3.269 \(\int x^m (A+B x^2) (b x^2+c x^4)^3 \, dx\)
Optimal. Leaf size=96 \[ \frac {A b^3 x^{m+7}}{m+7}+\frac {b^2 x^{m+9} (3 A c+b B)}{m+9}+\frac {c^2 x^{m+13} (A c+3 b B)}{m+13}+\frac {3 b c x^{m+11} (A c+b B)}{m+11}+\frac {B c^3 x^{m+15}}{m+15} \]
[Out]
A*b^3*x^(7+m)/(7+m)+b^2*(3*A*c+B*b)*x^(9+m)/(9+m)+3*b*c*(A*c+B*b)*x^(11+m)/(11+m)+c^2*(A*c+3*B*b)*x^(13+m)/(13
+m)+B*c^3*x^(15+m)/(15+m)
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Rubi [A] time = 0.07, antiderivative size = 96, normalized size of antiderivative = 1.00,
number of steps used = 3, number of rules used = 2, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used =
{1584, 448} \[ \frac {b^2 x^{m+9} (3 A c+b B)}{m+9}+\frac {A b^3 x^{m+7}}{m+7}+\frac {c^2 x^{m+13} (A c+3 b B)}{m+13}+\frac {3 b c x^{m+11} (A c+b B)}{m+11}+\frac {B c^3 x^{m+15}}{m+15} \]
Antiderivative was successfully verified.
[In]
Int[x^m*(A + B*x^2)*(b*x^2 + c*x^4)^3,x]
[Out]
(A*b^3*x^(7 + m))/(7 + m) + (b^2*(b*B + 3*A*c)*x^(9 + m))/(9 + m) + (3*b*c*(b*B + A*c)*x^(11 + m))/(11 + m) +
(c^2*(3*b*B + A*c)*x^(13 + m))/(13 + m) + (B*c^3*x^(15 + m))/(15 + m)
Rule 448
Int[((e_.)*(x_))^(m_.)*((a_) + (b_.)*(x_)^(n_))^(p_.)*((c_) + (d_.)*(x_)^(n_))^(q_.), x_Symbol] :> Int[ExpandI
ntegrand[(e*x)^m*(a + b*x^n)^p*(c + d*x^n)^q, x], x] /; FreeQ[{a, b, c, d, e, m, n}, x] && NeQ[b*c - a*d, 0] &
& IGtQ[p, 0] && IGtQ[q, 0]
Rule 1584
Int[(u_.)*(x_)^(m_.)*((a_.)*(x_)^(p_.) + (b_.)*(x_)^(q_.))^(n_.), x_Symbol] :> Int[u*x^(m + n*p)*(a + b*x^(q -
p))^n, x] /; FreeQ[{a, b, m, p, q}, x] && IntegerQ[n] && PosQ[q - p]
Rubi steps
\begin {align*} \int x^m \left (A+B x^2\right ) \left (b x^2+c x^4\right )^3 \, dx &=\int x^{6+m} \left (A+B x^2\right ) \left (b+c x^2\right )^3 \, dx\\ &=\int \left (A b^3 x^{6+m}+b^2 (b B+3 A c) x^{8+m}+3 b c (b B+A c) x^{10+m}+c^2 (3 b B+A c) x^{12+m}+B c^3 x^{14+m}\right ) \, dx\\ &=\frac {A b^3 x^{7+m}}{7+m}+\frac {b^2 (b B+3 A c) x^{9+m}}{9+m}+\frac {3 b c (b B+A c) x^{11+m}}{11+m}+\frac {c^2 (3 b B+A c) x^{13+m}}{13+m}+\frac {B c^3 x^{15+m}}{15+m}\\ \end {align*}
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Mathematica [A] time = 0.14, size = 89, normalized size = 0.93 \[ x^{m+7} \left (\frac {A b^3}{m+7}+\frac {b^2 x^2 (3 A c+b B)}{m+9}+\frac {c^2 x^6 (A c+3 b B)}{m+13}+\frac {3 b c x^4 (A c+b B)}{m+11}+\frac {B c^3 x^8}{m+15}\right ) \]
Antiderivative was successfully verified.
[In]
Integrate[x^m*(A + B*x^2)*(b*x^2 + c*x^4)^3,x]
[Out]
x^(7 + m)*((A*b^3)/(7 + m) + (b^2*(b*B + 3*A*c)*x^2)/(9 + m) + (3*b*c*(b*B + A*c)*x^4)/(11 + m) + (c^2*(3*b*B
+ A*c)*x^6)/(13 + m) + (B*c^3*x^8)/(15 + m))
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fricas [B] time = 0.91, size = 381, normalized size = 3.97 \[ \frac {{\left ({\left (B c^{3} m^{4} + 40 \, B c^{3} m^{3} + 590 \, B c^{3} m^{2} + 3800 \, B c^{3} m + 9009 \, B c^{3}\right )} x^{15} + {\left ({\left (3 \, B b c^{2} + A c^{3}\right )} m^{4} + 31185 \, B b c^{2} + 10395 \, A c^{3} + 42 \, {\left (3 \, B b c^{2} + A c^{3}\right )} m^{3} + 644 \, {\left (3 \, B b c^{2} + A c^{3}\right )} m^{2} + 4278 \, {\left (3 \, B b c^{2} + A c^{3}\right )} m\right )} x^{13} + 3 \, {\left ({\left (B b^{2} c + A b c^{2}\right )} m^{4} + 12285 \, B b^{2} c + 12285 \, A b c^{2} + 44 \, {\left (B b^{2} c + A b c^{2}\right )} m^{3} + 706 \, {\left (B b^{2} c + A b c^{2}\right )} m^{2} + 4884 \, {\left (B b^{2} c + A b c^{2}\right )} m\right )} x^{11} + {\left ({\left (B b^{3} + 3 \, A b^{2} c\right )} m^{4} + 15015 \, B b^{3} + 45045 \, A b^{2} c + 46 \, {\left (B b^{3} + 3 \, A b^{2} c\right )} m^{3} + 776 \, {\left (B b^{3} + 3 \, A b^{2} c\right )} m^{2} + 5666 \, {\left (B b^{3} + 3 \, A b^{2} c\right )} m\right )} x^{9} + {\left (A b^{3} m^{4} + 48 \, A b^{3} m^{3} + 854 \, A b^{3} m^{2} + 6672 \, A b^{3} m + 19305 \, A b^{3}\right )} x^{7}\right )} x^{m}}{m^{5} + 55 \, m^{4} + 1190 \, m^{3} + 12650 \, m^{2} + 66009 \, m + 135135} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(x^m*(B*x^2+A)*(c*x^4+b*x^2)^3,x, algorithm="fricas")
[Out]
((B*c^3*m^4 + 40*B*c^3*m^3 + 590*B*c^3*m^2 + 3800*B*c^3*m + 9009*B*c^3)*x^15 + ((3*B*b*c^2 + A*c^3)*m^4 + 3118
5*B*b*c^2 + 10395*A*c^3 + 42*(3*B*b*c^2 + A*c^3)*m^3 + 644*(3*B*b*c^2 + A*c^3)*m^2 + 4278*(3*B*b*c^2 + A*c^3)*
m)*x^13 + 3*((B*b^2*c + A*b*c^2)*m^4 + 12285*B*b^2*c + 12285*A*b*c^2 + 44*(B*b^2*c + A*b*c^2)*m^3 + 706*(B*b^2
*c + A*b*c^2)*m^2 + 4884*(B*b^2*c + A*b*c^2)*m)*x^11 + ((B*b^3 + 3*A*b^2*c)*m^4 + 15015*B*b^3 + 45045*A*b^2*c
+ 46*(B*b^3 + 3*A*b^2*c)*m^3 + 776*(B*b^3 + 3*A*b^2*c)*m^2 + 5666*(B*b^3 + 3*A*b^2*c)*m)*x^9 + (A*b^3*m^4 + 48
*A*b^3*m^3 + 854*A*b^3*m^2 + 6672*A*b^3*m + 19305*A*b^3)*x^7)*x^m/(m^5 + 55*m^4 + 1190*m^3 + 12650*m^2 + 66009
*m + 135135)
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giac [B] time = 0.22, size = 603, normalized size = 6.28 \[ \frac {B c^{3} m^{4} x^{15} x^{m} + 40 \, B c^{3} m^{3} x^{15} x^{m} + 3 \, B b c^{2} m^{4} x^{13} x^{m} + A c^{3} m^{4} x^{13} x^{m} + 590 \, B c^{3} m^{2} x^{15} x^{m} + 126 \, B b c^{2} m^{3} x^{13} x^{m} + 42 \, A c^{3} m^{3} x^{13} x^{m} + 3800 \, B c^{3} m x^{15} x^{m} + 3 \, B b^{2} c m^{4} x^{11} x^{m} + 3 \, A b c^{2} m^{4} x^{11} x^{m} + 1932 \, B b c^{2} m^{2} x^{13} x^{m} + 644 \, A c^{3} m^{2} x^{13} x^{m} + 9009 \, B c^{3} x^{15} x^{m} + 132 \, B b^{2} c m^{3} x^{11} x^{m} + 132 \, A b c^{2} m^{3} x^{11} x^{m} + 12834 \, B b c^{2} m x^{13} x^{m} + 4278 \, A c^{3} m x^{13} x^{m} + B b^{3} m^{4} x^{9} x^{m} + 3 \, A b^{2} c m^{4} x^{9} x^{m} + 2118 \, B b^{2} c m^{2} x^{11} x^{m} + 2118 \, A b c^{2} m^{2} x^{11} x^{m} + 31185 \, B b c^{2} x^{13} x^{m} + 10395 \, A c^{3} x^{13} x^{m} + 46 \, B b^{3} m^{3} x^{9} x^{m} + 138 \, A b^{2} c m^{3} x^{9} x^{m} + 14652 \, B b^{2} c m x^{11} x^{m} + 14652 \, A b c^{2} m x^{11} x^{m} + A b^{3} m^{4} x^{7} x^{m} + 776 \, B b^{3} m^{2} x^{9} x^{m} + 2328 \, A b^{2} c m^{2} x^{9} x^{m} + 36855 \, B b^{2} c x^{11} x^{m} + 36855 \, A b c^{2} x^{11} x^{m} + 48 \, A b^{3} m^{3} x^{7} x^{m} + 5666 \, B b^{3} m x^{9} x^{m} + 16998 \, A b^{2} c m x^{9} x^{m} + 854 \, A b^{3} m^{2} x^{7} x^{m} + 15015 \, B b^{3} x^{9} x^{m} + 45045 \, A b^{2} c x^{9} x^{m} + 6672 \, A b^{3} m x^{7} x^{m} + 19305 \, A b^{3} x^{7} x^{m}}{m^{5} + 55 \, m^{4} + 1190 \, m^{3} + 12650 \, m^{2} + 66009 \, m + 135135} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(x^m*(B*x^2+A)*(c*x^4+b*x^2)^3,x, algorithm="giac")
[Out]
(B*c^3*m^4*x^15*x^m + 40*B*c^3*m^3*x^15*x^m + 3*B*b*c^2*m^4*x^13*x^m + A*c^3*m^4*x^13*x^m + 590*B*c^3*m^2*x^15
*x^m + 126*B*b*c^2*m^3*x^13*x^m + 42*A*c^3*m^3*x^13*x^m + 3800*B*c^3*m*x^15*x^m + 3*B*b^2*c*m^4*x^11*x^m + 3*A
*b*c^2*m^4*x^11*x^m + 1932*B*b*c^2*m^2*x^13*x^m + 644*A*c^3*m^2*x^13*x^m + 9009*B*c^3*x^15*x^m + 132*B*b^2*c*m
^3*x^11*x^m + 132*A*b*c^2*m^3*x^11*x^m + 12834*B*b*c^2*m*x^13*x^m + 4278*A*c^3*m*x^13*x^m + B*b^3*m^4*x^9*x^m
+ 3*A*b^2*c*m^4*x^9*x^m + 2118*B*b^2*c*m^2*x^11*x^m + 2118*A*b*c^2*m^2*x^11*x^m + 31185*B*b*c^2*x^13*x^m + 103
95*A*c^3*x^13*x^m + 46*B*b^3*m^3*x^9*x^m + 138*A*b^2*c*m^3*x^9*x^m + 14652*B*b^2*c*m*x^11*x^m + 14652*A*b*c^2*
m*x^11*x^m + A*b^3*m^4*x^7*x^m + 776*B*b^3*m^2*x^9*x^m + 2328*A*b^2*c*m^2*x^9*x^m + 36855*B*b^2*c*x^11*x^m + 3
6855*A*b*c^2*x^11*x^m + 48*A*b^3*m^3*x^7*x^m + 5666*B*b^3*m*x^9*x^m + 16998*A*b^2*c*m*x^9*x^m + 854*A*b^3*m^2*
x^7*x^m + 15015*B*b^3*x^9*x^m + 45045*A*b^2*c*x^9*x^m + 6672*A*b^3*m*x^7*x^m + 19305*A*b^3*x^7*x^m)/(m^5 + 55*
m^4 + 1190*m^3 + 12650*m^2 + 66009*m + 135135)
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maple [B] time = 0.05, size = 474, normalized size = 4.94 \[ \frac {\left (B \,c^{3} m^{4} x^{8}+40 B \,c^{3} m^{3} x^{8}+A \,c^{3} m^{4} x^{6}+3 B b \,c^{2} m^{4} x^{6}+590 B \,c^{3} m^{2} x^{8}+42 A \,c^{3} m^{3} x^{6}+126 B b \,c^{2} m^{3} x^{6}+3800 B \,c^{3} m \,x^{8}+3 A b \,c^{2} m^{4} x^{4}+644 A \,c^{3} m^{2} x^{6}+3 B \,b^{2} c \,m^{4} x^{4}+1932 B b \,c^{2} m^{2} x^{6}+9009 B \,c^{3} x^{8}+132 A b \,c^{2} m^{3} x^{4}+4278 A \,c^{3} m \,x^{6}+132 B \,b^{2} c \,m^{3} x^{4}+12834 B b \,c^{2} m \,x^{6}+3 A \,b^{2} c \,m^{4} x^{2}+2118 A b \,c^{2} m^{2} x^{4}+10395 A \,c^{3} x^{6}+B \,b^{3} m^{4} x^{2}+2118 B \,b^{2} c \,m^{2} x^{4}+31185 B b \,c^{2} x^{6}+138 A \,b^{2} c \,m^{3} x^{2}+14652 A b \,c^{2} m \,x^{4}+46 B \,b^{3} m^{3} x^{2}+14652 B \,b^{2} c m \,x^{4}+A \,b^{3} m^{4}+2328 A \,b^{2} c \,m^{2} x^{2}+36855 A b \,c^{2} x^{4}+776 B \,b^{3} m^{2} x^{2}+36855 B \,b^{2} c \,x^{4}+48 A \,b^{3} m^{3}+16998 A \,b^{2} c m \,x^{2}+5666 B \,b^{3} m \,x^{2}+854 A \,b^{3} m^{2}+45045 A \,b^{2} c \,x^{2}+15015 B \,b^{3} x^{2}+6672 A \,b^{3} m +19305 A \,b^{3}\right ) x^{m +7}}{\left (m +15\right ) \left (m +13\right ) \left (m +11\right ) \left (m +9\right ) \left (m +7\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(x^m*(B*x^2+A)*(c*x^4+b*x^2)^3,x)
[Out]
x^(m+7)*(B*c^3*m^4*x^8+40*B*c^3*m^3*x^8+A*c^3*m^4*x^6+3*B*b*c^2*m^4*x^6+590*B*c^3*m^2*x^8+42*A*c^3*m^3*x^6+126
*B*b*c^2*m^3*x^6+3800*B*c^3*m*x^8+3*A*b*c^2*m^4*x^4+644*A*c^3*m^2*x^6+3*B*b^2*c*m^4*x^4+1932*B*b*c^2*m^2*x^6+9
009*B*c^3*x^8+132*A*b*c^2*m^3*x^4+4278*A*c^3*m*x^6+132*B*b^2*c*m^3*x^4+12834*B*b*c^2*m*x^6+3*A*b^2*c*m^4*x^2+2
118*A*b*c^2*m^2*x^4+10395*A*c^3*x^6+B*b^3*m^4*x^2+2118*B*b^2*c*m^2*x^4+31185*B*b*c^2*x^6+138*A*b^2*c*m^3*x^2+1
4652*A*b*c^2*m*x^4+46*B*b^3*m^3*x^2+14652*B*b^2*c*m*x^4+A*b^3*m^4+2328*A*b^2*c*m^2*x^2+36855*A*b*c^2*x^4+776*B
*b^3*m^2*x^2+36855*B*b^2*c*x^4+48*A*b^3*m^3+16998*A*b^2*c*m*x^2+5666*B*b^3*m*x^2+854*A*b^3*m^2+45045*A*b^2*c*x
^2+15015*B*b^3*x^2+6672*A*b^3*m+19305*A*b^3)/(m+15)/(m+13)/(m+11)/(m+9)/(m+7)
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maxima [A] time = 1.37, size = 129, normalized size = 1.34 \[ \frac {B c^{3} x^{m + 15}}{m + 15} + \frac {3 \, B b c^{2} x^{m + 13}}{m + 13} + \frac {A c^{3} x^{m + 13}}{m + 13} + \frac {3 \, B b^{2} c x^{m + 11}}{m + 11} + \frac {3 \, A b c^{2} x^{m + 11}}{m + 11} + \frac {B b^{3} x^{m + 9}}{m + 9} + \frac {3 \, A b^{2} c x^{m + 9}}{m + 9} + \frac {A b^{3} x^{m + 7}}{m + 7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(x^m*(B*x^2+A)*(c*x^4+b*x^2)^3,x, algorithm="maxima")
[Out]
B*c^3*x^(m + 15)/(m + 15) + 3*B*b*c^2*x^(m + 13)/(m + 13) + A*c^3*x^(m + 13)/(m + 13) + 3*B*b^2*c*x^(m + 11)/(
m + 11) + 3*A*b*c^2*x^(m + 11)/(m + 11) + B*b^3*x^(m + 9)/(m + 9) + 3*A*b^2*c*x^(m + 9)/(m + 9) + A*b^3*x^(m +
7)/(m + 7)
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mupad [B] time = 0.48, size = 291, normalized size = 3.03 \[ \frac {A\,b^3\,x^m\,x^7\,\left (m^4+48\,m^3+854\,m^2+6672\,m+19305\right )}{m^5+55\,m^4+1190\,m^3+12650\,m^2+66009\,m+135135}+\frac {B\,c^3\,x^m\,x^{15}\,\left (m^4+40\,m^3+590\,m^2+3800\,m+9009\right )}{m^5+55\,m^4+1190\,m^3+12650\,m^2+66009\,m+135135}+\frac {b^2\,x^m\,x^9\,\left (3\,A\,c+B\,b\right )\,\left (m^4+46\,m^3+776\,m^2+5666\,m+15015\right )}{m^5+55\,m^4+1190\,m^3+12650\,m^2+66009\,m+135135}+\frac {c^2\,x^m\,x^{13}\,\left (A\,c+3\,B\,b\right )\,\left (m^4+42\,m^3+644\,m^2+4278\,m+10395\right )}{m^5+55\,m^4+1190\,m^3+12650\,m^2+66009\,m+135135}+\frac {3\,b\,c\,x^m\,x^{11}\,\left (A\,c+B\,b\right )\,\left (m^4+44\,m^3+706\,m^2+4884\,m+12285\right )}{m^5+55\,m^4+1190\,m^3+12650\,m^2+66009\,m+135135} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(x^m*(A + B*x^2)*(b*x^2 + c*x^4)^3,x)
[Out]
(A*b^3*x^m*x^7*(6672*m + 854*m^2 + 48*m^3 + m^4 + 19305))/(66009*m + 12650*m^2 + 1190*m^3 + 55*m^4 + m^5 + 135
135) + (B*c^3*x^m*x^15*(3800*m + 590*m^2 + 40*m^3 + m^4 + 9009))/(66009*m + 12650*m^2 + 1190*m^3 + 55*m^4 + m^
5 + 135135) + (b^2*x^m*x^9*(3*A*c + B*b)*(5666*m + 776*m^2 + 46*m^3 + m^4 + 15015))/(66009*m + 12650*m^2 + 119
0*m^3 + 55*m^4 + m^5 + 135135) + (c^2*x^m*x^13*(A*c + 3*B*b)*(4278*m + 644*m^2 + 42*m^3 + m^4 + 10395))/(66009
*m + 12650*m^2 + 1190*m^3 + 55*m^4 + m^5 + 135135) + (3*b*c*x^m*x^11*(A*c + B*b)*(4884*m + 706*m^2 + 44*m^3 +
m^4 + 12285))/(66009*m + 12650*m^2 + 1190*m^3 + 55*m^4 + m^5 + 135135)
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sympy [A] time = 9.05, size = 2077, normalized size = 21.64 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(x**m*(B*x**2+A)*(c*x**4+b*x**2)**3,x)
[Out]
Piecewise((-A*b**3/(8*x**8) - A*b**2*c/(2*x**6) - 3*A*b*c**2/(4*x**4) - A*c**3/(2*x**2) - B*b**3/(6*x**6) - 3*
B*b**2*c/(4*x**4) - 3*B*b*c**2/(2*x**2) + B*c**3*log(x), Eq(m, -15)), (-A*b**3/(6*x**6) - 3*A*b**2*c/(4*x**4)
- 3*A*b*c**2/(2*x**2) + A*c**3*log(x) - B*b**3/(4*x**4) - 3*B*b**2*c/(2*x**2) + 3*B*b*c**2*log(x) + B*c**3*x**
2/2, Eq(m, -13)), (-A*b**3/(4*x**4) - 3*A*b**2*c/(2*x**2) + 3*A*b*c**2*log(x) + A*c**3*x**2/2 - B*b**3/(2*x**2
) + 3*B*b**2*c*log(x) + 3*B*b*c**2*x**2/2 + B*c**3*x**4/4, Eq(m, -11)), (-A*b**3/(2*x**2) + 3*A*b**2*c*log(x)
+ 3*A*b*c**2*x**2/2 + A*c**3*x**4/4 + B*b**3*log(x) + 3*B*b**2*c*x**2/2 + 3*B*b*c**2*x**4/4 + B*c**3*x**6/6, E
q(m, -9)), (A*b**3*log(x) + 3*A*b**2*c*x**2/2 + 3*A*b*c**2*x**4/4 + A*c**3*x**6/6 + B*b**3*x**2/2 + 3*B*b**2*c
*x**4/4 + B*b*c**2*x**6/2 + B*c**3*x**8/8, Eq(m, -7)), (A*b**3*m**4*x**7*x**m/(m**5 + 55*m**4 + 1190*m**3 + 12
650*m**2 + 66009*m + 135135) + 48*A*b**3*m**3*x**7*x**m/(m**5 + 55*m**4 + 1190*m**3 + 12650*m**2 + 66009*m + 1
35135) + 854*A*b**3*m**2*x**7*x**m/(m**5 + 55*m**4 + 1190*m**3 + 12650*m**2 + 66009*m + 135135) + 6672*A*b**3*
m*x**7*x**m/(m**5 + 55*m**4 + 1190*m**3 + 12650*m**2 + 66009*m + 135135) + 19305*A*b**3*x**7*x**m/(m**5 + 55*m
**4 + 1190*m**3 + 12650*m**2 + 66009*m + 135135) + 3*A*b**2*c*m**4*x**9*x**m/(m**5 + 55*m**4 + 1190*m**3 + 126
50*m**2 + 66009*m + 135135) + 138*A*b**2*c*m**3*x**9*x**m/(m**5 + 55*m**4 + 1190*m**3 + 12650*m**2 + 66009*m +
135135) + 2328*A*b**2*c*m**2*x**9*x**m/(m**5 + 55*m**4 + 1190*m**3 + 12650*m**2 + 66009*m + 135135) + 16998*A
*b**2*c*m*x**9*x**m/(m**5 + 55*m**4 + 1190*m**3 + 12650*m**2 + 66009*m + 135135) + 45045*A*b**2*c*x**9*x**m/(m
**5 + 55*m**4 + 1190*m**3 + 12650*m**2 + 66009*m + 135135) + 3*A*b*c**2*m**4*x**11*x**m/(m**5 + 55*m**4 + 1190
*m**3 + 12650*m**2 + 66009*m + 135135) + 132*A*b*c**2*m**3*x**11*x**m/(m**5 + 55*m**4 + 1190*m**3 + 12650*m**2
+ 66009*m + 135135) + 2118*A*b*c**2*m**2*x**11*x**m/(m**5 + 55*m**4 + 1190*m**3 + 12650*m**2 + 66009*m + 1351
35) + 14652*A*b*c**2*m*x**11*x**m/(m**5 + 55*m**4 + 1190*m**3 + 12650*m**2 + 66009*m + 135135) + 36855*A*b*c**
2*x**11*x**m/(m**5 + 55*m**4 + 1190*m**3 + 12650*m**2 + 66009*m + 135135) + A*c**3*m**4*x**13*x**m/(m**5 + 55*
m**4 + 1190*m**3 + 12650*m**2 + 66009*m + 135135) + 42*A*c**3*m**3*x**13*x**m/(m**5 + 55*m**4 + 1190*m**3 + 12
650*m**2 + 66009*m + 135135) + 644*A*c**3*m**2*x**13*x**m/(m**5 + 55*m**4 + 1190*m**3 + 12650*m**2 + 66009*m +
135135) + 4278*A*c**3*m*x**13*x**m/(m**5 + 55*m**4 + 1190*m**3 + 12650*m**2 + 66009*m + 135135) + 10395*A*c**
3*x**13*x**m/(m**5 + 55*m**4 + 1190*m**3 + 12650*m**2 + 66009*m + 135135) + B*b**3*m**4*x**9*x**m/(m**5 + 55*m
**4 + 1190*m**3 + 12650*m**2 + 66009*m + 135135) + 46*B*b**3*m**3*x**9*x**m/(m**5 + 55*m**4 + 1190*m**3 + 1265
0*m**2 + 66009*m + 135135) + 776*B*b**3*m**2*x**9*x**m/(m**5 + 55*m**4 + 1190*m**3 + 12650*m**2 + 66009*m + 13
5135) + 5666*B*b**3*m*x**9*x**m/(m**5 + 55*m**4 + 1190*m**3 + 12650*m**2 + 66009*m + 135135) + 15015*B*b**3*x*
*9*x**m/(m**5 + 55*m**4 + 1190*m**3 + 12650*m**2 + 66009*m + 135135) + 3*B*b**2*c*m**4*x**11*x**m/(m**5 + 55*m
**4 + 1190*m**3 + 12650*m**2 + 66009*m + 135135) + 132*B*b**2*c*m**3*x**11*x**m/(m**5 + 55*m**4 + 1190*m**3 +
12650*m**2 + 66009*m + 135135) + 2118*B*b**2*c*m**2*x**11*x**m/(m**5 + 55*m**4 + 1190*m**3 + 12650*m**2 + 6600
9*m + 135135) + 14652*B*b**2*c*m*x**11*x**m/(m**5 + 55*m**4 + 1190*m**3 + 12650*m**2 + 66009*m + 135135) + 368
55*B*b**2*c*x**11*x**m/(m**5 + 55*m**4 + 1190*m**3 + 12650*m**2 + 66009*m + 135135) + 3*B*b*c**2*m**4*x**13*x*
*m/(m**5 + 55*m**4 + 1190*m**3 + 12650*m**2 + 66009*m + 135135) + 126*B*b*c**2*m**3*x**13*x**m/(m**5 + 55*m**4
+ 1190*m**3 + 12650*m**2 + 66009*m + 135135) + 1932*B*b*c**2*m**2*x**13*x**m/(m**5 + 55*m**4 + 1190*m**3 + 12
650*m**2 + 66009*m + 135135) + 12834*B*b*c**2*m*x**13*x**m/(m**5 + 55*m**4 + 1190*m**3 + 12650*m**2 + 66009*m
+ 135135) + 31185*B*b*c**2*x**13*x**m/(m**5 + 55*m**4 + 1190*m**3 + 12650*m**2 + 66009*m + 135135) + B*c**3*m*
*4*x**15*x**m/(m**5 + 55*m**4 + 1190*m**3 + 12650*m**2 + 66009*m + 135135) + 40*B*c**3*m**3*x**15*x**m/(m**5 +
55*m**4 + 1190*m**3 + 12650*m**2 + 66009*m + 135135) + 590*B*c**3*m**2*x**15*x**m/(m**5 + 55*m**4 + 1190*m**3
+ 12650*m**2 + 66009*m + 135135) + 3800*B*c**3*m*x**15*x**m/(m**5 + 55*m**4 + 1190*m**3 + 12650*m**2 + 66009*
m + 135135) + 9009*B*c**3*x**15*x**m/(m**5 + 55*m**4 + 1190*m**3 + 12650*m**2 + 66009*m + 135135), True))
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