3.368 \(\int (d+e x)^m (3+2 x+5 x^2)^2 (2+x+3 x^2-5 x^3+4 x^4) \, dx\)
Optimal. Leaf size=432 \[ \frac{\left (5 d^2-2 d e+3 e^2\right )^2 \left (3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right ) (d+e x)^{m+1}}{e^9 (m+1)}-\frac{\left (5 d^2-2 d e+3 e^2\right ) \left (88 d^3 e^2-4 d^2 e^3+127 d^4 e+160 d^5+64 d e^4-11 e^5\right ) (d+e x)^{m+2}}{e^9 (m+2)}+\frac{\left (1665 d^4 e^2+370 d^3 e^3+888 d^2 e^4+945 d^5 e+2800 d^6-195 d e^5+107 e^6\right ) (d+e x)^{m+3}}{e^9 (m+3)}-\frac{\left (2220 d^3 e^2+370 d^2 e^3+1575 d^4 e+5600 d^5+592 d e^4-65 e^5\right ) (d+e x)^{m+4}}{e^9 (m+4)}+\frac{\left (1665 d^2 e^2+1575 d^3 e+7000 d^4+185 d e^3+148 e^4\right ) (d+e x)^{m+5}}{e^9 (m+5)}-\frac{\left (945 d^2 e+5600 d^3+666 d e^2+37 e^3\right ) (d+e x)^{m+6}}{e^9 (m+6)}+\frac{\left (2800 d^2+315 d e+111 e^2\right ) (d+e x)^{m+7}}{e^9 (m+7)}-\frac{5 (160 d+9 e) (d+e x)^{m+8}}{e^9 (m+8)}+\frac{100 (d+e x)^{m+9}}{e^9 (m+9)} \]
[Out]
((5*d^2 - 2*d*e + 3*e^2)^2*(4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4)*(d + e*x)^(1 + m))/(e^9*(1 + m)) - ((
5*d^2 - 2*d*e + 3*e^2)*(160*d^5 + 127*d^4*e + 88*d^3*e^2 - 4*d^2*e^3 + 64*d*e^4 - 11*e^5)*(d + e*x)^(2 + m))/(
e^9*(2 + m)) + ((2800*d^6 + 945*d^5*e + 1665*d^4*e^2 + 370*d^3*e^3 + 888*d^2*e^4 - 195*d*e^5 + 107*e^6)*(d + e
*x)^(3 + m))/(e^9*(3 + m)) - ((5600*d^5 + 1575*d^4*e + 2220*d^3*e^2 + 370*d^2*e^3 + 592*d*e^4 - 65*e^5)*(d + e
*x)^(4 + m))/(e^9*(4 + m)) + ((7000*d^4 + 1575*d^3*e + 1665*d^2*e^2 + 185*d*e^3 + 148*e^4)*(d + e*x)^(5 + m))/
(e^9*(5 + m)) - ((5600*d^3 + 945*d^2*e + 666*d*e^2 + 37*e^3)*(d + e*x)^(6 + m))/(e^9*(6 + m)) + ((2800*d^2 + 3
15*d*e + 111*e^2)*(d + e*x)^(7 + m))/(e^9*(7 + m)) - (5*(160*d + 9*e)*(d + e*x)^(8 + m))/(e^9*(8 + m)) + (100*
(d + e*x)^(9 + m))/(e^9*(9 + m))
________________________________________________________________________________________
Rubi [A] time = 0.242795, antiderivative size = 432, normalized size of antiderivative = 1.,
number of steps used = 2, number of rules used = 1, integrand size = 38, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.026, Rules used =
{1628} \[ \frac{\left (5 d^2-2 d e+3 e^2\right )^2 \left (3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right ) (d+e x)^{m+1}}{e^9 (m+1)}-\frac{\left (5 d^2-2 d e+3 e^2\right ) \left (88 d^3 e^2-4 d^2 e^3+127 d^4 e+160 d^5+64 d e^4-11 e^5\right ) (d+e x)^{m+2}}{e^9 (m+2)}+\frac{\left (1665 d^4 e^2+370 d^3 e^3+888 d^2 e^4+945 d^5 e+2800 d^6-195 d e^5+107 e^6\right ) (d+e x)^{m+3}}{e^9 (m+3)}-\frac{\left (2220 d^3 e^2+370 d^2 e^3+1575 d^4 e+5600 d^5+592 d e^4-65 e^5\right ) (d+e x)^{m+4}}{e^9 (m+4)}+\frac{\left (1665 d^2 e^2+1575 d^3 e+7000 d^4+185 d e^3+148 e^4\right ) (d+e x)^{m+5}}{e^9 (m+5)}-\frac{\left (945 d^2 e+5600 d^3+666 d e^2+37 e^3\right ) (d+e x)^{m+6}}{e^9 (m+6)}+\frac{\left (2800 d^2+315 d e+111 e^2\right ) (d+e x)^{m+7}}{e^9 (m+7)}-\frac{5 (160 d+9 e) (d+e x)^{m+8}}{e^9 (m+8)}+\frac{100 (d+e x)^{m+9}}{e^9 (m+9)} \]
Antiderivative was successfully verified.
[In]
Int[(d + e*x)^m*(3 + 2*x + 5*x^2)^2*(2 + x + 3*x^2 - 5*x^3 + 4*x^4),x]
[Out]
((5*d^2 - 2*d*e + 3*e^2)^2*(4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4)*(d + e*x)^(1 + m))/(e^9*(1 + m)) - ((
5*d^2 - 2*d*e + 3*e^2)*(160*d^5 + 127*d^4*e + 88*d^3*e^2 - 4*d^2*e^3 + 64*d*e^4 - 11*e^5)*(d + e*x)^(2 + m))/(
e^9*(2 + m)) + ((2800*d^6 + 945*d^5*e + 1665*d^4*e^2 + 370*d^3*e^3 + 888*d^2*e^4 - 195*d*e^5 + 107*e^6)*(d + e
*x)^(3 + m))/(e^9*(3 + m)) - ((5600*d^5 + 1575*d^4*e + 2220*d^3*e^2 + 370*d^2*e^3 + 592*d*e^4 - 65*e^5)*(d + e
*x)^(4 + m))/(e^9*(4 + m)) + ((7000*d^4 + 1575*d^3*e + 1665*d^2*e^2 + 185*d*e^3 + 148*e^4)*(d + e*x)^(5 + m))/
(e^9*(5 + m)) - ((5600*d^3 + 945*d^2*e + 666*d*e^2 + 37*e^3)*(d + e*x)^(6 + m))/(e^9*(6 + m)) + ((2800*d^2 + 3
15*d*e + 111*e^2)*(d + e*x)^(7 + m))/(e^9*(7 + m)) - (5*(160*d + 9*e)*(d + e*x)^(8 + m))/(e^9*(8 + m)) + (100*
(d + e*x)^(9 + m))/(e^9*(9 + m))
Rule 1628
Int[(Pq_)*((d_.) + (e_.)*(x_))^(m_.)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> Int[ExpandIntegra
nd[(d + e*x)^m*Pq*(a + b*x + c*x^2)^p, x], x] /; FreeQ[{a, b, c, d, e, m}, x] && PolyQ[Pq, x] && IGtQ[p, -2]
Rubi steps
\begin{align*} \int (d+e x)^m \left (3+2 x+5 x^2\right )^2 \left (2+x+3 x^2-5 x^3+4 x^4\right ) \, dx &=\int \left (\frac{\left (5 d^2-2 d e+3 e^2\right )^2 \left (4 d^4+5 d^3 e+3 d^2 e^2-d e^3+2 e^4\right ) (d+e x)^m}{e^8}+\frac{\left (-800 d^7-315 d^6 e-666 d^5 e^2-185 d^4 e^3-592 d^3 e^4+195 d^2 e^5-214 d e^6+33 e^7\right ) (d+e x)^{1+m}}{e^8}+\frac{\left (2800 d^6+945 d^5 e+1665 d^4 e^2+370 d^3 e^3+888 d^2 e^4-195 d e^5+107 e^6\right ) (d+e x)^{2+m}}{e^8}+\frac{\left (-5600 d^5-1575 d^4 e-2220 d^3 e^2-370 d^2 e^3-592 d e^4+65 e^5\right ) (d+e x)^{3+m}}{e^8}+\frac{\left (7000 d^4+1575 d^3 e+1665 d^2 e^2+185 d e^3+148 e^4\right ) (d+e x)^{4+m}}{e^8}+\frac{\left (-5600 d^3-945 d^2 e-666 d e^2-37 e^3\right ) (d+e x)^{5+m}}{e^8}+\frac{\left (2800 d^2+315 d e+111 e^2\right ) (d+e x)^{6+m}}{e^8}-\frac{5 (160 d+9 e) (d+e x)^{7+m}}{e^8}+\frac{100 (d+e x)^{8+m}}{e^8}\right ) \, dx\\ &=\frac{\left (5 d^2-2 d e+3 e^2\right )^2 \left (4 d^4+5 d^3 e+3 d^2 e^2-d e^3+2 e^4\right ) (d+e x)^{1+m}}{e^9 (1+m)}-\frac{\left (5 d^2-2 d e+3 e^2\right ) \left (160 d^5+127 d^4 e+88 d^3 e^2-4 d^2 e^3+64 d e^4-11 e^5\right ) (d+e x)^{2+m}}{e^9 (2+m)}+\frac{\left (2800 d^6+945 d^5 e+1665 d^4 e^2+370 d^3 e^3+888 d^2 e^4-195 d e^5+107 e^6\right ) (d+e x)^{3+m}}{e^9 (3+m)}-\frac{\left (5600 d^5+1575 d^4 e+2220 d^3 e^2+370 d^2 e^3+592 d e^4-65 e^5\right ) (d+e x)^{4+m}}{e^9 (4+m)}+\frac{\left (7000 d^4+1575 d^3 e+1665 d^2 e^2+185 d e^3+148 e^4\right ) (d+e x)^{5+m}}{e^9 (5+m)}-\frac{\left (5600 d^3+945 d^2 e+666 d e^2+37 e^3\right ) (d+e x)^{6+m}}{e^9 (6+m)}+\frac{\left (2800 d^2+315 d e+111 e^2\right ) (d+e x)^{7+m}}{e^9 (7+m)}-\frac{5 (160 d+9 e) (d+e x)^{8+m}}{e^9 (8+m)}+\frac{100 (d+e x)^{9+m}}{e^9 (9+m)}\\ \end{align*}
Mathematica [A] time = 0.255382, size = 391, normalized size = 0.91 \[ \frac{(d+e x)^{m+1} \left (\frac{\left (2800 d^2+315 d e+111 e^2\right ) (d+e x)^6}{m+7}-\frac{\left (945 d^2 e+5600 d^3+666 d e^2+37 e^3\right ) (d+e x)^5}{m+6}+\frac{\left (1665 d^2 e^2+1575 d^3 e+7000 d^4+185 d e^3+148 e^4\right ) (d+e x)^4}{m+5}-\frac{\left (2220 d^3 e^2+370 d^2 e^3+1575 d^4 e+5600 d^5+592 d e^4-65 e^5\right ) (d+e x)^3}{m+4}+\frac{\left (1665 d^4 e^2+370 d^3 e^3+888 d^2 e^4+945 d^5 e+2800 d^6-195 d e^5+107 e^6\right ) (d+e x)^2}{m+3}-\frac{\left (5 d^2-2 d e+3 e^2\right ) \left (88 d^3 e^2-4 d^2 e^3+127 d^4 e+160 d^5+64 d e^4-11 e^5\right ) (d+e x)}{m+2}+\frac{\left (5 d^2-2 d e+3 e^2\right )^2 \left (3 d^2 e^2+5 d^3 e+4 d^4-d e^3+2 e^4\right )}{m+1}+\frac{100 (d+e x)^8}{m+9}-\frac{5 (160 d+9 e) (d+e x)^7}{m+8}\right )}{e^9} \]
Antiderivative was successfully verified.
[In]
Integrate[(d + e*x)^m*(3 + 2*x + 5*x^2)^2*(2 + x + 3*x^2 - 5*x^3 + 4*x^4),x]
[Out]
((d + e*x)^(1 + m)*(((5*d^2 - 2*d*e + 3*e^2)^2*(4*d^4 + 5*d^3*e + 3*d^2*e^2 - d*e^3 + 2*e^4))/(1 + m) - ((5*d^
2 - 2*d*e + 3*e^2)*(160*d^5 + 127*d^4*e + 88*d^3*e^2 - 4*d^2*e^3 + 64*d*e^4 - 11*e^5)*(d + e*x))/(2 + m) + ((2
800*d^6 + 945*d^5*e + 1665*d^4*e^2 + 370*d^3*e^3 + 888*d^2*e^4 - 195*d*e^5 + 107*e^6)*(d + e*x)^2)/(3 + m) - (
(5600*d^5 + 1575*d^4*e + 2220*d^3*e^2 + 370*d^2*e^3 + 592*d*e^4 - 65*e^5)*(d + e*x)^3)/(4 + m) + ((7000*d^4 +
1575*d^3*e + 1665*d^2*e^2 + 185*d*e^3 + 148*e^4)*(d + e*x)^4)/(5 + m) - ((5600*d^3 + 945*d^2*e + 666*d*e^2 + 3
7*e^3)*(d + e*x)^5)/(6 + m) + ((2800*d^2 + 315*d*e + 111*e^2)*(d + e*x)^6)/(7 + m) - (5*(160*d + 9*e)*(d + e*x
)^7)/(8 + m) + (100*(d + e*x)^8)/(9 + m)))/e^9
________________________________________________________________________________________
Maple [B] time = 0.062, size = 3222, normalized size = 7.5 \begin{align*} \text{output too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((e*x+d)^m*(5*x^2+2*x+3)^2*(4*x^4-5*x^3+3*x^2+x+2),x)
[Out]
(e*x+d)^(1+m)*(100*e^8*m^8*x^8-45*e^8*m^8*x^7+3600*e^8*m^7*x^8-800*d*e^7*m^7*x^7+111*e^8*m^8*x^6-1665*e^8*m^7*
x^7+54600*e^8*m^6*x^8+315*d*e^7*m^7*x^6-22400*d*e^7*m^6*x^7-37*e^8*m^8*x^5+4218*e^8*m^7*x^6-25830*e^8*m^6*x^7+
453600*e^8*m^5*x^8+5600*d^2*e^6*m^6*x^6-666*d*e^7*m^7*x^5+9450*d*e^7*m^6*x^6-257600*d*e^7*m^5*x^7+148*e^8*m^8*
x^4-1443*e^8*m^7*x^5+67044*e^8*m^6*x^6-218610*e^8*m^5*x^7+2244900*e^8*m^4*x^8-1890*d^2*e^6*m^6*x^5+117600*d^2*
e^6*m^5*x^6+185*d*e^7*m^7*x^4-21312*d*e^7*m^6*x^5+114660*d*e^7*m^5*x^6-1568000*d*e^7*m^4*x^7+65*e^8*m^8*x^3+59
20*e^8*m^7*x^4-23532*e^8*m^6*x^5+579642*e^8*m^5*x^6-1098405*e^8*m^4*x^7+6728400*e^8*m^3*x^8-33600*d^3*e^5*m^5*
x^5+3330*d^2*e^6*m^6*x^4-45360*d^2*e^6*m^5*x^5+980000*d^2*e^6*m^4*x^6-592*d*e^7*m^7*x^3+6290*d*e^7*m^6*x^4-274
392*d*e^7*m^5*x^5+727650*d*e^7*m^4*x^6-5415200*d*e^7*m^3*x^7+107*e^8*m^8*x^2+2665*e^8*m^7*x^3+99160*e^8*m^6*x^
4-208458*e^8*m^5*x^5+2965809*e^8*m^4*x^6-3332385*e^8*m^3*x^7+11812400*e^8*m^2*x^8+9450*d^3*e^5*m^5*x^4-504000*
d^3*e^5*m^4*x^5-740*d^2*e^6*m^6*x^3+89910*d^2*e^6*m^5*x^4-415800*d^2*e^6*m^4*x^5+4116000*d^2*e^6*m^3*x^6-195*d
*e^7*m^7*x^2-21312*d*e^7*m^6*x^3+86210*d*e^7*m^5*x^4-1831500*d*e^7*m^4*x^5+2595285*d*e^7*m^3*x^6-10505600*d*e^
7*m^2*x^7+33*e^8*m^8*x+4494*e^8*m^7*x^2+45890*e^8*m^6*x^3+902800*e^8*m^5*x^4-1090353*e^8*m^4*x^5+9134412*e^8*m
^3*x^6-5906520*e^8*m^2*x^7+10958400*e^8*m*x^8+168000*d^4*e^4*m^4*x^4-13320*d^3*e^5*m^5*x^3+179550*d^3*e^5*m^4*
x^4-2856000*d^3*e^5*m^3*x^5+1776*d^2*e^6*m^6*x^2-22200*d^2*e^6*m^5*x^3+922410*d^2*e^6*m^4*x^4-1871100*d^2*e^6*
m^3*x^5+9094400*d^2*e^6*m^2*x^6-214*d*e^7*m^7*x-7410*d*e^7*m^6*x^2-311392*d*e^7*m^5*x^3+611240*d*e^7*m^4*x^4-6
805854*d*e^7*m^3*x^5+5159700*d*e^7*m^2*x^6-10454400*d*e^7*m*x^7+18*e^8*m^8+1419*e^8*m^7*x+79608*e^8*m^6*x^2+43
0690*e^8*m^5*x^3+4850404*e^8*m^4*x^4-3422907*e^8*m^3*x^5+16387596*e^8*m^2*x^6-5519340*e^8*m*x^7+4032000*e^8*x^
8-37800*d^4*e^4*m^4*x^3+1680000*d^4*e^4*m^3*x^4+2220*d^3*e^5*m^5*x^2-306360*d^3*e^5*m^4*x^3+1181250*d^3*e^5*m^
3*x^4-7560000*d^3*e^5*m^2*x^5+390*d^2*e^6*m^6*x+58608*d^2*e^6*m^5*x^2-256040*d^2*e^6*m^4*x^3+4545450*d^2*e^6*m
^3*x^4-4345110*d^2*e^6*m^2*x^5+9878400*d^2*e^6*m*x^6-33*d*e^7*m^7-8560*d*e^7*m^6*x-115440*d*e^7*m^5*x^2-236563
2*d*e^7*m^4*x^3+2395565*d*e^7*m^3*x^4-13971348*d*e^7*m^2*x^5+5227740*d*e^7*m*x^6-4032000*d*e^7*x^7+792*e^8*m^7
+25872*e^8*m^6*x+772326*e^8*m^5*x^2+2389985*e^8*m^4*x^3+15608080*e^8*m^3*x^4-6238718*e^8*m^2*x^5+15456528*e^8*
m*x^6-2041200*e^8*x^7-672000*d^5*e^3*m^3*x^3+39960*d^4*e^4*m^4*x^2-567000*d^4*e^4*m^3*x^3+5880000*d^4*e^4*m^2*
x^4-3552*d^3*e^5*m^5*x+59940*d^3*e^5*m^4*x^2-2464200*d^3*e^5*m^3*x^3+3449250*d^3*e^5*m^2*x^4-9206400*d^3*e^5*m
*x^5+214*d^2*e^6*m^6+14040*d^2*e^6*m^5*x+758352*d^2*e^6*m^4*x^2-1420800*d^2*e^6*m^3*x^3+11302020*d^2*e^6*m^2*x
^4-4887540*d^2*e^6*m*x^5+4032000*d^2*e^6*x^6-1386*d*e^7*m^6-142096*d*e^7*m^5*x-945750*d*e^7*m^4*x^2-9939088*d*
e^7*m^3*x^3+5136710*d*e^7*m^2*x^4-14497488*d*e^7*m*x^5+2041200*d*e^7*x^6+14868*e^8*m^6+260106*e^8*m^5*x+445323
3*e^8*m^4*x^2+7946185*e^8*m^3*x^3+29064240*e^8*m^2*x^4-5957592*e^8*m*x^5+5754240*e^8*x^6+113400*d^5*e^3*m^3*x^
2-4032000*d^5*e^3*m^2*x^3-4440*d^4*e^4*m^4*x+799200*d^4*e^4*m^3*x^2-2457000*d^4*e^4*m^2*x^3+8400000*d^4*e^4*m*
x^4-390*d^3*e^5*m^5-110112*d^3*e^5*m^4*x+588300*d^3*e^5*m^3*x^2-8325000*d^3*e^5*m^2*x^3+4479300*d^3*e^5*m*x^4-
4032000*d^3*e^5*x^5+8346*d^2*e^6*m^5+202800*d^2*e^6*m^4*x+4821840*d^2*e^6*m^3*x^2-3899060*d^2*e^6*m^2*x^3+1334
6640*d^2*e^6*m*x^4-2041200*d^2*e^6*x^5-24486*d*e^7*m^5-1260460*d*e^7*m^4*x-4332705*d*e^7*m^3*x^2-22675968*d*e^
7*m^2*x^3+5510040*d*e^7*m*x^4-5754240*d*e^7*x^5+155232*e^8*m^5+1567797*e^8*m^4*x+15458076*e^8*m^3*x^2+15254460
*e^8*m^2*x^3+28238400*e^8*m*x^4-2237760*e^8*x^5+2016000*d^6*e^2*m^2*x^2-79920*d^5*e^3*m^3*x+1360800*d^5*e^3*m^
2*x^2-7392000*d^5*e^3*m*x^3+3552*d^4*e^4*m^4-111000*d^4*e^4*m^3*x+4995000*d^4*e^4*m^2*x^2-3969000*d^4*e^4*m*x^
3+4032000*d^4*e^4*x^4-13650*d^3*e^5*m^4-1296480*d^3*e^5*m^3*x+2497500*d^3*e^5*m^2*x^2-11908080*d^3*e^5*m*x^3+2
041200*d^3*e^5*x^4+133750*d^2*e^6*m^4+1485900*d^2*e^6*m^3*x+15351744*d^2*e^6*m^2*x^2-4950600*d^2*e^6*m*x^3+575
4240*d^2*e^6*x^4-235620*d*e^7*m^4-6385546*d*e^7*m^3*x-10840440*d*e^7*m^2*x^2-25553088*d*e^7*m*x^3+2237760*d*e^
7*x^4+983682*e^8*m^4+5752131*e^8*m^3*x+31059532*e^8*m^2*x^2+15207660*e^8*m*x^3+10741248*e^8*x^4-226800*d^6*e^2
*m^2*x+6048000*d^6*e^2*m*x^2+4440*d^5*e^3*m^3-1438560*d^5*e^3*m^2*x+3288600*d^5*e^3*m*x^2-4032000*d^5*e^3*x^3+
106560*d^4*e^4*m^3-954600*d^4*e^4*m^2*x+9990000*d^4*e^4*m*x^2-2041200*d^4*e^4*x^3-189150*d^3*e^5*m^3-7050720*d
^3*e^5*m^2*x+4204680*d^3*e^5*m*x^2-5754240*d^3*e^5*x^3+1126710*d^2*e^6*m^3+5693610*d^2*e^6*m^2*x+21972672*d^2*
e^6*m*x^2-2237760*d^2*e^6*x^3-1332177*d*e^7*m^3-18145060*d*e^7*m^2*x-13242060*d*e^7*m*x^2-10741248*d*e^7*x^3+3
864168*e^8*m^3+12377178*e^8*m^2*x+32300304*e^8*m*x^2+5896800*e^8*x^3-4032000*d^7*e*m*x+79920*d^6*e^2*m^2-22680
00*d^6*e^2*m*x+4032000*d^6*e^2*x^2+106560*d^5*e^3*m^2-7112880*d^5*e^3*m*x+2041200*d^5*e^3*x^2+1189920*d^4*e^4*
m^2-3085800*d^4*e^4*m*x+5754240*d^4*e^4*x^2-1296750*d^3*e^5*m^2-16602048*d^3*e^5*m*x+2237760*d^3*e^5*x^2+52588
36*d^2*e^6*m^2+10293660*d^2*e^6*m*x+10741248*d^2*e^6*x^2-4419954*d*e^7*m^2-25828944*d*e^7*m*x-5896800*d*e^7*x^
2+9162072*e^8*m^2+13944744*e^8*m*x+12942720*e^8*x^2+226800*d^7*e*m-4032000*d^7*e*x+1358640*d^6*e^2*m-2041200*d
^6*e^2*x+848040*d^5*e^3*m-5754240*d^5*e^3*x+5860800*d^4*e^4*m-2237760*d^4*e^4*x-4396860*d^3*e^5*m-10741248*d^3
*e^5*x+12886224*d^2*e^6*m+5896800*d^2*e^6*x-7957224*d*e^7*m-12942720*d*e^7*x+11946528*e^8*m+5987520*e^8*x+4032
000*d^8+2041200*d^7*e+5754240*d^6*e^2+2237760*d^5*e^3+10741248*d^4*e^4-5896800*d^3*e^5+12942720*d^2*e^6-598752
0*d*e^7+6531840*e^8)/e^9/(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+36
2880)
________________________________________________________________________________________
Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((e*x+d)^m*(5*x^2+2*x+3)^2*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm="maxima")
[Out]
Exception raised: ValueError
________________________________________________________________________________________
Fricas [B] time = 1.58728, size = 7602, normalized size = 17.6 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((e*x+d)^m*(5*x^2+2*x+3)^2*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm="fricas")
[Out]
(18*d*e^8*m^8 + 100*(e^9*m^8 + 36*e^9*m^7 + 546*e^9*m^6 + 4536*e^9*m^5 + 22449*e^9*m^4 + 67284*e^9*m^3 + 11812
4*e^9*m^2 + 109584*e^9*m + 40320*e^9)*x^9 + 4032000*d^9 + 2041200*d^8*e + 5754240*d^7*e^2 + 2237760*d^6*e^3 +
10741248*d^5*e^4 - 5896800*d^4*e^5 + 12942720*d^3*e^6 - 5987520*d^2*e^7 + 6531840*d*e^8 - 5*(408240*e^9 - (20*
d*e^8 - 9*e^9)*m^8 - (560*d*e^8 - 333*e^9)*m^7 - 14*(460*d*e^8 - 369*e^9)*m^6 - 14*(2800*d*e^8 - 3123*e^9)*m^5
- 7*(19340*d*e^8 - 31383*e^9)*m^4 - 7*(37520*d*e^8 - 95211*e^9)*m^3 - 216*(1210*d*e^8 - 5469*e^9)*m^2 - 36*(2
800*d*e^8 - 30663*e^9)*m)*x^8 - 33*(d^2*e^7 - 24*d*e^8)*m^7 + (5754240*e^9 - 3*(15*d*e^8 - 37*e^9)*m^8 - 2*(40
0*d^2*e^7 + 675*d*e^8 - 2109*e^9)*m^7 - 12*(1400*d^2*e^7 + 1365*d*e^8 - 5587*e^9)*m^6 - 14*(10000*d^2*e^7 + 74
25*d*e^8 - 41403*e^9)*m^5 - 21*(28000*d^2*e^7 + 17655*d*e^8 - 141229*e^9)*m^4 - 28*(46400*d^2*e^7 + 26325*d*e^
8 - 326229*e^9)*m^3 - 36*(39200*d^2*e^7 + 20745*d*e^8 - 455211*e^9)*m^2 - 144*(4000*d^2*e^7 + 2025*d*e^8 - 107
337*e^9)*m)*x^7 + 2*(107*d^3*e^6 - 693*d^2*e^7 + 7434*d*e^8)*m^6 - (2237760*e^9 - 37*(3*d*e^8 - e^9)*m^8 - 3*(
105*d^2*e^7 + 1184*d*e^8 - 481*e^9)*m^7 - 4*(1400*d^3*e^6 + 1890*d^2*e^7 + 11433*d*e^8 - 5883*e^9)*m^6 - 6*(14
000*d^3*e^6 + 11550*d^2*e^7 + 50875*d*e^8 - 34743*e^9)*m^5 - (476000*d^3*e^6 + 311850*d^2*e^7 + 1134309*d*e^8
- 1090353*e^9)*m^4 - 3*(420000*d^3*e^6 + 241395*d^2*e^7 + 776186*d*e^8 - 1140969*e^9)*m^3 - 2*(767200*d^3*e^6
+ 407295*d^2*e^7 + 1208124*d*e^8 - 3119359*e^9)*m^2 - 24*(28000*d^3*e^6 + 14175*d^2*e^7 + 39960*d*e^8 - 248233
*e^9)*m)*x^6 - 6*(65*d^4*e^5 - 1391*d^3*e^6 + 4081*d^2*e^7 - 25872*d*e^8)*m^5 + (10741248*e^9 - 37*(d*e^8 - 4*
e^9)*m^8 - 74*(9*d^2*e^7 + 17*d*e^8 - 80*e^9)*m^7 - 2*(945*d^3*e^6 + 8991*d^2*e^7 + 8621*d*e^8 - 49580*e^9)*m^
6 - 2*(16800*d^4*e^5 + 17955*d^3*e^6 + 92241*d^2*e^7 + 61124*d*e^8 - 451400*e^9)*m^5 - (336000*d^4*e^5 + 23625
0*d^3*e^6 + 909090*d^2*e^7 + 479113*d*e^8 - 4850404*e^9)*m^4 - 2*(588000*d^4*e^5 + 344925*d^3*e^6 + 1130202*d^
2*e^7 + 513671*d*e^8 - 7804040*e^9)*m^3 - 12*(140000*d^4*e^5 + 74655*d^3*e^6 + 222444*d^2*e^7 + 91834*d*e^8 -
2422020*e^9)*m^2 - 144*(5600*d^4*e^5 + 2835*d^3*e^6 + 7992*d^2*e^7 + 3108*d*e^8 - 196100*e^9)*m)*x^5 + 2*(1776
*d^5*e^4 - 6825*d^4*e^5 + 66875*d^3*e^6 - 117810*d^2*e^7 + 491841*d*e^8)*m^4 + (5896800*e^9 + (148*d*e^8 + 65*
e^9)*m^8 + (185*d^2*e^7 + 5328*d*e^8 + 2665*e^9)*m^7 + 2*(1665*d^3*e^6 + 2775*d^2*e^7 + 38924*d*e^8 + 22945*e^
9)*m^6 + 2*(4725*d^4*e^5 + 38295*d^3*e^6 + 32005*d^2*e^7 + 295704*d*e^8 + 215345*e^9)*m^5 + (168000*d^5*e^4 +
141750*d^4*e^5 + 616050*d^3*e^6 + 355200*d^2*e^7 + 2484772*d*e^8 + 2389985*e^9)*m^4 + (1008000*d^5*e^4 + 61425
0*d^4*e^5 + 2081250*d^3*e^6 + 974765*d^2*e^7 + 5668992*d*e^8 + 7946185*e^9)*m^3 + 6*(308000*d^5*e^4 + 165375*d
^4*e^5 + 496170*d^3*e^6 + 206275*d^2*e^7 + 1064712*d*e^8 + 2542410*e^9)*m^2 + 36*(28000*d^5*e^4 + 14175*d^4*e^
5 + 39960*d^3*e^6 + 15540*d^2*e^7 + 74592*d*e^8 + 422435*e^9)*m)*x^4 + 3*(1480*d^6*e^3 + 35520*d^5*e^4 - 63050
*d^4*e^5 + 375570*d^3*e^6 - 444059*d^2*e^7 + 1288056*d*e^8)*m^3 + (12942720*e^9 + (65*d*e^8 + 107*e^9)*m^8 - 2
*(296*d^2*e^7 - 1235*d*e^8 - 2247*e^9)*m^7 - 4*(185*d^3*e^6 + 4884*d^2*e^7 - 9620*d*e^8 - 19902*e^9)*m^6 - 2*(
6660*d^4*e^5 + 9990*d^3*e^6 + 126392*d^2*e^7 - 157625*d*e^8 - 386163*e^9)*m^5 - (37800*d^5*e^4 + 266400*d^4*e^
5 + 196100*d^3*e^6 + 1607280*d^2*e^7 - 1444235*d*e^8 - 4453233*e^9)*m^4 - 4*(168000*d^6*e^3 + 113400*d^5*e^4 +
416250*d^4*e^5 + 208125*d^3*e^6 + 1279312*d^2*e^7 - 903370*d*e^8 - 3864519*e^9)*m^3 - 4*(504000*d^6*e^3 + 274
050*d^5*e^4 + 832500*d^4*e^5 + 350390*d^3*e^6 + 1831056*d^2*e^7 - 1103505*d*e^8 - 7764883*e^9)*m^2 - 48*(28000
*d^6*e^3 + 14175*d^5*e^4 + 39960*d^4*e^5 + 15540*d^3*e^6 + 74592*d^2*e^7 - 40950*d*e^8 - 672923*e^9)*m)*x^3 +
2*(39960*d^7*e^2 + 53280*d^6*e^3 + 594960*d^5*e^4 - 648375*d^4*e^5 + 2629418*d^3*e^6 - 2209977*d^2*e^7 + 45810
36*d*e^8)*m^2 + (5987520*e^9 + (107*d*e^8 + 33*e^9)*m^8 - (195*d^2*e^7 - 4280*d*e^8 - 1419*e^9)*m^7 + 4*(444*d
^3*e^6 - 1755*d^2*e^7 + 17762*d*e^8 + 6468*e^9)*m^6 + 2*(1110*d^4*e^5 + 27528*d^3*e^6 - 50700*d^2*e^7 + 315115
*d*e^8 + 130053*e^9)*m^5 + (39960*d^5*e^4 + 55500*d^4*e^5 + 648240*d^3*e^6 - 742950*d^2*e^7 + 3192773*d*e^8 +
1567797*e^9)*m^4 + (113400*d^6*e^3 + 719280*d^5*e^4 + 477300*d^4*e^5 + 3525360*d^3*e^6 - 2846805*d^2*e^7 + 907
2530*d*e^8 + 5752131*e^9)*m^3 + 6*(336000*d^7*e^2 + 189000*d^6*e^3 + 592740*d^5*e^4 + 257150*d^4*e^5 + 1383504
*d^3*e^6 - 857805*d^2*e^7 + 2152412*d*e^8 + 2062863*e^9)*m^2 + 72*(28000*d^7*e^2 + 14175*d^6*e^3 + 39960*d^5*e
^4 + 15540*d^4*e^5 + 74592*d^3*e^6 - 40950*d^2*e^7 + 89880*d*e^8 + 193677*e^9)*m)*x^2 + 12*(18900*d^8*e + 1132
20*d^7*e^2 + 70670*d^6*e^3 + 488400*d^5*e^4 - 366405*d^4*e^5 + 1073852*d^3*e^6 - 663102*d^2*e^7 + 995544*d*e^8
)*m + (6531840*e^9 + 3*(11*d*e^8 + 6*e^9)*m^8 - 2*(107*d^2*e^7 - 693*d*e^8 - 396*e^9)*m^7 + 6*(65*d^3*e^6 - 13
91*d^2*e^7 + 4081*d*e^8 + 2478*e^9)*m^6 - 2*(1776*d^4*e^5 - 6825*d^3*e^6 + 66875*d^2*e^7 - 117810*d*e^8 - 7761
6*e^9)*m^5 - 3*(1480*d^5*e^4 + 35520*d^4*e^5 - 63050*d^3*e^6 + 375570*d^2*e^7 - 444059*d*e^8 - 327894*e^9)*m^4
- 2*(39960*d^6*e^3 + 53280*d^5*e^4 + 594960*d^4*e^5 - 648375*d^3*e^6 + 2629418*d^2*e^7 - 2209977*d*e^8 - 1932
084*e^9)*m^3 - 12*(18900*d^7*e^2 + 113220*d^6*e^3 + 70670*d^5*e^4 + 488400*d^4*e^5 - 366405*d^3*e^6 + 1073852*
d^2*e^7 - 663102*d*e^8 - 763506*e^9)*m^2 - 144*(28000*d^8*e + 14175*d^7*e^2 + 39960*d^6*e^3 + 15540*d^5*e^4 +
74592*d^4*e^5 - 40950*d^3*e^6 + 89880*d^2*e^7 - 41580*d*e^8 - 82962*e^9)*m)*x)*(e*x + d)^m/(e^9*m^9 + 45*e^9*m
^8 + 870*e^9*m^7 + 9450*e^9*m^6 + 63273*e^9*m^5 + 269325*e^9*m^4 + 723680*e^9*m^3 + 1172700*e^9*m^2 + 1026576*
e^9*m + 362880*e^9)
________________________________________________________________________________________
Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((e*x+d)**m*(5*x**2+2*x+3)**2*(4*x**4-5*x**3+3*x**2+x+2),x)
[Out]
Timed out
________________________________________________________________________________________
Giac [B] time = 1.31855, size = 8401, normalized size = 19.45 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((e*x+d)^m*(5*x^2+2*x+3)^2*(4*x^4-5*x^3+3*x^2+x+2),x, algorithm="giac")
[Out]
(100*(x*e + d)^m*m^8*x^9*e^9 + 100*(x*e + d)^m*d*m^8*x^8*e^8 - 45*(x*e + d)^m*m^8*x^8*e^9 + 3600*(x*e + d)^m*m
^7*x^9*e^9 - 45*(x*e + d)^m*d*m^8*x^7*e^8 + 2800*(x*e + d)^m*d*m^7*x^8*e^8 - 800*(x*e + d)^m*d^2*m^7*x^7*e^7 +
111*(x*e + d)^m*m^8*x^7*e^9 - 1665*(x*e + d)^m*m^7*x^8*e^9 + 54600*(x*e + d)^m*m^6*x^9*e^9 + 111*(x*e + d)^m*
d*m^8*x^6*e^8 - 1350*(x*e + d)^m*d*m^7*x^7*e^8 + 32200*(x*e + d)^m*d*m^6*x^8*e^8 + 315*(x*e + d)^m*d^2*m^7*x^6
*e^7 - 16800*(x*e + d)^m*d^2*m^6*x^7*e^7 + 5600*(x*e + d)^m*d^3*m^6*x^6*e^6 - 37*(x*e + d)^m*m^8*x^6*e^9 + 421
8*(x*e + d)^m*m^7*x^7*e^9 - 25830*(x*e + d)^m*m^6*x^8*e^9 + 453600*(x*e + d)^m*m^5*x^9*e^9 - 37*(x*e + d)^m*d*
m^8*x^5*e^8 + 3552*(x*e + d)^m*d*m^7*x^6*e^8 - 16380*(x*e + d)^m*d*m^6*x^7*e^8 + 196000*(x*e + d)^m*d*m^5*x^8*
e^8 - 666*(x*e + d)^m*d^2*m^7*x^5*e^7 + 7560*(x*e + d)^m*d^2*m^6*x^6*e^7 - 140000*(x*e + d)^m*d^2*m^5*x^7*e^7
- 1890*(x*e + d)^m*d^3*m^6*x^5*e^6 + 84000*(x*e + d)^m*d^3*m^5*x^6*e^6 - 33600*(x*e + d)^m*d^4*m^5*x^5*e^5 + 1
48*(x*e + d)^m*m^8*x^5*e^9 - 1443*(x*e + d)^m*m^7*x^6*e^9 + 67044*(x*e + d)^m*m^6*x^7*e^9 - 218610*(x*e + d)^m
*m^5*x^8*e^9 + 2244900*(x*e + d)^m*m^4*x^9*e^9 + 148*(x*e + d)^m*d*m^8*x^4*e^8 - 1258*(x*e + d)^m*d*m^7*x^5*e^
8 + 45732*(x*e + d)^m*d*m^6*x^6*e^8 - 103950*(x*e + d)^m*d*m^5*x^7*e^8 + 676900*(x*e + d)^m*d*m^4*x^8*e^8 + 18
5*(x*e + d)^m*d^2*m^7*x^4*e^7 - 17982*(x*e + d)^m*d^2*m^6*x^5*e^7 + 69300*(x*e + d)^m*d^2*m^5*x^6*e^7 - 588000
*(x*e + d)^m*d^2*m^4*x^7*e^7 + 3330*(x*e + d)^m*d^3*m^6*x^4*e^6 - 35910*(x*e + d)^m*d^3*m^5*x^5*e^6 + 476000*(
x*e + d)^m*d^3*m^4*x^6*e^6 + 9450*(x*e + d)^m*d^4*m^5*x^4*e^5 - 336000*(x*e + d)^m*d^4*m^4*x^5*e^5 + 168000*(x
*e + d)^m*d^5*m^4*x^4*e^4 + 65*(x*e + d)^m*m^8*x^4*e^9 + 5920*(x*e + d)^m*m^7*x^5*e^9 - 23532*(x*e + d)^m*m^6*
x^6*e^9 + 579642*(x*e + d)^m*m^5*x^7*e^9 - 1098405*(x*e + d)^m*m^4*x^8*e^9 + 6728400*(x*e + d)^m*m^3*x^9*e^9 +
65*(x*e + d)^m*d*m^8*x^3*e^8 + 5328*(x*e + d)^m*d*m^7*x^4*e^8 - 17242*(x*e + d)^m*d*m^6*x^5*e^8 + 305250*(x*e
+ d)^m*d*m^5*x^6*e^8 - 370755*(x*e + d)^m*d*m^4*x^7*e^8 + 1313200*(x*e + d)^m*d*m^3*x^8*e^8 - 592*(x*e + d)^m
*d^2*m^7*x^3*e^7 + 5550*(x*e + d)^m*d^2*m^6*x^4*e^7 - 184482*(x*e + d)^m*d^2*m^5*x^5*e^7 + 311850*(x*e + d)^m*
d^2*m^4*x^6*e^7 - 1299200*(x*e + d)^m*d^2*m^3*x^7*e^7 - 740*(x*e + d)^m*d^3*m^6*x^3*e^6 + 76590*(x*e + d)^m*d^
3*m^5*x^4*e^6 - 236250*(x*e + d)^m*d^3*m^4*x^5*e^6 + 1260000*(x*e + d)^m*d^3*m^3*x^6*e^6 - 13320*(x*e + d)^m*d
^4*m^5*x^3*e^5 + 141750*(x*e + d)^m*d^4*m^4*x^4*e^5 - 1176000*(x*e + d)^m*d^4*m^3*x^5*e^5 - 37800*(x*e + d)^m*
d^5*m^4*x^3*e^4 + 1008000*(x*e + d)^m*d^5*m^3*x^4*e^4 - 672000*(x*e + d)^m*d^6*m^3*x^3*e^3 + 107*(x*e + d)^m*m
^8*x^3*e^9 + 2665*(x*e + d)^m*m^7*x^4*e^9 + 99160*(x*e + d)^m*m^6*x^5*e^9 - 208458*(x*e + d)^m*m^5*x^6*e^9 + 2
965809*(x*e + d)^m*m^4*x^7*e^9 - 3332385*(x*e + d)^m*m^3*x^8*e^9 + 11812400*(x*e + d)^m*m^2*x^9*e^9 + 107*(x*e
+ d)^m*d*m^8*x^2*e^8 + 2470*(x*e + d)^m*d*m^7*x^3*e^8 + 77848*(x*e + d)^m*d*m^6*x^4*e^8 - 122248*(x*e + d)^m*
d*m^5*x^5*e^8 + 1134309*(x*e + d)^m*d*m^4*x^6*e^8 - 737100*(x*e + d)^m*d*m^3*x^7*e^8 + 1306800*(x*e + d)^m*d*m
^2*x^8*e^8 - 195*(x*e + d)^m*d^2*m^7*x^2*e^7 - 19536*(x*e + d)^m*d^2*m^6*x^3*e^7 + 64010*(x*e + d)^m*d^2*m^5*x
^4*e^7 - 909090*(x*e + d)^m*d^2*m^4*x^5*e^7 + 724185*(x*e + d)^m*d^2*m^3*x^6*e^7 - 1411200*(x*e + d)^m*d^2*m^2
*x^7*e^7 + 1776*(x*e + d)^m*d^3*m^6*x^2*e^6 - 19980*(x*e + d)^m*d^3*m^5*x^3*e^6 + 616050*(x*e + d)^m*d^3*m^4*x
^4*e^6 - 689850*(x*e + d)^m*d^3*m^3*x^5*e^6 + 1534400*(x*e + d)^m*d^3*m^2*x^6*e^6 + 2220*(x*e + d)^m*d^4*m^5*x
^2*e^5 - 266400*(x*e + d)^m*d^4*m^4*x^3*e^5 + 614250*(x*e + d)^m*d^4*m^3*x^4*e^5 - 1680000*(x*e + d)^m*d^4*m^2
*x^5*e^5 + 39960*(x*e + d)^m*d^5*m^4*x^2*e^4 - 453600*(x*e + d)^m*d^5*m^3*x^3*e^4 + 1848000*(x*e + d)^m*d^5*m^
2*x^4*e^4 + 113400*(x*e + d)^m*d^6*m^3*x^2*e^3 - 2016000*(x*e + d)^m*d^6*m^2*x^3*e^3 + 2016000*(x*e + d)^m*d^7
*m^2*x^2*e^2 + 33*(x*e + d)^m*m^8*x^2*e^9 + 4494*(x*e + d)^m*m^7*x^3*e^9 + 45890*(x*e + d)^m*m^6*x^4*e^9 + 902
800*(x*e + d)^m*m^5*x^5*e^9 - 1090353*(x*e + d)^m*m^4*x^6*e^9 + 9134412*(x*e + d)^m*m^3*x^7*e^9 - 5906520*(x*e
+ d)^m*m^2*x^8*e^9 + 10958400*(x*e + d)^m*m*x^9*e^9 + 33*(x*e + d)^m*d*m^8*x*e^8 + 4280*(x*e + d)^m*d*m^7*x^2
*e^8 + 38480*(x*e + d)^m*d*m^6*x^3*e^8 + 591408*(x*e + d)^m*d*m^5*x^4*e^8 - 479113*(x*e + d)^m*d*m^4*x^5*e^8 +
2328558*(x*e + d)^m*d*m^3*x^6*e^8 - 746820*(x*e + d)^m*d*m^2*x^7*e^8 + 504000*(x*e + d)^m*d*m*x^8*e^8 - 214*(
x*e + d)^m*d^2*m^7*x*e^7 - 7020*(x*e + d)^m*d^2*m^6*x^2*e^7 - 252784*(x*e + d)^m*d^2*m^5*x^3*e^7 + 355200*(x*e
+ d)^m*d^2*m^4*x^4*e^7 - 2260404*(x*e + d)^m*d^2*m^3*x^5*e^7 + 814590*(x*e + d)^m*d^2*m^2*x^6*e^7 - 576000*(x
*e + d)^m*d^2*m*x^7*e^7 + 390*(x*e + d)^m*d^3*m^6*x*e^6 + 55056*(x*e + d)^m*d^3*m^5*x^2*e^6 - 196100*(x*e + d)
^m*d^3*m^4*x^3*e^6 + 2081250*(x*e + d)^m*d^3*m^3*x^4*e^6 - 895860*(x*e + d)^m*d^3*m^2*x^5*e^6 + 672000*(x*e +
d)^m*d^3*m*x^6*e^6 - 3552*(x*e + d)^m*d^4*m^5*x*e^5 + 55500*(x*e + d)^m*d^4*m^4*x^2*e^5 - 1665000*(x*e + d)^m*
d^4*m^3*x^3*e^5 + 992250*(x*e + d)^m*d^4*m^2*x^4*e^5 - 806400*(x*e + d)^m*d^4*m*x^5*e^5 - 4440*(x*e + d)^m*d^5
*m^4*x*e^4 + 719280*(x*e + d)^m*d^5*m^3*x^2*e^4 - 1096200*(x*e + d)^m*d^5*m^2*x^3*e^4 + 1008000*(x*e + d)^m*d^
5*m*x^4*e^4 - 79920*(x*e + d)^m*d^6*m^3*x*e^3 + 1134000*(x*e + d)^m*d^6*m^2*x^2*e^3 - 1344000*(x*e + d)^m*d^6*
m*x^3*e^3 - 226800*(x*e + d)^m*d^7*m^2*x*e^2 + 2016000*(x*e + d)^m*d^7*m*x^2*e^2 - 4032000*(x*e + d)^m*d^8*m*x
*e + 18*(x*e + d)^m*m^8*x*e^9 + 1419*(x*e + d)^m*m^7*x^2*e^9 + 79608*(x*e + d)^m*m^6*x^3*e^9 + 430690*(x*e + d
)^m*m^5*x^4*e^9 + 4850404*(x*e + d)^m*m^4*x^5*e^9 - 3422907*(x*e + d)^m*m^3*x^6*e^9 + 16387596*(x*e + d)^m*m^2
*x^7*e^9 - 5519340*(x*e + d)^m*m*x^8*e^9 + 4032000*(x*e + d)^m*x^9*e^9 + 18*(x*e + d)^m*d*m^8*e^8 + 1386*(x*e
+ d)^m*d*m^7*x*e^8 + 71048*(x*e + d)^m*d*m^6*x^2*e^8 + 315250*(x*e + d)^m*d*m^5*x^3*e^8 + 2484772*(x*e + d)^m*
d*m^4*x^4*e^8 - 1027342*(x*e + d)^m*d*m^3*x^5*e^8 + 2416248*(x*e + d)^m*d*m^2*x^6*e^8 - 291600*(x*e + d)^m*d*m
*x^7*e^8 - 33*(x*e + d)^m*d^2*m^7*e^7 - 8346*(x*e + d)^m*d^2*m^6*x*e^7 - 101400*(x*e + d)^m*d^2*m^5*x^2*e^7 -
1607280*(x*e + d)^m*d^2*m^4*x^3*e^7 + 974765*(x*e + d)^m*d^2*m^3*x^4*e^7 - 2669328*(x*e + d)^m*d^2*m^2*x^5*e^7
+ 340200*(x*e + d)^m*d^2*m*x^6*e^7 + 214*(x*e + d)^m*d^3*m^6*e^6 + 13650*(x*e + d)^m*d^3*m^5*x*e^6 + 648240*(
x*e + d)^m*d^3*m^4*x^2*e^6 - 832500*(x*e + d)^m*d^3*m^3*x^3*e^6 + 2977020*(x*e + d)^m*d^3*m^2*x^4*e^6 - 408240
*(x*e + d)^m*d^3*m*x^5*e^6 - 390*(x*e + d)^m*d^4*m^5*e^5 - 106560*(x*e + d)^m*d^4*m^4*x*e^5 + 477300*(x*e + d)
^m*d^4*m^3*x^2*e^5 - 3330000*(x*e + d)^m*d^4*m^2*x^3*e^5 + 510300*(x*e + d)^m*d^4*m*x^4*e^5 + 3552*(x*e + d)^m
*d^5*m^4*e^4 - 106560*(x*e + d)^m*d^5*m^3*x*e^4 + 3556440*(x*e + d)^m*d^5*m^2*x^2*e^4 - 680400*(x*e + d)^m*d^5
*m*x^3*e^4 + 4440*(x*e + d)^m*d^6*m^3*e^3 - 1358640*(x*e + d)^m*d^6*m^2*x*e^3 + 1020600*(x*e + d)^m*d^6*m*x^2*
e^3 + 79920*(x*e + d)^m*d^7*m^2*e^2 - 2041200*(x*e + d)^m*d^7*m*x*e^2 + 226800*(x*e + d)^m*d^8*m*e + 4032000*(
x*e + d)^m*d^9 + 792*(x*e + d)^m*m^7*x*e^9 + 25872*(x*e + d)^m*m^6*x^2*e^9 + 772326*(x*e + d)^m*m^5*x^3*e^9 +
2389985*(x*e + d)^m*m^4*x^4*e^9 + 15608080*(x*e + d)^m*m^3*x^5*e^9 - 6238718*(x*e + d)^m*m^2*x^6*e^9 + 1545652
8*(x*e + d)^m*m*x^7*e^9 - 2041200*(x*e + d)^m*x^8*e^9 + 792*(x*e + d)^m*d*m^7*e^8 + 24486*(x*e + d)^m*d*m^6*x*
e^8 + 630230*(x*e + d)^m*d*m^5*x^2*e^8 + 1444235*(x*e + d)^m*d*m^4*x^3*e^8 + 5668992*(x*e + d)^m*d*m^3*x^4*e^8
- 1102008*(x*e + d)^m*d*m^2*x^5*e^8 + 959040*(x*e + d)^m*d*m*x^6*e^8 - 1386*(x*e + d)^m*d^2*m^6*e^7 - 133750*
(x*e + d)^m*d^2*m^5*x*e^7 - 742950*(x*e + d)^m*d^2*m^4*x^2*e^7 - 5117248*(x*e + d)^m*d^2*m^3*x^3*e^7 + 1237650
*(x*e + d)^m*d^2*m^2*x^4*e^7 - 1150848*(x*e + d)^m*d^2*m*x^5*e^7 + 8346*(x*e + d)^m*d^3*m^5*e^6 + 189150*(x*e
+ d)^m*d^3*m^4*x*e^6 + 3525360*(x*e + d)^m*d^3*m^3*x^2*e^6 - 1401560*(x*e + d)^m*d^3*m^2*x^3*e^6 + 1438560*(x*
e + d)^m*d^3*m*x^4*e^6 - 13650*(x*e + d)^m*d^4*m^4*e^5 - 1189920*(x*e + d)^m*d^4*m^3*x*e^5 + 1542900*(x*e + d)
^m*d^4*m^2*x^2*e^5 - 1918080*(x*e + d)^m*d^4*m*x^3*e^5 + 106560*(x*e + d)^m*d^5*m^3*e^4 - 848040*(x*e + d)^m*d
^5*m^2*x*e^4 + 2877120*(x*e + d)^m*d^5*m*x^2*e^4 + 106560*(x*e + d)^m*d^6*m^2*e^3 - 5754240*(x*e + d)^m*d^6*m*
x*e^3 + 1358640*(x*e + d)^m*d^7*m*e^2 + 2041200*(x*e + d)^m*d^8*e + 14868*(x*e + d)^m*m^6*x*e^9 + 260106*(x*e
+ d)^m*m^5*x^2*e^9 + 4453233*(x*e + d)^m*m^4*x^3*e^9 + 7946185*(x*e + d)^m*m^3*x^4*e^9 + 29064240*(x*e + d)^m*
m^2*x^5*e^9 - 5957592*(x*e + d)^m*m*x^6*e^9 + 5754240*(x*e + d)^m*x^7*e^9 + 14868*(x*e + d)^m*d*m^6*e^8 + 2356
20*(x*e + d)^m*d*m^5*x*e^8 + 3192773*(x*e + d)^m*d*m^4*x^2*e^8 + 3613480*(x*e + d)^m*d*m^3*x^3*e^8 + 6388272*(
x*e + d)^m*d*m^2*x^4*e^8 - 447552*(x*e + d)^m*d*m*x^5*e^8 - 24486*(x*e + d)^m*d^2*m^5*e^7 - 1126710*(x*e + d)^
m*d^2*m^4*x*e^7 - 2846805*(x*e + d)^m*d^2*m^3*x^2*e^7 - 7324224*(x*e + d)^m*d^2*m^2*x^3*e^7 + 559440*(x*e + d)
^m*d^2*m*x^4*e^7 + 133750*(x*e + d)^m*d^3*m^4*e^6 + 1296750*(x*e + d)^m*d^3*m^3*x*e^6 + 8301024*(x*e + d)^m*d^
3*m^2*x^2*e^6 - 745920*(x*e + d)^m*d^3*m*x^3*e^6 - 189150*(x*e + d)^m*d^4*m^3*e^5 - 5860800*(x*e + d)^m*d^4*m^
2*x*e^5 + 1118880*(x*e + d)^m*d^4*m*x^2*e^5 + 1189920*(x*e + d)^m*d^5*m^2*e^4 - 2237760*(x*e + d)^m*d^5*m*x*e^
4 + 848040*(x*e + d)^m*d^6*m*e^3 + 5754240*(x*e + d)^m*d^7*e^2 + 155232*(x*e + d)^m*m^5*x*e^9 + 1567797*(x*e +
d)^m*m^4*x^2*e^9 + 15458076*(x*e + d)^m*m^3*x^3*e^9 + 15254460*(x*e + d)^m*m^2*x^4*e^9 + 28238400*(x*e + d)^m
*m*x^5*e^9 - 2237760*(x*e + d)^m*x^6*e^9 + 155232*(x*e + d)^m*d*m^5*e^8 + 1332177*(x*e + d)^m*d*m^4*x*e^8 + 90
72530*(x*e + d)^m*d*m^3*x^2*e^8 + 4414020*(x*e + d)^m*d*m^2*x^3*e^8 + 2685312*(x*e + d)^m*d*m*x^4*e^8 - 235620
*(x*e + d)^m*d^2*m^4*e^7 - 5258836*(x*e + d)^m*d^2*m^3*x*e^7 - 5146830*(x*e + d)^m*d^2*m^2*x^2*e^7 - 3580416*(
x*e + d)^m*d^2*m*x^3*e^7 + 1126710*(x*e + d)^m*d^3*m^3*e^6 + 4396860*(x*e + d)^m*d^3*m^2*x*e^6 + 5370624*(x*e
+ d)^m*d^3*m*x^2*e^6 - 1296750*(x*e + d)^m*d^4*m^2*e^5 - 10741248*(x*e + d)^m*d^4*m*x*e^5 + 5860800*(x*e + d)^
m*d^5*m*e^4 + 2237760*(x*e + d)^m*d^6*e^3 + 983682*(x*e + d)^m*m^4*x*e^9 + 5752131*(x*e + d)^m*m^3*x^2*e^9 + 3
1059532*(x*e + d)^m*m^2*x^3*e^9 + 15207660*(x*e + d)^m*m*x^4*e^9 + 10741248*(x*e + d)^m*x^5*e^9 + 983682*(x*e
+ d)^m*d*m^4*e^8 + 4419954*(x*e + d)^m*d*m^3*x*e^8 + 12914472*(x*e + d)^m*d*m^2*x^2*e^8 + 1965600*(x*e + d)^m*
d*m*x^3*e^8 - 1332177*(x*e + d)^m*d^2*m^3*e^7 - 12886224*(x*e + d)^m*d^2*m^2*x*e^7 - 2948400*(x*e + d)^m*d^2*m
*x^2*e^7 + 5258836*(x*e + d)^m*d^3*m^2*e^6 + 5896800*(x*e + d)^m*d^3*m*x*e^6 - 4396860*(x*e + d)^m*d^4*m*e^5 +
10741248*(x*e + d)^m*d^5*e^4 + 3864168*(x*e + d)^m*m^3*x*e^9 + 12377178*(x*e + d)^m*m^2*x^2*e^9 + 32300304*(x
*e + d)^m*m*x^3*e^9 + 5896800*(x*e + d)^m*x^4*e^9 + 3864168*(x*e + d)^m*d*m^3*e^8 + 7957224*(x*e + d)^m*d*m^2*
x*e^8 + 6471360*(x*e + d)^m*d*m*x^2*e^8 - 4419954*(x*e + d)^m*d^2*m^2*e^7 - 12942720*(x*e + d)^m*d^2*m*x*e^7 +
12886224*(x*e + d)^m*d^3*m*e^6 - 5896800*(x*e + d)^m*d^4*e^5 + 9162072*(x*e + d)^m*m^2*x*e^9 + 13944744*(x*e
+ d)^m*m*x^2*e^9 + 12942720*(x*e + d)^m*x^3*e^9 + 9162072*(x*e + d)^m*d*m^2*e^8 + 5987520*(x*e + d)^m*d*m*x*e^
8 - 7957224*(x*e + d)^m*d^2*m*e^7 + 12942720*(x*e + d)^m*d^3*e^6 + 11946528*(x*e + d)^m*m*x*e^9 + 5987520*(x*e
+ d)^m*x^2*e^9 + 11946528*(x*e + d)^m*d*m*e^8 - 5987520*(x*e + d)^m*d^2*e^7 + 6531840*(x*e + d)^m*x*e^9 + 653
1840*(x*e + d)^m*d*e^8)/(m^9*e^9 + 45*m^8*e^9 + 870*m^7*e^9 + 9450*m^6*e^9 + 63273*m^5*e^9 + 269325*m^4*e^9 +
723680*m^3*e^9 + 1172700*m^2*e^9 + 1026576*m*e^9 + 362880*e^9)