\(\int (e x)^m (A+B x) (a+c x^2)^4 \, dx\) [485]
Optimal result
Integrand size = 20, antiderivative size = 217 \[
\int (e x)^m (A+B x) \left (a+c x^2\right )^4 \, dx=\frac {a^4 A (e x)^{1+m}}{e (1+m)}+\frac {a^4 B (e x)^{2+m}}{e^2 (2+m)}+\frac {4 a^3 A c (e x)^{3+m}}{e^3 (3+m)}+\frac {4 a^3 B c (e x)^{4+m}}{e^4 (4+m)}+\frac {6 a^2 A c^2 (e x)^{5+m}}{e^5 (5+m)}+\frac {6 a^2 B c^2 (e x)^{6+m}}{e^6 (6+m)}+\frac {4 a A c^3 (e x)^{7+m}}{e^7 (7+m)}+\frac {4 a B c^3 (e x)^{8+m}}{e^8 (8+m)}+\frac {A c^4 (e x)^{9+m}}{e^9 (9+m)}+\frac {B c^4 (e x)^{10+m}}{e^{10} (10+m)}
\]
[Out]
a^4*A*(e*x)^(1+m)/e/(1+m)+a^4*B*(e*x)^(2+m)/e^2/(2+m)+4*a^3*A*c*(e*x)^(3+m)/e^3/(3+m)+4*a^3*B*c*(e*x)^(4+m)/e^
4/(4+m)+6*a^2*A*c^2*(e*x)^(5+m)/e^5/(5+m)+6*a^2*B*c^2*(e*x)^(6+m)/e^6/(6+m)+4*a*A*c^3*(e*x)^(7+m)/e^7/(7+m)+4*
a*B*c^3*(e*x)^(8+m)/e^8/(8+m)+A*c^4*(e*x)^(9+m)/e^9/(9+m)+B*c^4*(e*x)^(10+m)/e^10/(10+m)
Rubi [A] (verified)
Time = 0.11 (sec) , antiderivative size = 217, normalized size of antiderivative = 1.00,
number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {780}
\[
\int (e x)^m (A+B x) \left (a+c x^2\right )^4 \, dx=\frac {a^4 A (e x)^{m+1}}{e (m+1)}+\frac {a^4 B (e x)^{m+2}}{e^2 (m+2)}+\frac {4 a^3 A c (e x)^{m+3}}{e^3 (m+3)}+\frac {4 a^3 B c (e x)^{m+4}}{e^4 (m+4)}+\frac {6 a^2 A c^2 (e x)^{m+5}}{e^5 (m+5)}+\frac {6 a^2 B c^2 (e x)^{m+6}}{e^6 (m+6)}+\frac {4 a A c^3 (e x)^{m+7}}{e^7 (m+7)}+\frac {4 a B c^3 (e x)^{m+8}}{e^8 (m+8)}+\frac {A c^4 (e x)^{m+9}}{e^9 (m+9)}+\frac {B c^4 (e x)^{m+10}}{e^{10} (m+10)}
\]
[In]
Int[(e*x)^m*(A + B*x)*(a + c*x^2)^4,x]
[Out]
(a^4*A*(e*x)^(1 + m))/(e*(1 + m)) + (a^4*B*(e*x)^(2 + m))/(e^2*(2 + m)) + (4*a^3*A*c*(e*x)^(3 + m))/(e^3*(3 +
m)) + (4*a^3*B*c*(e*x)^(4 + m))/(e^4*(4 + m)) + (6*a^2*A*c^2*(e*x)^(5 + m))/(e^5*(5 + m)) + (6*a^2*B*c^2*(e*x)
^(6 + m))/(e^6*(6 + m)) + (4*a*A*c^3*(e*x)^(7 + m))/(e^7*(7 + m)) + (4*a*B*c^3*(e*x)^(8 + m))/(e^8*(8 + m)) +
(A*c^4*(e*x)^(9 + m))/(e^9*(9 + m)) + (B*c^4*(e*x)^(10 + m))/(e^10*(10 + m))
Rule 780
Int[((e_.)*(x_))^(m_.)*((f_.) + (g_.)*(x_))*((a_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> Int[ExpandIntegrand[(e*x
)^m*(f + g*x)*(a + c*x^2)^p, x], x] /; FreeQ[{a, c, e, f, g, m}, x] && IGtQ[p, 0]
Rubi steps \begin{align*}
\text {integral}& = \int \left (a^4 A (e x)^m+\frac {a^4 B (e x)^{1+m}}{e}+\frac {4 a^3 A c (e x)^{2+m}}{e^2}+\frac {4 a^3 B c (e x)^{3+m}}{e^3}+\frac {6 a^2 A c^2 (e x)^{4+m}}{e^4}+\frac {6 a^2 B c^2 (e x)^{5+m}}{e^5}+\frac {4 a A c^3 (e x)^{6+m}}{e^6}+\frac {4 a B c^3 (e x)^{7+m}}{e^7}+\frac {A c^4 (e x)^{8+m}}{e^8}+\frac {B c^4 (e x)^{9+m}}{e^9}\right ) \, dx \\ & = \frac {a^4 A (e x)^{1+m}}{e (1+m)}+\frac {a^4 B (e x)^{2+m}}{e^2 (2+m)}+\frac {4 a^3 A c (e x)^{3+m}}{e^3 (3+m)}+\frac {4 a^3 B c (e x)^{4+m}}{e^4 (4+m)}+\frac {6 a^2 A c^2 (e x)^{5+m}}{e^5 (5+m)}+\frac {6 a^2 B c^2 (e x)^{6+m}}{e^6 (6+m)}+\frac {4 a A c^3 (e x)^{7+m}}{e^7 (7+m)}+\frac {4 a B c^3 (e x)^{8+m}}{e^8 (8+m)}+\frac {A c^4 (e x)^{9+m}}{e^9 (9+m)}+\frac {B c^4 (e x)^{10+m}}{e^{10} (10+m)} \\
\end{align*}
Mathematica [A] (verified)
Time = 0.58 (sec) , antiderivative size = 128, normalized size of antiderivative = 0.59
\[
\int (e x)^m (A+B x) \left (a+c x^2\right )^4 \, dx=x (e x)^m \left (a^4 \left (\frac {A}{1+m}+\frac {B x}{2+m}\right )+4 a^3 c x^2 \left (\frac {A}{3+m}+\frac {B x}{4+m}\right )+6 a^2 c^2 x^4 \left (\frac {A}{5+m}+\frac {B x}{6+m}\right )+4 a c^3 x^6 \left (\frac {A}{7+m}+\frac {B x}{8+m}\right )+c^4 x^8 \left (\frac {A}{9+m}+\frac {B x}{10+m}\right )\right )
\]
[In]
Integrate[(e*x)^m*(A + B*x)*(a + c*x^2)^4,x]
[Out]
x*(e*x)^m*(a^4*(A/(1 + m) + (B*x)/(2 + m)) + 4*a^3*c*x^2*(A/(3 + m) + (B*x)/(4 + m)) + 6*a^2*c^2*x^4*(A/(5 + m
) + (B*x)/(6 + m)) + 4*a*c^3*x^6*(A/(7 + m) + (B*x)/(8 + m)) + c^4*x^8*(A/(9 + m) + (B*x)/(10 + m)))
Maple [B] (verified)
Leaf count of result is larger than twice the leaf count of optimal. \(1254\) vs. \(2(217)=434\).
Time = 0.24 (sec) , antiderivative size = 1255, normalized size of antiderivative =
5.78
| | |
method | result | size |
| | |
gosper |
\(\text {Expression too large to display}\) |
\(1255\) |
risch |
\(\text {Expression too large to display}\) |
\(1255\) |
parallelrisch |
\(\text {Expression too large to display}\) |
\(1779\) |
| | |
|
|
|
[In]
int((e*x)^m*(B*x+A)*(c*x^2+a)^4,x,method=_RETURNVERBOSE)
[Out]
x*(B*c^4*m^9*x^9+A*c^4*m^9*x^8+45*B*c^4*m^8*x^9+46*A*c^4*m^8*x^8+4*B*a*c^3*m^9*x^7+870*B*c^4*m^7*x^9+4*A*a*c^3
*m^9*x^6+906*A*c^4*m^7*x^8+188*B*a*c^3*m^8*x^7+9450*B*c^4*m^6*x^9+192*A*a*c^3*m^8*x^6+9996*A*c^4*m^6*x^8+6*B*a
^2*c^2*m^9*x^5+3776*B*a*c^3*m^7*x^7+63273*B*c^4*m^5*x^9+6*A*a^2*c^2*m^9*x^4+3936*A*a*c^3*m^7*x^6+67809*A*c^4*m
^5*x^8+294*B*a^2*c^2*m^8*x^5+42392*B*a*c^3*m^6*x^7+269325*B*c^4*m^4*x^9+300*A*a^2*c^2*m^8*x^4+45048*A*a*c^3*m^
6*x^6+291774*A*c^4*m^4*x^8+4*B*a^3*c*m^9*x^3+6156*B*a^2*c^2*m^7*x^5+291956*B*a*c^3*m^5*x^7+723680*B*c^4*m^3*x^
9+4*A*a^3*c*m^9*x^2+6420*A*a^2*c^2*m^7*x^4+315756*A*a*c^3*m^5*x^6+790964*A*c^4*m^3*x^8+204*B*a^3*c*m^8*x^3+719
64*B*a^2*c^2*m^6*x^5+1272572*B*a*c^3*m^4*x^7+1172700*B*c^4*m^2*x^9+208*A*a^3*c*m^8*x^2+76800*A*a^2*c^2*m^6*x^4
+1397928*A*a*c^3*m^4*x^6+1290824*A*c^4*m^2*x^8+B*a^4*m^9*x+4464*B*a^3*c*m^7*x^3+514854*B*a^2*c^2*m^5*x^5+34871
44*B*a*c^3*m^3*x^7+1026576*B*c^4*m*x^9+A*a^4*m^9+4656*A*a^3*c*m^7*x^2+562638*A*a^2*c^2*m^5*x^4+3882224*A*a*c^3
*m^3*x^6+1136160*A*c^4*m*x^8+53*B*a^4*m^8*x+54744*B*a^3*c*m^6*x^3+2323206*B*a^2*c^2*m^4*x^5+5740848*B*a*c^3*m^
2*x^7+362880*B*c^4*x^9+54*A*a^4*m^8+58632*A*a^3*c*m^6*x^2+2599140*A*a^2*c^2*m^4*x^4+6462432*A*a*c^3*m^2*x^6+40
3200*A*c^4*x^8+1214*B*a^4*m^7*x+412116*B*a^3*c*m^5*x^3+6562344*B*a^2*c^2*m^3*x^5+5087520*B*a*c^3*m*x^7+1266*A*
a^4*m^7+455196*A*a^3*c*m^5*x^2+7505880*A*a^2*c^2*m^3*x^4+5777280*A*a*c^3*m*x^6+15722*B*a^4*m^6*x+1959756*B*a^3
*c*m^4*x^3+11082936*B*a^2*c^2*m^2*x^5+1814400*B*a*c^3*x^7+16884*A*a^4*m^6+2242632*A*a^3*c*m^4*x^2+12927600*A*a
^2*c^2*m^2*x^4+2073600*A*a*c^3*x^6+126329*B*a^4*m^5*x+5828696*B*a^3*c*m^3*x^3+10023840*B*a^2*c^2*m*x^5+140889*
A*a^4*m^5+6939824*A*a^3*c*m^3*x^2+11883456*A*a^2*c^2*m*x^4+649397*B*a^4*m^4*x+10323216*B*a^3*c*m^2*x^3+3628800
*B*a^2*c^2*x^5+761166*A*a^4*m^4+12818528*A*a^3*c*m^2*x^2+4354560*A*a^2*c^2*x^4+2118136*B*a^4*m^3*x+9721440*B*a
^3*c*m*x^3+2655764*A*a^4*m^3+12558720*A*a^3*c*m*x^2+4173228*B*a^4*m^2*x+3628800*B*a^3*c*x^3+5753736*A*a^4*m^2+
4838400*A*a^3*c*x^2+4407120*B*a^4*m*x+6999840*A*a^4*m+1814400*B*a^4*x+3628800*A*a^4)*(e*x)^m/(10+m)/(9+m)/(8+m
)/(7+m)/(6+m)/(5+m)/(4+m)/(3+m)/(2+m)/(1+m)
Fricas [B] (verification not implemented)
Leaf count of result is larger than twice the leaf count of optimal. 1051 vs. \(2 (217) = 434\).
Time = 0.39 (sec) , antiderivative size = 1051, normalized size of antiderivative = 4.84
\[
\int (e x)^m (A+B x) \left (a+c x^2\right )^4 \, dx=\frac {{\left ({\left (B c^{4} m^{9} + 45 \, B c^{4} m^{8} + 870 \, B c^{4} m^{7} + 9450 \, B c^{4} m^{6} + 63273 \, B c^{4} m^{5} + 269325 \, B c^{4} m^{4} + 723680 \, B c^{4} m^{3} + 1172700 \, B c^{4} m^{2} + 1026576 \, B c^{4} m + 362880 \, B c^{4}\right )} x^{10} + {\left (A c^{4} m^{9} + 46 \, A c^{4} m^{8} + 906 \, A c^{4} m^{7} + 9996 \, A c^{4} m^{6} + 67809 \, A c^{4} m^{5} + 291774 \, A c^{4} m^{4} + 790964 \, A c^{4} m^{3} + 1290824 \, A c^{4} m^{2} + 1136160 \, A c^{4} m + 403200 \, A c^{4}\right )} x^{9} + 4 \, {\left (B a c^{3} m^{9} + 47 \, B a c^{3} m^{8} + 944 \, B a c^{3} m^{7} + 10598 \, B a c^{3} m^{6} + 72989 \, B a c^{3} m^{5} + 318143 \, B a c^{3} m^{4} + 871786 \, B a c^{3} m^{3} + 1435212 \, B a c^{3} m^{2} + 1271880 \, B a c^{3} m + 453600 \, B a c^{3}\right )} x^{8} + 4 \, {\left (A a c^{3} m^{9} + 48 \, A a c^{3} m^{8} + 984 \, A a c^{3} m^{7} + 11262 \, A a c^{3} m^{6} + 78939 \, A a c^{3} m^{5} + 349482 \, A a c^{3} m^{4} + 970556 \, A a c^{3} m^{3} + 1615608 \, A a c^{3} m^{2} + 1444320 \, A a c^{3} m + 518400 \, A a c^{3}\right )} x^{7} + 6 \, {\left (B a^{2} c^{2} m^{9} + 49 \, B a^{2} c^{2} m^{8} + 1026 \, B a^{2} c^{2} m^{7} + 11994 \, B a^{2} c^{2} m^{6} + 85809 \, B a^{2} c^{2} m^{5} + 387201 \, B a^{2} c^{2} m^{4} + 1093724 \, B a^{2} c^{2} m^{3} + 1847156 \, B a^{2} c^{2} m^{2} + 1670640 \, B a^{2} c^{2} m + 604800 \, B a^{2} c^{2}\right )} x^{6} + 6 \, {\left (A a^{2} c^{2} m^{9} + 50 \, A a^{2} c^{2} m^{8} + 1070 \, A a^{2} c^{2} m^{7} + 12800 \, A a^{2} c^{2} m^{6} + 93773 \, A a^{2} c^{2} m^{5} + 433190 \, A a^{2} c^{2} m^{4} + 1250980 \, A a^{2} c^{2} m^{3} + 2154600 \, A a^{2} c^{2} m^{2} + 1980576 \, A a^{2} c^{2} m + 725760 \, A a^{2} c^{2}\right )} x^{5} + 4 \, {\left (B a^{3} c m^{9} + 51 \, B a^{3} c m^{8} + 1116 \, B a^{3} c m^{7} + 13686 \, B a^{3} c m^{6} + 103029 \, B a^{3} c m^{5} + 489939 \, B a^{3} c m^{4} + 1457174 \, B a^{3} c m^{3} + 2580804 \, B a^{3} c m^{2} + 2430360 \, B a^{3} c m + 907200 \, B a^{3} c\right )} x^{4} + 4 \, {\left (A a^{3} c m^{9} + 52 \, A a^{3} c m^{8} + 1164 \, A a^{3} c m^{7} + 14658 \, A a^{3} c m^{6} + 113799 \, A a^{3} c m^{5} + 560658 \, A a^{3} c m^{4} + 1734956 \, A a^{3} c m^{3} + 3204632 \, A a^{3} c m^{2} + 3139680 \, A a^{3} c m + 1209600 \, A a^{3} c\right )} x^{3} + {\left (B a^{4} m^{9} + 53 \, B a^{4} m^{8} + 1214 \, B a^{4} m^{7} + 15722 \, B a^{4} m^{6} + 126329 \, B a^{4} m^{5} + 649397 \, B a^{4} m^{4} + 2118136 \, B a^{4} m^{3} + 4173228 \, B a^{4} m^{2} + 4407120 \, B a^{4} m + 1814400 \, B a^{4}\right )} x^{2} + {\left (A a^{4} m^{9} + 54 \, A a^{4} m^{8} + 1266 \, A a^{4} m^{7} + 16884 \, A a^{4} m^{6} + 140889 \, A a^{4} m^{5} + 761166 \, A a^{4} m^{4} + 2655764 \, A a^{4} m^{3} + 5753736 \, A a^{4} m^{2} + 6999840 \, A a^{4} m + 3628800 \, A a^{4}\right )} x\right )} \left (e x\right )^{m}}{m^{10} + 55 \, m^{9} + 1320 \, m^{8} + 18150 \, m^{7} + 157773 \, m^{6} + 902055 \, m^{5} + 3416930 \, m^{4} + 8409500 \, m^{3} + 12753576 \, m^{2} + 10628640 \, m + 3628800}
\]
[In]
integrate((e*x)^m*(B*x+A)*(c*x^2+a)^4,x, algorithm="fricas")
[Out]
((B*c^4*m^9 + 45*B*c^4*m^8 + 870*B*c^4*m^7 + 9450*B*c^4*m^6 + 63273*B*c^4*m^5 + 269325*B*c^4*m^4 + 723680*B*c^
4*m^3 + 1172700*B*c^4*m^2 + 1026576*B*c^4*m + 362880*B*c^4)*x^10 + (A*c^4*m^9 + 46*A*c^4*m^8 + 906*A*c^4*m^7 +
9996*A*c^4*m^6 + 67809*A*c^4*m^5 + 291774*A*c^4*m^4 + 790964*A*c^4*m^3 + 1290824*A*c^4*m^2 + 1136160*A*c^4*m
+ 403200*A*c^4)*x^9 + 4*(B*a*c^3*m^9 + 47*B*a*c^3*m^8 + 944*B*a*c^3*m^7 + 10598*B*a*c^3*m^6 + 72989*B*a*c^3*m^
5 + 318143*B*a*c^3*m^4 + 871786*B*a*c^3*m^3 + 1435212*B*a*c^3*m^2 + 1271880*B*a*c^3*m + 453600*B*a*c^3)*x^8 +
4*(A*a*c^3*m^9 + 48*A*a*c^3*m^8 + 984*A*a*c^3*m^7 + 11262*A*a*c^3*m^6 + 78939*A*a*c^3*m^5 + 349482*A*a*c^3*m^4
+ 970556*A*a*c^3*m^3 + 1615608*A*a*c^3*m^2 + 1444320*A*a*c^3*m + 518400*A*a*c^3)*x^7 + 6*(B*a^2*c^2*m^9 + 49*
B*a^2*c^2*m^8 + 1026*B*a^2*c^2*m^7 + 11994*B*a^2*c^2*m^6 + 85809*B*a^2*c^2*m^5 + 387201*B*a^2*c^2*m^4 + 109372
4*B*a^2*c^2*m^3 + 1847156*B*a^2*c^2*m^2 + 1670640*B*a^2*c^2*m + 604800*B*a^2*c^2)*x^6 + 6*(A*a^2*c^2*m^9 + 50*
A*a^2*c^2*m^8 + 1070*A*a^2*c^2*m^7 + 12800*A*a^2*c^2*m^6 + 93773*A*a^2*c^2*m^5 + 433190*A*a^2*c^2*m^4 + 125098
0*A*a^2*c^2*m^3 + 2154600*A*a^2*c^2*m^2 + 1980576*A*a^2*c^2*m + 725760*A*a^2*c^2)*x^5 + 4*(B*a^3*c*m^9 + 51*B*
a^3*c*m^8 + 1116*B*a^3*c*m^7 + 13686*B*a^3*c*m^6 + 103029*B*a^3*c*m^5 + 489939*B*a^3*c*m^4 + 1457174*B*a^3*c*m
^3 + 2580804*B*a^3*c*m^2 + 2430360*B*a^3*c*m + 907200*B*a^3*c)*x^4 + 4*(A*a^3*c*m^9 + 52*A*a^3*c*m^8 + 1164*A*
a^3*c*m^7 + 14658*A*a^3*c*m^6 + 113799*A*a^3*c*m^5 + 560658*A*a^3*c*m^4 + 1734956*A*a^3*c*m^3 + 3204632*A*a^3*
c*m^2 + 3139680*A*a^3*c*m + 1209600*A*a^3*c)*x^3 + (B*a^4*m^9 + 53*B*a^4*m^8 + 1214*B*a^4*m^7 + 15722*B*a^4*m^
6 + 126329*B*a^4*m^5 + 649397*B*a^4*m^4 + 2118136*B*a^4*m^3 + 4173228*B*a^4*m^2 + 4407120*B*a^4*m + 1814400*B*
a^4)*x^2 + (A*a^4*m^9 + 54*A*a^4*m^8 + 1266*A*a^4*m^7 + 16884*A*a^4*m^6 + 140889*A*a^4*m^5 + 761166*A*a^4*m^4
+ 2655764*A*a^4*m^3 + 5753736*A*a^4*m^2 + 6999840*A*a^4*m + 3628800*A*a^4)*x)*(e*x)^m/(m^10 + 55*m^9 + 1320*m^
8 + 18150*m^7 + 157773*m^6 + 902055*m^5 + 3416930*m^4 + 8409500*m^3 + 12753576*m^2 + 10628640*m + 3628800)
Sympy [B] (verification not implemented)
Leaf count of result is larger than twice the leaf count of optimal. 8032 vs. \(2 (207) = 414\).
Time = 1.01 (sec) , antiderivative size = 8032, normalized size of antiderivative = 37.01
\[
\int (e x)^m (A+B x) \left (a+c x^2\right )^4 \, dx=\text {Too large to display}
\]
[In]
integrate((e*x)**m*(B*x+A)*(c*x**2+a)**4,x)
[Out]
Piecewise(((-A*a**4/(9*x**9) - 4*A*a**3*c/(7*x**7) - 6*A*a**2*c**2/(5*x**5) - 4*A*a*c**3/(3*x**3) - A*c**4/x -
B*a**4/(8*x**8) - 2*B*a**3*c/(3*x**6) - 3*B*a**2*c**2/(2*x**4) - 2*B*a*c**3/x**2 + B*c**4*log(x))/e**10, Eq(m
, -10)), ((-A*a**4/(8*x**8) - 2*A*a**3*c/(3*x**6) - 3*A*a**2*c**2/(2*x**4) - 2*A*a*c**3/x**2 + A*c**4*log(x) -
B*a**4/(7*x**7) - 4*B*a**3*c/(5*x**5) - 2*B*a**2*c**2/x**3 - 4*B*a*c**3/x + B*c**4*x)/e**9, Eq(m, -9)), ((-A*
a**4/(7*x**7) - 4*A*a**3*c/(5*x**5) - 2*A*a**2*c**2/x**3 - 4*A*a*c**3/x + A*c**4*x - B*a**4/(6*x**6) - B*a**3*
c/x**4 - 3*B*a**2*c**2/x**2 + 4*B*a*c**3*log(x) + B*c**4*x**2/2)/e**8, Eq(m, -8)), ((-A*a**4/(6*x**6) - A*a**3
*c/x**4 - 3*A*a**2*c**2/x**2 + 4*A*a*c**3*log(x) + A*c**4*x**2/2 - B*a**4/(5*x**5) - 4*B*a**3*c/(3*x**3) - 6*B
*a**2*c**2/x + 4*B*a*c**3*x + B*c**4*x**3/3)/e**7, Eq(m, -7)), ((-A*a**4/(5*x**5) - 4*A*a**3*c/(3*x**3) - 6*A*
a**2*c**2/x + 4*A*a*c**3*x + A*c**4*x**3/3 - B*a**4/(4*x**4) - 2*B*a**3*c/x**2 + 6*B*a**2*c**2*log(x) + 2*B*a*
c**3*x**2 + B*c**4*x**4/4)/e**6, Eq(m, -6)), ((-A*a**4/(4*x**4) - 2*A*a**3*c/x**2 + 6*A*a**2*c**2*log(x) + 2*A
*a*c**3*x**2 + A*c**4*x**4/4 - B*a**4/(3*x**3) - 4*B*a**3*c/x + 6*B*a**2*c**2*x + 4*B*a*c**3*x**3/3 + B*c**4*x
**5/5)/e**5, Eq(m, -5)), ((-A*a**4/(3*x**3) - 4*A*a**3*c/x + 6*A*a**2*c**2*x + 4*A*a*c**3*x**3/3 + A*c**4*x**5
/5 - B*a**4/(2*x**2) + 4*B*a**3*c*log(x) + 3*B*a**2*c**2*x**2 + B*a*c**3*x**4 + B*c**4*x**6/6)/e**4, Eq(m, -4)
), ((-A*a**4/(2*x**2) + 4*A*a**3*c*log(x) + 3*A*a**2*c**2*x**2 + A*a*c**3*x**4 + A*c**4*x**6/6 - B*a**4/x + 4*
B*a**3*c*x + 2*B*a**2*c**2*x**3 + 4*B*a*c**3*x**5/5 + B*c**4*x**7/7)/e**3, Eq(m, -3)), ((-A*a**4/x + 4*A*a**3*
c*x + 2*A*a**2*c**2*x**3 + 4*A*a*c**3*x**5/5 + A*c**4*x**7/7 + B*a**4*log(x) + 2*B*a**3*c*x**2 + 3*B*a**2*c**2
*x**4/2 + 2*B*a*c**3*x**6/3 + B*c**4*x**8/8)/e**2, Eq(m, -2)), ((A*a**4*log(x) + 2*A*a**3*c*x**2 + 3*A*a**2*c*
*2*x**4/2 + 2*A*a*c**3*x**6/3 + A*c**4*x**8/8 + B*a**4*x + 4*B*a**3*c*x**3/3 + 6*B*a**2*c**2*x**5/5 + 4*B*a*c*
*3*x**7/7 + B*c**4*x**9/9)/e, Eq(m, -1)), (A*a**4*m**9*x*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 +
157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 54*A*a**4*m*
*8*x*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m
**3 + 12753576*m**2 + 10628640*m + 3628800) + 1266*A*a**4*m**7*x*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150
*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 1688
4*A*a**4*m**6*x*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4
+ 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 140889*A*a**4*m**5*x*(e*x)**m/(m**10 + 55*m**9 + 1320
*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 36
28800) + 761166*A*a**4*m**4*x*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 +
3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 2655764*A*a**4*m**3*x*(e*x)**m/(m**10 +
55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 +
10628640*m + 3628800) + 5753736*A*a**4*m**2*x*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6
+ 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 6999840*A*a**4*m*x*(e*x
)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 127
53576*m**2 + 10628640*m + 3628800) + 3628800*A*a**4*x*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157
773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 4*A*a**3*c*m**9
*x**3*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*
m**3 + 12753576*m**2 + 10628640*m + 3628800) + 208*A*a**3*c*m**8*x**3*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 +
18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) +
4656*A*a**3*c*m**7*x**3*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416
930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 58632*A*a**3*c*m**6*x**3*(e*x)**m/(m**10 + 5
5*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10
628640*m + 3628800) + 455196*A*a**3*c*m**5*x**3*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m*
*6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 2242632*A*a**3*c*m**4
*x**3*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*
m**3 + 12753576*m**2 + 10628640*m + 3628800) + 6939824*A*a**3*c*m**3*x**3*(e*x)**m/(m**10 + 55*m**9 + 1320*m**
8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 362880
0) + 12818528*A*a**3*c*m**2*x**3*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**
5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 12558720*A*a**3*c*m*x**3*(e*x)**m/(m
**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m
**2 + 10628640*m + 3628800) + 4838400*A*a**3*c*x**3*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 15777
3*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 6*A*a**2*c**2*m**
9*x**5*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500
*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 300*A*a**2*c**2*m**8*x**5*(e*x)**m/(m**10 + 55*m**9 + 1320*m**
8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 362880
0) + 6420*A*a**2*c**2*m**7*x**5*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5
+ 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 76800*A*a**2*c**2*m**6*x**5*(e*x)**m/
(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576
*m**2 + 10628640*m + 3628800) + 562638*A*a**2*c**2*m**5*x**5*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**
7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 2599140*
A*a**2*c**2*m**4*x**5*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930
*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 7505880*A*a**2*c**2*m**3*x**5*(e*x)**m/(m**10 +
55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 +
10628640*m + 3628800) + 12927600*A*a**2*c**2*m**2*x**5*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 15
7773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 11883456*A*a**
2*c**2*m*x**5*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 +
8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 4354560*A*a**2*c**2*x**5*(e*x)**m/(m**10 + 55*m**9 + 13
20*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m +
3628800) + 4*A*a*c**3*m**9*x**7*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5
+ 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 192*A*a*c**3*m**8*x**7*(e*x)**m/(m**1
0 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2
+ 10628640*m + 3628800) + 3936*A*a*c**3*m**7*x**7*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773
*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 45048*A*a*c**3*m**
6*x**7*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500
*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 315756*A*a*c**3*m**5*x**7*(e*x)**m/(m**10 + 55*m**9 + 1320*m**
8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 362880
0) + 1397928*A*a*c**3*m**4*x**7*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5
+ 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 3882224*A*a*c**3*m**3*x**7*(e*x)**m/(
m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*
m**2 + 10628640*m + 3628800) + 6462432*A*a*c**3*m**2*x**7*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 +
157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 5777280*A*a
*c**3*m*x**7*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8
409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 2073600*A*a*c**3*x**7*(e*x)**m/(m**10 + 55*m**9 + 1320*m
**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628
800) + A*c**4*m**9*x**9*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 34169
30*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 46*A*c**4*m**8*x**9*(e*x)**m/(m**10 + 55*m**9
+ 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640
*m + 3628800) + 906*A*c**4*m**7*x**9*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055
*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 9996*A*c**4*m**6*x**9*(e*x)**m/(
m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*
m**2 + 10628640*m + 3628800) + 67809*A*c**4*m**5*x**9*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157
773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 291774*A*c**4*m
**4*x**9*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 84095
00*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 790964*A*c**4*m**3*x**9*(e*x)**m/(m**10 + 55*m**9 + 1320*m**
8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 362880
0) + 1290824*A*c**4*m**2*x**9*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 +
3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 1136160*A*c**4*m*x**9*(e*x)**m/(m**10 +
55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 +
10628640*m + 3628800) + 403200*A*c**4*x**9*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 +
902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + B*a**4*m**9*x**2*(e*x)**m/
(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576
*m**2 + 10628640*m + 3628800) + 53*B*a**4*m**8*x**2*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 15777
3*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 1214*B*a**4*m**7*
x**2*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m
**3 + 12753576*m**2 + 10628640*m + 3628800) + 15722*B*a**4*m**6*x**2*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 1
8150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) +
126329*B*a**4*m**5*x**2*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 34169
30*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 649397*B*a**4*m**4*x**2*(e*x)**m/(m**10 + 55*
m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 1062
8640*m + 3628800) + 2118136*B*a**4*m**3*x**2*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6
+ 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 4173228*B*a**4*m**2*x**2
*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3
+ 12753576*m**2 + 10628640*m + 3628800) + 4407120*B*a**4*m*x**2*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*
m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 18144
00*B*a**4*x**2*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 +
8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 4*B*a**3*c*m**9*x**4*(e*x)**m/(m**10 + 55*m**9 + 1320*
m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 362
8800) + 204*B*a**3*c*m**8*x**4*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5
+ 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 4464*B*a**3*c*m**7*x**4*(e*x)**m/(m**1
0 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2
+ 10628640*m + 3628800) + 54744*B*a**3*c*m**6*x**4*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 15777
3*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 412116*B*a**3*c*m
**5*x**4*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 84095
00*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 1959756*B*a**3*c*m**4*x**4*(e*x)**m/(m**10 + 55*m**9 + 1320*
m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 362
8800) + 5828696*B*a**3*c*m**3*x**4*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m
**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 10323216*B*a**3*c*m**2*x**4*(e*x)*
*m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753
576*m**2 + 10628640*m + 3628800) + 9721440*B*a**3*c*m*x**4*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7
+ 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 3628800*B*
a**3*c*x**4*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 84
09500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 6*B*a**2*c**2*m**9*x**6*(e*x)**m/(m**10 + 55*m**9 + 1320*
m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 362
8800) + 294*B*a**2*c**2*m**8*x**6*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m*
*5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 6156*B*a**2*c**2*m**7*x**6*(e*x)**m
/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 1275357
6*m**2 + 10628640*m + 3628800) + 71964*B*a**2*c**2*m**6*x**6*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**
7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 514854*B
*a**2*c**2*m**5*x**6*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*
m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 2323206*B*a**2*c**2*m**4*x**6*(e*x)**m/(m**10 +
55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 1
0628640*m + 3628800) + 6562344*B*a**2*c**2*m**3*x**6*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 1577
73*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 11082936*B*a**2*
c**2*m**2*x**6*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 +
8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 10023840*B*a**2*c**2*m*x**6*(e*x)**m/(m**10 + 55*m**9
+ 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*
m + 3628800) + 3628800*B*a**2*c**2*x**6*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902
055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 4*B*a*c**3*m**9*x**8*(e*x)**m
/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 1275357
6*m**2 + 10628640*m + 3628800) + 188*B*a*c**3*m**8*x**8*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 1
57773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 3776*B*a*c**3
*m**7*x**8*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 840
9500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 42392*B*a*c**3*m**6*x**8*(e*x)**m/(m**10 + 55*m**9 + 1320*
m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 362
8800) + 291956*B*a*c**3*m**5*x**8*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m*
*5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 1272572*B*a*c**3*m**4*x**8*(e*x)**m
/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 1275357
6*m**2 + 10628640*m + 3628800) + 3487144*B*a*c**3*m**3*x**8*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7
+ 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 5740848*B
*a*c**3*m**2*x**8*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**
4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 5087520*B*a*c**3*m*x**8*(e*x)**m/(m**10 + 55*m**9 +
1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m
+ 3628800) + 1814400*B*a*c**3*x**8*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*
m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + B*c**4*m**9*x**10*(e*x)**m/(m**10
+ 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2
+ 10628640*m + 3628800) + 45*B*c**4*m**8*x**10*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**
6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 870*B*c**4*m**7*x**10*
(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 +
12753576*m**2 + 10628640*m + 3628800) + 9450*B*c**4*m**6*x**10*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*
m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 63273
*B*c**4*m**5*x**10*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m*
*4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 269325*B*c**4*m**4*x**10*(e*x)**m/(m**10 + 55*m**9
+ 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640
*m + 3628800) + 723680*B*c**4*m**3*x**10*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 90
2055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 1172700*B*c**4*m**2*x**10*(e
*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 1
2753576*m**2 + 10628640*m + 3628800) + 1026576*B*c**4*m*x**10*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m*
*7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8409500*m**3 + 12753576*m**2 + 10628640*m + 3628800) + 362880*
B*c**4*x**10*(e*x)**m/(m**10 + 55*m**9 + 1320*m**8 + 18150*m**7 + 157773*m**6 + 902055*m**5 + 3416930*m**4 + 8
409500*m**3 + 12753576*m**2 + 10628640*m + 3628800), True))
Maxima [A] (verification not implemented)
none
Time = 0.22 (sec) , antiderivative size = 208, normalized size of antiderivative = 0.96
\[
\int (e x)^m (A+B x) \left (a+c x^2\right )^4 \, dx=\frac {B c^{4} e^{m} x^{10} x^{m}}{m + 10} + \frac {A c^{4} e^{m} x^{9} x^{m}}{m + 9} + \frac {4 \, B a c^{3} e^{m} x^{8} x^{m}}{m + 8} + \frac {4 \, A a c^{3} e^{m} x^{7} x^{m}}{m + 7} + \frac {6 \, B a^{2} c^{2} e^{m} x^{6} x^{m}}{m + 6} + \frac {6 \, A a^{2} c^{2} e^{m} x^{5} x^{m}}{m + 5} + \frac {4 \, B a^{3} c e^{m} x^{4} x^{m}}{m + 4} + \frac {4 \, A a^{3} c e^{m} x^{3} x^{m}}{m + 3} + \frac {B a^{4} e^{m} x^{2} x^{m}}{m + 2} + \frac {\left (e x\right )^{m + 1} A a^{4}}{e {\left (m + 1\right )}}
\]
[In]
integrate((e*x)^m*(B*x+A)*(c*x^2+a)^4,x, algorithm="maxima")
[Out]
B*c^4*e^m*x^10*x^m/(m + 10) + A*c^4*e^m*x^9*x^m/(m + 9) + 4*B*a*c^3*e^m*x^8*x^m/(m + 8) + 4*A*a*c^3*e^m*x^7*x^
m/(m + 7) + 6*B*a^2*c^2*e^m*x^6*x^m/(m + 6) + 6*A*a^2*c^2*e^m*x^5*x^m/(m + 5) + 4*B*a^3*c*e^m*x^4*x^m/(m + 4)
+ 4*A*a^3*c*e^m*x^3*x^m/(m + 3) + B*a^4*e^m*x^2*x^m/(m + 2) + (e*x)^(m + 1)*A*a^4/(e*(m + 1))
Giac [B] (verification not implemented)
Leaf count of result is larger than twice the leaf count of optimal. 1778 vs. \(2 (217) = 434\).
Time = 0.28 (sec) , antiderivative size = 1778, normalized size of antiderivative = 8.19
\[
\int (e x)^m (A+B x) \left (a+c x^2\right )^4 \, dx=\text {Too large to display}
\]
[In]
integrate((e*x)^m*(B*x+A)*(c*x^2+a)^4,x, algorithm="giac")
[Out]
((e*x)^m*B*c^4*m^9*x^10 + (e*x)^m*A*c^4*m^9*x^9 + 45*(e*x)^m*B*c^4*m^8*x^10 + 4*(e*x)^m*B*a*c^3*m^9*x^8 + 46*(
e*x)^m*A*c^4*m^8*x^9 + 870*(e*x)^m*B*c^4*m^7*x^10 + 4*(e*x)^m*A*a*c^3*m^9*x^7 + 188*(e*x)^m*B*a*c^3*m^8*x^8 +
906*(e*x)^m*A*c^4*m^7*x^9 + 9450*(e*x)^m*B*c^4*m^6*x^10 + 6*(e*x)^m*B*a^2*c^2*m^9*x^6 + 192*(e*x)^m*A*a*c^3*m^
8*x^7 + 3776*(e*x)^m*B*a*c^3*m^7*x^8 + 9996*(e*x)^m*A*c^4*m^6*x^9 + 63273*(e*x)^m*B*c^4*m^5*x^10 + 6*(e*x)^m*A
*a^2*c^2*m^9*x^5 + 294*(e*x)^m*B*a^2*c^2*m^8*x^6 + 3936*(e*x)^m*A*a*c^3*m^7*x^7 + 42392*(e*x)^m*B*a*c^3*m^6*x^
8 + 67809*(e*x)^m*A*c^4*m^5*x^9 + 269325*(e*x)^m*B*c^4*m^4*x^10 + 4*(e*x)^m*B*a^3*c*m^9*x^4 + 300*(e*x)^m*A*a^
2*c^2*m^8*x^5 + 6156*(e*x)^m*B*a^2*c^2*m^7*x^6 + 45048*(e*x)^m*A*a*c^3*m^6*x^7 + 291956*(e*x)^m*B*a*c^3*m^5*x^
8 + 291774*(e*x)^m*A*c^4*m^4*x^9 + 723680*(e*x)^m*B*c^4*m^3*x^10 + 4*(e*x)^m*A*a^3*c*m^9*x^3 + 204*(e*x)^m*B*a
^3*c*m^8*x^4 + 6420*(e*x)^m*A*a^2*c^2*m^7*x^5 + 71964*(e*x)^m*B*a^2*c^2*m^6*x^6 + 315756*(e*x)^m*A*a*c^3*m^5*x
^7 + 1272572*(e*x)^m*B*a*c^3*m^4*x^8 + 790964*(e*x)^m*A*c^4*m^3*x^9 + 1172700*(e*x)^m*B*c^4*m^2*x^10 + (e*x)^m
*B*a^4*m^9*x^2 + 208*(e*x)^m*A*a^3*c*m^8*x^3 + 4464*(e*x)^m*B*a^3*c*m^7*x^4 + 76800*(e*x)^m*A*a^2*c^2*m^6*x^5
+ 514854*(e*x)^m*B*a^2*c^2*m^5*x^6 + 1397928*(e*x)^m*A*a*c^3*m^4*x^7 + 3487144*(e*x)^m*B*a*c^3*m^3*x^8 + 12908
24*(e*x)^m*A*c^4*m^2*x^9 + 1026576*(e*x)^m*B*c^4*m*x^10 + (e*x)^m*A*a^4*m^9*x + 53*(e*x)^m*B*a^4*m^8*x^2 + 465
6*(e*x)^m*A*a^3*c*m^7*x^3 + 54744*(e*x)^m*B*a^3*c*m^6*x^4 + 562638*(e*x)^m*A*a^2*c^2*m^5*x^5 + 2323206*(e*x)^m
*B*a^2*c^2*m^4*x^6 + 3882224*(e*x)^m*A*a*c^3*m^3*x^7 + 5740848*(e*x)^m*B*a*c^3*m^2*x^8 + 1136160*(e*x)^m*A*c^4
*m*x^9 + 362880*(e*x)^m*B*c^4*x^10 + 54*(e*x)^m*A*a^4*m^8*x + 1214*(e*x)^m*B*a^4*m^7*x^2 + 58632*(e*x)^m*A*a^3
*c*m^6*x^3 + 412116*(e*x)^m*B*a^3*c*m^5*x^4 + 2599140*(e*x)^m*A*a^2*c^2*m^4*x^5 + 6562344*(e*x)^m*B*a^2*c^2*m^
3*x^6 + 6462432*(e*x)^m*A*a*c^3*m^2*x^7 + 5087520*(e*x)^m*B*a*c^3*m*x^8 + 403200*(e*x)^m*A*c^4*x^9 + 1266*(e*x
)^m*A*a^4*m^7*x + 15722*(e*x)^m*B*a^4*m^6*x^2 + 455196*(e*x)^m*A*a^3*c*m^5*x^3 + 1959756*(e*x)^m*B*a^3*c*m^4*x
^4 + 7505880*(e*x)^m*A*a^2*c^2*m^3*x^5 + 11082936*(e*x)^m*B*a^2*c^2*m^2*x^6 + 5777280*(e*x)^m*A*a*c^3*m*x^7 +
1814400*(e*x)^m*B*a*c^3*x^8 + 16884*(e*x)^m*A*a^4*m^6*x + 126329*(e*x)^m*B*a^4*m^5*x^2 + 2242632*(e*x)^m*A*a^3
*c*m^4*x^3 + 5828696*(e*x)^m*B*a^3*c*m^3*x^4 + 12927600*(e*x)^m*A*a^2*c^2*m^2*x^5 + 10023840*(e*x)^m*B*a^2*c^2
*m*x^6 + 2073600*(e*x)^m*A*a*c^3*x^7 + 140889*(e*x)^m*A*a^4*m^5*x + 649397*(e*x)^m*B*a^4*m^4*x^2 + 6939824*(e*
x)^m*A*a^3*c*m^3*x^3 + 10323216*(e*x)^m*B*a^3*c*m^2*x^4 + 11883456*(e*x)^m*A*a^2*c^2*m*x^5 + 3628800*(e*x)^m*B
*a^2*c^2*x^6 + 761166*(e*x)^m*A*a^4*m^4*x + 2118136*(e*x)^m*B*a^4*m^3*x^2 + 12818528*(e*x)^m*A*a^3*c*m^2*x^3 +
9721440*(e*x)^m*B*a^3*c*m*x^4 + 4354560*(e*x)^m*A*a^2*c^2*x^5 + 2655764*(e*x)^m*A*a^4*m^3*x + 4173228*(e*x)^m
*B*a^4*m^2*x^2 + 12558720*(e*x)^m*A*a^3*c*m*x^3 + 3628800*(e*x)^m*B*a^3*c*x^4 + 5753736*(e*x)^m*A*a^4*m^2*x +
4407120*(e*x)^m*B*a^4*m*x^2 + 4838400*(e*x)^m*A*a^3*c*x^3 + 6999840*(e*x)^m*A*a^4*m*x + 1814400*(e*x)^m*B*a^4*
x^2 + 3628800*(e*x)^m*A*a^4*x)/(m^10 + 55*m^9 + 1320*m^8 + 18150*m^7 + 157773*m^6 + 902055*m^5 + 3416930*m^4 +
8409500*m^3 + 12753576*m^2 + 10628640*m + 3628800)
Mupad [B] (verification not implemented)
Time = 10.68 (sec) , antiderivative size = 1075, normalized size of antiderivative = 4.95
\[
\int (e x)^m (A+B x) \left (a+c x^2\right )^4 \, dx=\frac {B\,a^4\,x^2\,{\left (e\,x\right )}^m\,\left (m^9+53\,m^8+1214\,m^7+15722\,m^6+126329\,m^5+649397\,m^4+2118136\,m^3+4173228\,m^2+4407120\,m+1814400\right )}{m^{10}+55\,m^9+1320\,m^8+18150\,m^7+157773\,m^6+902055\,m^5+3416930\,m^4+8409500\,m^3+12753576\,m^2+10628640\,m+3628800}+\frac {A\,c^4\,x^9\,{\left (e\,x\right )}^m\,\left (m^9+46\,m^8+906\,m^7+9996\,m^6+67809\,m^5+291774\,m^4+790964\,m^3+1290824\,m^2+1136160\,m+403200\right )}{m^{10}+55\,m^9+1320\,m^8+18150\,m^7+157773\,m^6+902055\,m^5+3416930\,m^4+8409500\,m^3+12753576\,m^2+10628640\,m+3628800}+\frac {B\,c^4\,x^{10}\,{\left (e\,x\right )}^m\,\left (m^9+45\,m^8+870\,m^7+9450\,m^6+63273\,m^5+269325\,m^4+723680\,m^3+1172700\,m^2+1026576\,m+362880\right )}{m^{10}+55\,m^9+1320\,m^8+18150\,m^7+157773\,m^6+902055\,m^5+3416930\,m^4+8409500\,m^3+12753576\,m^2+10628640\,m+3628800}+\frac {A\,a^4\,x\,{\left (e\,x\right )}^m\,\left (m^9+54\,m^8+1266\,m^7+16884\,m^6+140889\,m^5+761166\,m^4+2655764\,m^3+5753736\,m^2+6999840\,m+3628800\right )}{m^{10}+55\,m^9+1320\,m^8+18150\,m^7+157773\,m^6+902055\,m^5+3416930\,m^4+8409500\,m^3+12753576\,m^2+10628640\,m+3628800}+\frac {4\,A\,a\,c^3\,x^7\,{\left (e\,x\right )}^m\,\left (m^9+48\,m^8+984\,m^7+11262\,m^6+78939\,m^5+349482\,m^4+970556\,m^3+1615608\,m^2+1444320\,m+518400\right )}{m^{10}+55\,m^9+1320\,m^8+18150\,m^7+157773\,m^6+902055\,m^5+3416930\,m^4+8409500\,m^3+12753576\,m^2+10628640\,m+3628800}+\frac {4\,A\,a^3\,c\,x^3\,{\left (e\,x\right )}^m\,\left (m^9+52\,m^8+1164\,m^7+14658\,m^6+113799\,m^5+560658\,m^4+1734956\,m^3+3204632\,m^2+3139680\,m+1209600\right )}{m^{10}+55\,m^9+1320\,m^8+18150\,m^7+157773\,m^6+902055\,m^5+3416930\,m^4+8409500\,m^3+12753576\,m^2+10628640\,m+3628800}+\frac {4\,B\,a\,c^3\,x^8\,{\left (e\,x\right )}^m\,\left (m^9+47\,m^8+944\,m^7+10598\,m^6+72989\,m^5+318143\,m^4+871786\,m^3+1435212\,m^2+1271880\,m+453600\right )}{m^{10}+55\,m^9+1320\,m^8+18150\,m^7+157773\,m^6+902055\,m^5+3416930\,m^4+8409500\,m^3+12753576\,m^2+10628640\,m+3628800}+\frac {4\,B\,a^3\,c\,x^4\,{\left (e\,x\right )}^m\,\left (m^9+51\,m^8+1116\,m^7+13686\,m^6+103029\,m^5+489939\,m^4+1457174\,m^3+2580804\,m^2+2430360\,m+907200\right )}{m^{10}+55\,m^9+1320\,m^8+18150\,m^7+157773\,m^6+902055\,m^5+3416930\,m^4+8409500\,m^3+12753576\,m^2+10628640\,m+3628800}+\frac {6\,A\,a^2\,c^2\,x^5\,{\left (e\,x\right )}^m\,\left (m^9+50\,m^8+1070\,m^7+12800\,m^6+93773\,m^5+433190\,m^4+1250980\,m^3+2154600\,m^2+1980576\,m+725760\right )}{m^{10}+55\,m^9+1320\,m^8+18150\,m^7+157773\,m^6+902055\,m^5+3416930\,m^4+8409500\,m^3+12753576\,m^2+10628640\,m+3628800}+\frac {6\,B\,a^2\,c^2\,x^6\,{\left (e\,x\right )}^m\,\left (m^9+49\,m^8+1026\,m^7+11994\,m^6+85809\,m^5+387201\,m^4+1093724\,m^3+1847156\,m^2+1670640\,m+604800\right )}{m^{10}+55\,m^9+1320\,m^8+18150\,m^7+157773\,m^6+902055\,m^5+3416930\,m^4+8409500\,m^3+12753576\,m^2+10628640\,m+3628800}
\]
[In]
int((e*x)^m*(a + c*x^2)^4*(A + B*x),x)
[Out]
(B*a^4*x^2*(e*x)^m*(4407120*m + 4173228*m^2 + 2118136*m^3 + 649397*m^4 + 126329*m^5 + 15722*m^6 + 1214*m^7 + 5
3*m^8 + m^9 + 1814400))/(10628640*m + 12753576*m^2 + 8409500*m^3 + 3416930*m^4 + 902055*m^5 + 157773*m^6 + 181
50*m^7 + 1320*m^8 + 55*m^9 + m^10 + 3628800) + (A*c^4*x^9*(e*x)^m*(1136160*m + 1290824*m^2 + 790964*m^3 + 2917
74*m^4 + 67809*m^5 + 9996*m^6 + 906*m^7 + 46*m^8 + m^9 + 403200))/(10628640*m + 12753576*m^2 + 8409500*m^3 + 3
416930*m^4 + 902055*m^5 + 157773*m^6 + 18150*m^7 + 1320*m^8 + 55*m^9 + m^10 + 3628800) + (B*c^4*x^10*(e*x)^m*(
1026576*m + 1172700*m^2 + 723680*m^3 + 269325*m^4 + 63273*m^5 + 9450*m^6 + 870*m^7 + 45*m^8 + m^9 + 362880))/(
10628640*m + 12753576*m^2 + 8409500*m^3 + 3416930*m^4 + 902055*m^5 + 157773*m^6 + 18150*m^7 + 1320*m^8 + 55*m^
9 + m^10 + 3628800) + (A*a^4*x*(e*x)^m*(6999840*m + 5753736*m^2 + 2655764*m^3 + 761166*m^4 + 140889*m^5 + 1688
4*m^6 + 1266*m^7 + 54*m^8 + m^9 + 3628800))/(10628640*m + 12753576*m^2 + 8409500*m^3 + 3416930*m^4 + 902055*m^
5 + 157773*m^6 + 18150*m^7 + 1320*m^8 + 55*m^9 + m^10 + 3628800) + (4*A*a*c^3*x^7*(e*x)^m*(1444320*m + 1615608
*m^2 + 970556*m^3 + 349482*m^4 + 78939*m^5 + 11262*m^6 + 984*m^7 + 48*m^8 + m^9 + 518400))/(10628640*m + 12753
576*m^2 + 8409500*m^3 + 3416930*m^4 + 902055*m^5 + 157773*m^6 + 18150*m^7 + 1320*m^8 + 55*m^9 + m^10 + 3628800
) + (4*A*a^3*c*x^3*(e*x)^m*(3139680*m + 3204632*m^2 + 1734956*m^3 + 560658*m^4 + 113799*m^5 + 14658*m^6 + 1164
*m^7 + 52*m^8 + m^9 + 1209600))/(10628640*m + 12753576*m^2 + 8409500*m^3 + 3416930*m^4 + 902055*m^5 + 157773*m
^6 + 18150*m^7 + 1320*m^8 + 55*m^9 + m^10 + 3628800) + (4*B*a*c^3*x^8*(e*x)^m*(1271880*m + 1435212*m^2 + 87178
6*m^3 + 318143*m^4 + 72989*m^5 + 10598*m^6 + 944*m^7 + 47*m^8 + m^9 + 453600))/(10628640*m + 12753576*m^2 + 84
09500*m^3 + 3416930*m^4 + 902055*m^5 + 157773*m^6 + 18150*m^7 + 1320*m^8 + 55*m^9 + m^10 + 3628800) + (4*B*a^3
*c*x^4*(e*x)^m*(2430360*m + 2580804*m^2 + 1457174*m^3 + 489939*m^4 + 103029*m^5 + 13686*m^6 + 1116*m^7 + 51*m^
8 + m^9 + 907200))/(10628640*m + 12753576*m^2 + 8409500*m^3 + 3416930*m^4 + 902055*m^5 + 157773*m^6 + 18150*m^
7 + 1320*m^8 + 55*m^9 + m^10 + 3628800) + (6*A*a^2*c^2*x^5*(e*x)^m*(1980576*m + 2154600*m^2 + 1250980*m^3 + 43
3190*m^4 + 93773*m^5 + 12800*m^6 + 1070*m^7 + 50*m^8 + m^9 + 725760))/(10628640*m + 12753576*m^2 + 8409500*m^3
+ 3416930*m^4 + 902055*m^5 + 157773*m^6 + 18150*m^7 + 1320*m^8 + 55*m^9 + m^10 + 3628800) + (6*B*a^2*c^2*x^6*
(e*x)^m*(1670640*m + 1847156*m^2 + 1093724*m^3 + 387201*m^4 + 85809*m^5 + 11994*m^6 + 1026*m^7 + 49*m^8 + m^9
+ 604800))/(10628640*m + 12753576*m^2 + 8409500*m^3 + 3416930*m^4 + 902055*m^5 + 157773*m^6 + 18150*m^7 + 1320
*m^8 + 55*m^9 + m^10 + 3628800)