3.1.27 \(\int x^m (A+B x) (b x+c x^2)^3 \, dx\)

Optimal. Leaf size=96 \[ \frac {A b^3 x^{m+4}}{m+4}+\frac {b^2 x^{m+5} (3 A c+b B)}{m+5}+\frac {c^2 x^{m+7} (A c+3 b B)}{m+7}+\frac {3 b c x^{m+6} (A c+b B)}{m+6}+\frac {B c^3 x^{m+8}}{m+8} \]

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Rubi [A]  time = 0.06, antiderivative size = 96, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {765} \begin {gather*} \frac {b^2 x^{m+5} (3 A c+b B)}{m+5}+\frac {A b^3 x^{m+4}}{m+4}+\frac {c^2 x^{m+7} (A c+3 b B)}{m+7}+\frac {3 b c x^{m+6} (A c+b B)}{m+6}+\frac {B c^3 x^{m+8}}{m+8} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[x^m*(A + B*x)*(b*x + c*x^2)^3,x]

[Out]

(A*b^3*x^(4 + m))/(4 + m) + (b^2*(b*B + 3*A*c)*x^(5 + m))/(5 + m) + (3*b*c*(b*B + A*c)*x^(6 + m))/(6 + m) + (c
^2*(3*b*B + A*c)*x^(7 + m))/(7 + m) + (B*c^3*x^(8 + m))/(8 + m)

Rule 765

Int[((e_.)*(x_))^(m_.)*((f_.) + (g_.)*(x_))*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> Int[Expand
Integrand[(e*x)^m*(f + g*x)*(a + b*x + c*x^2)^p, x], x] /; FreeQ[{a, b, c, e, f, g, m}, x] && IntegerQ[p] && (
GtQ[p, 0] || (EqQ[a, 0] && IntegerQ[m]))

Rubi steps

\begin {align*} \int x^m (A+B x) \left (b x+c x^2\right )^3 \, dx &=\int \left (A b^3 x^{3+m}+b^2 (b B+3 A c) x^{4+m}+3 b c (b B+A c) x^{5+m}+c^2 (3 b B+A c) x^{6+m}+B c^3 x^{7+m}\right ) \, dx\\ &=\frac {A b^3 x^{4+m}}{4+m}+\frac {b^2 (b B+3 A c) x^{5+m}}{5+m}+\frac {3 b c (b B+A c) x^{6+m}}{6+m}+\frac {c^2 (3 b B+A c) x^{7+m}}{7+m}+\frac {B c^3 x^{8+m}}{8+m}\\ \end {align*}

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Mathematica [A]  time = 0.11, size = 87, normalized size = 0.91 \begin {gather*} \frac {x^{m+4} \left (\left (\frac {b^3}{m+4}+\frac {3 b^2 c x}{m+5}+\frac {3 b c^2 x^2}{m+6}+\frac {c^3 x^3}{m+7}\right ) (A c (m+8)-b B (m+4))+B (b+c x)^4\right )}{c (m+8)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[x^m*(A + B*x)*(b*x + c*x^2)^3,x]

[Out]

(x^(4 + m)*(B*(b + c*x)^4 + (-(b*B*(4 + m)) + A*c*(8 + m))*(b^3/(4 + m) + (3*b^2*c*x)/(5 + m) + (3*b*c^2*x^2)/
(6 + m) + (c^3*x^3)/(7 + m))))/(c*(8 + m))

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IntegrateAlgebraic [F]  time = 0.42, size = 0, normalized size = 0.00 \begin {gather*} \int x^m (A+B x) \left (b x+c x^2\right )^3 \, dx \end {gather*}

Verification is not applicable to the result.

[In]

IntegrateAlgebraic[x^m*(A + B*x)*(b*x + c*x^2)^3,x]

[Out]

Defer[IntegrateAlgebraic][x^m*(A + B*x)*(b*x + c*x^2)^3, x]

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fricas [B]  time = 0.42, size = 381, normalized size = 3.97 \begin {gather*} \frac {{\left ({\left (B c^{3} m^{4} + 22 \, B c^{3} m^{3} + 179 \, B c^{3} m^{2} + 638 \, B c^{3} m + 840 \, B c^{3}\right )} x^{8} + {\left ({\left (3 \, B b c^{2} + A c^{3}\right )} m^{4} + 2880 \, B b c^{2} + 960 \, A c^{3} + 23 \, {\left (3 \, B b c^{2} + A c^{3}\right )} m^{3} + 194 \, {\left (3 \, B b c^{2} + A c^{3}\right )} m^{2} + 712 \, {\left (3 \, B b c^{2} + A c^{3}\right )} m\right )} x^{7} + 3 \, {\left ({\left (B b^{2} c + A b c^{2}\right )} m^{4} + 1120 \, B b^{2} c + 1120 \, A b c^{2} + 24 \, {\left (B b^{2} c + A b c^{2}\right )} m^{3} + 211 \, {\left (B b^{2} c + A b c^{2}\right )} m^{2} + 804 \, {\left (B b^{2} c + A b c^{2}\right )} m\right )} x^{6} + {\left ({\left (B b^{3} + 3 \, A b^{2} c\right )} m^{4} + 1344 \, B b^{3} + 4032 \, A b^{2} c + 25 \, {\left (B b^{3} + 3 \, A b^{2} c\right )} m^{3} + 230 \, {\left (B b^{3} + 3 \, A b^{2} c\right )} m^{2} + 920 \, {\left (B b^{3} + 3 \, A b^{2} c\right )} m\right )} x^{5} + {\left (A b^{3} m^{4} + 26 \, A b^{3} m^{3} + 251 \, A b^{3} m^{2} + 1066 \, A b^{3} m + 1680 \, A b^{3}\right )} x^{4}\right )} x^{m}}{m^{5} + 30 \, m^{4} + 355 \, m^{3} + 2070 \, m^{2} + 5944 \, m + 6720} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m*(B*x+A)*(c*x^2+b*x)^3,x, algorithm="fricas")

[Out]

((B*c^3*m^4 + 22*B*c^3*m^3 + 179*B*c^3*m^2 + 638*B*c^3*m + 840*B*c^3)*x^8 + ((3*B*b*c^2 + A*c^3)*m^4 + 2880*B*
b*c^2 + 960*A*c^3 + 23*(3*B*b*c^2 + A*c^3)*m^3 + 194*(3*B*b*c^2 + A*c^3)*m^2 + 712*(3*B*b*c^2 + A*c^3)*m)*x^7
+ 3*((B*b^2*c + A*b*c^2)*m^4 + 1120*B*b^2*c + 1120*A*b*c^2 + 24*(B*b^2*c + A*b*c^2)*m^3 + 211*(B*b^2*c + A*b*c
^2)*m^2 + 804*(B*b^2*c + A*b*c^2)*m)*x^6 + ((B*b^3 + 3*A*b^2*c)*m^4 + 1344*B*b^3 + 4032*A*b^2*c + 25*(B*b^3 +
3*A*b^2*c)*m^3 + 230*(B*b^3 + 3*A*b^2*c)*m^2 + 920*(B*b^3 + 3*A*b^2*c)*m)*x^5 + (A*b^3*m^4 + 26*A*b^3*m^3 + 25
1*A*b^3*m^2 + 1066*A*b^3*m + 1680*A*b^3)*x^4)*x^m/(m^5 + 30*m^4 + 355*m^3 + 2070*m^2 + 5944*m + 6720)

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giac [B]  time = 0.25, size = 603, normalized size = 6.28 \begin {gather*} \frac {B c^{3} m^{4} x^{8} x^{m} + 3 \, B b c^{2} m^{4} x^{7} x^{m} + A c^{3} m^{4} x^{7} x^{m} + 22 \, B c^{3} m^{3} x^{8} x^{m} + 3 \, B b^{2} c m^{4} x^{6} x^{m} + 3 \, A b c^{2} m^{4} x^{6} x^{m} + 69 \, B b c^{2} m^{3} x^{7} x^{m} + 23 \, A c^{3} m^{3} x^{7} x^{m} + 179 \, B c^{3} m^{2} x^{8} x^{m} + B b^{3} m^{4} x^{5} x^{m} + 3 \, A b^{2} c m^{4} x^{5} x^{m} + 72 \, B b^{2} c m^{3} x^{6} x^{m} + 72 \, A b c^{2} m^{3} x^{6} x^{m} + 582 \, B b c^{2} m^{2} x^{7} x^{m} + 194 \, A c^{3} m^{2} x^{7} x^{m} + 638 \, B c^{3} m x^{8} x^{m} + A b^{3} m^{4} x^{4} x^{m} + 25 \, B b^{3} m^{3} x^{5} x^{m} + 75 \, A b^{2} c m^{3} x^{5} x^{m} + 633 \, B b^{2} c m^{2} x^{6} x^{m} + 633 \, A b c^{2} m^{2} x^{6} x^{m} + 2136 \, B b c^{2} m x^{7} x^{m} + 712 \, A c^{3} m x^{7} x^{m} + 840 \, B c^{3} x^{8} x^{m} + 26 \, A b^{3} m^{3} x^{4} x^{m} + 230 \, B b^{3} m^{2} x^{5} x^{m} + 690 \, A b^{2} c m^{2} x^{5} x^{m} + 2412 \, B b^{2} c m x^{6} x^{m} + 2412 \, A b c^{2} m x^{6} x^{m} + 2880 \, B b c^{2} x^{7} x^{m} + 960 \, A c^{3} x^{7} x^{m} + 251 \, A b^{3} m^{2} x^{4} x^{m} + 920 \, B b^{3} m x^{5} x^{m} + 2760 \, A b^{2} c m x^{5} x^{m} + 3360 \, B b^{2} c x^{6} x^{m} + 3360 \, A b c^{2} x^{6} x^{m} + 1066 \, A b^{3} m x^{4} x^{m} + 1344 \, B b^{3} x^{5} x^{m} + 4032 \, A b^{2} c x^{5} x^{m} + 1680 \, A b^{3} x^{4} x^{m}}{m^{5} + 30 \, m^{4} + 355 \, m^{3} + 2070 \, m^{2} + 5944 \, m + 6720} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m*(B*x+A)*(c*x^2+b*x)^3,x, algorithm="giac")

[Out]

(B*c^3*m^4*x^8*x^m + 3*B*b*c^2*m^4*x^7*x^m + A*c^3*m^4*x^7*x^m + 22*B*c^3*m^3*x^8*x^m + 3*B*b^2*c*m^4*x^6*x^m
+ 3*A*b*c^2*m^4*x^6*x^m + 69*B*b*c^2*m^3*x^7*x^m + 23*A*c^3*m^3*x^7*x^m + 179*B*c^3*m^2*x^8*x^m + B*b^3*m^4*x^
5*x^m + 3*A*b^2*c*m^4*x^5*x^m + 72*B*b^2*c*m^3*x^6*x^m + 72*A*b*c^2*m^3*x^6*x^m + 582*B*b*c^2*m^2*x^7*x^m + 19
4*A*c^3*m^2*x^7*x^m + 638*B*c^3*m*x^8*x^m + A*b^3*m^4*x^4*x^m + 25*B*b^3*m^3*x^5*x^m + 75*A*b^2*c*m^3*x^5*x^m
+ 633*B*b^2*c*m^2*x^6*x^m + 633*A*b*c^2*m^2*x^6*x^m + 2136*B*b*c^2*m*x^7*x^m + 712*A*c^3*m*x^7*x^m + 840*B*c^3
*x^8*x^m + 26*A*b^3*m^3*x^4*x^m + 230*B*b^3*m^2*x^5*x^m + 690*A*b^2*c*m^2*x^5*x^m + 2412*B*b^2*c*m*x^6*x^m + 2
412*A*b*c^2*m*x^6*x^m + 2880*B*b*c^2*x^7*x^m + 960*A*c^3*x^7*x^m + 251*A*b^3*m^2*x^4*x^m + 920*B*b^3*m*x^5*x^m
+ 2760*A*b^2*c*m*x^5*x^m + 3360*B*b^2*c*x^6*x^m + 3360*A*b*c^2*x^6*x^m + 1066*A*b^3*m*x^4*x^m + 1344*B*b^3*x^
5*x^m + 4032*A*b^2*c*x^5*x^m + 1680*A*b^3*x^4*x^m)/(m^5 + 30*m^4 + 355*m^3 + 2070*m^2 + 5944*m + 6720)

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maple [B]  time = 0.05, size = 454, normalized size = 4.73 \begin {gather*} \frac {\left (B \,c^{3} m^{4} x^{4}+A \,c^{3} m^{4} x^{3}+3 B b \,c^{2} m^{4} x^{3}+22 B \,c^{3} m^{3} x^{4}+3 A b \,c^{2} m^{4} x^{2}+23 A \,c^{3} m^{3} x^{3}+3 B \,b^{2} c \,m^{4} x^{2}+69 B b \,c^{2} m^{3} x^{3}+179 B \,c^{3} m^{2} x^{4}+3 A \,b^{2} c \,m^{4} x +72 A b \,c^{2} m^{3} x^{2}+194 A \,c^{3} m^{2} x^{3}+B \,b^{3} m^{4} x +72 B \,b^{2} c \,m^{3} x^{2}+582 B b \,c^{2} m^{2} x^{3}+638 B \,c^{3} m \,x^{4}+A \,b^{3} m^{4}+75 A \,b^{2} c \,m^{3} x +633 A b \,c^{2} m^{2} x^{2}+712 A \,c^{3} m \,x^{3}+25 B \,b^{3} m^{3} x +633 B \,b^{2} c \,m^{2} x^{2}+2136 B b \,c^{2} m \,x^{3}+840 B \,c^{3} x^{4}+26 A \,b^{3} m^{3}+690 A \,b^{2} c \,m^{2} x +2412 A b \,c^{2} m \,x^{2}+960 A \,c^{3} x^{3}+230 B \,b^{3} m^{2} x +2412 B \,b^{2} c m \,x^{2}+2880 B b \,c^{2} x^{3}+251 A \,b^{3} m^{2}+2760 A \,b^{2} c m x +3360 A b \,c^{2} x^{2}+920 B \,b^{3} m x +3360 B \,b^{2} c \,x^{2}+1066 A \,b^{3} m +4032 A \,b^{2} c x +1344 B \,b^{3} x +1680 A \,b^{3}\right ) x^{m +4}}{\left (m +8\right ) \left (m +7\right ) \left (m +6\right ) \left (m +5\right ) \left (m +4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^m*(B*x+A)*(c*x^2+b*x)^3,x)

[Out]

x^(m+4)*(B*c^3*m^4*x^4+A*c^3*m^4*x^3+3*B*b*c^2*m^4*x^3+22*B*c^3*m^3*x^4+3*A*b*c^2*m^4*x^2+23*A*c^3*m^3*x^3+3*B
*b^2*c*m^4*x^2+69*B*b*c^2*m^3*x^3+179*B*c^3*m^2*x^4+3*A*b^2*c*m^4*x+72*A*b*c^2*m^3*x^2+194*A*c^3*m^2*x^3+B*b^3
*m^4*x+72*B*b^2*c*m^3*x^2+582*B*b*c^2*m^2*x^3+638*B*c^3*m*x^4+A*b^3*m^4+75*A*b^2*c*m^3*x+633*A*b*c^2*m^2*x^2+7
12*A*c^3*m*x^3+25*B*b^3*m^3*x+633*B*b^2*c*m^2*x^2+2136*B*b*c^2*m*x^3+840*B*c^3*x^4+26*A*b^3*m^3+690*A*b^2*c*m^
2*x+2412*A*b*c^2*m*x^2+960*A*c^3*x^3+230*B*b^3*m^2*x+2412*B*b^2*c*m*x^2+2880*B*b*c^2*x^3+251*A*b^3*m^2+2760*A*
b^2*c*m*x+3360*A*b*c^2*x^2+920*B*b^3*m*x+3360*B*b^2*c*x^2+1066*A*b^3*m+4032*A*b^2*c*x+1344*B*b^3*x+1680*A*b^3)
/(m+8)/(m+7)/(m+6)/(m+5)/(m+4)

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maxima [A]  time = 0.91, size = 129, normalized size = 1.34 \begin {gather*} \frac {B c^{3} x^{m + 8}}{m + 8} + \frac {3 \, B b c^{2} x^{m + 7}}{m + 7} + \frac {A c^{3} x^{m + 7}}{m + 7} + \frac {3 \, B b^{2} c x^{m + 6}}{m + 6} + \frac {3 \, A b c^{2} x^{m + 6}}{m + 6} + \frac {B b^{3} x^{m + 5}}{m + 5} + \frac {3 \, A b^{2} c x^{m + 5}}{m + 5} + \frac {A b^{3} x^{m + 4}}{m + 4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m*(B*x+A)*(c*x^2+b*x)^3,x, algorithm="maxima")

[Out]

B*c^3*x^(m + 8)/(m + 8) + 3*B*b*c^2*x^(m + 7)/(m + 7) + A*c^3*x^(m + 7)/(m + 7) + 3*B*b^2*c*x^(m + 6)/(m + 6)
+ 3*A*b*c^2*x^(m + 6)/(m + 6) + B*b^3*x^(m + 5)/(m + 5) + 3*A*b^2*c*x^(m + 5)/(m + 5) + A*b^3*x^(m + 4)/(m + 4
)

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mupad [B]  time = 1.28, size = 291, normalized size = 3.03 \begin {gather*} \frac {A\,b^3\,x^m\,x^4\,\left (m^4+26\,m^3+251\,m^2+1066\,m+1680\right )}{m^5+30\,m^4+355\,m^3+2070\,m^2+5944\,m+6720}+\frac {B\,c^3\,x^m\,x^8\,\left (m^4+22\,m^3+179\,m^2+638\,m+840\right )}{m^5+30\,m^4+355\,m^3+2070\,m^2+5944\,m+6720}+\frac {b^2\,x^m\,x^5\,\left (3\,A\,c+B\,b\right )\,\left (m^4+25\,m^3+230\,m^2+920\,m+1344\right )}{m^5+30\,m^4+355\,m^3+2070\,m^2+5944\,m+6720}+\frac {c^2\,x^m\,x^7\,\left (A\,c+3\,B\,b\right )\,\left (m^4+23\,m^3+194\,m^2+712\,m+960\right )}{m^5+30\,m^4+355\,m^3+2070\,m^2+5944\,m+6720}+\frac {3\,b\,c\,x^m\,x^6\,\left (A\,c+B\,b\right )\,\left (m^4+24\,m^3+211\,m^2+804\,m+1120\right )}{m^5+30\,m^4+355\,m^3+2070\,m^2+5944\,m+6720} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^m*(b*x + c*x^2)^3*(A + B*x),x)

[Out]

(A*b^3*x^m*x^4*(1066*m + 251*m^2 + 26*m^3 + m^4 + 1680))/(5944*m + 2070*m^2 + 355*m^3 + 30*m^4 + m^5 + 6720) +
(B*c^3*x^m*x^8*(638*m + 179*m^2 + 22*m^3 + m^4 + 840))/(5944*m + 2070*m^2 + 355*m^3 + 30*m^4 + m^5 + 6720) +
(b^2*x^m*x^5*(3*A*c + B*b)*(920*m + 230*m^2 + 25*m^3 + m^4 + 1344))/(5944*m + 2070*m^2 + 355*m^3 + 30*m^4 + m^
5 + 6720) + (c^2*x^m*x^7*(A*c + 3*B*b)*(712*m + 194*m^2 + 23*m^3 + m^4 + 960))/(5944*m + 2070*m^2 + 355*m^3 +
30*m^4 + m^5 + 6720) + (3*b*c*x^m*x^6*(A*c + B*b)*(804*m + 211*m^2 + 24*m^3 + m^4 + 1120))/(5944*m + 2070*m^2
+ 355*m^3 + 30*m^4 + m^5 + 6720)

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sympy [A]  time = 2.76, size = 2026, normalized size = 21.10

result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**m*(B*x+A)*(c*x**2+b*x)**3,x)

[Out]

Piecewise((-A*b**3/(4*x**4) - A*b**2*c/x**3 - 3*A*b*c**2/(2*x**2) - A*c**3/x - B*b**3/(3*x**3) - 3*B*b**2*c/(2
*x**2) - 3*B*b*c**2/x + B*c**3*log(x), Eq(m, -8)), (-A*b**3/(3*x**3) - 3*A*b**2*c/(2*x**2) - 3*A*b*c**2/x + A*
c**3*log(x) - B*b**3/(2*x**2) - 3*B*b**2*c/x + 3*B*b*c**2*log(x) + B*c**3*x, Eq(m, -7)), (-A*b**3/(2*x**2) - 3
*A*b**2*c/x + 3*A*b*c**2*log(x) + A*c**3*x - B*b**3/x + 3*B*b**2*c*log(x) + 3*B*b*c**2*x + B*c**3*x**2/2, Eq(m
, -6)), (-A*b**3/x + 3*A*b**2*c*log(x) + 3*A*b*c**2*x + A*c**3*x**2/2 + B*b**3*log(x) + 3*B*b**2*c*x + 3*B*b*c
**2*x**2/2 + B*c**3*x**3/3, Eq(m, -5)), (A*b**3*log(x) + 3*A*b**2*c*x + 3*A*b*c**2*x**2/2 + A*c**3*x**3/3 + B*
b**3*x + 3*B*b**2*c*x**2/2 + B*b*c**2*x**3 + B*c**3*x**4/4, Eq(m, -4)), (A*b**3*m**4*x**4*x**m/(m**5 + 30*m**4
+ 355*m**3 + 2070*m**2 + 5944*m + 6720) + 26*A*b**3*m**3*x**4*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5
944*m + 6720) + 251*A*b**3*m**2*x**4*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 1066*A*b**
3*m*x**4*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 1680*A*b**3*x**4*x**m/(m**5 + 30*m**4
+ 355*m**3 + 2070*m**2 + 5944*m + 6720) + 3*A*b**2*c*m**4*x**5*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5
944*m + 6720) + 75*A*b**2*c*m**3*x**5*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 690*A*b**
2*c*m**2*x**5*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 2760*A*b**2*c*m*x**5*x**m/(m**5 +
30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 4032*A*b**2*c*x**5*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m
**2 + 5944*m + 6720) + 3*A*b*c**2*m**4*x**6*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 72*
A*b*c**2*m**3*x**6*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 633*A*b*c**2*m**2*x**6*x**m/
(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 2412*A*b*c**2*m*x**6*x**m/(m**5 + 30*m**4 + 355*m**3
+ 2070*m**2 + 5944*m + 6720) + 3360*A*b*c**2*x**6*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720
) + A*c**3*m**4*x**7*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 23*A*c**3*m**3*x**7*x**m/(
m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 194*A*c**3*m**2*x**7*x**m/(m**5 + 30*m**4 + 355*m**3
+ 2070*m**2 + 5944*m + 6720) + 712*A*c**3*m*x**7*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720)
+ 960*A*c**3*x**7*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + B*b**3*m**4*x**5*x**m/(m**5 +
30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 25*B*b**3*m**3*x**5*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*
m**2 + 5944*m + 6720) + 230*B*b**3*m**2*x**5*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 92
0*B*b**3*m*x**5*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 1344*B*b**3*x**5*x**m/(m**5 + 3
0*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 3*B*b**2*c*m**4*x**6*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m
**2 + 5944*m + 6720) + 72*B*b**2*c*m**3*x**6*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 63
3*B*b**2*c*m**2*x**6*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 2412*B*b**2*c*m*x**6*x**m/
(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 3360*B*b**2*c*x**6*x**m/(m**5 + 30*m**4 + 355*m**3 +
2070*m**2 + 5944*m + 6720) + 3*B*b*c**2*m**4*x**7*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720
) + 69*B*b*c**2*m**3*x**7*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 582*B*b*c**2*m**2*x**
7*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 2136*B*b*c**2*m*x**7*x**m/(m**5 + 30*m**4 + 3
55*m**3 + 2070*m**2 + 5944*m + 6720) + 2880*B*b*c**2*x**7*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m
+ 6720) + B*c**3*m**4*x**8*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 22*B*c**3*m**3*x**8
*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720) + 179*B*c**3*m**2*x**8*x**m/(m**5 + 30*m**4 + 35
5*m**3 + 2070*m**2 + 5944*m + 6720) + 638*B*c**3*m*x**8*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m +
6720) + 840*B*c**3*x**8*x**m/(m**5 + 30*m**4 + 355*m**3 + 2070*m**2 + 5944*m + 6720), True))

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