3.16.80 \(\int (A+B x) (d+e x)^{7/2} (a^2+2 a b x+b^2 x^2)^3 \, dx\)
Optimal. Leaf size=308 \[ -\frac {2 b^5 (d+e x)^{21/2} (-6 a B e-A b e+7 b B d)}{21 e^8}+\frac {6 b^4 (d+e x)^{19/2} (b d-a e) (-5 a B e-2 A b e+7 b B d)}{19 e^8}-\frac {10 b^3 (d+e x)^{17/2} (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{17 e^8}+\frac {2 b^2 (d+e x)^{15/2} (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{3 e^8}-\frac {6 b (d+e x)^{13/2} (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{13 e^8}+\frac {2 (d+e x)^{11/2} (b d-a e)^5 (-a B e-6 A b e+7 b B d)}{11 e^8}-\frac {2 (d+e x)^{9/2} (b d-a e)^6 (B d-A e)}{9 e^8}+\frac {2 b^6 B (d+e x)^{23/2}}{23 e^8} \]
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Rubi [A] time = 0.21, antiderivative size = 308, normalized size of antiderivative = 1.00,
number of steps used = 3, number of rules used = 2, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.061, Rules used =
{27, 77} \begin {gather*} -\frac {2 b^5 (d+e x)^{21/2} (-6 a B e-A b e+7 b B d)}{21 e^8}+\frac {6 b^4 (d+e x)^{19/2} (b d-a e) (-5 a B e-2 A b e+7 b B d)}{19 e^8}-\frac {10 b^3 (d+e x)^{17/2} (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{17 e^8}+\frac {2 b^2 (d+e x)^{15/2} (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{3 e^8}-\frac {6 b (d+e x)^{13/2} (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{13 e^8}+\frac {2 (d+e x)^{11/2} (b d-a e)^5 (-a B e-6 A b e+7 b B d)}{11 e^8}-\frac {2 (d+e x)^{9/2} (b d-a e)^6 (B d-A e)}{9 e^8}+\frac {2 b^6 B (d+e x)^{23/2}}{23 e^8} \end {gather*}
Antiderivative was successfully verified.
[In]
Int[(A + B*x)*(d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]
[Out]
(-2*(b*d - a*e)^6*(B*d - A*e)*(d + e*x)^(9/2))/(9*e^8) + (2*(b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e)*(d + e*x
)^(11/2))/(11*e^8) - (6*b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e)*(d + e*x)^(13/2))/(13*e^8) + (2*b^2*(b*d
- a*e)^3*(7*b*B*d - 4*A*b*e - 3*a*B*e)*(d + e*x)^(15/2))/(3*e^8) - (10*b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e -
4*a*B*e)*(d + e*x)^(17/2))/(17*e^8) + (6*b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e)*(d + e*x)^(19/2))/(19*
e^8) - (2*b^5*(7*b*B*d - A*b*e - 6*a*B*e)*(d + e*x)^(21/2))/(21*e^8) + (2*b^6*B*(d + e*x)^(23/2))/(23*e^8)
Rule 27
Int[(u_.)*((a_) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> Int[u*Cancel[(b/2 + c*x)^(2*p)/c^p], x] /; Fr
eeQ[{a, b, c}, x] && EqQ[b^2 - 4*a*c, 0] && IntegerQ[p]
Rule 77
Int[((a_.) + (b_.)*(x_))*((c_) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandIntegran
d[(a + b*x)*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, n}, x] && NeQ[b*c - a*d, 0] && ((ILtQ[
n, 0] && ILtQ[p, 0]) || EqQ[p, 1] || (IGtQ[p, 0] && ( !IntegerQ[n] || LeQ[9*p + 5*(n + 2), 0] || GeQ[n + p + 1
, 0] || (GeQ[n + p + 2, 0] && RationalQ[a, b, c, d, e, f]))))
Rubi steps
\begin {align*} \int (A+B x) (d+e x)^{7/2} \left (a^2+2 a b x+b^2 x^2\right )^3 \, dx &=\int (a+b x)^6 (A+B x) (d+e x)^{7/2} \, dx\\ &=\int \left (\frac {(-b d+a e)^6 (-B d+A e) (d+e x)^{7/2}}{e^7}+\frac {(-b d+a e)^5 (-7 b B d+6 A b e+a B e) (d+e x)^{9/2}}{e^7}+\frac {3 b (b d-a e)^4 (-7 b B d+5 A b e+2 a B e) (d+e x)^{11/2}}{e^7}-\frac {5 b^2 (b d-a e)^3 (-7 b B d+4 A b e+3 a B e) (d+e x)^{13/2}}{e^7}+\frac {5 b^3 (b d-a e)^2 (-7 b B d+3 A b e+4 a B e) (d+e x)^{15/2}}{e^7}-\frac {3 b^4 (b d-a e) (-7 b B d+2 A b e+5 a B e) (d+e x)^{17/2}}{e^7}+\frac {b^5 (-7 b B d+A b e+6 a B e) (d+e x)^{19/2}}{e^7}+\frac {b^6 B (d+e x)^{21/2}}{e^7}\right ) \, dx\\ &=-\frac {2 (b d-a e)^6 (B d-A e) (d+e x)^{9/2}}{9 e^8}+\frac {2 (b d-a e)^5 (7 b B d-6 A b e-a B e) (d+e x)^{11/2}}{11 e^8}-\frac {6 b (b d-a e)^4 (7 b B d-5 A b e-2 a B e) (d+e x)^{13/2}}{13 e^8}+\frac {2 b^2 (b d-a e)^3 (7 b B d-4 A b e-3 a B e) (d+e x)^{15/2}}{3 e^8}-\frac {10 b^3 (b d-a e)^2 (7 b B d-3 A b e-4 a B e) (d+e x)^{17/2}}{17 e^8}+\frac {6 b^4 (b d-a e) (7 b B d-2 A b e-5 a B e) (d+e x)^{19/2}}{19 e^8}-\frac {2 b^5 (7 b B d-A b e-6 a B e) (d+e x)^{21/2}}{21 e^8}+\frac {2 b^6 B (d+e x)^{23/2}}{23 e^8}\\ \end {align*}
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Mathematica [A] time = 0.35, size = 259, normalized size = 0.84 \begin {gather*} \frac {2 (d+e x)^{9/2} \left (-3187041 b^5 (d+e x)^6 (-6 a B e-A b e+7 b B d)+10567557 b^4 (d+e x)^5 (b d-a e) (-5 a B e-2 A b e+7 b B d)-19684665 b^3 (d+e x)^4 (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)+22309287 b^2 (d+e x)^3 (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)-15444891 b (d+e x)^2 (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)+6084351 (d+e x) (b d-a e)^5 (-a B e-6 A b e+7 b B d)-7436429 (b d-a e)^6 (B d-A e)+2909907 b^6 B (d+e x)^7\right )}{66927861 e^8} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(A + B*x)*(d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]
[Out]
(2*(d + e*x)^(9/2)*(-7436429*(b*d - a*e)^6*(B*d - A*e) + 6084351*(b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e)*(d
+ e*x) - 15444891*b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e)*(d + e*x)^2 + 22309287*b^2*(b*d - a*e)^3*(7*b*
B*d - 4*A*b*e - 3*a*B*e)*(d + e*x)^3 - 19684665*b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e - 4*a*B*e)*(d + e*x)^4 +
10567557*b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e)*(d + e*x)^5 - 3187041*b^5*(7*b*B*d - A*b*e - 6*a*B*e)*(
d + e*x)^6 + 2909907*b^6*B*(d + e*x)^7))/(66927861*e^8)
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IntegrateAlgebraic [B] time = 0.47, size = 1069, normalized size = 3.47 \begin {gather*} \frac {2 (d+e x)^{9/2} \left (-7436429 b^6 B d^7+7436429 A b^6 e d^6+44618574 a b^5 B e d^6+42590457 b^6 B (d+e x) d^6-44618574 a A b^5 e^2 d^5-111546435 a^2 b^4 B e^2 d^5-108114237 b^6 B (d+e x)^2 d^5-36506106 A b^6 e (d+e x) d^5-219036636 a b^5 B e (d+e x) d^5+111546435 a^2 A b^4 e^3 d^4+148728580 a^3 b^3 B e^3 d^4+156165009 b^6 B (d+e x)^3 d^4+77224455 A b^6 e (d+e x)^2 d^4+463346730 a b^5 B e (d+e x)^2 d^4+182530530 a A b^5 e^2 (d+e x) d^4+456326325 a^2 b^4 B e^2 (d+e x) d^4-148728580 a^3 A b^3 e^4 d^3-111546435 a^4 b^2 B e^4 d^3-137792655 b^6 B (d+e x)^4 d^3-89237148 A b^6 e (d+e x)^3 d^3-535422888 a b^5 B e (d+e x)^3 d^3-308897820 a A b^5 e^2 (d+e x)^2 d^3-772244550 a^2 b^4 B e^2 (d+e x)^2 d^3-365061060 a^2 A b^4 e^3 (d+e x) d^3-486748080 a^3 b^3 B e^3 (d+e x) d^3+111546435 a^4 A b^2 e^5 d^2+44618574 a^5 b B e^5 d^2+73972899 b^6 B (d+e x)^5 d^2+59053995 A b^6 e (d+e x)^4 d^2+354323970 a b^5 B e (d+e x)^4 d^2+267711444 a A b^5 e^2 (d+e x)^3 d^2+669278610 a^2 b^4 B e^2 (d+e x)^3 d^2+463346730 a^2 A b^4 e^3 (d+e x)^2 d^2+617795640 a^3 b^3 B e^3 (d+e x)^2 d^2+365061060 a^3 A b^3 e^4 (d+e x) d^2+273795795 a^4 b^2 B e^4 (d+e x) d^2-44618574 a^5 A b e^6 d-7436429 a^6 B e^6 d-22309287 b^6 B (d+e x)^6 d-21135114 A b^6 e (d+e x)^5 d-126810684 a b^5 B e (d+e x)^5 d-118107990 a A b^5 e^2 (d+e x)^4 d-295269975 a^2 b^4 B e^2 (d+e x)^4 d-267711444 a^2 A b^4 e^3 (d+e x)^3 d-356948592 a^3 b^3 B e^3 (d+e x)^3 d-308897820 a^3 A b^3 e^4 (d+e x)^2 d-231673365 a^4 b^2 B e^4 (d+e x)^2 d-182530530 a^4 A b^2 e^5 (d+e x) d-73012212 a^5 b B e^5 (d+e x) d+7436429 a^6 A e^7+2909907 b^6 B (d+e x)^7+3187041 A b^6 e (d+e x)^6+19122246 a b^5 B e (d+e x)^6+21135114 a A b^5 e^2 (d+e x)^5+52837785 a^2 b^4 B e^2 (d+e x)^5+59053995 a^2 A b^4 e^3 (d+e x)^4+78738660 a^3 b^3 B e^3 (d+e x)^4+89237148 a^3 A b^3 e^4 (d+e x)^3+66927861 a^4 b^2 B e^4 (d+e x)^3+77224455 a^4 A b^2 e^5 (d+e x)^2+30889782 a^5 b B e^5 (d+e x)^2+36506106 a^5 A b e^6 (d+e x)+6084351 a^6 B e^6 (d+e x)\right )}{66927861 e^8} \end {gather*}
Antiderivative was successfully verified.
[In]
IntegrateAlgebraic[(A + B*x)*(d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]
[Out]
(2*(d + e*x)^(9/2)*(-7436429*b^6*B*d^7 + 7436429*A*b^6*d^6*e + 44618574*a*b^5*B*d^6*e - 44618574*a*A*b^5*d^5*e
^2 - 111546435*a^2*b^4*B*d^5*e^2 + 111546435*a^2*A*b^4*d^4*e^3 + 148728580*a^3*b^3*B*d^4*e^3 - 148728580*a^3*A
*b^3*d^3*e^4 - 111546435*a^4*b^2*B*d^3*e^4 + 111546435*a^4*A*b^2*d^2*e^5 + 44618574*a^5*b*B*d^2*e^5 - 44618574
*a^5*A*b*d*e^6 - 7436429*a^6*B*d*e^6 + 7436429*a^6*A*e^7 + 42590457*b^6*B*d^6*(d + e*x) - 36506106*A*b^6*d^5*e
*(d + e*x) - 219036636*a*b^5*B*d^5*e*(d + e*x) + 182530530*a*A*b^5*d^4*e^2*(d + e*x) + 456326325*a^2*b^4*B*d^4
*e^2*(d + e*x) - 365061060*a^2*A*b^4*d^3*e^3*(d + e*x) - 486748080*a^3*b^3*B*d^3*e^3*(d + e*x) + 365061060*a^3
*A*b^3*d^2*e^4*(d + e*x) + 273795795*a^4*b^2*B*d^2*e^4*(d + e*x) - 182530530*a^4*A*b^2*d*e^5*(d + e*x) - 73012
212*a^5*b*B*d*e^5*(d + e*x) + 36506106*a^5*A*b*e^6*(d + e*x) + 6084351*a^6*B*e^6*(d + e*x) - 108114237*b^6*B*d
^5*(d + e*x)^2 + 77224455*A*b^6*d^4*e*(d + e*x)^2 + 463346730*a*b^5*B*d^4*e*(d + e*x)^2 - 308897820*a*A*b^5*d^
3*e^2*(d + e*x)^2 - 772244550*a^2*b^4*B*d^3*e^2*(d + e*x)^2 + 463346730*a^2*A*b^4*d^2*e^3*(d + e*x)^2 + 617795
640*a^3*b^3*B*d^2*e^3*(d + e*x)^2 - 308897820*a^3*A*b^3*d*e^4*(d + e*x)^2 - 231673365*a^4*b^2*B*d*e^4*(d + e*x
)^2 + 77224455*a^4*A*b^2*e^5*(d + e*x)^2 + 30889782*a^5*b*B*e^5*(d + e*x)^2 + 156165009*b^6*B*d^4*(d + e*x)^3
- 89237148*A*b^6*d^3*e*(d + e*x)^3 - 535422888*a*b^5*B*d^3*e*(d + e*x)^3 + 267711444*a*A*b^5*d^2*e^2*(d + e*x)
^3 + 669278610*a^2*b^4*B*d^2*e^2*(d + e*x)^3 - 267711444*a^2*A*b^4*d*e^3*(d + e*x)^3 - 356948592*a^3*b^3*B*d*e
^3*(d + e*x)^3 + 89237148*a^3*A*b^3*e^4*(d + e*x)^3 + 66927861*a^4*b^2*B*e^4*(d + e*x)^3 - 137792655*b^6*B*d^3
*(d + e*x)^4 + 59053995*A*b^6*d^2*e*(d + e*x)^4 + 354323970*a*b^5*B*d^2*e*(d + e*x)^4 - 118107990*a*A*b^5*d*e^
2*(d + e*x)^4 - 295269975*a^2*b^4*B*d*e^2*(d + e*x)^4 + 59053995*a^2*A*b^4*e^3*(d + e*x)^4 + 78738660*a^3*b^3*
B*e^3*(d + e*x)^4 + 73972899*b^6*B*d^2*(d + e*x)^5 - 21135114*A*b^6*d*e*(d + e*x)^5 - 126810684*a*b^5*B*d*e*(d
+ e*x)^5 + 21135114*a*A*b^5*e^2*(d + e*x)^5 + 52837785*a^2*b^4*B*e^2*(d + e*x)^5 - 22309287*b^6*B*d*(d + e*x)
^6 + 3187041*A*b^6*e*(d + e*x)^6 + 19122246*a*b^5*B*e*(d + e*x)^6 + 2909907*b^6*B*(d + e*x)^7))/(66927861*e^8)
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fricas [B] time = 0.44, size = 1470, normalized size = 4.77
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((B*x+A)*(e*x+d)^(7/2)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm="fricas")
[Out]
2/66927861*(2909907*B*b^6*e^11*x^11 - 14336*B*b^6*d^11 + 7436429*A*a^6*d^4*e^7 + 23552*(6*B*a*b^5 + A*b^6)*d^1
0*e - 123648*(5*B*a^2*b^4 + 2*A*a*b^5)*d^9*e^2 + 391552*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^8*e^3 - 832048*(3*B*a^4*
b^2 + 4*A*a^3*b^3)*d^7*e^4 + 1248072*(2*B*a^5*b + 5*A*a^4*b^2)*d^6*e^5 - 1352078*(B*a^6 + 6*A*a^5*b)*d^5*e^6 +
138567*(70*B*b^6*d*e^10 + 23*(6*B*a*b^5 + A*b^6)*e^11)*x^10 + 7293*(1498*B*b^6*d^2*e^9 + 1472*(6*B*a*b^5 + A*
b^6)*d*e^10 + 1449*(5*B*a^2*b^4 + 2*A*a*b^5)*e^11)*x^9 + 1287*(3248*B*b^6*d^3*e^8 + 9522*(6*B*a*b^5 + A*b^6)*d
^2*e^9 + 28014*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^10 + 15295*(4*B*a^3*b^3 + 3*A*a^2*b^4)*e^11)*x^8 + 429*(7*B*b^6*d
^4*e^7 + 11132*(6*B*a*b^5 + A*b^6)*d^3*e^8 + 97566*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^9 + 159068*(4*B*a^3*b^3 + 3
*A*a^2*b^4)*d*e^10 + 52003*(3*B*a^4*b^2 + 4*A*a^3*b^3)*e^11)*x^7 - 231*(14*B*b^6*d^5*e^6 - 23*(6*B*a*b^5 + A*b
^6)*d^4*e^7 - 72312*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e^8 - 350474*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^9 - 341734*(3
*B*a^4*b^2 + 4*A*a^3*b^3)*d*e^10 - 66861*(2*B*a^5*b + 5*A*a^4*b^2)*e^11)*x^6 + 63*(56*B*b^6*d^6*e^5 - 92*(6*B*
a*b^5 + A*b^6)*d^5*e^6 + 483*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^7 + 529644*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^8 +
1530374*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^9 + 891480*(2*B*a^5*b + 5*A*a^4*b^2)*d*e^10 + 96577*(B*a^6 + 6*A*a^5
*b)*e^11)*x^5 - 7*(560*B*b^6*d^7*e^4 - 1062347*A*a^6*e^11 - 920*(6*B*a*b^5 + A*b^6)*d^6*e^5 + 4830*(5*B*a^2*b^
4 + 2*A*a*b^5)*d^5*e^6 - 15295*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^7 - 5943200*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e
^8 - 10207446*(2*B*a^5*b + 5*A*a^4*b^2)*d^2*e^9 - 3283618*(B*a^6 + 6*A*a^5*b)*d*e^10)*x^4 + (4480*B*b^6*d^8*e^
3 + 29745716*A*a^6*d*e^10 - 7360*(6*B*a*b^5 + A*b^6)*d^7*e^4 + 38640*(5*B*a^2*b^4 + 2*A*a*b^5)*d^6*e^5 - 12236
0*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^5*e^6 + 260015*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^4*e^7 + 33073908*(2*B*a^5*b + 5*A
*a^4*b^2)*d^3*e^8 + 31097794*(B*a^6 + 6*A*a^5*b)*d^2*e^9)*x^3 - 3*(1792*B*b^6*d^9*e^2 - 14872858*A*a^6*d^2*e^9
- 2944*(6*B*a*b^5 + A*b^6)*d^8*e^3 + 15456*(5*B*a^2*b^4 + 2*A*a*b^5)*d^7*e^4 - 48944*(4*B*a^3*b^3 + 3*A*a^2*b
^4)*d^6*e^5 + 104006*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^5*e^6 - 156009*(2*B*a^5*b + 5*A*a^4*b^2)*d^4*e^7 - 5408312*
(B*a^6 + 6*A*a^5*b)*d^3*e^8)*x^2 + (7168*B*b^6*d^10*e + 29745716*A*a^6*d^3*e^8 - 11776*(6*B*a*b^5 + A*b^6)*d^9
*e^2 + 61824*(5*B*a^2*b^4 + 2*A*a*b^5)*d^8*e^3 - 195776*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^7*e^4 + 416024*(3*B*a^4*
b^2 + 4*A*a^3*b^3)*d^6*e^5 - 624036*(2*B*a^5*b + 5*A*a^4*b^2)*d^5*e^6 + 676039*(B*a^6 + 6*A*a^5*b)*d^4*e^7)*x)
*sqrt(e*x + d)/e^8
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giac [B] time = 0.74, size = 6433, normalized size = 20.89
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((B*x+A)*(e*x+d)^(7/2)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm="giac")
[Out]
2/334639305*(111546435*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*B*a^6*d^4*e^(-1) + 669278610*((x*e + d)^(3/2) - 3
*sqrt(x*e + d)*d)*A*a^5*b*d^4*e^(-1) + 133855722*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*
d^2)*B*a^5*b*d^4*e^(-2) + 334639305*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^4*b^
2*d^4*e^(-2) + 143416845*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)
*d^3)*B*a^4*b^2*d^4*e^(-3) + 191222460*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35
*sqrt(x*e + d)*d^3)*A*a^3*b^3*d^4*e^(-3) + 21246940*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d
)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^3*b^3*d^4*e^(-4) + 15935205*(35*(x*e + d)^(
9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^
2*b^4*d^4*e^(-4) + 7243275*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e
+ d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^2*b^4*d^4*e^(-5) + 2897310*(63*(x*e + d
)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d
^4 - 693*sqrt(x*e + d)*d^5)*A*a*b^5*d^4*e^(-5) + 668610*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005
*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*s
qrt(x*e + d)*d^6)*B*a*b^5*d^4*e^(-6) + 111435*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)
^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e +
d)*d^6)*A*b^6*d^4*e^(-6) + 52003*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2
- 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^
6 - 6435*sqrt(x*e + d)*d^7)*B*b^6*d^4*e^(-7) + 89237148*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*
e + d)*d^2)*B*a^6*d^3*e^(-1) + 535422888*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a
^5*b*d^3*e^(-1) + 229466952*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e +
d)*d^3)*B*a^5*b*d^3*e^(-2) + 573667380*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 3
5*sqrt(x*e + d)*d^3)*A*a^4*b^2*d^3*e^(-2) + 63740820*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e +
d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^4*b^2*d^3*e^(-3) + 84987760*(35*(x*e + d)^
(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a
^3*b^3*d^3*e^(-3) + 38630800*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*
e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^3*b^3*d^3*e^(-4) + 28973100*(63*(x*e
+ d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2
)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a^2*b^4*d^3*e^(-4) + 6686100*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d
+ 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 +
3003*sqrt(x*e + d)*d^6)*B*a^2*b^4*d^3*e^(-5) + 2674440*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*
(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sq
rt(x*e + d)*d^6)*A*a*b^5*d^3*e^(-5) + 1248072*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d
)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e
+ d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*a*b^5*d^3*e^(-6) + 208012*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(1
3/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^
(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*A*b^6*d^3*e^(-6) + 12236*(6435*(x*e + d)^(17/2
) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9
/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x
*e + d)*d^8)*B*b^6*d^3*e^(-7) + 334639305*sqrt(x*e + d)*A*a^6*d^4 + 446185740*((x*e + d)^(3/2) - 3*sqrt(x*e +
d)*d)*A*a^6*d^3 + 57366738*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e +
d)*d^3)*B*a^6*d^2*e^(-1) + 344200428*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*s
qrt(x*e + d)*d^3)*A*a^5*b*d^2*e^(-1) + 38244492*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5
/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^5*b*d^2*e^(-2) + 95611230*(35*(x*e + d)^(9/2) -
180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^4*b^2*
d^2*e^(-2) + 43459650*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^
(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^4*b^2*d^2*e^(-3) + 57946200*(63*(x*e + d)^(1
1/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 -
693*sqrt(x*e + d)*d^5)*A*a^3*b^3*d^2*e^(-3) + 13372200*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005
*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*s
qrt(x*e + d)*d^6)*B*a^3*b^3*d^2*e^(-4) + 10029150*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e
+ d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*
e + d)*d^6)*A*a^2*b^4*d^2*e^(-4) + 4680270*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(
11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d
)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*a^2*b^4*d^2*e^(-5) + 1872108*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(1
3/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^
(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*A*a*b^5*d^2*e^(-5) + 110124*(6435*(x*e + d)^(1
7/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)
^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqr
t(x*e + d)*d^8)*B*a*b^5*d^2*e^(-6) + 18354*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d
)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*
(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*A*b^6*d^2*e^(-6) + 8694*(12155*(x
*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645
370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)
*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*B*b^6*d^2*e^(-7) + 133855722*(3*(x*e + d)^(5/2)
- 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*A*a^6*d^2 + 4249388*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d
+ 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*B*a^6*d*e^(-1) + 25496328*(35*(x
*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*
d^4)*A*a^5*b*d*e^(-1) + 11589240*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386
*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*B*a^5*b*d*e^(-2) + 28973100*(63*(x*e
+ d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2
)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a^4*b^2*d*e^(-2) + 6686100*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d +
5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 30
03*sqrt(x*e + d)*d^6)*B*a^4*b^2*d*e^(-3) + 8914800*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e
+ d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x
*e + d)*d^6)*A*a^3*b^3*d*e^(-3) + 4160240*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(1
1/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)
^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*a^3*b^3*d*e^(-4) + 3120180*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2
)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/
2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*A*a^2*b^4*d*e^(-4) + 183540*(6435*(x*e + d)^(17/2
) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9
/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x
*e + d)*d^8)*B*a^2*b^4*d*e^(-5) + 73416*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(
13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*
e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*A*a*b^5*d*e^(-5) + 34776*(12155*(x*e
+ d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 264537
0*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d
^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*B*a*b^5*d*e^(-6) + 5796*(12155*(x*e + d)^(19/2) -
122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11
/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*
e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*A*b^6*d*e^(-6) + 1380*(46189*(x*e + d)^(21/2) - 510510*(x*e + d)^
(19/2)*d + 2567565*(x*e + d)^(17/2)*d^2 - 7759752*(x*e + d)^(15/2)*d^3 + 15668730*(x*e + d)^(13/2)*d^4 - 22221
108*(x*e + d)^(11/2)*d^5 + 22632610*(x*e + d)^(9/2)*d^6 - 16628040*(x*e + d)^(7/2)*d^7 + 8729721*(x*e + d)^(5/
2)*d^8 - 3233230*(x*e + d)^(3/2)*d^9 + 969969*sqrt(x*e + d)*d^10)*B*b^6*d*e^(-7) + 38244492*(5*(x*e + d)^(7/2)
- 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*A*a^6*d + 482885*(63*(x*e + d)^(11/2)
- 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693
*sqrt(x*e + d)*d^5)*B*a^6*e^(-1) + 2897310*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*
d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*A*a^5*b*e^(-1) + 668610*(23
1*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e
+ d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*B*a^5*b*e^(-2) + 1671525*(231*(x*e + d)^(
13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d
^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*A*a^4*b^2*e^(-2) + 780045*(429*(x*e + d)^(15/2) - 3465
*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 270
27*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*B*a^4*b^2*e^(-3) + 1040060*(429*(
x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*
e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*A*a^3*b^3*e
^(-3) + 61180*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e +
d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*
(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*B*a^3*b^3*e^(-4) + 45885*(6435*(x*e + d)^(17/2) - 58344*(x*e +
d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160
*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*A*a
^2*b^4*e^(-4) + 21735*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492
260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2
)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*B*a^2*b^4*e^(-5)
+ 8694*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(
13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804
*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*A*a*b^5*e^(-5) + 2070*(46189*(x*
e + d)^(21/2) - 510510*(x*e + d)^(19/2)*d + 2567565*(x*e + d)^(17/2)*d^2 - 7759752*(x*e + d)^(15/2)*d^3 + 1566
8730*(x*e + d)^(13/2)*d^4 - 22221108*(x*e + d)^(11/2)*d^5 + 22632610*(x*e + d)^(9/2)*d^6 - 16628040*(x*e + d)^
(7/2)*d^7 + 8729721*(x*e + d)^(5/2)*d^8 - 3233230*(x*e + d)^(3/2)*d^9 + 969969*sqrt(x*e + d)*d^10)*B*a*b^5*e^(
-6) + 345*(46189*(x*e + d)^(21/2) - 510510*(x*e + d)^(19/2)*d + 2567565*(x*e + d)^(17/2)*d^2 - 7759752*(x*e +
d)^(15/2)*d^3 + 15668730*(x*e + d)^(13/2)*d^4 - 22221108*(x*e + d)^(11/2)*d^5 + 22632610*(x*e + d)^(9/2)*d^6 -
16628040*(x*e + d)^(7/2)*d^7 + 8729721*(x*e + d)^(5/2)*d^8 - 3233230*(x*e + d)^(3/2)*d^9 + 969969*sqrt(x*e +
d)*d^10)*A*b^6*e^(-6) + 165*(88179*(x*e + d)^(23/2) - 1062347*(x*e + d)^(21/2)*d + 5870865*(x*e + d)^(19/2)*d^
2 - 19684665*(x*e + d)^(17/2)*d^3 + 44618574*(x*e + d)^(15/2)*d^4 - 72076158*(x*e + d)^(13/2)*d^5 + 85180914*(
x*e + d)^(11/2)*d^6 - 74364290*(x*e + d)^(9/2)*d^7 + 47805615*(x*e + d)^(7/2)*d^8 - 22309287*(x*e + d)^(5/2)*d
^9 + 7436429*(x*e + d)^(3/2)*d^10 - 2028117*sqrt(x*e + d)*d^11)*B*b^6*e^(-7) + 1062347*(35*(x*e + d)^(9/2) - 1
80*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*A*a^6)*e^(-1
)
________________________________________________________________________________________
maple [B] time = 0.05, size = 913, normalized size = 2.96 \begin {gather*} \frac {2 \left (e x +d \right )^{\frac {9}{2}} \left (2909907 B \,b^{6} x^{7} e^{7}+3187041 A \,b^{6} e^{7} x^{6}+19122246 B a \,b^{5} e^{7} x^{6}-1939938 B \,b^{6} d \,e^{6} x^{6}+21135114 A a \,b^{5} e^{7} x^{5}-2012868 A \,b^{6} d \,e^{6} x^{5}+52837785 B \,a^{2} b^{4} e^{7} x^{5}-12077208 B a \,b^{5} d \,e^{6} x^{5}+1225224 B \,b^{6} d^{2} e^{5} x^{5}+59053995 A \,a^{2} b^{4} e^{7} x^{4}-12432420 A a \,b^{5} d \,e^{6} x^{4}+1184040 A \,b^{6} d^{2} e^{5} x^{4}+78738660 B \,a^{3} b^{3} e^{7} x^{4}-31081050 B \,a^{2} b^{4} d \,e^{6} x^{4}+7104240 B a \,b^{5} d^{2} e^{5} x^{4}-720720 B \,b^{6} d^{3} e^{4} x^{4}+89237148 A \,a^{3} b^{3} e^{7} x^{3}-31495464 A \,a^{2} b^{4} d \,e^{6} x^{3}+6630624 A a \,b^{5} d^{2} e^{5} x^{3}-631488 A \,b^{6} d^{3} e^{4} x^{3}+66927861 B \,a^{4} b^{2} e^{7} x^{3}-41993952 B \,a^{3} b^{3} d \,e^{6} x^{3}+16576560 B \,a^{2} b^{4} d^{2} e^{5} x^{3}-3788928 B a \,b^{5} d^{3} e^{4} x^{3}+384384 B \,b^{6} d^{4} e^{3} x^{3}+77224455 A \,a^{4} b^{2} e^{7} x^{2}-41186376 A \,a^{3} b^{3} d \,e^{6} x^{2}+14536368 A \,a^{2} b^{4} d^{2} e^{5} x^{2}-3060288 A a \,b^{5} d^{3} e^{4} x^{2}+291456 A \,b^{6} d^{4} e^{3} x^{2}+30889782 B \,a^{5} b \,e^{7} x^{2}-30889782 B \,a^{4} b^{2} d \,e^{6} x^{2}+19381824 B \,a^{3} b^{3} d^{2} e^{5} x^{2}-7650720 B \,a^{2} b^{4} d^{3} e^{4} x^{2}+1748736 B a \,b^{5} d^{4} e^{3} x^{2}-177408 B \,b^{6} d^{5} e^{2} x^{2}+36506106 A \,a^{5} b \,e^{7} x -28081620 A \,a^{4} b^{2} d \,e^{6} x +14976864 A \,a^{3} b^{3} d^{2} e^{5} x -5285952 A \,a^{2} b^{4} d^{3} e^{4} x +1112832 A a \,b^{5} d^{4} e^{3} x -105984 A \,b^{6} d^{5} e^{2} x +6084351 B \,a^{6} e^{7} x -11232648 B \,a^{5} b d \,e^{6} x +11232648 B \,a^{4} b^{2} d^{2} e^{5} x -7047936 B \,a^{3} b^{3} d^{3} e^{4} x +2782080 B \,a^{2} b^{4} d^{4} e^{3} x -635904 B a \,b^{5} d^{5} e^{2} x +64512 B \,b^{6} d^{6} e x +7436429 A \,a^{6} e^{7}-8112468 A \,a^{5} b d \,e^{6}+6240360 A \,a^{4} b^{2} d^{2} e^{5}-3328192 A \,a^{3} b^{3} d^{3} e^{4}+1174656 A \,a^{2} b^{4} d^{4} e^{3}-247296 A a \,b^{5} d^{5} e^{2}+23552 A \,b^{6} d^{6} e -1352078 B \,a^{6} d \,e^{6}+2496144 B \,a^{5} b \,d^{2} e^{5}-2496144 B \,a^{4} b^{2} d^{3} e^{4}+1566208 B \,a^{3} b^{3} d^{4} e^{3}-618240 B \,a^{2} b^{4} d^{5} e^{2}+141312 B a \,b^{5} d^{6} e -14336 B \,b^{6} d^{7}\right )}{66927861 e^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((B*x+A)*(e*x+d)^(7/2)*(b^2*x^2+2*a*b*x+a^2)^3,x)
[Out]
2/66927861*(e*x+d)^(9/2)*(2909907*B*b^6*e^7*x^7+3187041*A*b^6*e^7*x^6+19122246*B*a*b^5*e^7*x^6-1939938*B*b^6*d
*e^6*x^6+21135114*A*a*b^5*e^7*x^5-2012868*A*b^6*d*e^6*x^5+52837785*B*a^2*b^4*e^7*x^5-12077208*B*a*b^5*d*e^6*x^
5+1225224*B*b^6*d^2*e^5*x^5+59053995*A*a^2*b^4*e^7*x^4-12432420*A*a*b^5*d*e^6*x^4+1184040*A*b^6*d^2*e^5*x^4+78
738660*B*a^3*b^3*e^7*x^4-31081050*B*a^2*b^4*d*e^6*x^4+7104240*B*a*b^5*d^2*e^5*x^4-720720*B*b^6*d^3*e^4*x^4+892
37148*A*a^3*b^3*e^7*x^3-31495464*A*a^2*b^4*d*e^6*x^3+6630624*A*a*b^5*d^2*e^5*x^3-631488*A*b^6*d^3*e^4*x^3+6692
7861*B*a^4*b^2*e^7*x^3-41993952*B*a^3*b^3*d*e^6*x^3+16576560*B*a^2*b^4*d^2*e^5*x^3-3788928*B*a*b^5*d^3*e^4*x^3
+384384*B*b^6*d^4*e^3*x^3+77224455*A*a^4*b^2*e^7*x^2-41186376*A*a^3*b^3*d*e^6*x^2+14536368*A*a^2*b^4*d^2*e^5*x
^2-3060288*A*a*b^5*d^3*e^4*x^2+291456*A*b^6*d^4*e^3*x^2+30889782*B*a^5*b*e^7*x^2-30889782*B*a^4*b^2*d*e^6*x^2+
19381824*B*a^3*b^3*d^2*e^5*x^2-7650720*B*a^2*b^4*d^3*e^4*x^2+1748736*B*a*b^5*d^4*e^3*x^2-177408*B*b^6*d^5*e^2*
x^2+36506106*A*a^5*b*e^7*x-28081620*A*a^4*b^2*d*e^6*x+14976864*A*a^3*b^3*d^2*e^5*x-5285952*A*a^2*b^4*d^3*e^4*x
+1112832*A*a*b^5*d^4*e^3*x-105984*A*b^6*d^5*e^2*x+6084351*B*a^6*e^7*x-11232648*B*a^5*b*d*e^6*x+11232648*B*a^4*
b^2*d^2*e^5*x-7047936*B*a^3*b^3*d^3*e^4*x+2782080*B*a^2*b^4*d^4*e^3*x-635904*B*a*b^5*d^5*e^2*x+64512*B*b^6*d^6
*e*x+7436429*A*a^6*e^7-8112468*A*a^5*b*d*e^6+6240360*A*a^4*b^2*d^2*e^5-3328192*A*a^3*b^3*d^3*e^4+1174656*A*a^2
*b^4*d^4*e^3-247296*A*a*b^5*d^5*e^2+23552*A*b^6*d^6*e-1352078*B*a^6*d*e^6+2496144*B*a^5*b*d^2*e^5-2496144*B*a^
4*b^2*d^3*e^4+1566208*B*a^3*b^3*d^4*e^3-618240*B*a^2*b^4*d^5*e^2+141312*B*a*b^5*d^6*e-14336*B*b^6*d^7)/e^8
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maxima [B] time = 0.64, size = 767, normalized size = 2.49 \begin {gather*} \frac {2 \, {\left (2909907 \, {\left (e x + d\right )}^{\frac {23}{2}} B b^{6} - 3187041 \, {\left (7 \, B b^{6} d - {\left (6 \, B a b^{5} + A b^{6}\right )} e\right )} {\left (e x + d\right )}^{\frac {21}{2}} + 10567557 \, {\left (7 \, B b^{6} d^{2} - 2 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d e + {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} e^{2}\right )} {\left (e x + d\right )}^{\frac {19}{2}} - 19684665 \, {\left (7 \, B b^{6} d^{3} - 3 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{2} e + 3 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d e^{2} - {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} e^{3}\right )} {\left (e x + d\right )}^{\frac {17}{2}} + 22309287 \, {\left (7 \, B b^{6} d^{4} - 4 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{3} e + 6 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{2} e^{2} - 4 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d e^{3} + {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} e^{4}\right )} {\left (e x + d\right )}^{\frac {15}{2}} - 15444891 \, {\left (7 \, B b^{6} d^{5} - 5 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{4} e + 10 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{3} e^{2} - 10 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{2} e^{3} + 5 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d e^{4} - {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} e^{5}\right )} {\left (e x + d\right )}^{\frac {13}{2}} + 6084351 \, {\left (7 \, B b^{6} d^{6} - 6 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{5} e + 15 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{4} e^{2} - 20 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{3} e^{3} + 15 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{2} e^{4} - 6 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d e^{5} + {\left (B a^{6} + 6 \, A a^{5} b\right )} e^{6}\right )} {\left (e x + d\right )}^{\frac {11}{2}} - 7436429 \, {\left (B b^{6} d^{7} - A a^{6} e^{7} - {\left (6 \, B a b^{5} + A b^{6}\right )} d^{6} e + 3 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{5} e^{2} - 5 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{4} e^{3} + 5 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{3} e^{4} - 3 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d^{2} e^{5} + {\left (B a^{6} + 6 \, A a^{5} b\right )} d e^{6}\right )} {\left (e x + d\right )}^{\frac {9}{2}}\right )}}{66927861 \, e^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((B*x+A)*(e*x+d)^(7/2)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm="maxima")
[Out]
2/66927861*(2909907*(e*x + d)^(23/2)*B*b^6 - 3187041*(7*B*b^6*d - (6*B*a*b^5 + A*b^6)*e)*(e*x + d)^(21/2) + 10
567557*(7*B*b^6*d^2 - 2*(6*B*a*b^5 + A*b^6)*d*e + (5*B*a^2*b^4 + 2*A*a*b^5)*e^2)*(e*x + d)^(19/2) - 19684665*(
7*B*b^6*d^3 - 3*(6*B*a*b^5 + A*b^6)*d^2*e + 3*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^2 - (4*B*a^3*b^3 + 3*A*a^2*b^4)*e^
3)*(e*x + d)^(17/2) + 22309287*(7*B*b^6*d^4 - 4*(6*B*a*b^5 + A*b^6)*d^3*e + 6*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^
2 - 4*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d*e^3 + (3*B*a^4*b^2 + 4*A*a^3*b^3)*e^4)*(e*x + d)^(15/2) - 15444891*(7*B*b^
6*d^5 - 5*(6*B*a*b^5 + A*b^6)*d^4*e + 10*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e^2 - 10*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^
2*e^3 + 5*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d*e^4 - (2*B*a^5*b + 5*A*a^4*b^2)*e^5)*(e*x + d)^(13/2) + 6084351*(7*B*b
^6*d^6 - 6*(6*B*a*b^5 + A*b^6)*d^5*e + 15*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^2 - 20*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d
^3*e^3 + 15*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^4 - 6*(2*B*a^5*b + 5*A*a^4*b^2)*d*e^5 + (B*a^6 + 6*A*a^5*b)*e^6)
*(e*x + d)^(11/2) - 7436429*(B*b^6*d^7 - A*a^6*e^7 - (6*B*a*b^5 + A*b^6)*d^6*e + 3*(5*B*a^2*b^4 + 2*A*a*b^5)*d
^5*e^2 - 5*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^3 + 5*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^4 - 3*(2*B*a^5*b + 5*A*a^
4*b^2)*d^2*e^5 + (B*a^6 + 6*A*a^5*b)*d*e^6)*(e*x + d)^(9/2))/e^8
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mupad [B] time = 2.02, size = 279, normalized size = 0.91 \begin {gather*} \frac {{\left (d+e\,x\right )}^{21/2}\,\left (2\,A\,b^6\,e-14\,B\,b^6\,d+12\,B\,a\,b^5\,e\right )}{21\,e^8}+\frac {2\,{\left (a\,e-b\,d\right )}^5\,{\left (d+e\,x\right )}^{11/2}\,\left (6\,A\,b\,e+B\,a\,e-7\,B\,b\,d\right )}{11\,e^8}+\frac {2\,B\,b^6\,{\left (d+e\,x\right )}^{23/2}}{23\,e^8}+\frac {2\,\left (A\,e-B\,d\right )\,{\left (a\,e-b\,d\right )}^6\,{\left (d+e\,x\right )}^{9/2}}{9\,e^8}+\frac {6\,b\,{\left (a\,e-b\,d\right )}^4\,{\left (d+e\,x\right )}^{13/2}\,\left (5\,A\,b\,e+2\,B\,a\,e-7\,B\,b\,d\right )}{13\,e^8}+\frac {6\,b^4\,\left (a\,e-b\,d\right )\,{\left (d+e\,x\right )}^{19/2}\,\left (2\,A\,b\,e+5\,B\,a\,e-7\,B\,b\,d\right )}{19\,e^8}+\frac {2\,b^2\,{\left (a\,e-b\,d\right )}^3\,{\left (d+e\,x\right )}^{15/2}\,\left (4\,A\,b\,e+3\,B\,a\,e-7\,B\,b\,d\right )}{3\,e^8}+\frac {10\,b^3\,{\left (a\,e-b\,d\right )}^2\,{\left (d+e\,x\right )}^{17/2}\,\left (3\,A\,b\,e+4\,B\,a\,e-7\,B\,b\,d\right )}{17\,e^8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((A + B*x)*(d + e*x)^(7/2)*(a^2 + b^2*x^2 + 2*a*b*x)^3,x)
[Out]
((d + e*x)^(21/2)*(2*A*b^6*e - 14*B*b^6*d + 12*B*a*b^5*e))/(21*e^8) + (2*(a*e - b*d)^5*(d + e*x)^(11/2)*(6*A*b
*e + B*a*e - 7*B*b*d))/(11*e^8) + (2*B*b^6*(d + e*x)^(23/2))/(23*e^8) + (2*(A*e - B*d)*(a*e - b*d)^6*(d + e*x)
^(9/2))/(9*e^8) + (6*b*(a*e - b*d)^4*(d + e*x)^(13/2)*(5*A*b*e + 2*B*a*e - 7*B*b*d))/(13*e^8) + (6*b^4*(a*e -
b*d)*(d + e*x)^(19/2)*(2*A*b*e + 5*B*a*e - 7*B*b*d))/(19*e^8) + (2*b^2*(a*e - b*d)^3*(d + e*x)^(15/2)*(4*A*b*e
+ 3*B*a*e - 7*B*b*d))/(3*e^8) + (10*b^3*(a*e - b*d)^2*(d + e*x)^(17/2)*(3*A*b*e + 4*B*a*e - 7*B*b*d))/(17*e^8
)
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sympy [A] time = 163.18, size = 5414, normalized size = 17.58
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((B*x+A)*(e*x+d)**(7/2)*(b**2*x**2+2*a*b*x+a**2)**3,x)
[Out]
A*a**6*d**3*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 6*A*a**6*d**2*(-d*(d + e*x)**
(3/2)/3 + (d + e*x)**(5/2)/5)/e + 6*A*a**6*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7
/2)/7)/e + 2*A*a**6*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)
**(9/2)/9)/e + 12*A*a**5*b*d**3*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 36*A*a**5*b*d**2*(d**2*(d
+ e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 36*A*a**5*b*d*(-d**3*(d + e*x)**(3/2)/3
+ 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**2 + 12*A*a**5*b*(d**4*(d + e*x)*
*(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/
11)/e**2 + 30*A*a**4*b**2*d**3*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 +
90*A*a**4*b**2*d**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)
**(9/2)/9)/e**3 + 90*A*a**4*b**2*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7
/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**3 + 30*A*a**4*b**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*
(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e
*x)**(13/2)/13)/e**3 + 40*A*a**3*b**3*d**3*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*
x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 120*A*a**3*b**3*d**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/
2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 120*A*a**3*b**3*d*(-d
**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d
*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**4 + 40*A*a**3*b**3*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x
)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d +
e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**4 + 30*A*a**2*b**4*d**3*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x
)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 90*A*a**2*b**4*
d**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)
/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 90*A*a**2*b**4*d*(d**6*(d + e*x)**(3/2)/3 - 6*d**
5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11
- 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**5 + 30*A*a**2*b**4*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d
+ e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d*
*2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**5 + 12*A*a*b**5*d**3*(-d**5*(d +
e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*
x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**6 + 36*A*a*b**5*d**2*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/
2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)*
*(13/2)/13 + (d + e*x)**(15/2)/15)/e**6 + 36*A*a*b**5*d*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5
- 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13
/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**6 + 12*A*a*b**5*(d**8*(d + e*x)**(3/2)/3 - 8*d**7
*(d + e*x)**(5/2)/5 + 4*d**6*(d + e*x)**(7/2) - 56*d**5*(d + e*x)**(9/2)/9 + 70*d**4*(d + e*x)**(11/2)/11 - 56
*d**3*(d + e*x)**(13/2)/13 + 28*d**2*(d + e*x)**(15/2)/15 - 8*d*(d + e*x)**(17/2)/17 + (d + e*x)**(19/2)/19)/e
**6 + 2*A*b**6*d**3*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**
3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**7 +
6*A*b**6*d**2*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e
*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e
*x)**(17/2)/17)/e**7 + 6*A*b**6*d*(d**8*(d + e*x)**(3/2)/3 - 8*d**7*(d + e*x)**(5/2)/5 + 4*d**6*(d + e*x)**(7/
2) - 56*d**5*(d + e*x)**(9/2)/9 + 70*d**4*(d + e*x)**(11/2)/11 - 56*d**3*(d + e*x)**(13/2)/13 + 28*d**2*(d + e
*x)**(15/2)/15 - 8*d*(d + e*x)**(17/2)/17 + (d + e*x)**(19/2)/19)/e**7 + 2*A*b**6*(-d**9*(d + e*x)**(3/2)/3 +
9*d**8*(d + e*x)**(5/2)/5 - 36*d**7*(d + e*x)**(7/2)/7 + 28*d**6*(d + e*x)**(9/2)/3 - 126*d**5*(d + e*x)**(11/
2)/11 + 126*d**4*(d + e*x)**(13/2)/13 - 28*d**3*(d + e*x)**(15/2)/5 + 36*d**2*(d + e*x)**(17/2)/17 - 9*d*(d +
e*x)**(19/2)/19 + (d + e*x)**(21/2)/21)/e**7 + 2*B*a**6*d**3*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2
+ 6*B*a**6*d**2*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 6*B*a**6*d*(-d
**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**2 + 2*B*a
**6*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9
+ (d + e*x)**(11/2)/11)/e**2 + 12*B*a**5*b*d**3*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)*
*(7/2)/7)/e**3 + 36*B*a**5*b*d**2*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)
/7 + (d + e*x)**(9/2)/9)/e**3 + 36*B*a**5*b*d*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d
+ e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**3 + 12*B*a**5*b*(-d**5*(d + e*x)**(3/2)/3
+ d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11
+ (d + e*x)**(13/2)/13)/e**3 + 30*B*a**4*b**2*d**3*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d
*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 90*B*a**4*b**2*d**2*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*
x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 90*B*a**4*b**2
*d*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9
- 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**4 + 30*B*a**4*b**2*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d
+ e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*
d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**4 + 40*B*a**3*b**3*d**3*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d
+ e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**5 + 120*B*a**
3*b**3*d**2*(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)
**(9/2)/9 - 5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**5 + 120*B*a**3*b**3*d*(d**6*(d + e*x)**(3/2)/3
- 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(1
1/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**5 + 40*B*a**3*b**3*(-d**7*(d + e*x)**(3/2)/3 + 7
*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11
+ 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**5 + 30*B*a**2*b**4*d**3*
(-d**5*(d + e*x)**(3/2)/3 + d**4*(d + e*x)**(5/2) - 10*d**3*(d + e*x)**(7/2)/7 + 10*d**2*(d + e*x)**(9/2)/9 -
5*d*(d + e*x)**(11/2)/11 + (d + e*x)**(13/2)/13)/e**6 + 90*B*a**2*b**4*d**2*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*
(d + e*x)**(5/2)/5 + 15*d**4*(d + e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 -
6*d*(d + e*x)**(13/2)/13 + (d + e*x)**(15/2)/15)/e**6 + 90*B*a**2*b**4*d*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d
+ e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d*
*2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**6 + 30*B*a**2*b**4*(d**8*(d + e*
x)**(3/2)/3 - 8*d**7*(d + e*x)**(5/2)/5 + 4*d**6*(d + e*x)**(7/2) - 56*d**5*(d + e*x)**(9/2)/9 + 70*d**4*(d +
e*x)**(11/2)/11 - 56*d**3*(d + e*x)**(13/2)/13 + 28*d**2*(d + e*x)**(15/2)/15 - 8*d*(d + e*x)**(17/2)/17 + (d
+ e*x)**(19/2)/19)/e**6 + 12*B*a*b**5*d**3*(d**6*(d + e*x)**(3/2)/3 - 6*d**5*(d + e*x)**(5/2)/5 + 15*d**4*(d +
e*x)**(7/2)/7 - 20*d**3*(d + e*x)**(9/2)/9 + 15*d**2*(d + e*x)**(11/2)/11 - 6*d*(d + e*x)**(13/2)/13 + (d + e
*x)**(15/2)/15)/e**7 + 36*B*a*b**5*d**2*(-d**7*(d + e*x)**(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*
x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d
+ e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**7 + 36*B*a*b**5*d*(d**8*(d + e*x)**(3/2)/3 - 8*d**7*(d + e*x)**(5
/2)/5 + 4*d**6*(d + e*x)**(7/2) - 56*d**5*(d + e*x)**(9/2)/9 + 70*d**4*(d + e*x)**(11/2)/11 - 56*d**3*(d + e*x
)**(13/2)/13 + 28*d**2*(d + e*x)**(15/2)/15 - 8*d*(d + e*x)**(17/2)/17 + (d + e*x)**(19/2)/19)/e**7 + 12*B*a*b
**5*(-d**9*(d + e*x)**(3/2)/3 + 9*d**8*(d + e*x)**(5/2)/5 - 36*d**7*(d + e*x)**(7/2)/7 + 28*d**6*(d + e*x)**(9
/2)/3 - 126*d**5*(d + e*x)**(11/2)/11 + 126*d**4*(d + e*x)**(13/2)/13 - 28*d**3*(d + e*x)**(15/2)/5 + 36*d**2*
(d + e*x)**(17/2)/17 - 9*d*(d + e*x)**(19/2)/19 + (d + e*x)**(21/2)/21)/e**7 + 2*B*b**6*d**3*(-d**7*(d + e*x)*
*(3/2)/3 + 7*d**6*(d + e*x)**(5/2)/5 - 3*d**5*(d + e*x)**(7/2) + 35*d**4*(d + e*x)**(9/2)/9 - 35*d**3*(d + e*x
)**(11/2)/11 + 21*d**2*(d + e*x)**(13/2)/13 - 7*d*(d + e*x)**(15/2)/15 + (d + e*x)**(17/2)/17)/e**8 + 6*B*b**6
*d**2*(d**8*(d + e*x)**(3/2)/3 - 8*d**7*(d + e*x)**(5/2)/5 + 4*d**6*(d + e*x)**(7/2) - 56*d**5*(d + e*x)**(9/2
)/9 + 70*d**4*(d + e*x)**(11/2)/11 - 56*d**3*(d + e*x)**(13/2)/13 + 28*d**2*(d + e*x)**(15/2)/15 - 8*d*(d + e*
x)**(17/2)/17 + (d + e*x)**(19/2)/19)/e**8 + 6*B*b**6*d*(-d**9*(d + e*x)**(3/2)/3 + 9*d**8*(d + e*x)**(5/2)/5
- 36*d**7*(d + e*x)**(7/2)/7 + 28*d**6*(d + e*x)**(9/2)/3 - 126*d**5*(d + e*x)**(11/2)/11 + 126*d**4*(d + e*x)
**(13/2)/13 - 28*d**3*(d + e*x)**(15/2)/5 + 36*d**2*(d + e*x)**(17/2)/17 - 9*d*(d + e*x)**(19/2)/19 + (d + e*x
)**(21/2)/21)/e**8 + 2*B*b**6*(d**10*(d + e*x)**(3/2)/3 - 2*d**9*(d + e*x)**(5/2) + 45*d**8*(d + e*x)**(7/2)/7
- 40*d**7*(d + e*x)**(9/2)/3 + 210*d**6*(d + e*x)**(11/2)/11 - 252*d**5*(d + e*x)**(13/2)/13 + 14*d**4*(d + e
*x)**(15/2) - 120*d**3*(d + e*x)**(17/2)/17 + 45*d**2*(d + e*x)**(19/2)/19 - 10*d*(d + e*x)**(21/2)/21 + (d +
e*x)**(23/2)/23)/e**8
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