (a e g-4 b d g+b e f)+b^2 e^2 g-2 c^2 d (2 e f-5 d g)\right )}{e^6 (m+4)}+\frac {(d+e x)^{m+3} \left (2 c e (a e (e f-3 d g)-3 b d (e f-2 d g))+b e^2 (2 a e g-3 b d g+b e f)+2 c^2 d^2 (3 e f-5 d g)\right )}{e^6 (m+3)}+\frac {(e f-d g) (d+e x)^{m+1} \left (a e^2-b d e+c d^2\right )^2}{e^6 (m+1)}-\frac {(d+e x)^{m+2} \left (a e^2-b d e+c d^2\right ) (c d (4 e f-5 d g)-e (a e g-3 b d g+2 b e f))}{e^6 (m+2)}+\frac {c (d+e x)^{m+5} (2 b e g-5 c d g+c e f)}{e^6 (m+5)}+\frac {c^2 g (d+e x)^{m+6}}{e^6 (m+6)} \]

[In]

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

[Out]

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

Rule 785

Int[((d_.) + (e_.)*(x_))^(m_.)*((f_.) + (g_.)*(x_))*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> In
t[ExpandIntegrand[(d + e*x)^m*(f + g*x)*(a + b*x + c*x^2)^p, x], x] /; FreeQ[{a, b, c, d, e, f, g, m}, x] && N
eQ[b^2 - 4*a*c, 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 )^2 (e f-d g) (d+e x)^m}{e^5}+\frac {\left (c d^2-b d e+a e^2\right ) (-c d (4 e f-5 d g)+e (2 b e f-3 b d g+a e g)) (d+e x)^{1+m}}{e^5}+\frac {\left (2 c^2 d^2 (3 e f-5 d g)+b e^2 (b e f-3 b d g+2 a e g)+2 c e (a e (e f-3 d g)-3 b d (e f-2 d g))\right ) (d+e x)^{2+m}}{e^5}+\frac {\left (b^2 e^2 g-2 c^2 d (2 e f-5 d g)+2 c e (b e f-4 b d g+a e g)\right ) (d+e x)^{3+m}}{e^5}+\frac {c (c e f-5 c d g+2 b e g) (d+e x)^{4+m}}{e^5}+\frac {c^2 g (d+e x)^{5+m}}{e^5}\right ) \, dx \\ & = \frac {\left (c d^2-b d e+a e^2\right )^2 (e f-d g) (d+e x)^{1+m}}{e^6 (1+m)}-\frac {\left (c d^2-b d e+a e^2\right ) (c d (4 e f-5 d g)-e (2 b e f-3 b d g+a e g)) (d+e x)^{2+m}}{e^6 (2+m)}+\frac {\left (2 c^2 d^2 (3 e f-5 d g)+b e^2 (b e f-3 b d g+2 a e g)+2 c e (a e (e f-3 d g)-3 b d (e f-2 d g))\right ) (d+e x)^{3+m}}{e^6 (3+m)}+\frac {\left (b^2 e^2 g-2 c^2 d (2 e f-5 d g)+2 c e (b e f-4 b d g+a e g)\right ) (d+e x)^{4+m}}{e^6 (4+m)}+\frac {c (c e f-5 c d g+2 b e g) (d+e x)^{5+m}}{e^6 (5+m)}+\frac {c^2 g (d+e x)^{6+m}}{e^6 (6+m)} \\ \end{align*}

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(655\) vs. \(2(311)=622\).

Time = 1.11 (sec) , antiderivative size = 655, normalized size of antiderivative = 2.11 \[ \int (d+e x)^m (f+g x) \left (a+b x+c x^2\right )^2 \, dx=\frac {(d+e x)^{1+m} \left ((a+x (b+c x))^2 (2 b e g+c (-5 d g+e f (6+m)+e g (5+m) x))+\frac {2 \left (\frac {\left (c d^2+e (-b d+a e)\right ) \left (b^3 e^3 g \left (3+4 m+m^2\right )+12 c^3 d^2 (-5 d g+e f (6+m))-b c e^2 (1+m) (b d g (-6+m)+b e f (6+m)+2 a e g (9+2 m))+2 c^2 e \left (-3 b d (d g (-9+m)+2 e f (6+m))+2 a e \left (d g \left (-15+m+m^2\right )+e f \left (24+10 m+m^2\right )\right )\right )\right )}{e^2 (1+m)}+\frac {\left (b^4 e^4 g \left (6+5 m+m^2\right )+12 c^4 d^3 (5 d g-e f (6+m))-b^2 c e^3 (2+m) (b e f (6+m)+b d g (-3+2 m)+a e g (21+5 m))+2 c^3 d e \left (3 b d (d g (-14+m)+3 e f (6+m))-2 a e \left (d g \left (-30-4 m+m^2\right )+e f \left (42+19 m+2 m^2\right )\right )\right )+c^2 e^2 \left (4 a^2 e^2 g \left (15+8 m+m^2\right )+b^2 d \left (d g \left (6-13 m+m^2\right )+2 e f \left (-6+5 m+m^2\right )\right )+2 a b e \left (e f \left (42+19 m+2 m^2\right )+d g \left (-18+11 m+4 m^2\right )\right )\right )\right ) (d+e x)}{e^2 (2+m)}-\left (c e (4+m) \left (b d (-5 c d+2 b e) g-2 a c d e g m+a b e^2 g (1+m)+c e (b d-2 a e) f (6+m)\right )-(3 c d-b e) \left (b^2 e^2 g (3+m)+2 c^2 d (-5 d g+e f (6+m))-c e (b d g (-4+m)+2 a e g (5+m)+b e f (6+m))\right )+c e (3+m) \left (b^2 e^2 g (3+m)+2 c^2 d (-5 d g+e f (6+m))-c e (b d g (-4+m)+2 a e g (5+m)+b e f (6+m))\right ) x\right ) (a+x (b+c x))\right )}{c e^2 (3+m) (4+m)}\right )}{c e^2 (5+m) (6+m)} \]

[In]

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

[Out]

((d + e*x)^(1 + m)*((a + x*(b + c*x))^2*(2*b*e*g + c*(-5*d*g + e*f*(6 + m) + e*g*(5 + m)*x)) + (2*(((c*d^2 + e
*(-(b*d) + a*e))*(b^3*e^3*g*(3 + 4*m + m^2) + 12*c^3*d^2*(-5*d*g + e*f*(6 + m)) - b*c*e^2*(1 + m)*(b*d*g*(-6 +
m) + b*e*f*(6 + m) + 2*a*e*g*(9 + 2*m)) + 2*c^2*e*(-3*b*d*(d*g*(-9 + m) + 2*e*f*(6 + m)) + 2*a*e*(d*g*(-15 +
m + m^2) + e*f*(24 + 10*m + m^2)))))/(e^2*(1 + m)) + ((b^4*e^4*g*(6 + 5*m + m^2) + 12*c^4*d^3*(5*d*g - e*f*(6
+ m)) - b^2*c*e^3*(2 + m)*(b*e*f*(6 + m) + b*d*g*(-3 + 2*m) + a*e*g*(21 + 5*m)) + 2*c^3*d*e*(3*b*d*(d*g*(-14 +
m) + 3*e*f*(6 + m)) - 2*a*e*(d*g*(-30 - 4*m + m^2) + e*f*(42 + 19*m + 2*m^2))) + c^2*e^2*(4*a^2*e^2*g*(15 + 8
*m + m^2) + b^2*d*(d*g*(6 - 13*m + m^2) + 2*e*f*(-6 + 5*m + m^2)) + 2*a*b*e*(e*f*(42 + 19*m + 2*m^2) + d*g*(-1
8 + 11*m + 4*m^2))))*(d + e*x))/(e^2*(2 + m)) - (c*e*(4 + m)*(b*d*(-5*c*d + 2*b*e)*g - 2*a*c*d*e*g*m + a*b*e^2
*g*(1 + m) + c*e*(b*d - 2*a*e)*f*(6 + m)) - (3*c*d - b*e)*(b^2*e^2*g*(3 + m) + 2*c^2*d*(-5*d*g + e*f*(6 + m))
- c*e*(b*d*g*(-4 + m) + 2*a*e*g*(5 + m) + b*e*f*(6 + m))) + c*e*(3 + m)*(b^2*e^2*g*(3 + m) + 2*c^2*d*(-5*d*g +
e*f*(6 + m)) - c*e*(b*d*g*(-4 + m) + 2*a*e*g*(5 + m) + b*e*f*(6 + m)))*x)*(a + x*(b + c*x))))/(c*e^2*(3 + m)*
(4 + m))))/(c*e^2*(5 + m)*(6 + m))

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(2148\) vs. \(2(311)=622\).

Time = 0.64 (sec) , antiderivative size = 2149, normalized size of antiderivative = 6.91

method	result	size
norman	\(\text {Expression too large to display}\)	\(2149\)
gosper	\(\text {Expression too large to display}\)	\(2563\)
risch	\(\text {Expression too large to display}\)	\(3326\)
parallelrisch	\(\text {Expression too large to display}\)	\(5114\)

[In]

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

[Out]

g*c^2/(6+m)*x^6*exp(m*ln(e*x+d))+(2*a*c*e^2*g*m^2+b^2*e^2*g*m^2+2*b*c*d*e*g*m^2+2*b*c*e^2*f*m^2+c^2*d*e*f*m^2+
22*a*c*e^2*g*m+11*b^2*e^2*g*m+12*b*c*d*e*g*m+22*b*c*e^2*f*m-5*c^2*d^2*g*m+6*c^2*d*e*f*m+60*a*c*e^2*g+30*b^2*e^
2*g+60*b*c*e^2*f)/e^2/(m^3+15*m^2+74*m+120)*x^4*exp(m*ln(e*x+d))+(2*a*b*e^3*g*m^3+2*a*c*d*e^2*g*m^3+2*a*c*e^3*
f*m^3+b^2*d*e^2*g*m^3+b^2*e^3*f*m^3+2*b*c*d*e^2*f*m^3+30*a*b*e^3*g*m^2+22*a*c*d*e^2*g*m^2+30*a*c*e^3*f*m^2+11*
b^2*d*e^2*g*m^2+15*b^2*e^3*f*m^2-8*b*c*d^2*e*g*m^2+22*b*c*d*e^2*f*m^2-4*c^2*d^2*e*f*m^2+148*a*b*e^3*g*m+60*a*c
*d*e^2*g*m+148*a*c*e^3*f*m+30*b^2*d*e^2*g*m+74*b^2*e^3*f*m-48*b*c*d^2*e*g*m+60*b*c*d*e^2*f*m+20*c^2*d^3*g*m-24
*c^2*d^2*e*f*m+240*a*b*e^3*g+240*a*c*e^3*f+120*b^2*e^3*f)/e^3/(m^4+18*m^3+119*m^2+342*m+360)*x^3*exp(m*ln(e*x+
d))+(a^2*e^4*g*m^4+2*a*b*d*e^3*g*m^4+2*a*b*e^4*f*m^4+2*a*c*d*e^3*f*m^4+b^2*d*e^3*f*m^4+18*a^2*e^4*g*m^3+30*a*b
*d*e^3*g*m^3+36*a*b*e^4*f*m^3-6*a*c*d^2*e^2*g*m^3+30*a*c*d*e^3*f*m^3-3*b^2*d^2*e^2*g*m^3+15*b^2*d*e^3*f*m^3-6*
b*c*d^2*e^2*f*m^3+119*a^2*e^4*g*m^2+148*a*b*d*e^3*g*m^2+238*a*b*e^4*f*m^2-66*a*c*d^2*e^2*g*m^2+148*a*c*d*e^3*f
*m^2-33*b^2*d^2*e^2*g*m^2+74*b^2*d*e^3*f*m^2+24*b*c*d^3*e*g*m^2-66*b*c*d^2*e^2*f*m^2+12*c^2*d^3*e*f*m^2+342*a^
2*e^4*g*m+240*a*b*d*e^3*g*m+684*a*b*e^4*f*m-180*a*c*d^2*e^2*g*m+240*a*c*d*e^3*f*m-90*b^2*d^2*e^2*g*m+120*b^2*d
*e^3*f*m+144*b*c*d^3*e*g*m-180*b*c*d^2*e^2*f*m-60*c^2*d^4*g*m+72*c^2*d^3*e*f*m+360*a^2*e^4*g+720*a*b*e^4*f)/e^
4/(m^5+20*m^4+155*m^3+580*m^2+1044*m+720)*x^2*exp(m*ln(e*x+d))+(a^2*d*e^4*g*m^5+a^2*e^5*f*m^5+2*a*b*d*e^4*f*m^
5+18*a^2*d*e^4*g*m^4+20*a^2*e^5*f*m^4-4*a*b*d^2*e^3*g*m^4+36*a*b*d*e^4*f*m^4-4*a*c*d^2*e^3*f*m^4-2*b^2*d^2*e^3
*f*m^4+119*a^2*d*e^4*g*m^3+155*a^2*e^5*f*m^3-60*a*b*d^2*e^3*g*m^3+238*a*b*d*e^4*f*m^3+12*a*c*d^3*e^2*g*m^3-60*
a*c*d^2*e^3*f*m^3+6*b^2*d^3*e^2*g*m^3-30*b^2*d^2*e^3*f*m^3+12*b*c*d^3*e^2*f*m^3+342*a^2*d*e^4*g*m^2+580*a^2*e^
5*f*m^2-296*a*b*d^2*e^3*g*m^2+684*a*b*d*e^4*f*m^2+132*a*c*d^3*e^2*g*m^2-296*a*c*d^2*e^3*f*m^2+66*b^2*d^3*e^2*g
*m^2-148*b^2*d^2*e^3*f*m^2-48*b*c*d^4*e*g*m^2+132*b*c*d^3*e^2*f*m^2-24*c^2*d^4*e*f*m^2+360*a^2*d*e^4*g*m+1044*
a^2*e^5*f*m-480*a*b*d^2*e^3*g*m+720*a*b*d*e^4*f*m+360*a*c*d^3*e^2*g*m-480*a*c*d^2*e^3*f*m+180*b^2*d^3*e^2*g*m-
240*b^2*d^2*e^3*f*m-288*b*c*d^4*e*g*m+360*b*c*d^3*e^2*f*m+120*c^2*d^5*g*m-144*c^2*d^4*e*f*m+720*a^2*e^5*f)/e^5
/(m^6+21*m^5+175*m^4+735*m^3+1624*m^2+1764*m+720)*x*exp(m*ln(e*x+d))+(2*b*e*g*m+c*d*g*m+c*e*f*m+12*b*e*g+6*c*e
*f)*c/e/(m^2+11*m+30)*x^5*exp(m*ln(e*x+d))-d*(-a^2*e^5*f*m^5+a^2*d*e^4*g*m^4-20*a^2*e^5*f*m^4+2*a*b*d*e^4*f*m^
4+18*a^2*d*e^4*g*m^3-155*a^2*e^5*f*m^3-4*a*b*d^2*e^3*g*m^3+36*a*b*d*e^4*f*m^3-4*a*c*d^2*e^3*f*m^3-2*b^2*d^2*e^
3*f*m^3+119*a^2*d*e^4*g*m^2-580*a^2*e^5*f*m^2-60*a*b*d^2*e^3*g*m^2+238*a*b*d*e^4*f*m^2+12*a*c*d^3*e^2*g*m^2-60
*a*c*d^2*e^3*f*m^2+6*b^2*d^3*e^2*g*m^2-30*b^2*d^2*e^3*f*m^2+12*b*c*d^3*e^2*f*m^2+342*a^2*d*e^4*g*m-1044*a^2*e^
5*f*m-296*a*b*d^2*e^3*g*m+684*a*b*d*e^4*f*m+132*a*c*d^3*e^2*g*m-296*a*c*d^2*e^3*f*m+66*b^2*d^3*e^2*g*m-148*b^2
*d^2*e^3*f*m-48*b*c*d^4*e*g*m+132*b*c*d^3*e^2*f*m-24*c^2*d^4*e*f*m+360*a^2*d*e^4*g-720*a^2*e^5*f-480*a*b*d^2*e
^3*g+720*a*b*d*e^4*f+360*a*c*d^3*e^2*g-480*a*c*d^2*e^3*f+180*b^2*d^3*e^2*g-240*b^2*d^2*e^3*f-288*b*c*d^4*e*g+3
60*b*c*d^3*e^2*f+120*c^2*d^5*g-144*c^2*d^4*e*f)/e^6/(m^6+21*m^5+175*m^4+735*m^3+1624*m^2+1764*m+720)*exp(m*ln(
e*x+d))

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 2368 vs. \(2 (312) = 624\).

Time = 0.34 (sec) , antiderivative size = 2368, normalized size of antiderivative = 7.61 \[ \int (d+e x)^m (f+g x) \left (a+b x+c x^2\right )^2 \, dx=\text {Too large to display} \]

[In]

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

[Out]

(a^2*d*e^5*f*m^5 + (c^2*e^6*g*m^5 + 15*c^2*e^6*g*m^4 + 85*c^2*e^6*g*m^3 + 225*c^2*e^6*g*m^2 + 274*c^2*e^6*g*m
+ 120*c^2*e^6*g)*x^6 + (144*c^2*e^6*f + 288*b*c*e^6*g + (c^2*e^6*f + (c^2*d*e^5 + 2*b*c*e^6)*g)*m^5 + 2*(8*c^2
*e^6*f + (5*c^2*d*e^5 + 16*b*c*e^6)*g)*m^4 + 5*(19*c^2*e^6*f + (7*c^2*d*e^5 + 38*b*c*e^6)*g)*m^3 + 10*(26*c^2*
e^6*f + (5*c^2*d*e^5 + 52*b*c*e^6)*g)*m^2 + 12*(27*c^2*e^6*f + 2*(c^2*d*e^5 + 27*b*c*e^6)*g)*m)*x^5 - (a^2*d^2
*e^4*g + 2*(a*b*d^2*e^4 - 10*a^2*d*e^5)*f)*m^4 + (360*b*c*e^6*f + 180*(b^2 + 2*a*c)*e^6*g + ((c^2*d*e^5 + 2*b*
c*e^6)*f + (2*b*c*d*e^5 + (b^2 + 2*a*c)*e^6)*g)*m^5 + (2*(6*c^2*d*e^5 + 17*b*c*e^6)*f - (5*c^2*d^2*e^4 - 24*b*
c*d*e^5 - 17*(b^2 + 2*a*c)*e^6)*g)*m^4 + ((47*c^2*d*e^5 + 214*b*c*e^6)*f - (30*c^2*d^2*e^4 - 94*b*c*d*e^5 - 10
7*(b^2 + 2*a*c)*e^6)*g)*m^3 + (2*(36*c^2*d*e^5 + 307*b*c*e^6)*f - (55*c^2*d^2*e^4 - 144*b*c*d*e^5 - 307*(b^2 +
2*a*c)*e^6)*g)*m^2 + 6*(6*(c^2*d*e^5 + 22*b*c*e^6)*f - (5*c^2*d^2*e^4 - 12*b*c*d*e^5 - 66*(b^2 + 2*a*c)*e^6)*
g)*m)*x^4 - ((36*a*b*d^2*e^4 - 155*a^2*d*e^5 - 2*(b^2 + 2*a*c)*d^3*e^3)*f - 2*(2*a*b*d^3*e^3 - 9*a^2*d^2*e^4)*
g)*m^3 + (480*a*b*e^6*g + 240*(b^2 + 2*a*c)*e^6*f + ((2*b*c*d*e^5 + (b^2 + 2*a*c)*e^6)*f + (2*a*b*e^6 + (b^2 +
2*a*c)*d*e^5)*g)*m^5 - 2*((2*c^2*d^2*e^4 - 14*b*c*d*e^5 - 9*(b^2 + 2*a*c)*e^6)*f + (4*b*c*d^2*e^4 - 18*a*b*e^
6 - 7*(b^2 + 2*a*c)*d*e^5)*g)*m^4 - ((36*c^2*d^2*e^4 - 130*b*c*d*e^5 - 121*(b^2 + 2*a*c)*e^6)*f - (20*c^2*d^3*
e^3 - 72*b*c*d^2*e^4 + 242*a*b*e^6 + 65*(b^2 + 2*a*c)*d*e^5)*g)*m^3 - 4*((20*c^2*d^2*e^4 - 56*b*c*d*e^5 - 93*(
b^2 + 2*a*c)*e^6)*f - (15*c^2*d^3*e^3 - 40*b*c*d^2*e^4 + 186*a*b*e^6 + 28*(b^2 + 2*a*c)*d*e^5)*g)*m^2 - 4*((12
*c^2*d^2*e^4 - 30*b*c*d*e^5 - 127*(b^2 + 2*a*c)*e^6)*f - (10*c^2*d^3*e^3 - 24*b*c*d^2*e^4 + 254*a*b*e^6 + 15*(
b^2 + 2*a*c)*d*e^5)*g)*m)*x^3 - (2*(6*b*c*d^4*e^2 + 119*a*b*d^2*e^4 - 290*a^2*d*e^5 - 15*(b^2 + 2*a*c)*d^3*e^3
)*f - (60*a*b*d^3*e^3 - 119*a^2*d^2*e^4 - 6*(b^2 + 2*a*c)*d^4*e^2)*g)*m^2 + (720*a*b*e^6*f + 360*a^2*e^6*g + (
(2*a*b*e^6 + (b^2 + 2*a*c)*d*e^5)*f + (2*a*b*d*e^5 + a^2*e^6)*g)*m^5 - (2*(3*b*c*d^2*e^4 - 19*a*b*e^6 - 8*(b^2
+ 2*a*c)*d*e^5)*f - (32*a*b*d*e^5 + 19*a^2*e^6 - 3*(b^2 + 2*a*c)*d^2*e^4)*g)*m^4 + ((12*c^2*d^3*e^3 - 72*b*c*
d^2*e^4 + 274*a*b*e^6 + 89*(b^2 + 2*a*c)*d*e^5)*f + (24*b*c*d^3*e^3 + 178*a*b*d*e^5 + 137*a^2*e^6 - 36*(b^2 +
2*a*c)*d^2*e^4)*g)*m^3 + (2*(42*c^2*d^3*e^3 - 123*b*c*d^2*e^4 + 461*a*b*e^6 + 97*(b^2 + 2*a*c)*d*e^5)*f - (60*
c^2*d^4*e^2 - 168*b*c*d^3*e^3 - 388*a*b*d*e^5 - 461*a^2*e^6 + 123*(b^2 + 2*a*c)*d^2*e^4)*g)*m^2 + 6*(2*(6*c^2*
d^3*e^3 - 15*b*c*d^2*e^4 + 117*a*b*e^6 + 10*(b^2 + 2*a*c)*d*e^5)*f - (10*c^2*d^4*e^2 - 24*b*c*d^3*e^3 - 40*a*b
*d*e^5 - 117*a^2*e^6 + 15*(b^2 + 2*a*c)*d^2*e^4)*g)*m)*x^2 + 24*(6*c^2*d^5*e - 15*b*c*d^4*e^2 - 30*a*b*d^2*e^4
+ 30*a^2*d*e^5 + 10*(b^2 + 2*a*c)*d^3*e^3)*f - 12*(10*c^2*d^6 - 24*b*c*d^5*e - 40*a*b*d^3*e^3 + 30*a^2*d^2*e^
4 + 15*(b^2 + 2*a*c)*d^4*e^2)*g + 2*(2*(6*c^2*d^5*e - 33*b*c*d^4*e^2 - 171*a*b*d^2*e^4 + 261*a^2*d*e^5 + 37*(b
^2 + 2*a*c)*d^3*e^3)*f + (24*b*c*d^5*e + 148*a*b*d^3*e^3 - 171*a^2*d^2*e^4 - 33*(b^2 + 2*a*c)*d^4*e^2)*g)*m +
(720*a^2*e^6*f + (a^2*d*e^5*g + (2*a*b*d*e^5 + a^2*e^6)*f)*m^5 + 2*((18*a*b*d*e^5 + 10*a^2*e^6 - (b^2 + 2*a*c)
*d^2*e^4)*f - (2*a*b*d^2*e^4 - 9*a^2*d*e^5)*g)*m^4 + ((12*b*c*d^3*e^3 + 238*a*b*d*e^5 + 155*a^2*e^6 - 30*(b^2
+ 2*a*c)*d^2*e^4)*f - (60*a*b*d^2*e^4 - 119*a^2*d*e^5 - 6*(b^2 + 2*a*c)*d^3*e^3)*g)*m^3 - 2*(2*(6*c^2*d^4*e^2
- 33*b*c*d^3*e^3 - 171*a*b*d*e^5 - 145*a^2*e^6 + 37*(b^2 + 2*a*c)*d^2*e^4)*f + (24*b*c*d^4*e^2 + 148*a*b*d^2*e
^4 - 171*a^2*d*e^5 - 33*(b^2 + 2*a*c)*d^3*e^3)*g)*m^2 - 12*((12*c^2*d^4*e^2 - 30*b*c*d^3*e^3 - 60*a*b*d*e^5 -
87*a^2*e^6 + 20*(b^2 + 2*a*c)*d^2*e^4)*f - (10*c^2*d^5*e - 24*b*c*d^4*e^2 - 40*a*b*d^2*e^4 + 30*a^2*d*e^5 + 15
*(b^2 + 2*a*c)*d^3*e^3)*g)*m)*x)*(e*x + d)^m/(e^6*m^6 + 21*e^6*m^5 + 175*e^6*m^4 + 735*e^6*m^3 + 1624*e^6*m^2
+ 1764*e^6*m + 720*e^6)

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 32864 vs. \(2 (309) = 618\).

Time = 5.65 (sec) , antiderivative size = 32864, normalized size of antiderivative = 105.67 \[ \int (d+e x)^m (f+g x) \left (a+b x+c x^2\right )^2 \, dx=\text {Too large to display} \]

[In]

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

[Out]

Piecewise((d**m*(a**2*f*x + a**2*g*x**2/2 + a*b*f*x**2 + 2*a*b*g*x**3/3 + 2*a*c*f*x**3/3 + a*c*g*x**4/2 + b**2
*f*x**3/3 + b**2*g*x**4/4 + b*c*f*x**4/2 + 2*b*c*g*x**5/5 + c**2*f*x**5/5 + c**2*g*x**6/6), Eq(e, 0)), (-3*a**
2*d*e**4*g/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e
**11*x**5) - 12*a**2*e**5*f/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*
e**10*x**4 + 60*e**11*x**5) - 15*a**2*e**5*g*x/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2
*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 4*a*b*d**2*e**3*g/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*
e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 6*a*b*d*e**4*f/(60*d**5*e**6 + 300*d**4*e
**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 20*a*b*d*e**4*g*x/(60*d*
*5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 30*a
*b*e**5*f*x/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*
e**11*x**5) - 40*a*b*e**5*g*x**2/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 3
00*d*e**10*x**4 + 60*e**11*x**5) - 6*a*c*d**3*e**2*g/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 60
0*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 4*a*c*d**2*e**3*f/(60*d**5*e**6 + 300*d**4*e**7*x + 600
*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 30*a*c*d**2*e**3*g*x/(60*d**5*e**6
+ 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 20*a*c*d*e**
4*f*x/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*
x**5) - 60*a*c*d*e**4*g*x**2/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d
*e**10*x**4 + 60*e**11*x**5) - 40*a*c*e**5*f*x**2/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d
**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 60*a*c*e**5*g*x**3/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d
**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 3*b**2*d**3*e**2*g/(60*d**5*e**6 + 30
0*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 2*b**2*d**2*e**3
*f/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**
5) - 15*b**2*d**2*e**3*g*x/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e
**10*x**4 + 60*e**11*x**5) - 10*b**2*d*e**4*f*x/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**
2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 30*b**2*d*e**4*g*x**2/(60*d**5*e**6 + 300*d**4*e**7*x + 600*
d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 20*b**2*e**5*f*x**2/(60*d**5*e**6 +
300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 30*b**2*e**5*g
*x**3/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*
x**5) - 24*b*c*d**4*e*g/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**1
0*x**4 + 60*e**11*x**5) - 6*b*c*d**3*e**2*f/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e*
*9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 120*b*c*d**3*e**2*g*x/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3
*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 30*b*c*d**2*e**3*f*x/(60*d**5*e**6 + 300
*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 240*b*c*d**2*e**3
*g*x**2/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**1
1*x**5) - 60*b*c*d*e**4*f*x**2/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300
*d*e**10*x**4 + 60*e**11*x**5) - 240*b*c*d*e**4*g*x**3/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 +
600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 60*b*c*e**5*f*x**3/(60*d**5*e**6 + 300*d**4*e**7*x +
600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 120*b*c*e**5*g*x**4/(60*d**5*e**
6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) + 60*c**2*d*
*5*g*log(d/e + x)/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4
+ 60*e**11*x**5) + 137*c**2*d**5*g/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3
+ 300*d*e**10*x**4 + 60*e**11*x**5) - 12*c**2*d**4*e*f/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 +
600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) + 300*c**2*d**4*e*g*x*log(d/e + x)/(60*d**5*e**6 + 300*
d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) + 625*c**2*d**4*e*g*
x/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5
) - 60*c**2*d**3*e**2*f*x/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e*
*10*x**4 + 60*e**11*x**5) + 600*c**2*d**3*e**2*g*x**2*log(d/e + x)/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*
e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) + 1100*c**2*d**3*e**2*g*x**2/(60*d**5*e**6
+ 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 120*c**2*d**
2*e**3*f*x**2/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 6
0*e**11*x**5) + 600*c**2*d**2*e**3*g*x**3*log(d/e + x)/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 +
600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) + 900*c**2*d**2*e**3*g*x**3/(60*d**5*e**6 + 300*d**4*e*
*7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 120*c**2*d*e**4*f*x**3/(6
0*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) +
300*c**2*d*e**4*g*x**4*log(d/e + x)/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3
+ 300*d*e**10*x**4 + 60*e**11*x**5) + 300*c**2*d*e**4*g*x**4/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x
**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) - 60*c**2*e**5*f*x**4/(60*d**5*e**6 + 300*d**4*e*
*7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**11*x**5) + 60*c**2*e**5*g*x**5*log(d
/e + x)/(60*d**5*e**6 + 300*d**4*e**7*x + 600*d**3*e**8*x**2 + 600*d**2*e**9*x**3 + 300*d*e**10*x**4 + 60*e**1
1*x**5), Eq(m, -6)), (-a**2*d*e**4*g/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*
e**10*x**4) - 3*a**2*e**5*f/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**
4) - 4*a**2*e**5*g*x/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 2*
a*b*d**2*e**3*g/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 2*a*b*d
*e**4*f/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 8*a*b*d*e**4*g*
x/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 8*a*b*e**5*f*x/(12*d*
*4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 12*a*b*e**5*g*x**2/(12*d**4*e
**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 6*a*c*d**3*e**2*g/(12*d**4*e**6 +
48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 2*a*c*d**2*e**3*f/(12*d**4*e**6 + 48*d
**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 24*a*c*d**2*e**3*g*x/(12*d**4*e**6 + 48*d**
3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 8*a*c*d*e**4*f*x/(12*d**4*e**6 + 48*d**3*e**7
*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 36*a*c*d*e**4*g*x**2/(12*d**4*e**6 + 48*d**3*e**7*x
+ 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 12*a*c*e**5*f*x**2/(12*d**4*e**6 + 48*d**3*e**7*x + 7
2*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 24*a*c*e**5*g*x**3/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d*
*2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 3*b**2*d**3*e**2*g/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e
**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - b**2*d**2*e**3*f/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x*
*2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 12*b**2*d**2*e**3*g*x/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**
2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 4*b**2*d*e**4*f*x/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 4
8*d*e**9*x**3 + 12*e**10*x**4) - 18*b**2*d*e**4*g*x**2/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48
*d*e**9*x**3 + 12*e**10*x**4) - 6*b**2*e**5*f*x**2/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e
**9*x**3 + 12*e**10*x**4) - 12*b**2*e**5*g*x**3/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9
*x**3 + 12*e**10*x**4) + 24*b*c*d**4*e*g*log(d/e + x)/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*
d*e**9*x**3 + 12*e**10*x**4) + 50*b*c*d**4*e*g/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*
x**3 + 12*e**10*x**4) - 6*b*c*d**3*e**2*f/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3
+ 12*e**10*x**4) + 96*b*c*d**3*e**2*g*x*log(d/e + x)/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d
*e**9*x**3 + 12*e**10*x**4) + 176*b*c*d**3*e**2*g*x/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*
e**9*x**3 + 12*e**10*x**4) - 24*b*c*d**2*e**3*f*x/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e*
*9*x**3 + 12*e**10*x**4) + 144*b*c*d**2*e**3*g*x**2*log(d/e + x)/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8
*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) + 216*b*c*d**2*e**3*g*x**2/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e*
*8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 36*b*c*d*e**4*f*x**2/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8
*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) + 96*b*c*d*e**4*g*x**3*log(d/e + x)/(12*d**4*e**6 + 48*d**3*e**7*x + 7
2*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) + 96*b*c*d*e**4*g*x**3/(12*d**4*e**6 + 48*d**3*e**7*x + 72*
d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 24*b*c*e**5*f*x**3/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2
*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) + 24*b*c*e**5*g*x**4*log(d/e + x)/(12*d**4*e**6 + 48*d**3*e**7*x
+ 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 60*c**2*d**5*g*log(d/e + x)/(12*d**4*e**6 + 48*d**3*e*
*7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 125*c**2*d**5*g/(12*d**4*e**6 + 48*d**3*e**7*x +
72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) + 12*c**2*d**4*e*f*log(d/e + x)/(12*d**4*e**6 + 48*d**3*e*
*7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) + 25*c**2*d**4*e*f/(12*d**4*e**6 + 48*d**3*e**7*x +
72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 240*c**2*d**4*e*g*x*log(d/e + x)/(12*d**4*e**6 + 48*d**
3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 440*c**2*d**4*e*g*x/(12*d**4*e**6 + 48*d**3*e
**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) + 48*c**2*d**3*e**2*f*x*log(d/e + x)/(12*d**4*e**6
+ 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) + 88*c**2*d**3*e**2*f*x/(12*d**4*e**6
+ 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 360*c**2*d**3*e**2*g*x**2*log(d/e + x
)/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) - 540*c**2*d**3*e**2*g*
x**2/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) + 72*c**2*d**2*e**3*
f*x**2*log(d/e + x)/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) + 108
*c**2*d**2*e**3*f*x**2/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) -
240*c**2*d**2*e**3*g*x**3*log(d/e + x)/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3 + 1
2*e**10*x**4) - 240*c**2*d**2*e**3*g*x**3/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d*e**9*x**3
+ 12*e**10*x**4) + 48*c**2*d*e**4*f*x**3*log(d/e + x)/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*
d*e**9*x**3 + 12*e**10*x**4) + 48*c**2*d*e**4*f*x**3/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8*x**2 + 48*d
*e**9*x**3 + 12*e**10*x**4) - 60*c**2*d*e**4*g*x**4*log(d/e + x)/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d**2*e**8
*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) + 12*c**2*e**5*f*x**4*log(d/e + x)/(12*d**4*e**6 + 48*d**3*e**7*x + 72
*d**2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4) + 12*c**2*e**5*g*x**5/(12*d**4*e**6 + 48*d**3*e**7*x + 72*d*
*2*e**8*x**2 + 48*d*e**9*x**3 + 12*e**10*x**4), Eq(m, -5)), (-a**2*d*e**4*g/(6*d**3*e**6 + 18*d**2*e**7*x + 18
*d*e**8*x**2 + 6*e**9*x**3) - 2*a**2*e**5*f/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 3*
a**2*e**5*g*x/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 4*a*b*d**2*e**3*g/(6*d**3*e**6 +
18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 2*a*b*d*e**4*f/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**
2 + 6*e**9*x**3) - 12*a*b*d*e**4*g*x/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 6*a*b*e**
5*f*x/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 12*a*b*e**5*g*x**2/(6*d**3*e**6 + 18*d**
2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 12*a*c*d**3*e**2*g*log(d/e + x)/(6*d**3*e**6 + 18*d**2*e**7*x + 18*
d*e**8*x**2 + 6*e**9*x**3) + 22*a*c*d**3*e**2*g/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3)
- 4*a*c*d**2*e**3*f/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 36*a*c*d**2*e**3*g*x*log(d
/e + x)/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 54*a*c*d**2*e**3*g*x/(6*d**3*e**6 + 18
*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 12*a*c*d*e**4*f*x/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**
2 + 6*e**9*x**3) + 36*a*c*d*e**4*g*x**2*log(d/e + x)/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x
**3) + 36*a*c*d*e**4*g*x**2/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 12*a*c*e**5*f*x**2
/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 12*a*c*e**5*g*x**3*log(d/e + x)/(6*d**3*e**6
+ 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 6*b**2*d**3*e**2*g*log(d/e + x)/(6*d**3*e**6 + 18*d**2*e**7
*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 11*b**2*d**3*e**2*g/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e*
*9*x**3) - 2*b**2*d**2*e**3*f/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 18*b**2*d**2*e**
3*g*x*log(d/e + x)/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 27*b**2*d**2*e**3*g*x/(6*d*
*3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 6*b**2*d*e**4*f*x/(6*d**3*e**6 + 18*d**2*e**7*x + 1
8*d*e**8*x**2 + 6*e**9*x**3) + 18*b**2*d*e**4*g*x**2*log(d/e + x)/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x*
*2 + 6*e**9*x**3) + 18*b**2*d*e**4*g*x**2/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 6*b*
*2*e**5*f*x**2/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 6*b**2*e**5*g*x**3*log(d/e + x)
/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 48*b*c*d**4*e*g*log(d/e + x)/(6*d**3*e**6 + 1
8*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 88*b*c*d**4*e*g/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2
+ 6*e**9*x**3) + 12*b*c*d**3*e**2*f*log(d/e + x)/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3
) + 22*b*c*d**3*e**2*f/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 144*b*c*d**3*e**2*g*x*l
og(d/e + x)/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 216*b*c*d**3*e**2*g*x/(6*d**3*e**6
+ 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 36*b*c*d**2*e**3*f*x*log(d/e + x)/(6*d**3*e**6 + 18*d**2*e
**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 54*b*c*d**2*e**3*f*x/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 +
6*e**9*x**3) - 144*b*c*d**2*e**3*g*x**2*log(d/e + x)/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x
**3) - 144*b*c*d**2*e**3*g*x**2/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 36*b*c*d*e**4*
f*x**2*log(d/e + x)/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 36*b*c*d*e**4*f*x**2/(6*d*
*3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 48*b*c*d*e**4*g*x**3*log(d/e + x)/(6*d**3*e**6 + 18
*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 12*b*c*e**5*f*x**3*log(d/e + x)/(6*d**3*e**6 + 18*d**2*e**7*x +
18*d*e**8*x**2 + 6*e**9*x**3) + 12*b*c*e**5*g*x**4/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x*
*3) + 60*c**2*d**5*g*log(d/e + x)/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 110*c**2*d**
5*g/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 24*c**2*d**4*e*f*log(d/e + x)/(6*d**3*e**6
+ 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 44*c**2*d**4*e*f/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8
*x**2 + 6*e**9*x**3) + 180*c**2*d**4*e*g*x*log(d/e + x)/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**
9*x**3) + 270*c**2*d**4*e*g*x/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 72*c**2*d**3*e**
2*f*x*log(d/e + x)/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 108*c**2*d**3*e**2*f*x/(6*d
**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 180*c**2*d**3*e**2*g*x**2*log(d/e + x)/(6*d**3*e**
6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 180*c**2*d**3*e**2*g*x**2/(6*d**3*e**6 + 18*d**2*e**7*x +
18*d*e**8*x**2 + 6*e**9*x**3) - 72*c**2*d**2*e**3*f*x**2*log(d/e + x)/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e*
*8*x**2 + 6*e**9*x**3) - 72*c**2*d**2*e**3*f*x**2/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3
) + 60*c**2*d**2*e**3*g*x**3*log(d/e + x)/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 24*c
**2*d*e**4*f*x**3*log(d/e + x)/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) - 15*c**2*d*e**4*
g*x**4/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 6*c**2*e**5*f*x**4/(6*d**3*e**6 + 18*d*
*2*e**7*x + 18*d*e**8*x**2 + 6*e**9*x**3) + 3*c**2*e**5*g*x**5/(6*d**3*e**6 + 18*d**2*e**7*x + 18*d*e**8*x**2
+ 6*e**9*x**3), Eq(m, -4)), (-3*a**2*d*e**4*g/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 3*a**2*e**5*f/(6*d**
2*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 6*a**2*e**5*g*x/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 12*a*b*d**2*
e**3*g*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 18*a*b*d**2*e**3*g/(6*d**2*e**6 + 12*d*e**7*x
+ 6*e**8*x**2) - 6*a*b*d*e**4*f/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 24*a*b*d*e**4*g*x*log(d/e + x)/(6*
d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 24*a*b*d*e**4*g*x/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 12*a*b*
e**5*f*x/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 12*a*b*e**5*g*x**2*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*
x + 6*e**8*x**2) - 36*a*c*d**3*e**2*g*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 54*a*c*d**3*e**
2*g/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 12*a*c*d**2*e**3*f*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6
*e**8*x**2) + 18*a*c*d**2*e**3*f/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 72*a*c*d**2*e**3*g*x*log(d/e + x)
/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 72*a*c*d**2*e**3*g*x/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) +
24*a*c*d*e**4*f*x*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 24*a*c*d*e**4*f*x/(6*d**2*e**6 + 12
*d*e**7*x + 6*e**8*x**2) - 36*a*c*d*e**4*g*x**2*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 12*a*
c*e**5*f*x**2*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 12*a*c*e**5*g*x**3/(6*d**2*e**6 + 12*d*
e**7*x + 6*e**8*x**2) - 18*b**2*d**3*e**2*g*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 27*b**2*d
**3*e**2*g/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 6*b**2*d**2*e**3*f*log(d/e + x)/(6*d**2*e**6 + 12*d*e**
7*x + 6*e**8*x**2) + 9*b**2*d**2*e**3*f/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 36*b**2*d**2*e**3*g*x*log(
d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 36*b**2*d**2*e**3*g*x/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8
*x**2) + 12*b**2*d*e**4*f*x*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 12*b**2*d*e**4*f*x/(6*d**
2*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 18*b**2*d*e**4*g*x**2*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x
**2) + 6*b**2*e**5*f*x**2*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 6*b**2*e**5*g*x**3/(6*d**2*
e**6 + 12*d*e**7*x + 6*e**8*x**2) + 72*b*c*d**4*e*g*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 1
08*b*c*d**4*e*g/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 36*b*c*d**3*e**2*f*log(d/e + x)/(6*d**2*e**6 + 12*
d*e**7*x + 6*e**8*x**2) - 54*b*c*d**3*e**2*f/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 144*b*c*d**3*e**2*g*x
*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 144*b*c*d**3*e**2*g*x/(6*d**2*e**6 + 12*d*e**7*x + 6
*e**8*x**2) - 72*b*c*d**2*e**3*f*x*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 72*b*c*d**2*e**3*f
*x/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 72*b*c*d**2*e**3*g*x**2*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x
+ 6*e**8*x**2) - 36*b*c*d*e**4*f*x**2*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 24*b*c*d*e**4*
g*x**3/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 12*b*c*e**5*f*x**3/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2
) + 6*b*c*e**5*g*x**4/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 60*c**2*d**5*g*log(d/e + x)/(6*d**2*e**6 + 1
2*d*e**7*x + 6*e**8*x**2) - 90*c**2*d**5*g/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 36*c**2*d**4*e*f*log(d/
e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 54*c**2*d**4*e*f/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2)
- 120*c**2*d**4*e*g*x*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 120*c**2*d**4*e*g*x/(6*d**2*e**
6 + 12*d*e**7*x + 6*e**8*x**2) + 72*c**2*d**3*e**2*f*x*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2)
+ 72*c**2*d**3*e**2*f*x/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 60*c**2*d**3*e**2*g*x**2*log(d/e + x)/(6*d
**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 36*c**2*d**2*e**3*f*x**2*log(d/e + x)/(6*d**2*e**6 + 12*d*e**7*x + 6*e
**8*x**2) + 20*c**2*d**2*e**3*g*x**3/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 12*c**2*d*e**4*f*x**3/(6*d**2
*e**6 + 12*d*e**7*x + 6*e**8*x**2) - 5*c**2*d*e**4*g*x**4/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 3*c**2*e
**5*f*x**4/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*x**2) + 2*c**2*e**5*g*x**5/(6*d**2*e**6 + 12*d*e**7*x + 6*e**8*
x**2), Eq(m, -3)), (12*a**2*d*e**4*g*log(d/e + x)/(12*d*e**6 + 12*e**7*x) + 12*a**2*d*e**4*g/(12*d*e**6 + 12*e
**7*x) - 12*a**2*e**5*f/(12*d*e**6 + 12*e**7*x) + 12*a**2*e**5*g*x*log(d/e + x)/(12*d*e**6 + 12*e**7*x) - 48*a
*b*d**2*e**3*g*log(d/e + x)/(12*d*e**6 + 12*e**7*x) - 48*a*b*d**2*e**3*g/(12*d*e**6 + 12*e**7*x) + 24*a*b*d*e*
*4*f*log(d/e + x)/(12*d*e**6 + 12*e**7*x) + 24*a*b*d*e**4*f/(12*d*e**6 + 12*e**7*x) - 48*a*b*d*e**4*g*x*log(d/
e + x)/(12*d*e**6 + 12*e**7*x) + 24*a*b*e**5*f*x*log(d/e + x)/(12*d*e**6 + 12*e**7*x) + 24*a*b*e**5*g*x**2/(12
*d*e**6 + 12*e**7*x) + 72*a*c*d**3*e**2*g*log(d/e + x)/(12*d*e**6 + 12*e**7*x) + 72*a*c*d**3*e**2*g/(12*d*e**6
+ 12*e**7*x) - 48*a*c*d**2*e**3*f*log(d/e + x)/(12*d*e**6 + 12*e**7*x) - 48*a*c*d**2*e**3*f/(12*d*e**6 + 12*e
**7*x) + 72*a*c*d**2*e**3*g*x*log(d/e + x)/(12*d*e**6 + 12*e**7*x) - 48*a*c*d*e**4*f*x*log(d/e + x)/(12*d*e**6
+ 12*e**7*x) - 36*a*c*d*e**4*g*x**2/(12*d*e**6 + 12*e**7*x) + 24*a*c*e**5*f*x**2/(12*d*e**6 + 12*e**7*x) + 12
*a*c*e**5*g*x**3/(12*d*e**6 + 12*e**7*x) + 36*b**2*d**3*e**2*g*log(d/e + x)/(12*d*e**6 + 12*e**7*x) + 36*b**2*
d**3*e**2*g/(12*d*e**6 + 12*e**7*x) - 24*b**2*d**2*e**3*f*log(d/e + x)/(12*d*e**6 + 12*e**7*x) - 24*b**2*d**2*
e**3*f/(12*d*e**6 + 12*e**7*x) + 36*b**2*d**2*e**3*g*x*log(d/e + x)/(12*d*e**6 + 12*e**7*x) - 24*b**2*d*e**4*f
*x*log(d/e + x)/(12*d*e**6 + 12*e**7*x) - 18*b**2*d*e**4*g*x**2/(12*d*e**6 + 12*e**7*x) + 12*b**2*e**5*f*x**2/
(12*d*e**6 + 12*e**7*x) + 6*b**2*e**5*g*x**3/(12*d*e**6 + 12*e**7*x) - 96*b*c*d**4*e*g*log(d/e + x)/(12*d*e**6
+ 12*e**7*x) - 96*b*c*d**4*e*g/(12*d*e**6 + 12*e**7*x) + 72*b*c*d**3*e**2*f*log(d/e + x)/(12*d*e**6 + 12*e**7
*x) + 72*b*c*d**3*e**2*f/(12*d*e**6 + 12*e**7*x) - 96*b*c*d**3*e**2*g*x*log(d/e + x)/(12*d*e**6 + 12*e**7*x) +
72*b*c*d**2*e**3*f*x*log(d/e + x)/(12*d*e**6 + 12*e**7*x) + 48*b*c*d**2*e**3*g*x**2/(12*d*e**6 + 12*e**7*x) -
36*b*c*d*e**4*f*x**2/(12*d*e**6 + 12*e**7*x) - 16*b*c*d*e**4*g*x**3/(12*d*e**6 + 12*e**7*x) + 12*b*c*e**5*f*x
**3/(12*d*e**6 + 12*e**7*x) + 8*b*c*e**5*g*x**4/(12*d*e**6 + 12*e**7*x) + 60*c**2*d**5*g*log(d/e + x)/(12*d*e*
*6 + 12*e**7*x) + 60*c**2*d**5*g/(12*d*e**6 + 12*e**7*x) - 48*c**2*d**4*e*f*log(d/e + x)/(12*d*e**6 + 12*e**7*
x) - 48*c**2*d**4*e*f/(12*d*e**6 + 12*e**7*x) + 60*c**2*d**4*e*g*x*log(d/e + x)/(12*d*e**6 + 12*e**7*x) - 48*c
**2*d**3*e**2*f*x*log(d/e + x)/(12*d*e**6 + 12*e**7*x) - 30*c**2*d**3*e**2*g*x**2/(12*d*e**6 + 12*e**7*x) + 24
*c**2*d**2*e**3*f*x**2/(12*d*e**6 + 12*e**7*x) + 10*c**2*d**2*e**3*g*x**3/(12*d*e**6 + 12*e**7*x) - 8*c**2*d*e
**4*f*x**3/(12*d*e**6 + 12*e**7*x) - 5*c**2*d*e**4*g*x**4/(12*d*e**6 + 12*e**7*x) + 4*c**2*e**5*f*x**4/(12*d*e
**6 + 12*e**7*x) + 3*c**2*e**5*g*x**5/(12*d*e**6 + 12*e**7*x), Eq(m, -2)), (-a**2*d*g*log(d/e + x)/e**2 + a**2
*f*log(d/e + x)/e + a**2*g*x/e + 2*a*b*d**2*g*log(d/e + x)/e**3 - 2*a*b*d*f*log(d/e + x)/e**2 - 2*a*b*d*g*x/e*
*2 + 2*a*b*f*x/e + a*b*g*x**2/e - 2*a*c*d**3*g*log(d/e + x)/e**4 + 2*a*c*d**2*f*log(d/e + x)/e**3 + 2*a*c*d**2
*g*x/e**3 - 2*a*c*d*f*x/e**2 - a*c*d*g*x**2/e**2 + a*c*f*x**2/e + 2*a*c*g*x**3/(3*e) - b**2*d**3*g*log(d/e + x
)/e**4 + b**2*d**2*f*log(d/e + x)/e**3 + b**2*d**2*g*x/e**3 - b**2*d*f*x/e**2 - b**2*d*g*x**2/(2*e**2) + b**2*
f*x**2/(2*e) + b**2*g*x**3/(3*e) + 2*b*c*d**4*g*log(d/e + x)/e**5 - 2*b*c*d**3*f*log(d/e + x)/e**4 - 2*b*c*d**
3*g*x/e**4 + 2*b*c*d**2*f*x/e**3 + b*c*d**2*g*x**2/e**3 - b*c*d*f*x**2/e**2 - 2*b*c*d*g*x**3/(3*e**2) + 2*b*c*
f*x**3/(3*e) + b*c*g*x**4/(2*e) - c**2*d**5*g*log(d/e + x)/e**6 + c**2*d**4*f*log(d/e + x)/e**5 + c**2*d**4*g*
x/e**5 - c**2*d**3*f*x/e**4 - c**2*d**3*g*x**2/(2*e**4) + c**2*d**2*f*x**2/(2*e**3) + c**2*d**2*g*x**3/(3*e**3
) - c**2*d*f*x**3/(3*e**2) - c**2*d*g*x**4/(4*e**2) + c**2*f*x**4/(4*e) + c**2*g*x**5/(5*e), Eq(m, -1)), (-a**
2*d**2*e**4*g*m**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1
764*e**6*m + 720*e**6) - 18*a**2*d**2*e**4*g*m**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735
*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 119*a**2*d**2*e**4*g*m**2*(d + e*x)**m/(e**6*m**6 + 21
*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 342*a**2*d**2*e**4*g*m
*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e
**6) - 360*a**2*d**2*e**4*g*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6
*m**2 + 1764*e**6*m + 720*e**6) + a**2*d*e**5*f*m**5*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 +
735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 20*a**2*d*e**5*f*m**4*(d + e*x)**m/(e**6*m**6 + 21*
e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 155*a**2*d*e**5*f*m**3*
(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e*
*6) + 580*a**2*d*e**5*f*m**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**
6*m**2 + 1764*e**6*m + 720*e**6) + 1044*a**2*d*e**5*f*m*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4
+ 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 720*a**2*d*e**5*f*(d + e*x)**m/(e**6*m**6 + 21*e
**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + a**2*d*e**5*g*m**5*x*(d
+ e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6)
+ 18*a**2*d*e**5*g*m**4*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*
m**2 + 1764*e**6*m + 720*e**6) + 119*a**2*d*e**5*g*m**3*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m*
*4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 342*a**2*d*e**5*g*m**2*x*(d + e*x)**m/(e**6*m*
*6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 360*a**2*d*e**5
*g*m*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m +
720*e**6) + a**2*e**6*f*m**5*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*
e**6*m**2 + 1764*e**6*m + 720*e**6) + 20*a**2*e**6*f*m**4*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*
m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 155*a**2*e**6*f*m**3*x*(d + e*x)**m/(e**6*m*
*6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 580*a**2*e**6*f
*m**2*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m
+ 720*e**6) + 1044*a**2*e**6*f*m*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 16
24*e**6*m**2 + 1764*e**6*m + 720*e**6) + 720*a**2*e**6*f*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m
**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + a**2*e**6*g*m**5*x**2*(d + e*x)**m/(e**6*m**6
+ 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 19*a**2*e**6*g*m*
*4*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m
+ 720*e**6) + 137*a**2*e**6*g*m**3*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3
+ 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 461*a**2*e**6*g*m**2*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5
+ 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 702*a**2*e**6*g*m*x**2*(d + e*x)
**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 360
*a**2*e**6*g*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 17
64*e**6*m + 720*e**6) + 4*a*b*d**3*e**3*g*m**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e*
*6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 60*a*b*d**3*e**3*g*m**2*(d + e*x)**m/(e**6*m**6 + 21*e**6
*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 296*a*b*d**3*e**3*g*m*(d +
e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) +
480*a*b*d**3*e**3*g*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 +
1764*e**6*m + 720*e**6) - 2*a*b*d**2*e**4*f*m**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735
*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 36*a*b*d**2*e**4*f*m**3*(d + e*x)**m/(e**6*m**6 + 21*e
**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 238*a*b*d**2*e**4*f*m**2
*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e
**6) - 684*a*b*d**2*e**4*f*m*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**
6*m**2 + 1764*e**6*m + 720*e**6) - 720*a*b*d**2*e**4*f*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4
+ 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 4*a*b*d**2*e**4*g*m**4*x*(d + e*x)**m/(e**6*m**6
+ 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 60*a*b*d**2*e**4*g
*m**3*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m
+ 720*e**6) - 296*a*b*d**2*e**4*g*m**2*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**
3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 480*a*b*d**2*e**4*g*m*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5
+ 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 2*a*b*d*e**5*f*m**5*x*(d + e*x)**
m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 36*a*
b*d*e**5*f*m**4*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 17
64*e**6*m + 720*e**6) + 238*a*b*d*e**5*f*m**3*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e
**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 684*a*b*d*e**5*f*m**2*x*(d + e*x)**m/(e**6*m**6 + 21*e**
6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 720*a*b*d*e**5*f*m*x*(d +
e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) +
2*a*b*d*e**5*g*m**5*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m
**2 + 1764*e**6*m + 720*e**6) + 32*a*b*d*e**5*g*m**4*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m*
*4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 178*a*b*d*e**5*g*m**3*x**2*(d + e*x)**m/(e**6*
m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 388*a*b*d*e**
5*g*m**2*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e
**6*m + 720*e**6) + 240*a*b*d*e**5*g*m*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*
m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 2*a*b*e**6*f*m**5*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**
5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 38*a*b*e**6*f*m**4*x**2*(d + e*
x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 2
74*a*b*e**6*f*m**3*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**
2 + 1764*e**6*m + 720*e**6) + 922*a*b*e**6*f*m**2*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4
+ 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 1404*a*b*e**6*f*m*x**2*(d + e*x)**m/(e**6*m**6 +
21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 720*a*b*e**6*f*x**2*
(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e*
*6) + 2*a*b*e**6*g*m**5*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**
6*m**2 + 1764*e**6*m + 720*e**6) + 36*a*b*e**6*g*m**4*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m
**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 242*a*b*e**6*g*m**3*x**3*(d + e*x)**m/(e**6*m
**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 744*a*b*e**6*g
*m**2*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6
*m + 720*e**6) + 1016*a*b*e**6*g*m*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3
+ 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 480*a*b*e**6*g*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175
*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 12*a*c*d**4*e**2*g*m**2*(d + e*x)**m/(
e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 132*a*c*
d**4*e**2*g*m*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e
**6*m + 720*e**6) - 360*a*c*d**4*e**2*g*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3
+ 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 4*a*c*d**3*e**3*f*m**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 +
175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 60*a*c*d**3*e**3*f*m**2*(d + e*x)**
m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 296*a
*c*d**3*e**3*f*m*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 176
4*e**6*m + 720*e**6) + 480*a*c*d**3*e**3*f*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m
**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 12*a*c*d**3*e**3*g*m**3*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m
**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 132*a*c*d**3*e**3*g*m**2*x*(d
+ e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6
) + 360*a*c*d**3*e**3*g*m*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6
*m**2 + 1764*e**6*m + 720*e**6) - 4*a*c*d**2*e**4*f*m**4*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m
**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 60*a*c*d**2*e**4*f*m**3*x*(d + e*x)**m/(e**6*
m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 296*a*c*d**2*
e**4*f*m**2*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e
**6*m + 720*e**6) - 480*a*c*d**2*e**4*f*m*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*
m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 6*a*c*d**2*e**4*g*m**4*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**
6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 72*a*c*d**2*e**4*g*m**3*x*
*2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720
*e**6) - 246*a*c*d**2*e**4*g*m**2*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3
+ 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 180*a*c*d**2*e**4*g*m*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5
+ 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 2*a*c*d*e**5*f*m**5*x**2*(d + e*
x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 3
2*a*c*d*e**5*f*m**4*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m*
*2 + 1764*e**6*m + 720*e**6) + 178*a*c*d*e**5*f*m**3*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m*
*4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 388*a*c*d*e**5*f*m**2*x**2*(d + e*x)**m/(e**6*
m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 240*a*c*d*e**
5*f*m*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6
*m + 720*e**6) + 2*a*c*d*e**5*g*m**5*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m*
*3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 28*a*c*d*e**5*g*m**4*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m*
*5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 130*a*c*d*e**5*g*m**3*x**3*(d
+ e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6)
+ 224*a*c*d*e**5*g*m**2*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e*
*6*m**2 + 1764*e**6*m + 720*e**6) + 120*a*c*d*e**5*g*m*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*
m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 2*a*c*e**6*f*m**5*x**3*(d + e*x)**m/(e**6*m*
*6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 36*a*c*e**6*f*m
**4*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m
+ 720*e**6) + 242*a*c*e**6*f*m**3*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3
+ 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 744*a*c*e**6*f*m**2*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5
+ 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 1016*a*c*e**6*f*m*x**3*(d + e*x)*
*m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 480*
a*c*e**6*f*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764
*e**6*m + 720*e**6) + 2*a*c*e**6*g*m**5*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6
*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 34*a*c*e**6*g*m**4*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m
**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 214*a*c*e**6*g*m**3*x**4*(d +
e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6)
+ 614*a*c*e**6*g*m**2*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*
m**2 + 1764*e**6*m + 720*e**6) + 792*a*c*e**6*g*m*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4
+ 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 360*a*c*e**6*g*x**4*(d + e*x)**m/(e**6*m**6 + 21*
e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 6*b**2*d**4*e**2*g*m**2
*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e
**6) - 66*b**2*d**4*e**2*g*m*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**
6*m**2 + 1764*e**6*m + 720*e**6) - 180*b**2*d**4*e**2*g*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4
+ 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 2*b**2*d**3*e**3*f*m**3*(d + e*x)**m/(e**6*m**6
+ 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 30*b**2*d**3*e**3*
f*m**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m +
720*e**6) + 148*b**2*d**3*e**3*f*m*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1
624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 240*b**2*d**3*e**3*f*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e*
*6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 6*b**2*d**3*e**3*g*m**3*x*(d + e*x)**m/(e
**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 66*b**2*d
**3*e**3*g*m**2*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 17
64*e**6*m + 720*e**6) + 180*b**2*d**3*e**3*g*m*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*
e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 2*b**2*d**2*e**4*f*m**4*x*(d + e*x)**m/(e**6*m**6 + 21*
e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 30*b**2*d**2*e**4*f*m**
3*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 72
0*e**6) - 148*b**2*d**2*e**4*f*m**2*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 +
1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 240*b**2*d**2*e**4*f*m*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 +
175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 3*b**2*d**2*e**4*g*m**4*x**2*(d + e
*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) -
36*b**2*d**2*e**4*g*m**3*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e*
*6*m**2 + 1764*e**6*m + 720*e**6) - 123*b**2*d**2*e**4*g*m**2*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 17
5*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 90*b**2*d**2*e**4*g*m*x**2*(d + e*x)*
*m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + b**2
*d*e**5*f*m**5*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 +
1764*e**6*m + 720*e**6) + 16*b**2*d*e**5*f*m**4*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 +
735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 89*b**2*d*e**5*f*m**3*x**2*(d + e*x)**m/(e**6*m**6
+ 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 194*b**2*d*e**5*f*
m**2*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*
m + 720*e**6) + 120*b**2*d*e**5*f*m*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**
3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + b**2*d*e**5*g*m**5*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5
+ 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 14*b**2*d*e**5*g*m**4*x**3*(d + e
*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) +
65*b**2*d*e**5*g*m**3*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*
m**2 + 1764*e**6*m + 720*e**6) + 112*b**2*d*e**5*g*m**2*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6
*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 60*b**2*d*e**5*g*m*x**3*(d + e*x)**m/(e**6*
m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + b**2*e**6*f*m
**5*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m
+ 720*e**6) + 18*b**2*e**6*f*m**4*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3
+ 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 121*b**2*e**6*f*m**3*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5
+ 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 372*b**2*e**6*f*m**2*x**3*(d + e
*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) +
508*b**2*e**6*f*m*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2
+ 1764*e**6*m + 720*e**6) + 240*b**2*e**6*f*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735
*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + b**2*e**6*g*m**5*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**
6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 17*b**2*e**6*g*m**4*x**4*(
d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**
6) + 107*b**2*e**6*g*m**3*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e
**6*m**2 + 1764*e**6*m + 720*e**6) + 307*b**2*e**6*g*m**2*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e*
*6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 396*b**2*e**6*g*m*x**4*(d + e*x)**m/(e**6
*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 180*b**2*e**
6*g*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m
+ 720*e**6) + 48*b*c*d**5*e*g*m*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624
*e**6*m**2 + 1764*e**6*m + 720*e**6) + 288*b*c*d**5*e*g*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4
+ 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 12*b*c*d**4*e**2*f*m**2*(d + e*x)**m/(e**6*m**6
+ 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 132*b*c*d**4*e**2*
f*m*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 72
0*e**6) - 360*b*c*d**4*e**2*f*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e*
*6*m**2 + 1764*e**6*m + 720*e**6) - 48*b*c*d**4*e**2*g*m**2*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**
6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 288*b*c*d**4*e**2*g*m*x*(d + e*x)**m/(e**6
*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 12*b*c*d**3*
e**3*f*m**3*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e
**6*m + 720*e**6) + 132*b*c*d**3*e**3*f*m**2*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e*
*6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 360*b*c*d**3*e**3*f*m*x*(d + e*x)**m/(e**6*m**6 + 21*e**6
*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 24*b*c*d**3*e**3*g*m**3*x**
2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*
e**6) + 168*b*c*d**3*e**3*g*m**2*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 +
1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 144*b*c*d**3*e**3*g*m*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5
+ 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 6*b*c*d**2*e**4*f*m**4*x**2*(d +
e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) -
72*b*c*d**2*e**4*f*m**3*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e*
*6*m**2 + 1764*e**6*m + 720*e**6) - 246*b*c*d**2*e**4*f*m**2*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175
*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 180*b*c*d**2*e**4*f*m*x**2*(d + e*x)**
m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 8*b*c
*d**2*e**4*g*m**4*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2
+ 1764*e**6*m + 720*e**6) - 72*b*c*d**2*e**4*g*m**3*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m*
*4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 160*b*c*d**2*e**4*g*m**2*x**3*(d + e*x)**m/(e*
*6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 96*b*c*d**
2*e**4*g*m*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764
*e**6*m + 720*e**6) + 2*b*c*d*e**5*f*m**5*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e*
*6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 28*b*c*d*e**5*f*m**4*x**3*(d + e*x)**m/(e**6*m**6 + 21*e*
*6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 130*b*c*d*e**5*f*m**3*x**
3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*
e**6) + 224*b*c*d*e**5*f*m**2*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 16
24*e**6*m**2 + 1764*e**6*m + 720*e**6) + 120*b*c*d*e**5*f*m*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*
e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 2*b*c*d*e**5*g*m**5*x**4*(d + e*x)**m/(
e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 24*b*c*d
*e**5*g*m**4*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 17
64*e**6*m + 720*e**6) + 94*b*c*d*e**5*g*m**3*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735
*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 144*b*c*d*e**5*g*m**2*x**4*(d + e*x)**m/(e**6*m**6 + 2
1*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 72*b*c*d*e**5*g*m*x**
4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*
e**6) + 2*b*c*e**6*f*m**5*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e
**6*m**2 + 1764*e**6*m + 720*e**6) + 34*b*c*e**6*f*m**4*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6
*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 214*b*c*e**6*f*m**3*x**4*(d + e*x)**m/(e**6
*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 614*b*c*e**6
*f*m**2*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e*
*6*m + 720*e**6) + 792*b*c*e**6*f*m*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**
3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 360*b*c*e**6*f*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 17
5*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 2*b*c*e**6*g*m**5*x**5*(d + e*x)**m/(
e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 32*b*c*e
**6*g*m**4*x**5*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764
*e**6*m + 720*e**6) + 190*b*c*e**6*g*m**3*x**5*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e*
*6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 520*b*c*e**6*g*m**2*x**5*(d + e*x)**m/(e**6*m**6 + 21*e**
6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 648*b*c*e**6*g*m*x**5*(d +
e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6)
+ 288*b*c*e**6*g*x**5*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2
+ 1764*e**6*m + 720*e**6) - 120*c**2*d**6*g*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*
m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 24*c**2*d**5*e*f*m*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 +
175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 144*c**2*d**5*e*f*(d + e*x)**m/(e**
6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 120*c**2*d*
*5*e*g*m*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6
*m + 720*e**6) - 24*c**2*d**4*e**2*f*m**2*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*
m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 144*c**2*d**4*e**2*f*m*x*(d + e*x)**m/(e**6*m**6 + 21*e**6*m
**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 60*c**2*d**4*e**2*g*m**2*x**2
*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e
**6) - 60*c**2*d**4*e**2*g*m*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 162
4*e**6*m**2 + 1764*e**6*m + 720*e**6) + 12*c**2*d**3*e**3*f*m**3*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 +
175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 84*c**2*d**3*e**3*f*m**2*x**2*(d +
e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6)
+ 72*c**2*d**3*e**3*f*m*x**2*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**
6*m**2 + 1764*e**6*m + 720*e**6) + 20*c**2*d**3*e**3*g*m**3*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*
e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 60*c**2*d**3*e**3*g*m**2*x**3*(d + e*x)
**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 40*
c**2*d**3*e**3*g*m*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**
2 + 1764*e**6*m + 720*e**6) - 4*c**2*d**2*e**4*f*m**4*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m
**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 36*c**2*d**2*e**4*f*m**3*x**3*(d + e*x)**m/(e
**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 80*c**2*d
**2*e**4*f*m**2*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 +
1764*e**6*m + 720*e**6) - 48*c**2*d**2*e**4*f*m*x**3*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 +
735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 5*c**2*d**2*e**4*g*m**4*x**4*(d + e*x)**m/(e**6*m*
*6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 30*c**2*d**2*e*
*4*g*m**3*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*
e**6*m + 720*e**6) - 55*c**2*d**2*e**4*g*m**2*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 73
5*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) - 30*c**2*d**2*e**4*g*m*x**4*(d + e*x)**m/(e**6*m**6 +
21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + c**2*d*e**5*f*m**5*x
**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 72
0*e**6) + 12*c**2*d*e**5*f*m**4*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 +
1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 47*c**2*d*e**5*f*m**3*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 +
175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 72*c**2*d*e**5*f*m**2*x**4*(d + e*
x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 3
6*c**2*d*e**5*f*m*x**4*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2
+ 1764*e**6*m + 720*e**6) + c**2*d*e**5*g*m**5*x**5*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 +
735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 10*c**2*d*e**5*g*m**4*x**5*(d + e*x)**m/(e**6*m**6
+ 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 35*c**2*d*e**5*g*m
**3*x**5*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m
+ 720*e**6) + 50*c**2*d*e**5*g*m**2*x**5*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m*
*3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 24*c**2*d*e**5*g*m*x**5*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5
+ 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + c**2*e**6*f*m**5*x**5*(d + e*x)*
*m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 16*c
**2*e**6*f*m**4*x**5*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 +
1764*e**6*m + 720*e**6) + 95*c**2*e**6*f*m**3*x**5*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 7
35*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 260*c**2*e**6*f*m**2*x**5*(d + e*x)**m/(e**6*m**6 +
21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 324*c**2*e**6*f*m*x*
*5*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720
*e**6) + 144*c**2*e**6*f*x**5*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e*
*6*m**2 + 1764*e**6*m + 720*e**6) + c**2*e**6*g*m**5*x**6*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m*
*4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 15*c**2*e**6*g*m**4*x**6*(d + e*x)**m/(e**6*m*
*6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 85*c**2*e**6*g*
m**3*x**6*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*
m + 720*e**6) + 225*c**2*e**6*g*m**2*x**6*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m*
*3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 274*c**2*e**6*g*m*x**6*(d + e*x)**m/(e**6*m**6 + 21*e**6*m**5
+ 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6) + 120*c**2*e**6*g*x**6*(d + e*x)**m
/(e**6*m**6 + 21*e**6*m**5 + 175*e**6*m**4 + 735*e**6*m**3 + 1624*e**6*m**2 + 1764*e**6*m + 720*e**6), True))

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 1118 vs. \(2 (312) = 624\).

Time = 0.24 (sec) , antiderivative size = 1118, normalized size of antiderivative = 3.59 \[ \int (d+e x)^m (f+g x) \left (a+b x+c x^2\right )^2 \, dx=\text {Too large to display} \]

[In]

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

[Out]

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

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 4936 vs. \(2 (312) = 624\).

Time = 0.32 (sec) , antiderivative size = 4936, normalized size of antiderivative = 15.87 \[ \int (d+e x)^m (f+g x) \left (a+b x+c x^2\right )^2 \, dx=\text {Too large to display} \]

[In]

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

[Out]

((e*x + d)^m*c^2*e^6*g*m^5*x^6 + (e*x + d)^m*c^2*e^6*f*m^5*x^5 + (e*x + d)^m*c^2*d*e^5*g*m^5*x^5 + 2*(e*x + d)
^m*b*c*e^6*g*m^5*x^5 + 15*(e*x + d)^m*c^2*e^6*g*m^4*x^6 + (e*x + d)^m*c^2*d*e^5*f*m^5*x^4 + 2*(e*x + d)^m*b*c*
e^6*f*m^5*x^4 + 2*(e*x + d)^m*b*c*d*e^5*g*m^5*x^4 + (e*x + d)^m*b^2*e^6*g*m^5*x^4 + 2*(e*x + d)^m*a*c*e^6*g*m^
5*x^4 + 16*(e*x + d)^m*c^2*e^6*f*m^4*x^5 + 10*(e*x + d)^m*c^2*d*e^5*g*m^4*x^5 + 32*(e*x + d)^m*b*c*e^6*g*m^4*x
^5 + 85*(e*x + d)^m*c^2*e^6*g*m^3*x^6 + 2*(e*x + d)^m*b*c*d*e^5*f*m^5*x^3 + (e*x + d)^m*b^2*e^6*f*m^5*x^3 + 2*
(e*x + d)^m*a*c*e^6*f*m^5*x^3 + (e*x + d)^m*b^2*d*e^5*g*m^5*x^3 + 2*(e*x + d)^m*a*c*d*e^5*g*m^5*x^3 + 2*(e*x +
d)^m*a*b*e^6*g*m^5*x^3 + 12*(e*x + d)^m*c^2*d*e^5*f*m^4*x^4 + 34*(e*x + d)^m*b*c*e^6*f*m^4*x^4 - 5*(e*x + d)^
m*c^2*d^2*e^4*g*m^4*x^4 + 24*(e*x + d)^m*b*c*d*e^5*g*m^4*x^4 + 17*(e*x + d)^m*b^2*e^6*g*m^4*x^4 + 34*(e*x + d)
^m*a*c*e^6*g*m^4*x^4 + 95*(e*x + d)^m*c^2*e^6*f*m^3*x^5 + 35*(e*x + d)^m*c^2*d*e^5*g*m^3*x^5 + 190*(e*x + d)^m
*b*c*e^6*g*m^3*x^5 + 225*(e*x + d)^m*c^2*e^6*g*m^2*x^6 + (e*x + d)^m*b^2*d*e^5*f*m^5*x^2 + 2*(e*x + d)^m*a*c*d
*e^5*f*m^5*x^2 + 2*(e*x + d)^m*a*b*e^6*f*m^5*x^2 + 2*(e*x + d)^m*a*b*d*e^5*g*m^5*x^2 + (e*x + d)^m*a^2*e^6*g*m
^5*x^2 - 4*(e*x + d)^m*c^2*d^2*e^4*f*m^4*x^3 + 28*(e*x + d)^m*b*c*d*e^5*f*m^4*x^3 + 18*(e*x + d)^m*b^2*e^6*f*m
^4*x^3 + 36*(e*x + d)^m*a*c*e^6*f*m^4*x^3 - 8*(e*x + d)^m*b*c*d^2*e^4*g*m^4*x^3 + 14*(e*x + d)^m*b^2*d*e^5*g*m
^4*x^3 + 28*(e*x + d)^m*a*c*d*e^5*g*m^4*x^3 + 36*(e*x + d)^m*a*b*e^6*g*m^4*x^3 + 47*(e*x + d)^m*c^2*d*e^5*f*m^
3*x^4 + 214*(e*x + d)^m*b*c*e^6*f*m^3*x^4 - 30*(e*x + d)^m*c^2*d^2*e^4*g*m^3*x^4 + 94*(e*x + d)^m*b*c*d*e^5*g*
m^3*x^4 + 107*(e*x + d)^m*b^2*e^6*g*m^3*x^4 + 214*(e*x + d)^m*a*c*e^6*g*m^3*x^4 + 260*(e*x + d)^m*c^2*e^6*f*m^
2*x^5 + 50*(e*x + d)^m*c^2*d*e^5*g*m^2*x^5 + 520*(e*x + d)^m*b*c*e^6*g*m^2*x^5 + 274*(e*x + d)^m*c^2*e^6*g*m*x
^6 + 2*(e*x + d)^m*a*b*d*e^5*f*m^5*x + (e*x + d)^m*a^2*e^6*f*m^5*x + (e*x + d)^m*a^2*d*e^5*g*m^5*x - 6*(e*x +
d)^m*b*c*d^2*e^4*f*m^4*x^2 + 16*(e*x + d)^m*b^2*d*e^5*f*m^4*x^2 + 32*(e*x + d)^m*a*c*d*e^5*f*m^4*x^2 + 38*(e*x
+ d)^m*a*b*e^6*f*m^4*x^2 - 3*(e*x + d)^m*b^2*d^2*e^4*g*m^4*x^2 - 6*(e*x + d)^m*a*c*d^2*e^4*g*m^4*x^2 + 32*(e*
x + d)^m*a*b*d*e^5*g*m^4*x^2 + 19*(e*x + d)^m*a^2*e^6*g*m^4*x^2 - 36*(e*x + d)^m*c^2*d^2*e^4*f*m^3*x^3 + 130*(
e*x + d)^m*b*c*d*e^5*f*m^3*x^3 + 121*(e*x + d)^m*b^2*e^6*f*m^3*x^3 + 242*(e*x + d)^m*a*c*e^6*f*m^3*x^3 + 20*(e
*x + d)^m*c^2*d^3*e^3*g*m^3*x^3 - 72*(e*x + d)^m*b*c*d^2*e^4*g*m^3*x^3 + 65*(e*x + d)^m*b^2*d*e^5*g*m^3*x^3 +
130*(e*x + d)^m*a*c*d*e^5*g*m^3*x^3 + 242*(e*x + d)^m*a*b*e^6*g*m^3*x^3 + 72*(e*x + d)^m*c^2*d*e^5*f*m^2*x^4 +
614*(e*x + d)^m*b*c*e^6*f*m^2*x^4 - 55*(e*x + d)^m*c^2*d^2*e^4*g*m^2*x^4 + 144*(e*x + d)^m*b*c*d*e^5*g*m^2*x^
4 + 307*(e*x + d)^m*b^2*e^6*g*m^2*x^4 + 614*(e*x + d)^m*a*c*e^6*g*m^2*x^4 + 324*(e*x + d)^m*c^2*e^6*f*m*x^5 +
24*(e*x + d)^m*c^2*d*e^5*g*m*x^5 + 648*(e*x + d)^m*b*c*e^6*g*m*x^5 + 120*(e*x + d)^m*c^2*e^6*g*x^6 + (e*x + d)
^m*a^2*d*e^5*f*m^5 - 2*(e*x + d)^m*b^2*d^2*e^4*f*m^4*x - 4*(e*x + d)^m*a*c*d^2*e^4*f*m^4*x + 36*(e*x + d)^m*a*
b*d*e^5*f*m^4*x + 20*(e*x + d)^m*a^2*e^6*f*m^4*x - 4*(e*x + d)^m*a*b*d^2*e^4*g*m^4*x + 18*(e*x + d)^m*a^2*d*e^
5*g*m^4*x + 12*(e*x + d)^m*c^2*d^3*e^3*f*m^3*x^2 - 72*(e*x + d)^m*b*c*d^2*e^4*f*m^3*x^2 + 89*(e*x + d)^m*b^2*d
*e^5*f*m^3*x^2 + 178*(e*x + d)^m*a*c*d*e^5*f*m^3*x^2 + 274*(e*x + d)^m*a*b*e^6*f*m^3*x^2 + 24*(e*x + d)^m*b*c*
d^3*e^3*g*m^3*x^2 - 36*(e*x + d)^m*b^2*d^2*e^4*g*m^3*x^2 - 72*(e*x + d)^m*a*c*d^2*e^4*g*m^3*x^2 + 178*(e*x + d
)^m*a*b*d*e^5*g*m^3*x^2 + 137*(e*x + d)^m*a^2*e^6*g*m^3*x^2 - 80*(e*x + d)^m*c^2*d^2*e^4*f*m^2*x^3 + 224*(e*x
+ d)^m*b*c*d*e^5*f*m^2*x^3 + 372*(e*x + d)^m*b^2*e^6*f*m^2*x^3 + 744*(e*x + d)^m*a*c*e^6*f*m^2*x^3 + 60*(e*x +
d)^m*c^2*d^3*e^3*g*m^2*x^3 - 160*(e*x + d)^m*b*c*d^2*e^4*g*m^2*x^3 + 112*(e*x + d)^m*b^2*d*e^5*g*m^2*x^3 + 22
4*(e*x + d)^m*a*c*d*e^5*g*m^2*x^3 + 744*(e*x + d)^m*a*b*e^6*g*m^2*x^3 + 36*(e*x + d)^m*c^2*d*e^5*f*m*x^4 + 792
*(e*x + d)^m*b*c*e^6*f*m*x^4 - 30*(e*x + d)^m*c^2*d^2*e^4*g*m*x^4 + 72*(e*x + d)^m*b*c*d*e^5*g*m*x^4 + 396*(e*
x + d)^m*b^2*e^6*g*m*x^4 + 792*(e*x + d)^m*a*c*e^6*g*m*x^4 + 144*(e*x + d)^m*c^2*e^6*f*x^5 + 288*(e*x + d)^m*b
*c*e^6*g*x^5 - 2*(e*x + d)^m*a*b*d^2*e^4*f*m^4 + 20*(e*x + d)^m*a^2*d*e^5*f*m^4 - (e*x + d)^m*a^2*d^2*e^4*g*m^
4 + 12*(e*x + d)^m*b*c*d^3*e^3*f*m^3*x - 30*(e*x + d)^m*b^2*d^2*e^4*f*m^3*x - 60*(e*x + d)^m*a*c*d^2*e^4*f*m^3
*x + 238*(e*x + d)^m*a*b*d*e^5*f*m^3*x + 155*(e*x + d)^m*a^2*e^6*f*m^3*x + 6*(e*x + d)^m*b^2*d^3*e^3*g*m^3*x +
12*(e*x + d)^m*a*c*d^3*e^3*g*m^3*x - 60*(e*x + d)^m*a*b*d^2*e^4*g*m^3*x + 119*(e*x + d)^m*a^2*d*e^5*g*m^3*x +
84*(e*x + d)^m*c^2*d^3*e^3*f*m^2*x^2 - 246*(e*x + d)^m*b*c*d^2*e^4*f*m^2*x^2 + 194*(e*x + d)^m*b^2*d*e^5*f*m^
2*x^2 + 388*(e*x + d)^m*a*c*d*e^5*f*m^2*x^2 + 922*(e*x + d)^m*a*b*e^6*f*m^2*x^2 - 60*(e*x + d)^m*c^2*d^4*e^2*g
*m^2*x^2 + 168*(e*x + d)^m*b*c*d^3*e^3*g*m^2*x^2 - 123*(e*x + d)^m*b^2*d^2*e^4*g*m^2*x^2 - 246*(e*x + d)^m*a*c
*d^2*e^4*g*m^2*x^2 + 388*(e*x + d)^m*a*b*d*e^5*g*m^2*x^2 + 461*(e*x + d)^m*a^2*e^6*g*m^2*x^2 - 48*(e*x + d)^m*
c^2*d^2*e^4*f*m*x^3 + 120*(e*x + d)^m*b*c*d*e^5*f*m*x^3 + 508*(e*x + d)^m*b^2*e^6*f*m*x^3 + 1016*(e*x + d)^m*a
*c*e^6*f*m*x^3 + 40*(e*x + d)^m*c^2*d^3*e^3*g*m*x^3 - 96*(e*x + d)^m*b*c*d^2*e^4*g*m*x^3 + 60*(e*x + d)^m*b^2*
d*e^5*g*m*x^3 + 120*(e*x + d)^m*a*c*d*e^5*g*m*x^3 + 1016*(e*x + d)^m*a*b*e^6*g*m*x^3 + 360*(e*x + d)^m*b*c*e^6
*f*x^4 + 180*(e*x + d)^m*b^2*e^6*g*x^4 + 360*(e*x + d)^m*a*c*e^6*g*x^4 + 2*(e*x + d)^m*b^2*d^3*e^3*f*m^3 + 4*(
e*x + d)^m*a*c*d^3*e^3*f*m^3 - 36*(e*x + d)^m*a*b*d^2*e^4*f*m^3 + 155*(e*x + d)^m*a^2*d*e^5*f*m^3 + 4*(e*x + d
)^m*a*b*d^3*e^3*g*m^3 - 18*(e*x + d)^m*a^2*d^2*e^4*g*m^3 - 24*(e*x + d)^m*c^2*d^4*e^2*f*m^2*x + 132*(e*x + d)^
m*b*c*d^3*e^3*f*m^2*x - 148*(e*x + d)^m*b^2*d^2*e^4*f*m^2*x - 296*(e*x + d)^m*a*c*d^2*e^4*f*m^2*x + 684*(e*x +
d)^m*a*b*d*e^5*f*m^2*x + 580*(e*x + d)^m*a^2*e^6*f*m^2*x - 48*(e*x + d)^m*b*c*d^4*e^2*g*m^2*x + 66*(e*x + d)^
m*b^2*d^3*e^3*g*m^2*x + 132*(e*x + d)^m*a*c*d^3*e^3*g*m^2*x - 296*(e*x + d)^m*a*b*d^2*e^4*g*m^2*x + 342*(e*x +
d)^m*a^2*d*e^5*g*m^2*x + 72*(e*x + d)^m*c^2*d^3*e^3*f*m*x^2 - 180*(e*x + d)^m*b*c*d^2*e^4*f*m*x^2 + 120*(e*x
+ d)^m*b^2*d*e^5*f*m*x^2 + 240*(e*x + d)^m*a*c*d*e^5*f*m*x^2 + 1404*(e*x + d)^m*a*b*e^6*f*m*x^2 - 60*(e*x + d)
^m*c^2*d^4*e^2*g*m*x^2 + 144*(e*x + d)^m*b*c*d^3*e^3*g*m*x^2 - 90*(e*x + d)^m*b^2*d^2*e^4*g*m*x^2 - 180*(e*x +
d)^m*a*c*d^2*e^4*g*m*x^2 + 240*(e*x + d)^m*a*b*d*e^5*g*m*x^2 + 702*(e*x + d)^m*a^2*e^6*g*m*x^2 + 240*(e*x + d
)^m*b^2*e^6*f*x^3 + 480*(e*x + d)^m*a*c*e^6*f*x^3 + 480*(e*x + d)^m*a*b*e^6*g*x^3 - 12*(e*x + d)^m*b*c*d^4*e^2
*f*m^2 + 30*(e*x + d)^m*b^2*d^3*e^3*f*m^2 + 60*(e*x + d)^m*a*c*d^3*e^3*f*m^2 - 238*(e*x + d)^m*a*b*d^2*e^4*f*m
^2 + 580*(e*x + d)^m*a^2*d*e^5*f*m^2 - 6*(e*x + d)^m*b^2*d^4*e^2*g*m^2 - 12*(e*x + d)^m*a*c*d^4*e^2*g*m^2 + 60
*(e*x + d)^m*a*b*d^3*e^3*g*m^2 - 119*(e*x + d)^m*a^2*d^2*e^4*g*m^2 - 144*(e*x + d)^m*c^2*d^4*e^2*f*m*x + 360*(
e*x + d)^m*b*c*d^3*e^3*f*m*x - 240*(e*x + d)^m*b^2*d^2*e^4*f*m*x - 480*(e*x + d)^m*a*c*d^2*e^4*f*m*x + 720*(e*
x + d)^m*a*b*d*e^5*f*m*x + 1044*(e*x + d)^m*a^2*e^6*f*m*x + 120*(e*x + d)^m*c^2*d^5*e*g*m*x - 288*(e*x + d)^m*
b*c*d^4*e^2*g*m*x + 180*(e*x + d)^m*b^2*d^3*e^3*g*m*x + 360*(e*x + d)^m*a*c*d^3*e^3*g*m*x - 480*(e*x + d)^m*a*
b*d^2*e^4*g*m*x + 360*(e*x + d)^m*a^2*d*e^5*g*m*x + 720*(e*x + d)^m*a*b*e^6*f*x^2 + 360*(e*x + d)^m*a^2*e^6*g*
x^2 + 24*(e*x + d)^m*c^2*d^5*e*f*m - 132*(e*x + d)^m*b*c*d^4*e^2*f*m + 148*(e*x + d)^m*b^2*d^3*e^3*f*m + 296*(
e*x + d)^m*a*c*d^3*e^3*f*m - 684*(e*x + d)^m*a*b*d^2*e^4*f*m + 1044*(e*x + d)^m*a^2*d*e^5*f*m + 48*(e*x + d)^m
*b*c*d^5*e*g*m - 66*(e*x + d)^m*b^2*d^4*e^2*g*m - 132*(e*x + d)^m*a*c*d^4*e^2*g*m + 296*(e*x + d)^m*a*b*d^3*e^
3*g*m - 342*(e*x + d)^m*a^2*d^2*e^4*g*m + 720*(e*x + d)^m*a^2*e^6*f*x + 144*(e*x + d)^m*c^2*d^5*e*f - 360*(e*x
+ d)^m*b*c*d^4*e^2*f + 240*(e*x + d)^m*b^2*d^3*e^3*f + 480*(e*x + d)^m*a*c*d^3*e^3*f - 720*(e*x + d)^m*a*b*d^
2*e^4*f + 720*(e*x + d)^m*a^2*d*e^5*f - 120*(e*x + d)^m*c^2*d^6*g + 288*(e*x + d)^m*b*c*d^5*e*g - 180*(e*x + d
)^m*b^2*d^4*e^2*g - 360*(e*x + d)^m*a*c*d^4*e^2*g + 480*(e*x + d)^m*a*b*d^3*e^3*g - 360*(e*x + d)^m*a^2*d^2*e^
4*g)/(e^6*m^6 + 21*e^6*m^5 + 175*e^6*m^4 + 735*e^6*m^3 + 1624*e^6*m^2 + 1764*e^6*m + 720*e^6)

Mupad [B] (verification not implemented)

Time = 13.68 (sec) , antiderivative size = 2307, normalized size of antiderivative = 7.42 \[ \int (d+e x)^m (f+g x) \left (a+b x+c x^2\right )^2 \, dx=\text {Too large to display} \]

[In]

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

[Out]

((d + e*x)^m*(240*b^2*d^3*e^3*f - 360*a^2*d^2*e^4*g - 120*c^2*d^6*g - 180*b^2*d^4*e^2*g + 720*a^2*d*e^5*f + 14
4*c^2*d^5*e*f - 720*a*b*d^2*e^4*f + 480*a*b*d^3*e^3*g + 480*a*c*d^3*e^3*f - 360*a*c*d^4*e^2*g - 360*b*c*d^4*e^
2*f + 1044*a^2*d*e^5*f*m + 24*c^2*d^5*e*f*m + 580*a^2*d*e^5*f*m^2 + 155*a^2*d*e^5*f*m^3 + 20*a^2*d*e^5*f*m^4 +
a^2*d*e^5*f*m^5 - 342*a^2*d^2*e^4*g*m + 148*b^2*d^3*e^3*f*m - 66*b^2*d^4*e^2*g*m + 288*b*c*d^5*e*g - 119*a^2*
d^2*e^4*g*m^2 + 30*b^2*d^3*e^3*f*m^2 - 18*a^2*d^2*e^4*g*m^3 + 2*b^2*d^3*e^3*f*m^3 - a^2*d^2*e^4*g*m^4 - 6*b^2*
d^4*e^2*g*m^2 + 48*b*c*d^5*e*g*m - 684*a*b*d^2*e^4*f*m + 296*a*b*d^3*e^3*g*m + 296*a*c*d^3*e^3*f*m - 132*a*c*d
^4*e^2*g*m - 132*b*c*d^4*e^2*f*m - 238*a*b*d^2*e^4*f*m^2 - 36*a*b*d^2*e^4*f*m^3 - 2*a*b*d^2*e^4*f*m^4 + 60*a*b
*d^3*e^3*g*m^2 + 60*a*c*d^3*e^3*f*m^2 + 4*a*b*d^3*e^3*g*m^3 + 4*a*c*d^3*e^3*f*m^3 - 12*a*c*d^4*e^2*g*m^2 - 12*
b*c*d^4*e^2*f*m^2))/(e^6*(1764*m + 1624*m^2 + 735*m^3 + 175*m^4 + 21*m^5 + m^6 + 720)) + (x*(d + e*x)^m*(720*a
^2*e^6*f + 580*a^2*e^6*f*m^2 + 155*a^2*e^6*f*m^3 + 20*a^2*e^6*f*m^4 + a^2*e^6*f*m^5 + 1044*a^2*e^6*f*m + 360*a
^2*d*e^5*g*m + 120*c^2*d^5*e*g*m - 240*b^2*d^2*e^4*f*m + 342*a^2*d*e^5*g*m^2 + 119*a^2*d*e^5*g*m^3 + 18*a^2*d*
e^5*g*m^4 + a^2*d*e^5*g*m^5 + 180*b^2*d^3*e^3*g*m - 144*c^2*d^4*e^2*f*m - 148*b^2*d^2*e^4*f*m^2 - 30*b^2*d^2*e
^4*f*m^3 - 2*b^2*d^2*e^4*f*m^4 + 66*b^2*d^3*e^3*g*m^2 - 24*c^2*d^4*e^2*f*m^2 + 6*b^2*d^3*e^3*g*m^3 + 720*a*b*d
*e^5*f*m + 684*a*b*d*e^5*f*m^2 + 238*a*b*d*e^5*f*m^3 + 36*a*b*d*e^5*f*m^4 + 2*a*b*d*e^5*f*m^5 - 480*a*b*d^2*e^
4*g*m - 480*a*c*d^2*e^4*f*m + 360*a*c*d^3*e^3*g*m + 360*b*c*d^3*e^3*f*m - 288*b*c*d^4*e^2*g*m - 296*a*b*d^2*e^
4*g*m^2 - 296*a*c*d^2*e^4*f*m^2 - 60*a*b*d^2*e^4*g*m^3 - 60*a*c*d^2*e^4*f*m^3 - 4*a*b*d^2*e^4*g*m^4 - 4*a*c*d^
2*e^4*f*m^4 + 132*a*c*d^3*e^3*g*m^2 + 132*b*c*d^3*e^3*f*m^2 + 12*a*c*d^3*e^3*g*m^3 + 12*b*c*d^3*e^3*f*m^3 - 48
*b*c*d^4*e^2*g*m^2))/(e^6*(1764*m + 1624*m^2 + 735*m^3 + 175*m^4 + 21*m^5 + m^6 + 720)) + (x^3*(d + e*x)^m*(3*
m + m^2 + 2)*(120*b^2*e^3*f + 15*b^2*e^3*f*m^2 + b^2*e^3*f*m^3 + 240*a*b*e^3*g + 240*a*c*e^3*f + 74*b^2*e^3*f*
m + 20*c^2*d^3*g*m + 30*a*b*e^3*g*m^2 + 30*a*c*e^3*f*m^2 + 2*a*b*e^3*g*m^3 + 2*a*c*e^3*f*m^3 + 30*b^2*d*e^2*g*
m - 24*c^2*d^2*e*f*m + 11*b^2*d*e^2*g*m^2 - 4*c^2*d^2*e*f*m^2 + b^2*d*e^2*g*m^3 + 148*a*b*e^3*g*m + 148*a*c*e^
3*f*m + 60*a*c*d*e^2*g*m + 60*b*c*d*e^2*f*m - 48*b*c*d^2*e*g*m + 22*a*c*d*e^2*g*m^2 + 22*b*c*d*e^2*f*m^2 + 2*a
*c*d*e^2*g*m^3 + 2*b*c*d*e^2*f*m^3 - 8*b*c*d^2*e*g*m^2))/(e^3*(1764*m + 1624*m^2 + 735*m^3 + 175*m^4 + 21*m^5
+ m^6 + 720)) + (x^4*(d + e*x)^m*(11*m + 6*m^2 + m^3 + 6)*(30*b^2*e^2*g + b^2*e^2*g*m^2 + 60*a*c*e^2*g + 60*b*
c*e^2*f + 11*b^2*e^2*g*m - 5*c^2*d^2*g*m + 2*a*c*e^2*g*m^2 + 2*b*c*e^2*f*m^2 + c^2*d*e*f*m^2 + 22*a*c*e^2*g*m
+ 22*b*c*e^2*f*m + 6*c^2*d*e*f*m + 2*b*c*d*e*g*m^2 + 12*b*c*d*e*g*m))/(e^2*(1764*m + 1624*m^2 + 735*m^3 + 175*
m^4 + 21*m^5 + m^6 + 720)) + (c^2*g*x^6*(d + e*x)^m*(274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5 + 120))/(1764*m +
1624*m^2 + 735*m^3 + 175*m^4 + 21*m^5 + m^6 + 720) + (x^2*(m + 1)*(d + e*x)^m*(360*a^2*e^4*g + 119*a^2*e^4*g*
m^2 + 18*a^2*e^4*g*m^3 + a^2*e^4*g*m^4 + 720*a*b*e^4*f + 342*a^2*e^4*g*m - 60*c^2*d^4*g*m + 238*a*b*e^4*f*m^2
+ 36*a*b*e^4*f*m^3 + 2*a*b*e^4*f*m^4 + 120*b^2*d*e^3*f*m + 72*c^2*d^3*e*f*m + 74*b^2*d*e^3*f*m^2 + 15*b^2*d*e^
3*f*m^3 + b^2*d*e^3*f*m^4 - 90*b^2*d^2*e^2*g*m + 12*c^2*d^3*e*f*m^2 + 684*a*b*e^4*f*m - 33*b^2*d^2*e^2*g*m^2 -
3*b^2*d^2*e^2*g*m^3 + 240*a*b*d*e^3*g*m + 240*a*c*d*e^3*f*m + 144*b*c*d^3*e*g*m + 148*a*b*d*e^3*g*m^2 + 148*a
*c*d*e^3*f*m^2 + 30*a*b*d*e^3*g*m^3 + 30*a*c*d*e^3*f*m^3 + 2*a*b*d*e^3*g*m^4 + 2*a*c*d*e^3*f*m^4 - 180*a*c*d^2
*e^2*g*m - 180*b*c*d^2*e^2*f*m + 24*b*c*d^3*e*g*m^2 - 66*a*c*d^2*e^2*g*m^2 - 66*b*c*d^2*e^2*f*m^2 - 6*a*c*d^2*
e^2*g*m^3 - 6*b*c*d^2*e^2*f*m^3))/(e^4*(1764*m + 1624*m^2 + 735*m^3 + 175*m^4 + 21*m^5 + m^6 + 720)) + (c*x^5*
(d + e*x)^m*(50*m + 35*m^2 + 10*m^3 + m^4 + 24)*(12*b*e*g + 6*c*e*f + 2*b*e*g*m + c*d*g*m + c*e*f*m))/(e*(1764
*m + 1624*m^2 + 735*m^3 + 175*m^4 + 21*m^5 + m^6 + 720))