\(\int (a+b x) (d+e x)^6 (a^2+2 a b x+b^2 x^2)^{3/2} \, dx\) [1969]

Optimal result

Integrand size = 33, antiderivative size = 254 \[ \int (a+b x) (d+e x)^6 \left (a^2+2 a b x+b^2 x^2\right )^{3/2} \, dx=\frac {(b d-a e)^4 (d+e x)^7 \sqrt {a^2+2 a b x+b^2 x^2}}{7 e^5 (a+b x)}-\frac {b (b d-a e)^3 (d+e x)^8 \sqrt {a^2+2 a b x+b^2 x^2}}{2 e^5 (a+b x)}+\frac {2 b^2 (b d-a e)^2 (d+e x)^9 \sqrt {a^2+2 a b x+b^2 x^2}}{3 e^5 (a+b x)}-\frac {2 b^3 (b d-a e) (d+e x)^{10} \sqrt {a^2+2 a b x+b^2 x^2}}{5 e^5 (a+b x)}+\frac {b^4 (d+e x)^{11} \sqrt {a^2+2 a b x+b^2 x^2}}{11 e^5 (a+b x)} \]

[Out]

1/7*(-a*e+b*d)^4*(e*x+d)^7*((b*x+a)^2)^(1/2)/e^5/(b*x+a)-1/2*b*(-a*e+b*d)^3*(e*x+d)^8*((b*x+a)^2)^(1/2)/e^5/(b
*x+a)+2/3*b^2*(-a*e+b*d)^2*(e*x+d)^9*((b*x+a)^2)^(1/2)/e^5/(b*x+a)-2/5*b^3*(-a*e+b*d)*(e*x+d)^10*((b*x+a)^2)^(
1/2)/e^5/(b*x+a)+1/11*b^4*(e*x+d)^11*((b*x+a)^2)^(1/2)/e^5/(b*x+a)

Rubi [A] (verified)

Time = 0.21 (sec) , antiderivative size = 254, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {784, 21, 45} \[ \int (a+b x) (d+e x)^6 \left (a^2+2 a b x+b^2 x^2\right )^{3/2} \, dx=\frac {2 b^2 \sqrt {a^2+2 a b x+b^2 x^2} (d+e x)^9 (b d-a e)^2}{3 e^5 (a+b x)}-\frac {b \sqrt {a^2+2 a b x+b^2 x^2} (d+e x)^8 (b d-a e)^3}{2 e^5 (a+b x)}+\frac {\sqrt {a^2+2 a b x+b^2 x^2} (d+e x)^7 (b d-a e)^4}{7 e^5 (a+b x)}+\frac {b^4 \sqrt {a^2+2 a b x+b^2 x^2} (d+e x)^{11}}{11 e^5 (a+b x)}-\frac {2 b^3 \sqrt {a^2+2 a b x+b^2 x^2} (d+e x)^{10} (b d-a e)}{5 e^5 (a+b x)} \]

[In]

Int[(a + b*x)*(d + e*x)^6*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]

[Out]

((b*d - a*e)^4*(d + e*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^5*(a + b*x)) - (b*(b*d - a*e)^3*(d + e*x)^8*Sqr
t[a^2 + 2*a*b*x + b^2*x^2])/(2*e^5*(a + b*x)) + (2*b^2*(b*d - a*e)^2*(d + e*x)^9*Sqrt[a^2 + 2*a*b*x + b^2*x^2]
)/(3*e^5*(a + b*x)) - (2*b^3*(b*d - a*e)*(d + e*x)^10*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^5*(a + b*x)) + (b^4*
(d + e*x)^11*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^5*(a + b*x))

Rule 21

Int[(u_.)*((a_) + (b_.)*(v_))^(m_.)*((c_) + (d_.)*(v_))^(n_.), x_Symbol] :> Dist[(b/d)^m, Int[u*(c + d*v)^(m +
n), x], x] /; FreeQ[{a, b, c, d, n}, x] && EqQ[b*c - a*d, 0] && IntegerQ[m] && ( !IntegerQ[n] || SimplerQ[c +
d*x, a + b*x])

Rule 45

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d
*x)^n, x], x] /; FreeQ[{a, b, c, d, n}, x] && NeQ[b*c - a*d, 0] && IGtQ[m, 0] && ( !IntegerQ[n] || (EqQ[c, 0]
&& LeQ[7*m + 4*n + 4, 0]) || LtQ[9*m + 5*(n + 1), 0] || GtQ[m + n + 2, 0])

Rule 784

Int[((d_.) + (e_.)*(x_))^(m_.)*((f_.) + (g_.)*(x_))*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Dis
t[(a + b*x + c*x^2)^FracPart[p]/(c^IntPart[p]*(b/2 + c*x)^(2*FracPart[p])), Int[(d + e*x)^m*(f + g*x)*(b/2 + c
*x)^(2*p), x], x] /; FreeQ[{a, b, c, d, e, f, g, m}, x] && EqQ[b^2 - 4*a*c, 0]

Rubi steps \begin{align*} \text {integral}& = \frac {\sqrt {a^2+2 a b x+b^2 x^2} \int (a+b x) \left (a b+b^2 x\right )^3 (d+e x)^6 \, dx}{b^2 \left (a b+b^2 x\right )} \\ & = \frac {\left (b \sqrt {a^2+2 a b x+b^2 x^2}\right ) \int (a+b x)^4 (d+e x)^6 \, dx}{a b+b^2 x} \\ & = \frac {\left (b \sqrt {a^2+2 a b x+b^2 x^2}\right ) \int \left (\frac {(-b d+a e)^4 (d+e x)^6}{e^4}-\frac {4 b (b d-a e)^3 (d+e x)^7}{e^4}+\frac {6 b^2 (b d-a e)^2 (d+e x)^8}{e^4}-\frac {4 b^3 (b d-a e) (d+e x)^9}{e^4}+\frac {b^4 (d+e x)^{10}}{e^4}\right ) \, dx}{a b+b^2 x} \\ & = \frac {(b d-a e)^4 (d+e x)^7 \sqrt {a^2+2 a b x+b^2 x^2}}{7 e^5 (a+b x)}-\frac {b (b d-a e)^3 (d+e x)^8 \sqrt {a^2+2 a b x+b^2 x^2}}{2 e^5 (a+b x)}+\frac {2 b^2 (b d-a e)^2 (d+e x)^9 \sqrt {a^2+2 a b x+b^2 x^2}}{3 e^5 (a+b x)}-\frac {2 b^3 (b d-a e) (d+e x)^{10} \sqrt {a^2+2 a b x+b^2 x^2}}{5 e^5 (a+b x)}+\frac {b^4 (d+e x)^{11} \sqrt {a^2+2 a b x+b^2 x^2}}{11 e^5 (a+b x)} \\ \end{align*}

Mathematica [A] (verified)

Time = 1.08 (sec) , antiderivative size = 377, normalized size of antiderivative = 1.48 \[ \int (a+b x) (d+e x)^6 \left (a^2+2 a b x+b^2 x^2\right )^{3/2} \, dx=\frac {x \sqrt {(a+b x)^2} \left (330 a^4 \left (7 d^6+21 d^5 e x+35 d^4 e^2 x^2+35 d^3 e^3 x^3+21 d^2 e^4 x^4+7 d e^5 x^5+e^6 x^6\right )+165 a^3 b x \left (28 d^6+112 d^5 e x+210 d^4 e^2 x^2+224 d^3 e^3 x^3+140 d^2 e^4 x^4+48 d e^5 x^5+7 e^6 x^6\right )+55 a^2 b^2 x^2 \left (84 d^6+378 d^5 e x+756 d^4 e^2 x^2+840 d^3 e^3 x^3+540 d^2 e^4 x^4+189 d e^5 x^5+28 e^6 x^6\right )+11 a b^3 x^3 \left (210 d^6+1008 d^5 e x+2100 d^4 e^2 x^2+2400 d^3 e^3 x^3+1575 d^2 e^4 x^4+560 d e^5 x^5+84 e^6 x^6\right )+b^4 x^4 \left (462 d^6+2310 d^5 e x+4950 d^4 e^2 x^2+5775 d^3 e^3 x^3+3850 d^2 e^4 x^4+1386 d e^5 x^5+210 e^6 x^6\right )\right )}{2310 (a+b x)} \]

[In]

Integrate[(a + b*x)*(d + e*x)^6*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]

[Out]

(x*Sqrt[(a + b*x)^2]*(330*a^4*(7*d^6 + 21*d^5*e*x + 35*d^4*e^2*x^2 + 35*d^3*e^3*x^3 + 21*d^2*e^4*x^4 + 7*d*e^5
*x^5 + e^6*x^6) + 165*a^3*b*x*(28*d^6 + 112*d^5*e*x + 210*d^4*e^2*x^2 + 224*d^3*e^3*x^3 + 140*d^2*e^4*x^4 + 48
*d*e^5*x^5 + 7*e^6*x^6) + 55*a^2*b^2*x^2*(84*d^6 + 378*d^5*e*x + 756*d^4*e^2*x^2 + 840*d^3*e^3*x^3 + 540*d^2*e
^4*x^4 + 189*d*e^5*x^5 + 28*e^6*x^6) + 11*a*b^3*x^3*(210*d^6 + 1008*d^5*e*x + 2100*d^4*e^2*x^2 + 2400*d^3*e^3*
x^3 + 1575*d^2*e^4*x^4 + 560*d*e^5*x^5 + 84*e^6*x^6) + b^4*x^4*(462*d^6 + 2310*d^5*e*x + 4950*d^4*e^2*x^2 + 57
75*d^3*e^3*x^3 + 3850*d^2*e^4*x^4 + 1386*d*e^5*x^5 + 210*e^6*x^6)))/(2310*(a + b*x))

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(488\) vs. \(2(189)=378\).

Time = 0.79 (sec) , antiderivative size = 489, normalized size of antiderivative = 1.93

method	result	size
gosper	\(\frac {x \left (210 b^{4} e^{6} x^{10}+924 x^{9} b^{3} a \,e^{6}+1386 x^{9} b^{4} d \,e^{5}+1540 x^{8} a^{2} b^{2} e^{6}+6160 x^{8} a \,b^{3} d \,e^{5}+3850 x^{8} b^{4} d^{2} e^{4}+1155 x^{7} b \,a^{3} e^{6}+10395 x^{7} b^{2} a^{2} d \,e^{5}+17325 x^{7} b^{3} a \,d^{2} e^{4}+5775 x^{7} b^{4} d^{3} e^{3}+330 x^{6} a^{4} e^{6}+7920 x^{6} b \,a^{3} d \,e^{5}+29700 x^{6} b^{2} a^{2} d^{2} e^{4}+26400 x^{6} b^{3} a \,d^{3} e^{3}+4950 x^{6} b^{4} d^{4} e^{2}+2310 a^{4} d \,e^{5} x^{5}+23100 a^{3} b \,d^{2} e^{4} x^{5}+46200 a^{2} b^{2} d^{3} e^{3} x^{5}+23100 a \,b^{3} d^{4} e^{2} x^{5}+2310 b^{4} d^{5} e \,x^{5}+6930 x^{4} a^{4} d^{2} e^{4}+36960 x^{4} b \,a^{3} d^{3} e^{3}+41580 x^{4} b^{2} a^{2} d^{4} e^{2}+11088 x^{4} b^{3} a \,d^{5} e +462 x^{4} b^{4} d^{6}+11550 a^{4} d^{3} e^{3} x^{3}+34650 a^{3} b \,d^{4} e^{2} x^{3}+20790 a^{2} b^{2} d^{5} e \,x^{3}+2310 a \,b^{3} d^{6} x^{3}+11550 a^{4} d^{4} e^{2} x^{2}+18480 a^{3} b \,d^{5} e \,x^{2}+4620 a^{2} b^{2} d^{6} x^{2}+6930 a^{4} d^{5} e x +4620 a^{3} b \,d^{6} x +2310 a^{4} d^{6}\right ) \left (\left (b x +a \right )^{2}\right )^{\frac {3}{2}}}{2310 \left (b x +a \right )^{3}}\)	\(489\)
default	\(\frac {x \left (210 b^{4} e^{6} x^{10}+924 x^{9} b^{3} a \,e^{6}+1386 x^{9} b^{4} d \,e^{5}+1540 x^{8} a^{2} b^{2} e^{6}+6160 x^{8} a \,b^{3} d \,e^{5}+3850 x^{8} b^{4} d^{2} e^{4}+1155 x^{7} b \,a^{3} e^{6}+10395 x^{7} b^{2} a^{2} d \,e^{5}+17325 x^{7} b^{3} a \,d^{2} e^{4}+5775 x^{7} b^{4} d^{3} e^{3}+330 x^{6} a^{4} e^{6}+7920 x^{6} b \,a^{3} d \,e^{5}+29700 x^{6} b^{2} a^{2} d^{2} e^{4}+26400 x^{6} b^{3} a \,d^{3} e^{3}+4950 x^{6} b^{4} d^{4} e^{2}+2310 a^{4} d \,e^{5} x^{5}+23100 a^{3} b \,d^{2} e^{4} x^{5}+46200 a^{2} b^{2} d^{3} e^{3} x^{5}+23100 a \,b^{3} d^{4} e^{2} x^{5}+2310 b^{4} d^{5} e \,x^{5}+6930 x^{4} a^{4} d^{2} e^{4}+36960 x^{4} b \,a^{3} d^{3} e^{3}+41580 x^{4} b^{2} a^{2} d^{4} e^{2}+11088 x^{4} b^{3} a \,d^{5} e +462 x^{4} b^{4} d^{6}+11550 a^{4} d^{3} e^{3} x^{3}+34650 a^{3} b \,d^{4} e^{2} x^{3}+20790 a^{2} b^{2} d^{5} e \,x^{3}+2310 a \,b^{3} d^{6} x^{3}+11550 a^{4} d^{4} e^{2} x^{2}+18480 a^{3} b \,d^{5} e \,x^{2}+4620 a^{2} b^{2} d^{6} x^{2}+6930 a^{4} d^{5} e x +4620 a^{3} b \,d^{6} x +2310 a^{4} d^{6}\right ) \left (\left (b x +a \right )^{2}\right )^{\frac {3}{2}}}{2310 \left (b x +a \right )^{3}}\)	\(489\)
risch	\(\frac {\sqrt {\left (b x +a \right )^{2}}\, b^{4} e^{6} x^{11}}{11 b x +11 a}+\frac {\sqrt {\left (b x +a \right )^{2}}\, \left (4 b^{3} a \,e^{6}+6 b^{4} d \,e^{5}\right ) x^{10}}{10 b x +10 a}+\frac {\sqrt {\left (b x +a \right )^{2}}\, \left (6 a^{2} b^{2} e^{6}+24 a \,b^{3} d \,e^{5}+15 b^{4} d^{2} e^{4}\right ) x^{9}}{9 b x +9 a}+\frac {\sqrt {\left (b x +a \right )^{2}}\, \left (4 b \,a^{3} e^{6}+36 b^{2} a^{2} d \,e^{5}+60 b^{3} a \,d^{2} e^{4}+20 b^{4} d^{3} e^{3}\right ) x^{8}}{8 b x +8 a}+\frac {\sqrt {\left (b x +a \right )^{2}}\, \left (a^{4} e^{6}+24 b \,a^{3} d \,e^{5}+90 b^{2} a^{2} d^{2} e^{4}+80 b^{3} a \,d^{3} e^{3}+15 b^{4} d^{4} e^{2}\right ) x^{7}}{7 b x +7 a}+\frac {\sqrt {\left (b x +a \right )^{2}}\, \left (6 a^{4} d \,e^{5}+60 b \,a^{3} d^{2} e^{4}+120 b^{2} a^{2} d^{3} e^{3}+60 b^{3} a \,d^{4} e^{2}+6 b^{4} d^{5} e \right ) x^{6}}{6 b x +6 a}+\frac {\sqrt {\left (b x +a \right )^{2}}\, \left (15 a^{4} d^{2} e^{4}+80 b \,a^{3} d^{3} e^{3}+90 b^{2} a^{2} d^{4} e^{2}+24 b^{3} a \,d^{5} e +b^{4} d^{6}\right ) x^{5}}{5 b x +5 a}+\frac {\sqrt {\left (b x +a \right )^{2}}\, \left (20 a^{4} d^{3} e^{3}+60 b \,a^{3} d^{4} e^{2}+36 b^{2} a^{2} d^{5} e +4 b^{3} a \,d^{6}\right ) x^{4}}{4 b x +4 a}+\frac {\sqrt {\left (b x +a \right )^{2}}\, \left (15 a^{4} d^{4} e^{2}+24 b \,a^{3} d^{5} e +6 b^{2} a^{2} d^{6}\right ) x^{3}}{3 b x +3 a}+\frac {\sqrt {\left (b x +a \right )^{2}}\, \left (6 a^{4} d^{5} e +4 b \,a^{3} d^{6}\right ) x^{2}}{2 b x +2 a}+\frac {\sqrt {\left (b x +a \right )^{2}}\, a^{4} d^{6} x}{b x +a}\)	\(603\)

[In]

int((b*x+a)*(e*x+d)^6*(b^2*x^2+2*a*b*x+a^2)^(3/2),x,method=_RETURNVERBOSE)

[Out]

1/2310*x*(210*b^4*e^6*x^10+924*a*b^3*e^6*x^9+1386*b^4*d*e^5*x^9+1540*a^2*b^2*e^6*x^8+6160*a*b^3*d*e^5*x^8+3850
*b^4*d^2*e^4*x^8+1155*a^3*b*e^6*x^7+10395*a^2*b^2*d*e^5*x^7+17325*a*b^3*d^2*e^4*x^7+5775*b^4*d^3*e^3*x^7+330*a
^4*e^6*x^6+7920*a^3*b*d*e^5*x^6+29700*a^2*b^2*d^2*e^4*x^6+26400*a*b^3*d^3*e^3*x^6+4950*b^4*d^4*e^2*x^6+2310*a^
4*d*e^5*x^5+23100*a^3*b*d^2*e^4*x^5+46200*a^2*b^2*d^3*e^3*x^5+23100*a*b^3*d^4*e^2*x^5+2310*b^4*d^5*e*x^5+6930*
a^4*d^2*e^4*x^4+36960*a^3*b*d^3*e^3*x^4+41580*a^2*b^2*d^4*e^2*x^4+11088*a*b^3*d^5*e*x^4+462*b^4*d^6*x^4+11550*
a^4*d^3*e^3*x^3+34650*a^3*b*d^4*e^2*x^3+20790*a^2*b^2*d^5*e*x^3+2310*a*b^3*d^6*x^3+11550*a^4*d^4*e^2*x^2+18480
*a^3*b*d^5*e*x^2+4620*a^2*b^2*d^6*x^2+6930*a^4*d^5*e*x+4620*a^3*b*d^6*x+2310*a^4*d^6)*((b*x+a)^2)^(3/2)/(b*x+a
)^3

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 418 vs. \(2 (189) = 378\).

Time = 0.36 (sec) , antiderivative size = 418, normalized size of antiderivative = 1.65 \[ \int (a+b x) (d+e x)^6 \left (a^2+2 a b x+b^2 x^2\right )^{3/2} \, dx=\frac {1}{11} \, b^{4} e^{6} x^{11} + a^{4} d^{6} x + \frac {1}{5} \, {\left (3 \, b^{4} d e^{5} + 2 \, a b^{3} e^{6}\right )} x^{10} + \frac {1}{3} \, {\left (5 \, b^{4} d^{2} e^{4} + 8 \, a b^{3} d e^{5} + 2 \, a^{2} b^{2} e^{6}\right )} x^{9} + \frac {1}{2} \, {\left (5 \, b^{4} d^{3} e^{3} + 15 \, a b^{3} d^{2} e^{4} + 9 \, a^{2} b^{2} d e^{5} + a^{3} b e^{6}\right )} x^{8} + \frac {1}{7} \, {\left (15 \, b^{4} d^{4} e^{2} + 80 \, a b^{3} d^{3} e^{3} + 90 \, a^{2} b^{2} d^{2} e^{4} + 24 \, a^{3} b d e^{5} + a^{4} e^{6}\right )} x^{7} + {\left (b^{4} d^{5} e + 10 \, a b^{3} d^{4} e^{2} + 20 \, a^{2} b^{2} d^{3} e^{3} + 10 \, a^{3} b d^{2} e^{4} + a^{4} d e^{5}\right )} x^{6} + \frac {1}{5} \, {\left (b^{4} d^{6} + 24 \, a b^{3} d^{5} e + 90 \, a^{2} b^{2} d^{4} e^{2} + 80 \, a^{3} b d^{3} e^{3} + 15 \, a^{4} d^{2} e^{4}\right )} x^{5} + {\left (a b^{3} d^{6} + 9 \, a^{2} b^{2} d^{5} e + 15 \, a^{3} b d^{4} e^{2} + 5 \, a^{4} d^{3} e^{3}\right )} x^{4} + {\left (2 \, a^{2} b^{2} d^{6} + 8 \, a^{3} b d^{5} e + 5 \, a^{4} d^{4} e^{2}\right )} x^{3} + {\left (2 \, a^{3} b d^{6} + 3 \, a^{4} d^{5} e\right )} x^{2} \]

[In]

integrate((b*x+a)*(e*x+d)^6*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm="fricas")

[Out]

1/11*b^4*e^6*x^11 + a^4*d^6*x + 1/5*(3*b^4*d*e^5 + 2*a*b^3*e^6)*x^10 + 1/3*(5*b^4*d^2*e^4 + 8*a*b^3*d*e^5 + 2*
a^2*b^2*e^6)*x^9 + 1/2*(5*b^4*d^3*e^3 + 15*a*b^3*d^2*e^4 + 9*a^2*b^2*d*e^5 + a^3*b*e^6)*x^8 + 1/7*(15*b^4*d^4*
e^2 + 80*a*b^3*d^3*e^3 + 90*a^2*b^2*d^2*e^4 + 24*a^3*b*d*e^5 + a^4*e^6)*x^7 + (b^4*d^5*e + 10*a*b^3*d^4*e^2 +
20*a^2*b^2*d^3*e^3 + 10*a^3*b*d^2*e^4 + a^4*d*e^5)*x^6 + 1/5*(b^4*d^6 + 24*a*b^3*d^5*e + 90*a^2*b^2*d^4*e^2 +
80*a^3*b*d^3*e^3 + 15*a^4*d^2*e^4)*x^5 + (a*b^3*d^6 + 9*a^2*b^2*d^5*e + 15*a^3*b*d^4*e^2 + 5*a^4*d^3*e^3)*x^4
+ (2*a^2*b^2*d^6 + 8*a^3*b*d^5*e + 5*a^4*d^4*e^2)*x^3 + (2*a^3*b*d^6 + 3*a^4*d^5*e)*x^2

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 29211 vs. \(2 (182) = 364\).

Time = 1.79 (sec) , antiderivative size = 29211, normalized size of antiderivative = 115.00 \[ \int (a+b x) (d+e x)^6 \left (a^2+2 a b x+b^2 x^2\right )^{3/2} \, dx=\text {Too large to display} \]

[In]

integrate((b*x+a)*(e*x+d)**6*(b**2*x**2+2*a*b*x+a**2)**(3/2),x)

[Out]

Piecewise((sqrt(a**2 + 2*a*b*x + b**2*x**2)*(b**3*e**6*x**10/11 + x**9*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10
*b**2) + x**8*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15
*b**5*d**2*e**4)/(9*b**2) + x**7*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5
*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e*
*6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b**2) + x**6*(5*a**4*b*e**6 +
60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a
*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**
2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17
*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*
e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b**2) + x**5*(a**5*e**6 + 30*a**4*b*d*e**5 + 15
0*a**3*b**2*d**2*e**4 + 200*a**2*b**3*d**3*e**3 - 7*a**2*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34
*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e
**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b**2)
+ 75*a*b**4*d**4*e**2 - 13*a*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**
2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b*
*2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**
5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e
**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b
) + 6*b**5*d**5*e)/(6*b**2) + x**4*(6*a**5*d*e**5 + 75*a**4*b*d**2*e**4 + 200*a**3*b**2*d**3*e**3 + 150*a**2*b
**3*d**4*e**2 - 6*a**2*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*
e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 1
00*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**
5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11
+ 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b**2) +
30*a*b**4*d**5*e - 11*a*(a**5*e**6 + 30*a**4*b*d*e**5 + 150*a**3*b**2*d**2*e**4 + 200*a**2*b**3*d**3*e**3 - 7*
a**2*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b*
*4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b
) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b**2) + 75*a*b**4*d**4*e**2 - 13*a*(5*a**4*b*e**6 + 60*a*
*3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*
e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6
+ 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(10
0*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/
(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b) + 6*b**5*d**5*e)/(6*b) + b**5*d**6)/(5*b**2) + x**
3*(15*a**5*d**2*e**4 + 100*a**4*b*d**3*e**3 + 150*a**3*b**2*d**4*e**2 + 60*a**2*b**3*d**5*e - 5*a**2*(a**5*e**
6 + 30*a**4*b*d*e**5 + 150*a**3*b**2*d**2*e**4 + 200*a**2*b**3*d**3*e**3 - 7*a**2*(10*a**3*b**2*e**6 + 60*a**2
*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**
3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20
*b**5*d**3*e**3)/(8*b**2) + 75*a*b**4*d**4*e**2 - 13*a*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d*
*2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) +
15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(
34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d
*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b)
+ 15*b**5*d**4*e**2)/(7*b) + 6*b**5*d**5*e)/(6*b**2) + 5*a*b**4*d**6 - 9*a*(6*a**5*d*e**5 + 75*a**4*b*d**2*e**
4 + 200*a**3*b**2*d**3*e**3 + 150*a**2*b**3*d**4*e**2 - 6*a**2*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2
*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/
(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 -
9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*
a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3
)/(8*b) + 15*b**5*d**4*e**2)/(7*b**2) + 30*a*b**4*d**5*e - 11*a*(a**5*e**6 + 30*a**4*b*d*e**5 + 150*a**3*b**2*
d**2*e**4 + 200*a**2*b**3*d**3*e**3 - 7*a**2*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6
/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(
34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b**2) + 75*a*b**4
*d**4*e**2 - 13*a*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/
11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*
b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(1
0*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b
**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b) + 6*b**5*d
**5*e)/(6*b) + b**5*d**6)/(5*b))/(4*b**2) + x**2*(20*a**5*d**3*e**3 + 75*a**4*b*d**4*e**2 + 60*a**3*b**2*d**5*
e + 10*a**2*b**3*d**6 - 4*a**2*(6*a**5*d*e**5 + 75*a**4*b*d**2*e**4 + 200*a**3*b**2*d**3*e**3 + 150*a**2*b**3*
d**4*e**2 - 6*a**2*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6
/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a
*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(
10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*
b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b**2) + 30*a
*b**4*d**5*e - 11*a*(a**5*e**6 + 30*a**4*b*d*e**5 + 150*a**3*b**2*d**2*e**4 + 200*a**2*b**3*d**3*e**3 - 7*a**2
*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d
**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) +
15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b**2) + 75*a*b**4*d**4*e**2 - 13*a*(5*a**4*b*e**6 + 60*a**3*b
**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6
/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 6
0*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a*
*2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b
) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b) + 6*b**5*d**5*e)/(6*b) + b**5*d**6)/(5*b**2) - 7*a*(15
*a**5*d**2*e**4 + 100*a**4*b*d**3*e**3 + 150*a**3*b**2*d**4*e**2 + 60*a**2*b**3*d**5*e - 5*a**2*(a**5*e**6 + 3
0*a**4*b*d*e**5 + 150*a**3*b**2*d**2*e**4 + 200*a**2*b**3*d**3*e**3 - 7*a**2*(10*a**3*b**2*e**6 + 60*a**2*b**3
*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**
6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5
*d**3*e**3)/(8*b**2) + 75*a*b**4*d**4*e**2 - 13*a*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e*
*4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b
**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*
b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5
- 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*
b**5*d**4*e**2)/(7*b) + 6*b**5*d**5*e)/(6*b**2) + 5*a*b**4*d**6 - 9*a*(6*a**5*d*e**5 + 75*a**4*b*d**2*e**4 + 2
00*a**3*b**2*d**3*e**3 + 150*a**2*b**3*d**4*e**2 - 6*a**2*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3
*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b
) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**
2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**
4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*
b) + 15*b**5*d**4*e**2)/(7*b**2) + 30*a*b**4*d**5*e - 11*a*(a**5*e**6 + 30*a**4*b*d*e**5 + 150*a**3*b**2*d**2*
e**4 + 200*a**2*b**3*d**3*e**3 - 7*a**2*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 +
6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*
b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b**2) + 75*a*b**4*d**4
*e**2 - 13*a*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 +
30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*
d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**
2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d
*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b) + 6*b**5*d**5*e
)/(6*b) + b**5*d**6)/(5*b))/(4*b))/(3*b**2) + x*(15*a**5*d**4*e**2 + 30*a**4*b*d**5*e + 10*a**3*b**2*d**6 - 3*
a**2*(15*a**5*d**2*e**4 + 100*a**4*b*d**3*e**3 + 150*a**3*b**2*d**4*e**2 + 60*a**2*b**3*d**5*e - 5*a**2*(a**5*
e**6 + 30*a**4*b*d*e**5 + 150*a**3*b**2*d**2*e**4 + 200*a**2*b**3*d**3*e**3 - 7*a**2*(10*a**3*b**2*e**6 + 60*a
**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*
b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) +
20*b**5*d**3*e**3)/(8*b**2) + 75*a*b**4*d**4*e**2 - 13*a*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3
*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b
) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**
2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**
4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*
b) + 15*b**5*d**4*e**2)/(7*b) + 6*b**5*d**5*e)/(6*b**2) + 5*a*b**4*d**6 - 9*a*(6*a**5*d*e**5 + 75*a**4*b*d**2*
e**4 + 200*a**3*b**2*d**3*e**3 + 150*a**2*b**3*d**4*e**2 - 6*a**2*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a
**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**
5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5
- 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 +
30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e
**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b**2) + 30*a*b**4*d**5*e - 11*a*(a**5*e**6 + 30*a**4*b*d*e**5 + 150*a**3*b*
*2*d**2*e**4 + 200*a**2*b**3*d**3*e**3 - 7*a**2*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e
**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*
a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b**2) + 75*a*b
**4*d**4*e**2 - 13*a*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e*
*6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100
*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)
/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 +
6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b) + 6*b**
5*d**5*e)/(6*b) + b**5*d**6)/(5*b))/(4*b**2) - 5*a*(20*a**5*d**3*e**3 + 75*a**4*b*d**4*e**2 + 60*a**3*b**2*d**
5*e + 10*a**2*b**3*d**6 - 4*a**2*(6*a**5*d*e**5 + 75*a**4*b*d**2*e**4 + 200*a**3*b**2*d**3*e**3 + 150*a**2*b**
3*d**4*e**2 - 6*a**2*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e*
*6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100
*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)
/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 +
6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b**2) + 30
*a*b**4*d**5*e - 11*a*(a**5*e**6 + 30*a**4*b*d*e**5 + 150*a**3*b**2*d**2*e**4 + 200*a**2*b**3*d**3*e**3 - 7*a*
*2*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4
*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b)
+ 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b**2) + 75*a*b**4*d**4*e**2 - 13*a*(5*a**4*b*e**6 + 60*a**3
*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e*
*6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 +
60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*
a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9
*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b) + 6*b**5*d**5*e)/(6*b) + b**5*d**6)/(5*b**2) - 7*a*(
15*a**5*d**2*e**4 + 100*a**4*b*d**3*e**3 + 150*a**3*b**2*d**4*e**2 + 60*a**2*b**3*d**5*e - 5*a**2*(a**5*e**6 +
30*a**4*b*d*e**5 + 150*a**3*b**2*d**2*e**4 + 200*a**2*b**3*d**3*e**3 - 7*a**2*(10*a**3*b**2*e**6 + 60*a**2*b*
*3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e
**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b*
*5*d**3*e**3)/(8*b**2) + 75*a*b**4*d**4*e**2 - 13*a*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*
e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15
*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*
a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e*
*5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 1
5*b**5*d**4*e**2)/(7*b) + 6*b**5*d**5*e)/(6*b**2) + 5*a*b**4*d**6 - 9*a*(6*a**5*d*e**5 + 75*a**4*b*d**2*e**4 +
200*a**3*b**2*d**3*e**3 + 150*a**2*b**3*d**4*e**2 - 6*a**2*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b*
*3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10
*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a
**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b
**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(
8*b) + 15*b**5*d**4*e**2)/(7*b**2) + 30*a*b**4*d**5*e - 11*a*(a**5*e**6 + 30*a**4*b*d*e**5 + 150*a**3*b**2*d**
2*e**4 + 200*a**2*b**3*d**3*e**3 - 7*a**2*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11
+ 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*
a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b**2) + 75*a*b**4*d*
*4*e**2 - 13*a*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11
+ 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**
4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b
**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5
*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b) + 6*b**5*d**5
*e)/(6*b) + b**5*d**6)/(5*b))/(4*b))/(3*b))/(2*b**2) + (6*a**5*d**5*e + 5*a**4*b*d**6 - 2*a**2*(20*a**5*d**3*e
**3 + 75*a**4*b*d**4*e**2 + 60*a**3*b**2*d**5*e + 10*a**2*b**3*d**6 - 4*a**2*(6*a**5*d*e**5 + 75*a**4*b*d**2*e
**4 + 200*a**3*b**2*d**3*e**3 + 150*a**2*b**3*d**4*e**2 - 6*a**2*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a*
*2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5
)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5
- 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 3
0*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e*
*3)/(8*b) + 15*b**5*d**4*e**2)/(7*b**2) + 30*a*b**4*d**5*e - 11*a*(a**5*e**6 + 30*a**4*b*d*e**5 + 150*a**3*b**
2*d**2*e**4 + 200*a**2*b**3*d**3*e**3 - 7*a**2*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e*
*6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a
*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b**2) + 75*a*b*
*4*d**4*e**2 - 13*a*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**
6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*
a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/
(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6
*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b) + 6*b**5
*d**5*e)/(6*b) + b**5*d**6)/(5*b**2) - 7*a*(15*a**5*d**2*e**4 + 100*a**4*b*d**3*e**3 + 150*a**3*b**2*d**4*e**2
+ 60*a**2*b**3*d**5*e - 5*a**2*(a**5*e**6 + 30*a**4*b*d*e**5 + 150*a**3*b**2*d**2*e**4 + 200*a**2*b**3*d**3*e
**3 - 7*a**2*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) +
75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**
5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b**2) + 75*a*b**4*d**4*e**2 - 13*a*(5*a**4*b*e**6
+ 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34
*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b
**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 -
17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**
2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b) + 6*b**5*d**5*e)/(6*b**2) + 5*a*b**4*d**6
- 9*a*(6*a**5*d*e**5 + 75*a**4*b*d**2*e**4 + 200*a**3*b**2*d**3*e**3 + 150*a**2*b**3*d**4*e**2 - 6*a**2*(5*a**
4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 -
19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(1
0*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2
*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*
b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b**2) + 30*a*b**4*d**5*e - 11*a*(a**5
*e**6 + 30*a**4*b*d*e**5 + 150*a**3*b**2*d**2*e**4 + 200*a**2*b**3*d**3*e**3 - 7*a**2*(10*a**3*b**2*e**6 + 60*
a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2
*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b)
+ 20*b**5*d**3*e**3)/(8*b**2) + 75*a*b**4*d**4*e**2 - 13*a*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**
3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*
b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a*
*2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b*
*4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8
*b) + 15*b**5*d**4*e**2)/(7*b) + 6*b**5*d**5*e)/(6*b) + b**5*d**6)/(5*b))/(4*b))/(3*b**2) - 3*a*(15*a**5*d**4*
e**2 + 30*a**4*b*d**5*e + 10*a**3*b**2*d**6 - 3*a**2*(15*a**5*d**2*e**4 + 100*a**4*b*d**3*e**3 + 150*a**3*b**2
*d**4*e**2 + 60*a**2*b**3*d**5*e - 5*a**2*(a**5*e**6 + 30*a**4*b*d*e**5 + 150*a**3*b**2*d**2*e**4 + 200*a**2*b
**3*d**3*e**3 - 7*a**2*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(
10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*
b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b**2) + 75*a*b**4*d**4*e**2 - 13*a*(5*a
**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5
- 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*
(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d*
*2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 1
5*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b) + 6*b**5*d**5*e)/(6*b**2) + 5*a*
b**4*d**6 - 9*a*(6*a**5*d*e**5 + 75*a**4*b*d**2*e**4 + 200*a**3*b**2*d**3*e**3 + 150*a**2*b**3*d**4*e**2 - 6*a
**2*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4
*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3
- 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a
*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(1
0*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b**2) + 30*a*b**4*d**5*e -
11*a*(a**5*e**6 + 30*a**4*b*d*e**5 + 150*a**3*b**2*d**2*e**4 + 200*a**2*b**3*d**3*e**3 - 7*a**2*(10*a**3*b**2*
e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a
*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e*
*4)/(9*b) + 20*b**5*d**3*e**3)/(8*b**2) + 75*a*b**4*d**4*e**2 - 13*a*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 15
0*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*
e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e
**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11
+ 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**
3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b) + 6*b**5*d**5*e)/(6*b) + b**5*d**6)/(5*b))/(4*b**2) - 5*a*(20*a**5*d*
*3*e**3 + 75*a**4*b*d**4*e**2 + 60*a**3*b**2*d**5*e + 10*a**2*b**3*d**6 - 4*a**2*(6*a**5*d*e**5 + 75*a**4*b*d*
*2*e**4 + 200*a**3*b**2*d**3*e**3 + 150*a**2*b**3*d**4*e**2 - 6*a**2*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 15
0*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*
e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e
**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11
+ 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**
3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b**2) + 30*a*b**4*d**5*e - 11*a*(a**5*e**6 + 30*a**4*b*d*e**5 + 150*a**3
*b**2*d**2*e**4 + 200*a**2*b**3*d**3*e**3 - 7*a**2*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**
4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 -
19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b**2) + 75*
a*b**4*d**4*e**2 - 13*a*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3
*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) +
100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e*
*5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11
+ 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b) + 6*
b**5*d**5*e)/(6*b) + b**5*d**6)/(5*b**2) - 7*a*(15*a**5*d**2*e**4 + 100*a**4*b*d**3*e**3 + 150*a**3*b**2*d**4*
e**2 + 60*a**2*b**3*d**5*e - 5*a**2*(a**5*e**6 + 30*a**4*b*d*e**5 + 150*a**3*b**2*d**2*e**4 + 200*a**2*b**3*d*
*3*e**3 - 7*a**2*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**
2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d
*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b**2) + 75*a*b**4*d**4*e**2 - 13*a*(5*a**4*b*
e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a
*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a*
*3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**
4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5
*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b) + 6*b**5*d**5*e)/(6*b**2) + 5*a*b**4*d
**6 - 9*a*(6*a**5*d*e**5 + 75*a**4*b*d**2*e**4 + 200*a**3*b**2*d**3*e**3 + 150*a**2*b**3*d**4*e**2 - 6*a**2*(5
*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**
5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*
a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*
d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) +
15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b**2) + 30*a*b**4*d**5*e - 11*a*(
a**5*e**6 + 30*a**4*b*d*e**5 + 150*a**3*b**2*d**2*e**4 + 200*a**2*b**3*d**3*e**3 - 7*a**2*(10*a**3*b**2*e**6 +
60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*
a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9
*b) + 20*b**5*d**3*e**3)/(8*b**2) + 75*a*b**4*d**4*e**2 - 13*a*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2
*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/
(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 -
9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*
a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3
)/(8*b) + 15*b**5*d**4*e**2)/(7*b) + 6*b**5*d**5*e)/(6*b) + b**5*d**6)/(5*b))/(4*b))/(3*b))/(2*b))/b**2) + (a/
b + x)*(a**5*d**6 - a**2*(15*a**5*d**4*e**2 + 30*a**4*b*d**5*e + 10*a**3*b**2*d**6 - 3*a**2*(15*a**5*d**2*e**4
+ 100*a**4*b*d**3*e**3 + 150*a**3*b**2*d**4*e**2 + 60*a**2*b**3*d**5*e - 5*a**2*(a**5*e**6 + 30*a**4*b*d*e**5
+ 150*a**3*b**2*d**2*e**4 + 200*a**2*b**3*d**3*e**3 - 7*a**2*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**
2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**
4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*
b**2) + 75*a*b**4*d**4*e**2 - 13*a*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(10
0*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/
(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 +
6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b
**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)
/(7*b) + 6*b**5*d**5*e)/(6*b**2) + 5*a*b**4*d**6 - 9*a*(6*a**5*d*e**5 + 75*a**4*b*d**2*e**4 + 200*a**3*b**2*d*
*3*e**3 + 150*a**2*b**3*d**4*e**2 - 6*a**2*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*
a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**
2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e*
*6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a
*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d*
*4*e**2)/(7*b**2) + 30*a*b**4*d**5*e - 11*a*(a**5*e**6 + 30*a**4*b*d*e**5 + 150*a**3*b**2*d**2*e**4 + 200*a**2
*b**3*d**3*e**3 - 7*a**2*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)
/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 +
6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b**2) + 75*a*b**4*d**4*e**2 - 13*a*(5
*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**
5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*
a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*
d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) +
15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b) + 6*b**5*d**5*e)/(6*b) + b**5*
d**6)/(5*b))/(4*b**2) - 5*a*(20*a**5*d**3*e**3 + 75*a**4*b*d**4*e**2 + 60*a**3*b**2*d**5*e + 10*a**2*b**3*d**6
- 4*a**2*(6*a**5*d*e**5 + 75*a**4*b*d**2*e**4 + 200*a**3*b**2*d**3*e**3 + 150*a**2*b**3*d**4*e**2 - 6*a**2*(5
*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**
5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*
a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*
d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) +
15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b**2) + 30*a*b**4*d**5*e - 11*a*(
a**5*e**6 + 30*a**4*b*d*e**5 + 150*a**3*b**2*d**2*e**4 + 200*a**2*b**3*d**3*e**3 - 7*a**2*(10*a**3*b**2*e**6 +
60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*
a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9
*b) + 20*b**5*d**3*e**3)/(8*b**2) + 75*a*b**4*d**4*e**2 - 13*a*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2
*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/
(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 -
9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*
a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3
)/(8*b) + 15*b**5*d**4*e**2)/(7*b) + 6*b**5*d**5*e)/(6*b) + b**5*d**6)/(5*b**2) - 7*a*(15*a**5*d**2*e**4 + 100
*a**4*b*d**3*e**3 + 150*a**3*b**2*d**4*e**2 + 60*a**2*b**3*d**5*e - 5*a**2*(a**5*e**6 + 30*a**4*b*d*e**5 + 150
*a**3*b**2*d**2*e**4 + 200*a**2*b**3*d**3*e**3 - 7*a**2*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*
a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e*
*5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b**2)
+ 75*a*b**4*d**4*e**2 - 13*a*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2
*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**
2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5
*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e*
*6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b)
+ 6*b**5*d**5*e)/(6*b**2) + 5*a*b**4*d**6 - 9*a*(6*a**5*d*e**5 + 75*a**4*b*d**2*e**4 + 200*a**3*b**2*d**3*e**
3 + 150*a**2*b**3*d**4*e**2 - 6*a**2*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(
100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4
)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11
+ 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a
*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**
2)/(7*b**2) + 30*a*b**4*d**5*e - 11*a*(a**5*e**6 + 30*a**4*b*d*e**5 + 150*a**3*b**2*d**2*e**4 + 200*a**2*b**3*
d**3*e**3 - 7*a**2*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b
**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5
*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b**2) + 75*a*b**4*d**4*e**2 - 13*a*(5*a**4*
b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19
*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*
a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e
**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b*
*5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b) + 6*b**5*d**5*e)/(6*b) + b**5*d**6)/
(5*b))/(4*b))/(3*b))/(2*b**2) - a*(6*a**5*d**5*e + 5*a**4*b*d**6 - 2*a**2*(20*a**5*d**3*e**3 + 75*a**4*b*d**4*
e**2 + 60*a**3*b**2*d**5*e + 10*a**2*b**3*d**6 - 4*a**2*(6*a**5*d*e**5 + 75*a**4*b*d**2*e**4 + 200*a**3*b**2*d
**3*e**3 + 150*a**2*b**3*d**4*e**2 - 6*a**2*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8
*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d*
*2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e
**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*
a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d
**4*e**2)/(7*b**2) + 30*a*b**4*d**5*e - 11*a*(a**5*e**6 + 30*a**4*b*d*e**5 + 150*a**3*b**2*d**2*e**4 + 200*a**
2*b**3*d**3*e**3 - 7*a**2*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5
)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 +
6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b**2) + 75*a*b**4*d**4*e**2 - 13*a*(
5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e*
*5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15
*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4
*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b)
+ 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b) + 6*b**5*d**5*e)/(6*b) + b**5
*d**6)/(5*b**2) - 7*a*(15*a**5*d**2*e**4 + 100*a**4*b*d**3*e**3 + 150*a**3*b**2*d**4*e**2 + 60*a**2*b**3*d**5*
e - 5*a**2*(a**5*e**6 + 30*a**4*b*d*e**5 + 150*a**3*b**2*d**2*e**4 + 200*a**2*b**3*d**3*e**3 - 7*a**2*(10*a**3
*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4
- 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d
**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b**2) + 75*a*b**4*d**4*e**2 - 13*a*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**
5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b
**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b*
*3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e
**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b*
*5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b) + 6*b**5*d**5*e)/(6*b**2) + 5*a*b**4*d**6 - 9*a*(6*a**5*d*e**5
+ 75*a**4*b*d**2*e**4 + 200*a**3*b**2*d**3*e**3 + 150*a**2*b**3*d**4*e**2 - 6*a**2*(5*a**4*b*e**6 + 60*a**3*b*
*2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/
11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60
*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**
2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b)
+ 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b**2) + 30*a*b**4*d**5*e - 11*a*(a**5*e**6 + 30*a**4*b*d*e
**5 + 150*a**3*b**2*d**2*e**4 + 200*a**2*b**3*d**3*e**3 - 7*a**2*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*
a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*
b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/
(8*b**2) + 75*a*b**4*d**4*e**2 - 13*a*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*
(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**
4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11
+ 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*
a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e*
*2)/(7*b) + 6*b**5*d**5*e)/(6*b) + b**5*d**6)/(5*b))/(4*b))/(3*b**2) - 3*a*(15*a**5*d**4*e**2 + 30*a**4*b*d**5
*e + 10*a**3*b**2*d**6 - 3*a**2*(15*a**5*d**2*e**4 + 100*a**4*b*d**3*e**3 + 150*a**3*b**2*d**4*e**2 + 60*a**2*
b**3*d**5*e - 5*a**2*(a**5*e**6 + 30*a**4*b*d*e**5 + 150*a**3*b**2*d**2*e**4 + 200*a**2*b**3*d**3*e**3 - 7*a**
2*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*
d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) +
15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b**2) + 75*a*b**4*d**4*e**2 - 13*a*(5*a**4*b*e**6 + 60*a**3*
b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**
6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 +
60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a
**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*
b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b) + 6*b**5*d**5*e)/(6*b**2) + 5*a*b**4*d**6 - 9*a*(6*a*
*5*d*e**5 + 75*a**4*b*d**2*e**4 + 200*a**3*b**2*d**3*e**3 + 150*a**2*b**3*d**4*e**2 - 6*a**2*(5*a**4*b*e**6 +
60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*
b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2
*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*
a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e
**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b**2) + 30*a*b**4*d**5*e - 11*a*(a**5*e**6 + 30*
a**4*b*d*e**5 + 150*a**3*b**2*d**2*e**4 + 200*a**2*b**3*d**3*e**3 - 7*a**2*(10*a**3*b**2*e**6 + 60*a**2*b**3*d
*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/
11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d
**3*e**3)/(8*b**2) + 75*a*b**4*d**4*e**2 - 13*a*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4
- 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**
5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b*
*4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 -
19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b*
*5*d**4*e**2)/(7*b) + 6*b**5*d**5*e)/(6*b) + b**5*d**6)/(5*b))/(4*b**2) - 5*a*(20*a**5*d**3*e**3 + 75*a**4*b*d
**4*e**2 + 60*a**3*b**2*d**5*e + 10*a**2*b**3*d**6 - 4*a**2*(6*a**5*d*e**5 + 75*a**4*b*d**2*e**4 + 200*a**3*b*
*2*d**3*e**3 + 150*a**2*b**3*d**4*e**2 - 6*a**2*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4
- 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**
5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b*
*4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 -
19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b*
*5*d**4*e**2)/(7*b**2) + 30*a*b**4*d**5*e - 11*a*(a**5*e**6 + 30*a**4*b*d*e**5 + 150*a**3*b**2*d**2*e**4 + 200
*a**2*b**3*d**3*e**3 - 7*a**2*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*
e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/
11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b**2) + 75*a*b**4*d**4*e**2 - 13
*a*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*
d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3
- 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*
b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10
*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b) + 6*b**5*d**5*e)/(6*b) +
b**5*d**6)/(5*b**2) - 7*a*(15*a**5*d**2*e**4 + 100*a**4*b*d**3*e**3 + 150*a**3*b**2*d**4*e**2 + 60*a**2*b**3*d
**5*e - 5*a**2*(a**5*e**6 + 30*a**4*b*d*e**5 + 150*a**3*b**2*d**2*e**4 + 200*a**2*b**3*d**3*e**3 - 7*a**2*(10*
a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e
**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b*
*5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b**2) + 75*a*b**4*d**4*e**2 - 13*a*(5*a**4*b*e**6 + 60*a**3*b**2*d
*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 +
6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**
2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b*
*3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 2
0*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b) + 6*b**5*d**5*e)/(6*b**2) + 5*a*b**4*d**6 - 9*a*(6*a**5*d*e
**5 + 75*a**4*b*d**2*e**4 + 200*a**3*b**2*d**3*e**3 + 150*a**2*b**3*d**4*e**2 - 6*a**2*(5*a**4*b*e**6 + 60*a**
3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e
**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6
+ 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100
*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(
9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**4*e**2)/(7*b**2) + 30*a*b**4*d**5*e - 11*a*(a**5*e**6 + 30*a**4*b
*d*e**5 + 150*a**3*b**2*d**2*e**4 + 200*a**2*b**3*d**3*e**3 - 7*a**2*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5
- 9*a**2*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 3
0*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e*
*3)/(8*b**2) + 75*a*b**4*d**4*e**2 - 13*a*(5*a**4*b*e**6 + 60*a**3*b**2*d*e**5 + 150*a**2*b**3*d**2*e**4 - 8*a
**2*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2
*e**4)/(9*b**2) + 100*a*b**4*d**3*e**3 - 15*a*(10*a**3*b**2*e**6 + 60*a**2*b**3*d*e**5 - 9*a**2*(34*a*b**4*e**
6/11 + 6*b**5*d*e**5)/(10*b**2) + 75*a*b**4*d**2*e**4 - 17*a*(100*a**2*b**3*e**6/11 + 30*a*b**4*d*e**5 - 19*a*
(34*a*b**4*e**6/11 + 6*b**5*d*e**5)/(10*b) + 15*b**5*d**2*e**4)/(9*b) + 20*b**5*d**3*e**3)/(8*b) + 15*b**5*d**
4*e**2)/(7*b) + 6*b**5*d**5*e)/(6*b) + b**5*d**6)/(5*b))/(4*b))/(3*b))/(2*b))/b)*log(a/b + x)/sqrt(b**2*(a/b +
x)**2), Ne(b**2, 0)), (((a**2 + 2*a*b*x)**(5/2)*(a**7*e**6 - 12*a**6*b*d*e**5 + 60*a**5*b**2*d**2*e**4 - 160*
a**4*b**3*d**3*e**3 + 240*a**3*b**4*d**4*e**2 - 192*a**2*b**5*d**5*e + 64*a*b**6*d**6)/(640*b**6) + (a**2 + 2*
a*b*x)**(7/2)*(-5*a**6*e**6 + 48*a**5*b*d*e**5 - 180*a**4*b**2*d**2*e**4 + 320*a**3*b**3*d**3*e**3 - 240*a**2*
b**4*d**4*e**2 + 64*b**6*d**6)/(896*a*b**6) + (a**2 + 2*a*b*x)**(9/2)*(9*a**5*e**6 - 60*a**4*b*d*e**5 + 120*a*
*3*b**2*d**2*e**4 - 240*a*b**4*d**4*e**2 + 192*b**5*d**5*e)/(1152*a**2*b**6) + (a**2 + 2*a*b*x)**(11/2)*(-5*a*
*4*e**6 + 120*a**2*b**2*d**2*e**4 - 320*a*b**3*d**3*e**3 + 240*b**4*d**4*e**2)/(1408*a**3*b**6) + (a**2 + 2*a*
b*x)**(13/2)*(-5*a**3*e**6 + 60*a**2*b*d*e**5 - 180*a*b**2*d**2*e**4 + 160*b**3*d**3*e**3)/(1664*a**4*b**6) +
(a**2 + 2*a*b*x)**(15/2)*(9*a**2*e**6 - 48*a*b*d*e**5 + 60*b**2*d**2*e**4)/(1920*a**5*b**6) + (a**2 + 2*a*b*x)
**(17/2)*(-5*a*e**6 + 12*b*d*e**5)/(2176*a**6*b**6) + e**6*(a**2 + 2*a*b*x)**(19/2)/(2432*a**7*b**6))/(a*b), N
e(a*b, 0)), ((a*d**6*x + b*e**6*x**8/8 + x**7*(a*e**6 + 6*b*d*e**5)/7 + x**6*(6*a*d*e**5 + 15*b*d**2*e**4)/6 +
x**5*(15*a*d**2*e**4 + 20*b*d**3*e**3)/5 + x**4*(20*a*d**3*e**3 + 15*b*d**4*e**2)/4 + x**3*(15*a*d**4*e**2 +
6*b*d**5*e)/3 + x**2*(6*a*d**5*e + b*d**6)/2)*(a**2)**(3/2), True))

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 1736 vs. \(2 (189) = 378\).

Time = 0.22 (sec) , antiderivative size = 1736, normalized size of antiderivative = 6.83 \[ \int (a+b x) (d+e x)^6 \left (a^2+2 a b x+b^2 x^2\right )^{3/2} \, dx=\text {Too large to display} \]

[In]

integrate((b*x+a)*(e*x+d)^6*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm="maxima")

[Out]

1/11*(b^2*x^2 + 2*a*b*x + a^2)^(5/2)*e^6*x^6/b - 17/110*(b^2*x^2 + 2*a*b*x + a^2)^(5/2)*a*e^6*x^5/b^2 + 13/66*
(b^2*x^2 + 2*a*b*x + a^2)^(5/2)*a^2*e^6*x^4/b^3 - 59/264*(b^2*x^2 + 2*a*b*x + a^2)^(5/2)*a^3*e^6*x^3/b^4 + 1/4
*(b^2*x^2 + 2*a*b*x + a^2)^(3/2)*a*d^6*x - 1/4*(b^2*x^2 + 2*a*b*x + a^2)^(3/2)*a^7*e^6*x/b^6 + 21/88*(b^2*x^2
+ 2*a*b*x + a^2)^(5/2)*a^4*e^6*x^2/b^5 + 1/4*(b^2*x^2 + 2*a*b*x + a^2)^(3/2)*a^2*d^6/b - 1/4*(b^2*x^2 + 2*a*b*
x + a^2)^(3/2)*a^8*e^6/b^7 - 65/264*(b^2*x^2 + 2*a*b*x + a^2)^(5/2)*a^5*e^6*x/b^6 + 329/1320*(b^2*x^2 + 2*a*b*
x + a^2)^(5/2)*a^6*e^6/b^7 + 1/10*(6*b*d*e^5 + a*e^6)*(b^2*x^2 + 2*a*b*x + a^2)^(5/2)*x^5/b^2 - 1/6*(6*b*d*e^5
+ a*e^6)*(b^2*x^2 + 2*a*b*x + a^2)^(5/2)*a*x^4/b^3 + 1/3*(5*b*d^2*e^4 + 2*a*d*e^5)*(b^2*x^2 + 2*a*b*x + a^2)^
(5/2)*x^4/b^2 + 5/24*(6*b*d*e^5 + a*e^6)*(b^2*x^2 + 2*a*b*x + a^2)^(5/2)*a^2*x^3/b^4 - 13/24*(5*b*d^2*e^4 + 2*
a*d*e^5)*(b^2*x^2 + 2*a*b*x + a^2)^(5/2)*a*x^3/b^3 + 5/8*(4*b*d^3*e^3 + 3*a*d^2*e^4)*(b^2*x^2 + 2*a*b*x + a^2)
^(5/2)*x^3/b^2 + 1/4*(6*b*d*e^5 + a*e^6)*(b^2*x^2 + 2*a*b*x + a^2)^(3/2)*a^6*x/b^6 - 3/4*(5*b*d^2*e^4 + 2*a*d*
e^5)*(b^2*x^2 + 2*a*b*x + a^2)^(3/2)*a^5*x/b^5 + 5/4*(4*b*d^3*e^3 + 3*a*d^2*e^4)*(b^2*x^2 + 2*a*b*x + a^2)^(3/
2)*a^4*x/b^4 - 5/4*(3*b*d^4*e^2 + 4*a*d^3*e^3)*(b^2*x^2 + 2*a*b*x + a^2)^(3/2)*a^3*x/b^3 + 3/4*(2*b*d^5*e + 5*
a*d^4*e^2)*(b^2*x^2 + 2*a*b*x + a^2)^(3/2)*a^2*x/b^2 - 1/4*(b*d^6 + 6*a*d^5*e)*(b^2*x^2 + 2*a*b*x + a^2)^(3/2)
*a*x/b - 13/56*(6*b*d*e^5 + a*e^6)*(b^2*x^2 + 2*a*b*x + a^2)^(5/2)*a^3*x^2/b^5 + 37/56*(5*b*d^2*e^4 + 2*a*d*e^
5)*(b^2*x^2 + 2*a*b*x + a^2)^(5/2)*a^2*x^2/b^4 - 55/56*(4*b*d^3*e^3 + 3*a*d^2*e^4)*(b^2*x^2 + 2*a*b*x + a^2)^(
5/2)*a*x^2/b^3 + 5/7*(3*b*d^4*e^2 + 4*a*d^3*e^3)*(b^2*x^2 + 2*a*b*x + a^2)^(5/2)*x^2/b^2 + 1/4*(6*b*d*e^5 + a*
e^6)*(b^2*x^2 + 2*a*b*x + a^2)^(3/2)*a^7/b^7 - 3/4*(5*b*d^2*e^4 + 2*a*d*e^5)*(b^2*x^2 + 2*a*b*x + a^2)^(3/2)*a
^6/b^6 + 5/4*(4*b*d^3*e^3 + 3*a*d^2*e^4)*(b^2*x^2 + 2*a*b*x + a^2)^(3/2)*a^5/b^5 - 5/4*(3*b*d^4*e^2 + 4*a*d^3*
e^3)*(b^2*x^2 + 2*a*b*x + a^2)^(3/2)*a^4/b^4 + 3/4*(2*b*d^5*e + 5*a*d^4*e^2)*(b^2*x^2 + 2*a*b*x + a^2)^(3/2)*a
^3/b^3 - 1/4*(b*d^6 + 6*a*d^5*e)*(b^2*x^2 + 2*a*b*x + a^2)^(3/2)*a^2/b^2 + 41/168*(6*b*d*e^5 + a*e^6)*(b^2*x^2
+ 2*a*b*x + a^2)^(5/2)*a^4*x/b^6 - 121/168*(5*b*d^2*e^4 + 2*a*d*e^5)*(b^2*x^2 + 2*a*b*x + a^2)^(5/2)*a^3*x/b^
5 + 65/56*(4*b*d^3*e^3 + 3*a*d^2*e^4)*(b^2*x^2 + 2*a*b*x + a^2)^(5/2)*a^2*x/b^4 - 15/14*(3*b*d^4*e^2 + 4*a*d^3
*e^3)*(b^2*x^2 + 2*a*b*x + a^2)^(5/2)*a*x/b^3 + 1/2*(2*b*d^5*e + 5*a*d^4*e^2)*(b^2*x^2 + 2*a*b*x + a^2)^(5/2)*
x/b^2 - 209/840*(6*b*d*e^5 + a*e^6)*(b^2*x^2 + 2*a*b*x + a^2)^(5/2)*a^5/b^7 + 125/168*(5*b*d^2*e^4 + 2*a*d*e^5
)*(b^2*x^2 + 2*a*b*x + a^2)^(5/2)*a^4/b^6 - 69/56*(4*b*d^3*e^3 + 3*a*d^2*e^4)*(b^2*x^2 + 2*a*b*x + a^2)^(5/2)*
a^3/b^5 + 17/14*(3*b*d^4*e^2 + 4*a*d^3*e^3)*(b^2*x^2 + 2*a*b*x + a^2)^(5/2)*a^2/b^4 - 7/10*(2*b*d^5*e + 5*a*d^
4*e^2)*(b^2*x^2 + 2*a*b*x + a^2)^(5/2)*a/b^3 + 1/5*(b*d^6 + 6*a*d^5*e)*(b^2*x^2 + 2*a*b*x + a^2)^(5/2)/b^2

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 774 vs. \(2 (189) = 378\).

Time = 0.28 (sec) , antiderivative size = 774, normalized size of antiderivative = 3.05 \[ \int (a+b x) (d+e x)^6 \left (a^2+2 a b x+b^2 x^2\right )^{3/2} \, dx=\frac {1}{11} \, b^{4} e^{6} x^{11} \mathrm {sgn}\left (b x + a\right ) + \frac {3}{5} \, b^{4} d e^{5} x^{10} \mathrm {sgn}\left (b x + a\right ) + \frac {2}{5} \, a b^{3} e^{6} x^{10} \mathrm {sgn}\left (b x + a\right ) + \frac {5}{3} \, b^{4} d^{2} e^{4} x^{9} \mathrm {sgn}\left (b x + a\right ) + \frac {8}{3} \, a b^{3} d e^{5} x^{9} \mathrm {sgn}\left (b x + a\right ) + \frac {2}{3} \, a^{2} b^{2} e^{6} x^{9} \mathrm {sgn}\left (b x + a\right ) + \frac {5}{2} \, b^{4} d^{3} e^{3} x^{8} \mathrm {sgn}\left (b x + a\right ) + \frac {15}{2} \, a b^{3} d^{2} e^{4} x^{8} \mathrm {sgn}\left (b x + a\right ) + \frac {9}{2} \, a^{2} b^{2} d e^{5} x^{8} \mathrm {sgn}\left (b x + a\right ) + \frac {1}{2} \, a^{3} b e^{6} x^{8} \mathrm {sgn}\left (b x + a\right ) + \frac {15}{7} \, b^{4} d^{4} e^{2} x^{7} \mathrm {sgn}\left (b x + a\right ) + \frac {80}{7} \, a b^{3} d^{3} e^{3} x^{7} \mathrm {sgn}\left (b x + a\right ) + \frac {90}{7} \, a^{2} b^{2} d^{2} e^{4} x^{7} \mathrm {sgn}\left (b x + a\right ) + \frac {24}{7} \, a^{3} b d e^{5} x^{7} \mathrm {sgn}\left (b x + a\right ) + \frac {1}{7} \, a^{4} e^{6} x^{7} \mathrm {sgn}\left (b x + a\right ) + b^{4} d^{5} e x^{6} \mathrm {sgn}\left (b x + a\right ) + 10 \, a b^{3} d^{4} e^{2} x^{6} \mathrm {sgn}\left (b x + a\right ) + 20 \, a^{2} b^{2} d^{3} e^{3} x^{6} \mathrm {sgn}\left (b x + a\right ) + 10 \, a^{3} b d^{2} e^{4} x^{6} \mathrm {sgn}\left (b x + a\right ) + a^{4} d e^{5} x^{6} \mathrm {sgn}\left (b x + a\right ) + \frac {1}{5} \, b^{4} d^{6} x^{5} \mathrm {sgn}\left (b x + a\right ) + \frac {24}{5} \, a b^{3} d^{5} e x^{5} \mathrm {sgn}\left (b x + a\right ) + 18 \, a^{2} b^{2} d^{4} e^{2} x^{5} \mathrm {sgn}\left (b x + a\right ) + 16 \, a^{3} b d^{3} e^{3} x^{5} \mathrm {sgn}\left (b x + a\right ) + 3 \, a^{4} d^{2} e^{4} x^{5} \mathrm {sgn}\left (b x + a\right ) + a b^{3} d^{6} x^{4} \mathrm {sgn}\left (b x + a\right ) + 9 \, a^{2} b^{2} d^{5} e x^{4} \mathrm {sgn}\left (b x + a\right ) + 15 \, a^{3} b d^{4} e^{2} x^{4} \mathrm {sgn}\left (b x + a\right ) + 5 \, a^{4} d^{3} e^{3} x^{4} \mathrm {sgn}\left (b x + a\right ) + 2 \, a^{2} b^{2} d^{6} x^{3} \mathrm {sgn}\left (b x + a\right ) + 8 \, a^{3} b d^{5} e x^{3} \mathrm {sgn}\left (b x + a\right ) + 5 \, a^{4} d^{4} e^{2} x^{3} \mathrm {sgn}\left (b x + a\right ) + 2 \, a^{3} b d^{6} x^{2} \mathrm {sgn}\left (b x + a\right ) + 3 \, a^{4} d^{5} e x^{2} \mathrm {sgn}\left (b x + a\right ) + a^{4} d^{6} x \mathrm {sgn}\left (b x + a\right ) + \frac {{\left (462 \, a^{5} b^{6} d^{6} - 462 \, a^{6} b^{5} d^{5} e + 330 \, a^{7} b^{4} d^{4} e^{2} - 165 \, a^{8} b^{3} d^{3} e^{3} + 55 \, a^{9} b^{2} d^{2} e^{4} - 11 \, a^{10} b d e^{5} + a^{11} e^{6}\right )} \mathrm {sgn}\left (b x + a\right )}{2310 \, b^{7}} \]

[In]

integrate((b*x+a)*(e*x+d)^6*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm="giac")

[Out]

1/11*b^4*e^6*x^11*sgn(b*x + a) + 3/5*b^4*d*e^5*x^10*sgn(b*x + a) + 2/5*a*b^3*e^6*x^10*sgn(b*x + a) + 5/3*b^4*d
^2*e^4*x^9*sgn(b*x + a) + 8/3*a*b^3*d*e^5*x^9*sgn(b*x + a) + 2/3*a^2*b^2*e^6*x^9*sgn(b*x + a) + 5/2*b^4*d^3*e^
3*x^8*sgn(b*x + a) + 15/2*a*b^3*d^2*e^4*x^8*sgn(b*x + a) + 9/2*a^2*b^2*d*e^5*x^8*sgn(b*x + a) + 1/2*a^3*b*e^6*
x^8*sgn(b*x + a) + 15/7*b^4*d^4*e^2*x^7*sgn(b*x + a) + 80/7*a*b^3*d^3*e^3*x^7*sgn(b*x + a) + 90/7*a^2*b^2*d^2*
e^4*x^7*sgn(b*x + a) + 24/7*a^3*b*d*e^5*x^7*sgn(b*x + a) + 1/7*a^4*e^6*x^7*sgn(b*x + a) + b^4*d^5*e*x^6*sgn(b*
x + a) + 10*a*b^3*d^4*e^2*x^6*sgn(b*x + a) + 20*a^2*b^2*d^3*e^3*x^6*sgn(b*x + a) + 10*a^3*b*d^2*e^4*x^6*sgn(b*
x + a) + a^4*d*e^5*x^6*sgn(b*x + a) + 1/5*b^4*d^6*x^5*sgn(b*x + a) + 24/5*a*b^3*d^5*e*x^5*sgn(b*x + a) + 18*a^
2*b^2*d^4*e^2*x^5*sgn(b*x + a) + 16*a^3*b*d^3*e^3*x^5*sgn(b*x + a) + 3*a^4*d^2*e^4*x^5*sgn(b*x + a) + a*b^3*d^
6*x^4*sgn(b*x + a) + 9*a^2*b^2*d^5*e*x^4*sgn(b*x + a) + 15*a^3*b*d^4*e^2*x^4*sgn(b*x + a) + 5*a^4*d^3*e^3*x^4*
sgn(b*x + a) + 2*a^2*b^2*d^6*x^3*sgn(b*x + a) + 8*a^3*b*d^5*e*x^3*sgn(b*x + a) + 5*a^4*d^4*e^2*x^3*sgn(b*x + a
) + 2*a^3*b*d^6*x^2*sgn(b*x + a) + 3*a^4*d^5*e*x^2*sgn(b*x + a) + a^4*d^6*x*sgn(b*x + a) + 1/2310*(462*a^5*b^6
*d^6 - 462*a^6*b^5*d^5*e + 330*a^7*b^4*d^4*e^2 - 165*a^8*b^3*d^3*e^3 + 55*a^9*b^2*d^2*e^4 - 11*a^10*b*d*e^5 +
a^11*e^6)*sgn(b*x + a)/b^7

Mupad [F(-1)]

Timed out. \[ \int (a+b x) (d+e x)^6 \left (a^2+2 a b x+b^2 x^2\right )^{3/2} \, dx=\int \left (a+b\,x\right )\,{\left (d+e\,x\right )}^6\,{\left (a^2+2\,a\,b\,x+b^2\,x^2\right )}^{3/2} \,d x \]

[In]

int((a + b*x)*(d + e*x)^6*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2),x)

[Out]

int((a + b*x)*(d + e*x)^6*(a^2 + b^2*x^2 + 2*a*b*x)^(3/2), x)