3.11.94 \(\int \frac {(a+b x)^{10} (A+B x)}{(d+e x)^6} \, dx\) [1094]

Optimal. Leaf size=447 \[ -\frac {42 b^5 (b d-a e)^4 (11 b B d-5 A b e-6 a B e) x}{e^{11}}+\frac {(b d-a e)^{10} (B d-A e)}{5 e^{12} (d+e x)^5}-\frac {(b d-a e)^9 (11 b B d-10 A b e-a B e)}{4 e^{12} (d+e x)^4}+\frac {5 b (b d-a e)^8 (11 b B d-9 A b e-2 a B e)}{3 e^{12} (d+e x)^3}-\frac {15 b^2 (b d-a e)^7 (11 b B d-8 A b e-3 a B e)}{2 e^{12} (d+e x)^2}+\frac {30 b^3 (b d-a e)^6 (11 b B d-7 A b e-4 a B e)}{e^{12} (d+e x)}+\frac {15 b^6 (b d-a e)^3 (11 b B d-4 A b e-7 a B e) (d+e x)^2}{e^{12}}-\frac {5 b^7 (b d-a e)^2 (11 b B d-3 A b e-8 a B e) (d+e x)^3}{e^{12}}+\frac {5 b^8 (b d-a e) (11 b B d-2 A b e-9 a B e) (d+e x)^4}{4 e^{12}}-\frac {b^9 (11 b B d-A b e-10 a B e) (d+e x)^5}{5 e^{12}}+\frac {b^{10} B (d+e x)^6}{6 e^{12}}+\frac {42 b^4 (b d-a e)^5 (11 b B d-6 A b e-5 a B e) \log (d+e x)}{e^{12}} \]

[Out]

-42*b^5*(-a*e+b*d)^4*(-5*A*b*e-6*B*a*e+11*B*b*d)*x/e^11+1/5*(-a*e+b*d)^10*(-A*e+B*d)/e^12/(e*x+d)^5-1/4*(-a*e+
b*d)^9*(-10*A*b*e-B*a*e+11*B*b*d)/e^12/(e*x+d)^4+5/3*b*(-a*e+b*d)^8*(-9*A*b*e-2*B*a*e+11*B*b*d)/e^12/(e*x+d)^3
-15/2*b^2*(-a*e+b*d)^7*(-8*A*b*e-3*B*a*e+11*B*b*d)/e^12/(e*x+d)^2+30*b^3*(-a*e+b*d)^6*(-7*A*b*e-4*B*a*e+11*B*b
*d)/e^12/(e*x+d)+15*b^6*(-a*e+b*d)^3*(-4*A*b*e-7*B*a*e+11*B*b*d)*(e*x+d)^2/e^12-5*b^7*(-a*e+b*d)^2*(-3*A*b*e-8
*B*a*e+11*B*b*d)*(e*x+d)^3/e^12+5/4*b^8*(-a*e+b*d)*(-2*A*b*e-9*B*a*e+11*B*b*d)*(e*x+d)^4/e^12-1/5*b^9*(-A*b*e-
10*B*a*e+11*B*b*d)*(e*x+d)^5/e^12+1/6*b^10*B*(e*x+d)^6/e^12+42*b^4*(-a*e+b*d)^5*(-6*A*b*e-5*B*a*e+11*B*b*d)*ln
(e*x+d)/e^12

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Rubi [A]
time = 0.80, antiderivative size = 447, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78} \begin {gather*} -\frac {b^9 (d+e x)^5 (-10 a B e-A b e+11 b B d)}{5 e^{12}}+\frac {5 b^8 (d+e x)^4 (b d-a e) (-9 a B e-2 A b e+11 b B d)}{4 e^{12}}-\frac {5 b^7 (d+e x)^3 (b d-a e)^2 (-8 a B e-3 A b e+11 b B d)}{e^{12}}+\frac {15 b^6 (d+e x)^2 (b d-a e)^3 (-7 a B e-4 A b e+11 b B d)}{e^{12}}-\frac {42 b^5 x (b d-a e)^4 (-6 a B e-5 A b e+11 b B d)}{e^{11}}+\frac {42 b^4 (b d-a e)^5 \log (d+e x) (-5 a B e-6 A b e+11 b B d)}{e^{12}}+\frac {30 b^3 (b d-a e)^6 (-4 a B e-7 A b e+11 b B d)}{e^{12} (d+e x)}-\frac {15 b^2 (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{2 e^{12} (d+e x)^2}+\frac {5 b (b d-a e)^8 (-2 a B e-9 A b e+11 b B d)}{3 e^{12} (d+e x)^3}-\frac {(b d-a e)^9 (-a B e-10 A b e+11 b B d)}{4 e^{12} (d+e x)^4}+\frac {(b d-a e)^{10} (B d-A e)}{5 e^{12} (d+e x)^5}+\frac {b^{10} B (d+e x)^6}{6 e^{12}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[((a + b*x)^10*(A + B*x))/(d + e*x)^6,x]

[Out]

(-42*b^5*(b*d - a*e)^4*(11*b*B*d - 5*A*b*e - 6*a*B*e)*x)/e^11 + ((b*d - a*e)^10*(B*d - A*e))/(5*e^12*(d + e*x)
^5) - ((b*d - a*e)^9*(11*b*B*d - 10*A*b*e - a*B*e))/(4*e^12*(d + e*x)^4) + (5*b*(b*d - a*e)^8*(11*b*B*d - 9*A*
b*e - 2*a*B*e))/(3*e^12*(d + e*x)^3) - (15*b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b*e - 3*a*B*e))/(2*e^12*(d + e*x)
^2) + (30*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*e - 4*a*B*e))/(e^12*(d + e*x)) + (15*b^6*(b*d - a*e)^3*(11*b*B*d
- 4*A*b*e - 7*a*B*e)*(d + e*x)^2)/e^12 - (5*b^7*(b*d - a*e)^2*(11*b*B*d - 3*A*b*e - 8*a*B*e)*(d + e*x)^3)/e^1
2 + (5*b^8*(b*d - a*e)*(11*b*B*d - 2*A*b*e - 9*a*B*e)*(d + e*x)^4)/(4*e^12) - (b^9*(11*b*B*d - A*b*e - 10*a*B*
e)*(d + e*x)^5)/(5*e^12) + (b^10*B*(d + e*x)^6)/(6*e^12) + (42*b^4*(b*d - a*e)^5*(11*b*B*d - 6*A*b*e - 5*a*B*e
)*Log[d + e*x])/e^12

Rule 78

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 \frac {(a+b x)^{10} (A+B x)}{(d+e x)^6} \, dx &=\int \left (\frac {42 b^5 (b d-a e)^4 (-11 b B d+5 A b e+6 a B e)}{e^{11}}+\frac {(-b d+a e)^{10} (-B d+A e)}{e^{11} (d+e x)^6}+\frac {(-b d+a e)^9 (-11 b B d+10 A b e+a B e)}{e^{11} (d+e x)^5}+\frac {5 b (b d-a e)^8 (-11 b B d+9 A b e+2 a B e)}{e^{11} (d+e x)^4}-\frac {15 b^2 (b d-a e)^7 (-11 b B d+8 A b e+3 a B e)}{e^{11} (d+e x)^3}+\frac {30 b^3 (b d-a e)^6 (-11 b B d+7 A b e+4 a B e)}{e^{11} (d+e x)^2}-\frac {42 b^4 (b d-a e)^5 (-11 b B d+6 A b e+5 a B e)}{e^{11} (d+e x)}-\frac {30 b^6 (b d-a e)^3 (-11 b B d+4 A b e+7 a B e) (d+e x)}{e^{11}}+\frac {15 b^7 (b d-a e)^2 (-11 b B d+3 A b e+8 a B e) (d+e x)^2}{e^{11}}-\frac {5 b^8 (b d-a e) (-11 b B d+2 A b e+9 a B e) (d+e x)^3}{e^{11}}+\frac {b^9 (-11 b B d+A b e+10 a B e) (d+e x)^4}{e^{11}}+\frac {b^{10} B (d+e x)^5}{e^{11}}\right ) \, dx\\ &=-\frac {42 b^5 (b d-a e)^4 (11 b B d-5 A b e-6 a B e) x}{e^{11}}+\frac {(b d-a e)^{10} (B d-A e)}{5 e^{12} (d+e x)^5}-\frac {(b d-a e)^9 (11 b B d-10 A b e-a B e)}{4 e^{12} (d+e x)^4}+\frac {5 b (b d-a e)^8 (11 b B d-9 A b e-2 a B e)}{3 e^{12} (d+e x)^3}-\frac {15 b^2 (b d-a e)^7 (11 b B d-8 A b e-3 a B e)}{2 e^{12} (d+e x)^2}+\frac {30 b^3 (b d-a e)^6 (11 b B d-7 A b e-4 a B e)}{e^{12} (d+e x)}+\frac {15 b^6 (b d-a e)^3 (11 b B d-4 A b e-7 a B e) (d+e x)^2}{e^{12}}-\frac {5 b^7 (b d-a e)^2 (11 b B d-3 A b e-8 a B e) (d+e x)^3}{e^{12}}+\frac {5 b^8 (b d-a e) (11 b B d-2 A b e-9 a B e) (d+e x)^4}{4 e^{12}}-\frac {b^9 (11 b B d-A b e-10 a B e) (d+e x)^5}{5 e^{12}}+\frac {b^{10} B (d+e x)^6}{6 e^{12}}+\frac {42 b^4 (b d-a e)^5 (11 b B d-6 A b e-5 a B e) \log (d+e x)}{e^{12}}\\ \end {align*}

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Mathematica [A]
time = 0.31, size = 587, normalized size = 1.31 \begin {gather*} \frac {60 b^5 e \left (252 a^5 B e^5+140 a b^4 d^3 e (9 B d-4 A e)-315 a^2 b^3 d^2 e^2 (8 B d-3 A e)+360 a^3 b^2 d e^3 (7 B d-2 A e)-126 b^5 d^4 (2 B d-A e)+210 a^4 b e^4 (-6 B d+A e)\right ) x-30 b^6 e^2 \left (-210 a^4 B e^4-14 b^4 d^3 (9 B d-4 A e)+70 a b^3 d^2 e (8 B d-3 A e)-135 a^2 b^2 d e^2 (7 B d-2 A e)-120 a^3 b e^3 (-6 B d+A e)\right ) x^2+20 b^7 e^3 \left (120 a^3 B e^3-7 b^3 d^2 (8 B d-3 A e)+30 a b^2 d e (7 B d-2 A e)+45 a^2 b e^2 (-6 B d+A e)\right ) x^3-15 b^8 e^4 \left (-45 a^2 B e^2-10 a b e (-6 B d+A e)+3 b^2 d (-7 B d+2 A e)\right ) x^4+12 b^9 e^5 (-6 b B d+A b e+10 a B e) x^5+10 b^{10} B e^6 x^6+\frac {12 (b d-a e)^{10} (B d-A e)}{(d+e x)^5}-\frac {15 (b d-a e)^9 (11 b B d-10 A b e-a B e)}{(d+e x)^4}+\frac {100 b (b d-a e)^8 (11 b B d-9 A b e-2 a B e)}{(d+e x)^3}-\frac {450 b^2 (b d-a e)^7 (11 b B d-8 A b e-3 a B e)}{(d+e x)^2}+\frac {1800 b^3 (b d-a e)^6 (11 b B d-7 A b e-4 a B e)}{d+e x}+2520 b^4 (b d-a e)^5 (11 b B d-6 A b e-5 a B e) \log (d+e x)}{60 e^{12}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((a + b*x)^10*(A + B*x))/(d + e*x)^6,x]

[Out]

(60*b^5*e*(252*a^5*B*e^5 + 140*a*b^4*d^3*e*(9*B*d - 4*A*e) - 315*a^2*b^3*d^2*e^2*(8*B*d - 3*A*e) + 360*a^3*b^2
*d*e^3*(7*B*d - 2*A*e) - 126*b^5*d^4*(2*B*d - A*e) + 210*a^4*b*e^4*(-6*B*d + A*e))*x - 30*b^6*e^2*(-210*a^4*B*
e^4 - 14*b^4*d^3*(9*B*d - 4*A*e) + 70*a*b^3*d^2*e*(8*B*d - 3*A*e) - 135*a^2*b^2*d*e^2*(7*B*d - 2*A*e) - 120*a^
3*b*e^3*(-6*B*d + A*e))*x^2 + 20*b^7*e^3*(120*a^3*B*e^3 - 7*b^3*d^2*(8*B*d - 3*A*e) + 30*a*b^2*d*e*(7*B*d - 2*
A*e) + 45*a^2*b*e^2*(-6*B*d + A*e))*x^3 - 15*b^8*e^4*(-45*a^2*B*e^2 - 10*a*b*e*(-6*B*d + A*e) + 3*b^2*d*(-7*B*
d + 2*A*e))*x^4 + 12*b^9*e^5*(-6*b*B*d + A*b*e + 10*a*B*e)*x^5 + 10*b^10*B*e^6*x^6 + (12*(b*d - a*e)^10*(B*d -
A*e))/(d + e*x)^5 - (15*(b*d - a*e)^9*(11*b*B*d - 10*A*b*e - a*B*e))/(d + e*x)^4 + (100*b*(b*d - a*e)^8*(11*b
*B*d - 9*A*b*e - 2*a*B*e))/(d + e*x)^3 - (450*b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b*e - 3*a*B*e))/(d + e*x)^2 +
(1800*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*e - 4*a*B*e))/(d + e*x) + 2520*b^4*(b*d - a*e)^5*(11*b*B*d - 6*A*b*e
- 5*a*B*e)*Log[d + e*x])/(60*e^12)

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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(2000\) vs. \(2(433)=866\).
time = 0.10, size = 2001, normalized size = 4.48

method	result	size
norman	\(\text {Expression too large to display}\)	\(1916\)
default	\(\text {Expression too large to display}\)	\(2001\)
risch	\(\text {Expression too large to display}\)	\(2079\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((b*x+a)^10*(B*x+A)/(e*x+d)^6,x,method=_RETURNVERBOSE)

[Out]

b^5/e^11*(-1260*B*a^4*b*d*e^4*x+2520*B*a^3*b^2*d^2*e^3*x-2520*B*a^2*b^3*d^3*e^2*x+1260*B*a*b^4*d^4*e*x-135*A*a
^2*b^3*d*e^4*x^2+105*A*a*b^4*d^2*e^3*x^2-360*B*a^3*b^2*d*e^4*x^2+945/2*B*a^2*b^3*d^2*e^3*x^2-280*B*a*b^4*d^3*e
^2*x^2-720*A*a^3*b^2*d*e^4*x+945*A*a^2*b^3*d^2*e^3*x-560*A*a*b^4*d^3*e^2*x-90*B*a^2*b^3*d*e^4*x^3+70*B*a*b^4*d
^2*e^3*x^3-15*B*a*b^4*d*e^4*x^4-20*A*a*b^4*d*e^4*x^3+7*A*b^5*d^2*e^3*x^3+252*B*a^5*e^5*x-252*B*b^5*d^5*x+1/6*b
^5*B*x^6*e^5+1/5*A*b^5*e^5*x^5+2*B*a*b^4*e^5*x^5-6/5*B*b^5*d*e^4*x^5+5/2*A*a*b^4*e^5*x^4-3/2*A*b^5*d*e^4*x^4+4
5/4*B*a^2*b^3*e^5*x^4+21/4*B*b^5*d^2*e^3*x^4+15*A*a^2*b^3*e^5*x^3+40*B*a^3*b^2*e^5*x^3-56/3*B*b^5*d^3*e^2*x^3+
60*A*a^3*b^2*e^5*x^2-28*A*b^5*d^3*e^2*x^2+105*B*a^4*b*e^5*x^2+63*B*b^5*d^4*e*x^2+210*A*a^4*b*e^5*x+126*A*b^5*d
^4*e*x)-15/2*b^2/e^12*(8*A*a^7*b*e^8-56*A*a^6*b^2*d*e^7+168*A*a^5*b^3*d^2*e^6-280*A*a^4*b^4*d^3*e^5+280*A*a^3*
b^5*d^4*e^4-168*A*a^2*b^6*d^5*e^3+56*A*a*b^7*d^6*e^2-8*A*b^8*d^7*e+3*B*a^8*e^8-32*B*a^7*b*d*e^7+140*B*a^6*b^2*
d^2*e^6-336*B*a^5*b^3*d^3*e^5+490*B*a^4*b^4*d^4*e^4-448*B*a^3*b^5*d^5*e^3+252*B*a^2*b^6*d^6*e^2-80*B*a*b^7*d^7
*e+11*B*b^8*d^8)/(e*x+d)^2-1/4/e^12*(10*A*a^9*b*e^10-90*A*a^8*b^2*d*e^9+360*A*a^7*b^3*d^2*e^8-840*A*a^6*b^4*d^
3*e^7+1260*A*a^5*b^5*d^4*e^6-1260*A*a^4*b^6*d^5*e^5+840*A*a^3*b^7*d^6*e^4-360*A*a^2*b^8*d^7*e^3+90*A*a*b^9*d^8
*e^2-10*A*b^10*d^9*e+B*a^10*e^10-20*B*a^9*b*d*e^9+135*B*a^8*b^2*d^2*e^8-480*B*a^7*b^3*d^3*e^7+1050*B*a^6*b^4*d
^4*e^6-1512*B*a^5*b^5*d^5*e^5+1470*B*a^4*b^6*d^6*e^4-960*B*a^3*b^7*d^7*e^3+405*B*a^2*b^8*d^8*e^2-100*B*a*b^9*d
^9*e+11*B*b^10*d^10)/(e*x+d)^4-30*b^3/e^12*(7*A*a^6*b*e^7-42*A*a^5*b^2*d*e^6+105*A*a^4*b^3*d^2*e^5-140*A*a^3*b
^4*d^3*e^4+105*A*a^2*b^5*d^4*e^3-42*A*a*b^6*d^5*e^2+7*A*b^7*d^6*e+4*B*a^7*e^7-35*B*a^6*b*d*e^6+126*B*a^5*b^2*d
^2*e^5-245*B*a^4*b^3*d^3*e^4+280*B*a^3*b^4*d^4*e^3-189*B*a^2*b^5*d^5*e^2+70*B*a*b^6*d^6*e-11*B*b^7*d^7)/(e*x+d
)-1/5*(A*a^10*e^11-10*A*a^9*b*d*e^10+45*A*a^8*b^2*d^2*e^9-120*A*a^7*b^3*d^3*e^8+210*A*a^6*b^4*d^4*e^7-252*A*a^
5*b^5*d^5*e^6+210*A*a^4*b^6*d^6*e^5-120*A*a^3*b^7*d^7*e^4+45*A*a^2*b^8*d^8*e^3-10*A*a*b^9*d^9*e^2+A*b^10*d^10*
e-B*a^10*d*e^10+10*B*a^9*b*d^2*e^9-45*B*a^8*b^2*d^3*e^8+120*B*a^7*b^3*d^4*e^7-210*B*a^6*b^4*d^5*e^6+252*B*a^5*
b^5*d^6*e^5-210*B*a^4*b^6*d^7*e^4+120*B*a^3*b^7*d^8*e^3-45*B*a^2*b^8*d^9*e^2+10*B*a*b^9*d^10*e-B*b^10*d^11)/e^
12/(e*x+d)^5-5/3*b/e^12*(9*A*a^8*b*e^9-72*A*a^7*b^2*d*e^8+252*A*a^6*b^3*d^2*e^7-504*A*a^5*b^4*d^3*e^6+630*A*a^
4*b^5*d^4*e^5-504*A*a^3*b^6*d^5*e^4+252*A*a^2*b^7*d^6*e^3-72*A*a*b^8*d^7*e^2+9*A*b^9*d^8*e+2*B*a^9*e^9-27*B*a^
8*b*d*e^8+144*B*a^7*b^2*d^2*e^7-420*B*a^6*b^3*d^3*e^6+756*B*a^5*b^4*d^4*e^5-882*B*a^4*b^5*d^5*e^4+672*B*a^3*b^
6*d^6*e^3-324*B*a^2*b^7*d^7*e^2+90*B*a*b^8*d^8*e-11*B*b^9*d^9)/(e*x+d)^3+42*b^4/e^12*(6*A*a^5*b*e^6-30*A*a^4*b
^2*d*e^5+60*A*a^3*b^3*d^2*e^4-60*A*a^2*b^4*d^3*e^3+30*A*a*b^5*d^4*e^2-6*A*b^6*d^5*e+5*B*a^6*e^6-36*B*a^5*b*d*e
^5+105*B*a^4*b^2*d^2*e^4-160*B*a^3*b^3*d^3*e^3+135*B*a^2*b^4*d^4*e^2-60*B*a*b^5*d^5*e+11*B*b^6*d^6)*ln(e*x+d)

________________________________________________________________________________________

Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 1892 vs. \(2 (463) = 926\).
time = 0.52, size = 1892, normalized size = 4.23 \begin {gather*} \text {Too large to display} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)^10*(B*x+A)/(e*x+d)^6,x, algorithm="maxima")

[Out]

42*(11*B*b^10*d^6 + 5*B*a^6*b^4*e^6 + 6*A*a^5*b^5*e^6 - 6*(10*B*a*b^9*e + A*b^10*e)*d^5 + 15*(9*B*a^2*b^8*e^2
+ 2*A*a*b^9*e^2)*d^4 - 20*(8*B*a^3*b^7*e^3 + 3*A*a^2*b^8*e^3)*d^3 + 15*(7*B*a^4*b^6*e^4 + 4*A*a^3*b^7*e^4)*d^2
- 6*(6*B*a^5*b^5*e^5 + 5*A*a^4*b^6*e^5)*d)*e^(-12)*log(x*e + d) + 1/60*(10*B*b^10*x^6*e^5 - 12*(6*B*b^10*d*e^
4 - 10*B*a*b^9*e^5 - A*b^10*e^5)*x^5 + 15*(21*B*b^10*d^2*e^3 + 45*B*a^2*b^8*e^5 + 10*A*a*b^9*e^5 - 6*(10*B*a*b
^9*e^4 + A*b^10*e^4)*d)*x^4 - 20*(56*B*b^10*d^3*e^2 - 120*B*a^3*b^7*e^5 - 45*A*a^2*b^8*e^5 - 21*(10*B*a*b^9*e^
3 + A*b^10*e^3)*d^2 + 30*(9*B*a^2*b^8*e^4 + 2*A*a*b^9*e^4)*d)*x^3 + 30*(126*B*b^10*d^4*e + 210*B*a^4*b^6*e^5 +
120*A*a^3*b^7*e^5 - 56*(10*B*a*b^9*e^2 + A*b^10*e^2)*d^3 + 105*(9*B*a^2*b^8*e^3 + 2*A*a*b^9*e^3)*d^2 - 90*(8*
B*a^3*b^7*e^4 + 3*A*a^2*b^8*e^4)*d)*x^2 - 60*(252*B*b^10*d^5 - 252*B*a^5*b^5*e^5 - 210*A*a^4*b^6*e^5 - 126*(10
*B*a*b^9*e + A*b^10*e)*d^4 + 280*(9*B*a^2*b^8*e^2 + 2*A*a*b^9*e^2)*d^3 - 315*(8*B*a^3*b^7*e^3 + 3*A*a^2*b^8*e^
3)*d^2 + 180*(7*B*a^4*b^6*e^4 + 4*A*a^3*b^7*e^4)*d)*x)*e^(-11) + 1/60*(15797*B*b^10*d^11 - 12*A*a^10*e^11 - 97
62*(10*B*a*b^9*e + A*b^10*e)*d^10 + 28185*(9*B*a^2*b^8*e^2 + 2*A*a*b^9*e^2)*d^9 - 44580*(8*B*a^3*b^7*e^3 + 3*A
*a^2*b^8*e^3)*d^8 + 41310*(7*B*a^4*b^6*e^4 + 4*A*a^3*b^7*e^4)*d^7 - 21924*(6*B*a^5*b^5*e^5 + 5*A*a^4*b^6*e^5)*
d^6 + 5754*(5*B*a^6*b^4*e^6 + 6*A*a^5*b^5*e^6)*d^5 - 360*(4*B*a^7*b^3*e^7 + 7*A*a^6*b^4*e^7)*d^4 + 1800*(11*B*
b^10*d^7*e^4 - 4*B*a^7*b^3*e^11 - 7*A*a^6*b^4*e^11 - 7*(10*B*a*b^9*e^5 + A*b^10*e^5)*d^6 + 21*(9*B*a^2*b^8*e^6
+ 2*A*a*b^9*e^6)*d^5 - 35*(8*B*a^3*b^7*e^7 + 3*A*a^2*b^8*e^7)*d^4 + 35*(7*B*a^4*b^6*e^8 + 4*A*a^3*b^7*e^8)*d^
3 - 21*(6*B*a^5*b^5*e^9 + 5*A*a^4*b^6*e^9)*d^2 + 7*(5*B*a^6*b^4*e^10 + 6*A*a^5*b^5*e^10)*d)*x^4 - 45*(3*B*a^8*
b^2*e^8 + 8*A*a^7*b^3*e^8)*d^3 + 450*(165*B*b^10*d^8*e^3 - 3*B*a^8*b^2*e^11 - 8*A*a^7*b^3*e^11 - 104*(10*B*a*b
^9*e^4 + A*b^10*e^4)*d^7 + 308*(9*B*a^2*b^8*e^5 + 2*A*a*b^9*e^5)*d^6 - 504*(8*B*a^3*b^7*e^6 + 3*A*a^2*b^8*e^6)
*d^5 + 490*(7*B*a^4*b^6*e^7 + 4*A*a^3*b^7*e^7)*d^4 - 280*(6*B*a^5*b^5*e^8 + 5*A*a^4*b^6*e^8)*d^3 + 84*(5*B*a^6
*b^4*e^9 + 6*A*a^5*b^5*e^9)*d^2 - 8*(4*B*a^7*b^3*e^10 + 7*A*a^6*b^4*e^10)*d)*x^3 - 10*(2*B*a^9*b*e^9 + 9*A*a^8
*b^2*e^9)*d^2 + 50*(2101*B*b^10*d^9*e^2 - 4*B*a^9*b*e^11 - 18*A*a^8*b^2*e^11 - 1314*(10*B*a*b^9*e^3 + A*b^10*e
^3)*d^8 + 3852*(9*B*a^2*b^8*e^4 + 2*A*a*b^9*e^4)*d^7 - 6216*(8*B*a^3*b^7*e^5 + 3*A*a^2*b^8*e^5)*d^6 + 5922*(7*
B*a^4*b^6*e^6 + 4*A*a^3*b^7*e^6)*d^5 - 3276*(6*B*a^5*b^5*e^7 + 5*A*a^4*b^6*e^7)*d^4 + 924*(5*B*a^6*b^4*e^8 + 6
*A*a^5*b^5*e^8)*d^3 - 72*(4*B*a^7*b^3*e^9 + 7*A*a^6*b^4*e^9)*d^2 - 9*(3*B*a^8*b^2*e^10 + 8*A*a^7*b^3*e^10)*d)*
x^2 - 3*(B*a^10*e^10 + 10*A*a^9*b*e^10)*d + 5*(13277*B*b^10*d^10*e - 3*B*a^10*e^11 - 30*A*a^9*b*e^11 - 8250*(1
0*B*a*b^9*e^2 + A*b^10*e^2)*d^9 + 23985*(9*B*a^2*b^8*e^3 + 2*A*a*b^9*e^3)*d^8 - 38280*(8*B*a^3*b^7*e^4 + 3*A*a
^2*b^8*e^4)*d^7 + 35910*(7*B*a^4*b^6*e^5 + 4*A*a^3*b^7*e^5)*d^6 - 19404*(6*B*a^5*b^5*e^6 + 5*A*a^4*b^6*e^6)*d^
5 + 5250*(5*B*a^6*b^4*e^7 + 6*A*a^5*b^5*e^7)*d^4 - 360*(4*B*a^7*b^3*e^8 + 7*A*a^6*b^4*e^8)*d^3 - 45*(3*B*a^8*b
^2*e^9 + 8*A*a^7*b^3*e^9)*d^2 - 10*(2*B*a^9*b*e^10 + 9*A*a^8*b^2*e^10)*d)*x)/(x^5*e^17 + 5*d*x^4*e^16 + 10*d^2
*x^3*e^15 + 10*d^3*x^2*e^14 + 5*d^4*x*e^13 + d^5*e^12)

________________________________________________________________________________________

Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 2786 vs. \(2 (463) = 926\).
time = 1.18, size = 2786, normalized size = 6.23 \begin {gather*} \text {Too large to display} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)^10*(B*x+A)/(e*x+d)^6,x, algorithm="fricas")

[Out]

1/60*(15797*B*b^10*d^11 + (10*B*b^10*x^11 - 12*A*a^10 + 12*(10*B*a*b^9 + A*b^10)*x^10 + 75*(9*B*a^2*b^8 + 2*A*
a*b^9)*x^9 + 300*(8*B*a^3*b^7 + 3*A*a^2*b^8)*x^8 + 900*(7*B*a^4*b^6 + 4*A*a^3*b^7)*x^7 + 2520*(6*B*a^5*b^5 + 5
*A*a^4*b^6)*x^6 - 1800*(4*B*a^7*b^3 + 7*A*a^6*b^4)*x^4 - 450*(3*B*a^8*b^2 + 8*A*a^7*b^3)*x^3 - 100*(2*B*a^9*b
+ 9*A*a^8*b^2)*x^2 - 15*(B*a^10 + 10*A*a^9*b)*x)*e^11 - (22*B*b^10*d*x^10 + 30*(10*B*a*b^9 + A*b^10)*d*x^9 + 2
25*(9*B*a^2*b^8 + 2*A*a*b^9)*d*x^8 + 1200*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*x^7 + 6300*(7*B*a^4*b^6 + 4*A*a^3*b^7)
*d*x^6 - 12600*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*x^5 - 12600*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*x^4 + 3600*(4*B*a^7*b^3
+ 7*A*a^6*b^4)*d*x^3 + 450*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*x^2 + 50*(2*B*a^9*b + 9*A*a^8*b^2)*d*x + 3*(B*a^10 +
10*A*a^9*b)*d)*e^10 + 5*(11*B*b^10*d^2*x^9 + 18*(10*B*a*b^9 + A*b^10)*d^2*x^8 + 180*(9*B*a^2*b^8 + 2*A*a*b^9)
*d^2*x^7 + 1680*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*x^6 - 9000*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*x^5 - 2520*(6*B*a^5
*b^5 + 5*A*a^4*b^6)*d^2*x^4 + 7560*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*x^3 - 720*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*x
^2 - 45*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*x - 2*(2*B*a^9*b + 9*A*a^8*b^2)*d^2)*e^9 - 15*(11*B*b^10*d^3*x^8 + 24*
(10*B*a*b^9 + A*b^10)*d^3*x^7 + 420*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*x^6 - 4700*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*x
^5 + 2400*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*x^4 + 6720*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*x^3 - 3080*(5*B*a^6*b^4 +
6*A*a^5*b^5)*d^3*x^2 + 120*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*x + 3*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3)*e^8 + 15*(4
4*B*b^10*d^4*x^7 + 168*(10*B*a*b^9 + A*b^10)*d^4*x^6 - 3875*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*x^5 + 6700*(8*B*a^3*
b^7 + 3*A*a^2*b^8)*d^4*x^4 + 7800*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*x^3 - 10080*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*
x^2 + 1750*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*x - 24*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4)*e^7 - 3*(1540*B*b^10*d^5*x^
6 - 8254*(10*B*a*b^9 + A*b^10)*d^5*x^5 + 33875*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*x^4 + 17000*(8*B*a^3*b^7 + 3*A*a^
2*b^8)*d^5*x^3 - 81000*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*x^2 + 31500*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*x - 1918*(5
*B*a^6*b^4 + 6*A*a^5*b^5)*d^5)*e^6 - (47497*B*b^10*d^6*x^5 - 48210*(10*B*a*b^9 + A*b^10)*d^6*x^4 + 14250*(9*B*
a^2*b^8 + 2*A*a*b^9)*d^6*x^3 + 219000*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*x^2 - 168750*(7*B*a^4*b^6 + 4*A*a^3*b^7)
*d^6*x + 21924*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6)*e^5 - 5*(19777*B*b^10*d^7*x^4 - 4164*(10*B*a*b^9 + A*b^10)*d^7
*x^3 - 22350*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*x^2 + 34500*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*x - 8262*(7*B*a^4*b^6 +
4*A*a^3*b^7)*d^7)*e^4 - 5*(11834*B*b^10*d^8*x^3 + 5916*(10*B*a*b^9 + A*b^10)*d^8*x^2 - 20625*(9*B*a^2*b^8 + 2
*A*a*b^9)*d^8*x + 8916*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8)*e^3 + 5*(6646*B*b^10*d^9*x^2 - 6738*(10*B*a*b^9 + A*b^
10)*d^9*x + 5637*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9)*e^2 + (51265*B*b^10*d^10*x - 9762*(10*B*a*b^9 + A*b^10)*d^10)*
e + 2520*(11*B*b^10*d^11 + (5*B*a^6*b^4 + 6*A*a^5*b^5)*x^5*e^11 - (6*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*x^5 - 5*(5*
B*a^6*b^4 + 6*A*a^5*b^5)*d*x^4)*e^10 + 5*(3*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*x^5 - 6*(6*B*a^5*b^5 + 5*A*a^4*b^6
)*d^2*x^4 + 2*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*x^3)*e^9 - 5*(4*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*x^5 - 15*(7*B*a^
4*b^6 + 4*A*a^3*b^7)*d^3*x^4 + 12*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*x^3 - 2*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*x^2)
*e^8 + 5*(3*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*x^5 - 20*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*x^4 + 30*(7*B*a^4*b^6 + 4*A
*a^3*b^7)*d^4*x^3 - 12*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*x^2 + (5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*x)*e^7 - (6*(10*B
*a*b^9 + A*b^10)*d^5*x^5 - 75*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*x^4 + 200*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*x^3 - 15
0*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*x^2 + 30*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*x - (5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5
)*e^6 + (11*B*b^10*d^6*x^5 - 30*(10*B*a*b^9 + A*b^10)*d^6*x^4 + 150*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*x^3 - 200*(8
*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*x^2 + 75*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*x - 6*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6)*
e^5 + 5*(11*B*b^10*d^7*x^4 - 12*(10*B*a*b^9 + A*b^10)*d^7*x^3 + 30*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*x^2 - 20*(8*B
*a^3*b^7 + 3*A*a^2*b^8)*d^7*x + 3*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7)*e^4 + 5*(22*B*b^10*d^8*x^3 - 12*(10*B*a*b^9
+ A*b^10)*d^8*x^2 + 15*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*x - 4*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8)*e^3 + 5*(22*B*b^1
0*d^9*x^2 - 6*(10*B*a*b^9 + A*b^10)*d^9*x + 3*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9)*e^2 + (55*B*b^10*d^10*x - 6*(10*B
*a*b^9 + A*b^10)*d^10)*e)*log(x*e + d))/(x^5*e^17 + 5*d*x^4*e^16 + 10*d^2*x^3*e^15 + 10*d^3*x^2*e^14 + 5*d^4*x
*e^13 + d^5*e^12)

________________________________________________________________________________________

Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)**10*(B*x+A)/(e*x+d)**6,x)

[Out]

Timed out

________________________________________________________________________________________

Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 1900 vs. \(2 (463) = 926\).
time = 1.63, size = 1900, normalized size = 4.25 \begin {gather*} \text {Too large to display} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)^10*(B*x+A)/(e*x+d)^6,x, algorithm="giac")

[Out]

42*(11*B*b^10*d^6 - 60*B*a*b^9*d^5*e - 6*A*b^10*d^5*e + 135*B*a^2*b^8*d^4*e^2 + 30*A*a*b^9*d^4*e^2 - 160*B*a^3
*b^7*d^3*e^3 - 60*A*a^2*b^8*d^3*e^3 + 105*B*a^4*b^6*d^2*e^4 + 60*A*a^3*b^7*d^2*e^4 - 36*B*a^5*b^5*d*e^5 - 30*A
*a^4*b^6*d*e^5 + 5*B*a^6*b^4*e^6 + 6*A*a^5*b^5*e^6)*e^(-12)*log(abs(x*e + d)) + 1/60*(10*B*b^10*x^6*e^30 - 72*
B*b^10*d*x^5*e^29 + 315*B*b^10*d^2*x^4*e^28 - 1120*B*b^10*d^3*x^3*e^27 + 3780*B*b^10*d^4*x^2*e^26 - 15120*B*b^
10*d^5*x*e^25 + 120*B*a*b^9*x^5*e^30 + 12*A*b^10*x^5*e^30 - 900*B*a*b^9*d*x^4*e^29 - 90*A*b^10*d*x^4*e^29 + 42
00*B*a*b^9*d^2*x^3*e^28 + 420*A*b^10*d^2*x^3*e^28 - 16800*B*a*b^9*d^3*x^2*e^27 - 1680*A*b^10*d^3*x^2*e^27 + 75
600*B*a*b^9*d^4*x*e^26 + 7560*A*b^10*d^4*x*e^26 + 675*B*a^2*b^8*x^4*e^30 + 150*A*a*b^9*x^4*e^30 - 5400*B*a^2*b
^8*d*x^3*e^29 - 1200*A*a*b^9*d*x^3*e^29 + 28350*B*a^2*b^8*d^2*x^2*e^28 + 6300*A*a*b^9*d^2*x^2*e^28 - 151200*B*
a^2*b^8*d^3*x*e^27 - 33600*A*a*b^9*d^3*x*e^27 + 2400*B*a^3*b^7*x^3*e^30 + 900*A*a^2*b^8*x^3*e^30 - 21600*B*a^3
*b^7*d*x^2*e^29 - 8100*A*a^2*b^8*d*x^2*e^29 + 151200*B*a^3*b^7*d^2*x*e^28 + 56700*A*a^2*b^8*d^2*x*e^28 + 6300*
B*a^4*b^6*x^2*e^30 + 3600*A*a^3*b^7*x^2*e^30 - 75600*B*a^4*b^6*d*x*e^29 - 43200*A*a^3*b^7*d*x*e^29 + 15120*B*a
^5*b^5*x*e^30 + 12600*A*a^4*b^6*x*e^30)*e^(-36) + 1/60*(15797*B*b^10*d^11 - 97620*B*a*b^9*d^10*e - 9762*A*b^10
*d^10*e + 253665*B*a^2*b^8*d^9*e^2 + 56370*A*a*b^9*d^9*e^2 - 356640*B*a^3*b^7*d^8*e^3 - 133740*A*a^2*b^8*d^8*e
^3 + 289170*B*a^4*b^6*d^7*e^4 + 165240*A*a^3*b^7*d^7*e^4 - 131544*B*a^5*b^5*d^6*e^5 - 109620*A*a^4*b^6*d^6*e^5
+ 28770*B*a^6*b^4*d^5*e^6 + 34524*A*a^5*b^5*d^5*e^6 - 1440*B*a^7*b^3*d^4*e^7 - 2520*A*a^6*b^4*d^4*e^7 - 135*B
*a^8*b^2*d^3*e^8 - 360*A*a^7*b^3*d^3*e^8 - 20*B*a^9*b*d^2*e^9 - 90*A*a^8*b^2*d^2*e^9 - 3*B*a^10*d*e^10 - 30*A*
a^9*b*d*e^10 - 12*A*a^10*e^11 + 1800*(11*B*b^10*d^7*e^4 - 70*B*a*b^9*d^6*e^5 - 7*A*b^10*d^6*e^5 + 189*B*a^2*b^
8*d^5*e^6 + 42*A*a*b^9*d^5*e^6 - 280*B*a^3*b^7*d^4*e^7 - 105*A*a^2*b^8*d^4*e^7 + 245*B*a^4*b^6*d^3*e^8 + 140*A
*a^3*b^7*d^3*e^8 - 126*B*a^5*b^5*d^2*e^9 - 105*A*a^4*b^6*d^2*e^9 + 35*B*a^6*b^4*d*e^10 + 42*A*a^5*b^5*d*e^10 -
4*B*a^7*b^3*e^11 - 7*A*a^6*b^4*e^11)*x^4 + 450*(165*B*b^10*d^8*e^3 - 1040*B*a*b^9*d^7*e^4 - 104*A*b^10*d^7*e^
4 + 2772*B*a^2*b^8*d^6*e^5 + 616*A*a*b^9*d^6*e^5 - 4032*B*a^3*b^7*d^5*e^6 - 1512*A*a^2*b^8*d^5*e^6 + 3430*B*a^
4*b^6*d^4*e^7 + 1960*A*a^3*b^7*d^4*e^7 - 1680*B*a^5*b^5*d^3*e^8 - 1400*A*a^4*b^6*d^3*e^8 + 420*B*a^6*b^4*d^2*e
^9 + 504*A*a^5*b^5*d^2*e^9 - 32*B*a^7*b^3*d*e^10 - 56*A*a^6*b^4*d*e^10 - 3*B*a^8*b^2*e^11 - 8*A*a^7*b^3*e^11)*
x^3 + 50*(2101*B*b^10*d^9*e^2 - 13140*B*a*b^9*d^8*e^3 - 1314*A*b^10*d^8*e^3 + 34668*B*a^2*b^8*d^7*e^4 + 7704*A
*a*b^9*d^7*e^4 - 49728*B*a^3*b^7*d^6*e^5 - 18648*A*a^2*b^8*d^6*e^5 + 41454*B*a^4*b^6*d^5*e^6 + 23688*A*a^3*b^7
*d^5*e^6 - 19656*B*a^5*b^5*d^4*e^7 - 16380*A*a^4*b^6*d^4*e^7 + 4620*B*a^6*b^4*d^3*e^8 + 5544*A*a^5*b^5*d^3*e^8
- 288*B*a^7*b^3*d^2*e^9 - 504*A*a^6*b^4*d^2*e^9 - 27*B*a^8*b^2*d*e^10 - 72*A*a^7*b^3*d*e^10 - 4*B*a^9*b*e^11
- 18*A*a^8*b^2*e^11)*x^2 + 5*(13277*B*b^10*d^10*e - 82500*B*a*b^9*d^9*e^2 - 8250*A*b^10*d^9*e^2 + 215865*B*a^2
*b^8*d^8*e^3 + 47970*A*a*b^9*d^8*e^3 - 306240*B*a^3*b^7*d^7*e^4 - 114840*A*a^2*b^8*d^7*e^4 + 251370*B*a^4*b^6*
d^6*e^5 + 143640*A*a^3*b^7*d^6*e^5 - 116424*B*a^5*b^5*d^5*e^6 - 97020*A*a^4*b^6*d^5*e^6 + 26250*B*a^6*b^4*d^4*
e^7 + 31500*A*a^5*b^5*d^4*e^7 - 1440*B*a^7*b^3*d^3*e^8 - 2520*A*a^6*b^4*d^3*e^8 - 135*B*a^8*b^2*d^2*e^9 - 360*
A*a^7*b^3*d^2*e^9 - 20*B*a^9*b*d*e^10 - 90*A*a^8*b^2*d*e^10 - 3*B*a^10*e^11 - 30*A*a^9*b*e^11)*x)*e^(-12)/(x*e
+ d)^5

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Mupad [B]
time = 0.42, size = 2681, normalized size = 6.00 \begin {gather*} \text {Too large to display} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((A + B*x)*(a + b*x)^10)/(d + e*x)^6,x)

[Out]

x^5*((A*b^10 + 10*B*a*b^9)/(5*e^6) - (6*B*b^10*d)/(5*e^7)) - x^4*((3*d*((A*b^10 + 10*B*a*b^9)/e^6 - (6*B*b^10*
d)/e^7))/(2*e) - (5*a*b^8*(2*A*b + 9*B*a))/(4*e^6) + (15*B*b^10*d^2)/(4*e^8)) - (x^4*(210*A*a^6*b^4*e^10 + 120
*B*a^7*b^3*e^10 + 210*A*b^10*d^6*e^4 - 330*B*b^10*d^7*e^3 - 1260*A*a*b^9*d^5*e^5 - 1260*A*a^5*b^5*d*e^9 + 2100
*B*a*b^9*d^6*e^4 - 1050*B*a^6*b^4*d*e^9 + 3150*A*a^2*b^8*d^4*e^6 - 4200*A*a^3*b^7*d^3*e^7 + 3150*A*a^4*b^6*d^2
*e^8 - 5670*B*a^2*b^8*d^5*e^5 + 8400*B*a^3*b^7*d^4*e^6 - 7350*B*a^4*b^6*d^3*e^7 + 3780*B*a^5*b^5*d^2*e^8) + x^
3*(60*A*a^7*b^3*e^10 + (45*B*a^8*b^2*e^10)/2 + 780*A*b^10*d^7*e^3 - (2475*B*b^10*d^8*e^2)/2 - 4620*A*a*b^9*d^6
*e^4 + 420*A*a^6*b^4*d*e^9 + 7800*B*a*b^9*d^7*e^3 + 240*B*a^7*b^3*d*e^9 + 11340*A*a^2*b^8*d^5*e^5 - 14700*A*a^
3*b^7*d^4*e^6 + 10500*A*a^4*b^6*d^3*e^7 - 3780*A*a^5*b^5*d^2*e^8 - 20790*B*a^2*b^8*d^6*e^4 + 30240*B*a^3*b^7*d
^5*e^5 - 25725*B*a^4*b^6*d^4*e^6 + 12600*B*a^5*b^5*d^3*e^7 - 3150*B*a^6*b^4*d^2*e^8) + (12*A*a^10*e^11 - 15797
*B*b^10*d^11 + 9762*A*b^10*d^10*e + 3*B*a^10*d*e^10 - 56370*A*a*b^9*d^9*e^2 + 20*B*a^9*b*d^2*e^9 + 133740*A*a^
2*b^8*d^8*e^3 - 165240*A*a^3*b^7*d^7*e^4 + 109620*A*a^4*b^6*d^6*e^5 - 34524*A*a^5*b^5*d^5*e^6 + 2520*A*a^6*b^4
*d^4*e^7 + 360*A*a^7*b^3*d^3*e^8 + 90*A*a^8*b^2*d^2*e^9 - 253665*B*a^2*b^8*d^9*e^2 + 356640*B*a^3*b^7*d^8*e^3
- 289170*B*a^4*b^6*d^7*e^4 + 131544*B*a^5*b^5*d^6*e^5 - 28770*B*a^6*b^4*d^5*e^6 + 1440*B*a^7*b^3*d^4*e^7 + 135
*B*a^8*b^2*d^3*e^8 + 30*A*a^9*b*d*e^10 + 97620*B*a*b^9*d^10*e)/(60*e) + x*((B*a^10*e^10)/4 - (13277*B*b^10*d^1
0)/12 + (5*A*a^9*b*e^10)/2 + (1375*A*b^10*d^9*e)/2 - (7995*A*a*b^9*d^8*e^2)/2 + (15*A*a^8*b^2*d*e^9)/2 + 9570*
A*a^2*b^8*d^7*e^3 - 11970*A*a^3*b^7*d^6*e^4 + 8085*A*a^4*b^6*d^5*e^5 - 2625*A*a^5*b^5*d^4*e^6 + 210*A*a^6*b^4*
d^3*e^7 + 30*A*a^7*b^3*d^2*e^8 - (71955*B*a^2*b^8*d^8*e^2)/4 + 25520*B*a^3*b^7*d^7*e^3 - (41895*B*a^4*b^6*d^6*
e^4)/2 + 9702*B*a^5*b^5*d^5*e^5 - (4375*B*a^6*b^4*d^4*e^6)/2 + 120*B*a^7*b^3*d^3*e^7 + (45*B*a^8*b^2*d^2*e^8)/
4 + 6875*B*a*b^9*d^9*e + (5*B*a^9*b*d*e^9)/3) + x^2*((10*B*a^9*b*e^10)/3 - (10505*B*b^10*d^9*e)/6 + 15*A*a^8*b
^2*e^10 + 1095*A*b^10*d^8*e^2 - 6420*A*a*b^9*d^7*e^3 + 60*A*a^7*b^3*d*e^9 + 10950*B*a*b^9*d^8*e^2 + (45*B*a^8*
b^2*d*e^9)/2 + 15540*A*a^2*b^8*d^6*e^4 - 19740*A*a^3*b^7*d^5*e^5 + 13650*A*a^4*b^6*d^4*e^6 - 4620*A*a^5*b^5*d^
3*e^7 + 420*A*a^6*b^4*d^2*e^8 - 28890*B*a^2*b^8*d^7*e^3 + 41440*B*a^3*b^7*d^6*e^4 - 34545*B*a^4*b^6*d^5*e^5 +
16380*B*a^5*b^5*d^4*e^6 - 3850*B*a^6*b^4*d^3*e^7 + 240*B*a^7*b^3*d^2*e^8))/(d^5*e^11 + e^16*x^5 + 5*d^4*e^12*x
+ 5*d*e^15*x^4 + 10*d^3*e^13*x^2 + 10*d^2*e^14*x^3) - x^3*((5*d^2*((A*b^10 + 10*B*a*b^9)/e^6 - (6*B*b^10*d)/e
^7))/e^2 - (2*d*((6*d*((A*b^10 + 10*B*a*b^9)/e^6 - (6*B*b^10*d)/e^7))/e - (5*a*b^8*(2*A*b + 9*B*a))/e^6 + (15*
B*b^10*d^2)/e^8))/e - (5*a^2*b^7*(3*A*b + 8*B*a))/e^6 + (20*B*b^10*d^3)/(3*e^9)) - x*((6*d*((6*d*((15*d^2*((A*
b^10 + 10*B*a*b^9)/e^6 - (6*B*b^10*d)/e^7))/e^2 - (6*d*((6*d*((A*b^10 + 10*B*a*b^9)/e^6 - (6*B*b^10*d)/e^7))/e
- (5*a*b^8*(2*A*b + 9*B*a))/e^6 + (15*B*b^10*d^2)/e^8))/e - (15*a^2*b^7*(3*A*b + 8*B*a))/e^6 + (20*B*b^10*d^3
)/e^9))/e - (20*d^3*((A*b^10 + 10*B*a*b^9)/e^6 - (6*B*b^10*d)/e^7))/e^3 + (15*d^2*((6*d*((A*b^10 + 10*B*a*b^9)
/e^6 - (6*B*b^10*d)/e^7))/e - (5*a*b^8*(2*A*b + 9*B*a))/e^6 + (15*B*b^10*d^2)/e^8))/e^2 + (30*a^3*b^6*(4*A*b +
7*B*a))/e^6 - (15*B*b^10*d^4)/e^10))/e - (15*d^2*((15*d^2*((A*b^10 + 10*B*a*b^9)/e^6 - (6*B*b^10*d)/e^7))/e^2
- (6*d*((6*d*((A*b^10 + 10*B*a*b^9)/e^6 - (6*B*b^10*d)/e^7))/e - (5*a*b^8*(2*A*b + 9*B*a))/e^6 + (15*B*b^10*d
^2)/e^8))/e - (15*a^2*b^7*(3*A*b + 8*B*a))/e^6 + (20*B*b^10*d^3)/e^9))/e^2 + (15*d^4*((A*b^10 + 10*B*a*b^9)/e^
6 - (6*B*b^10*d)/e^7))/e^4 - (20*d^3*((6*d*((A*b^10 + 10*B*a*b^9)/e^6 - (6*B*b^10*d)/e^7))/e - (5*a*b^8*(2*A*b
+ 9*B*a))/e^6 + (15*B*b^10*d^2)/e^8))/e^3 - (42*a^4*b^5*(5*A*b + 6*B*a))/e^6 + (6*B*b^10*d^5)/e^11) + x^2*((3
*d*((15*d^2*((A*b^10 + 10*B*a*b^9)/e^6 - (6*B*b^10*d)/e^7))/e^2 - (6*d*((6*d*((A*b^10 + 10*B*a*b^9)/e^6 - (6*B
*b^10*d)/e^7))/e - (5*a*b^8*(2*A*b + 9*B*a))/e^6 + (15*B*b^10*d^2)/e^8))/e - (15*a^2*b^7*(3*A*b + 8*B*a))/e^6
+ (20*B*b^10*d^3)/e^9))/e - (10*d^3*((A*b^10 + 10*B*a*b^9)/e^6 - (6*B*b^10*d)/e^7))/e^3 + (15*d^2*((6*d*((A*b^
10 + 10*B*a*b^9)/e^6 - (6*B*b^10*d)/e^7))/e - (5*a*b^8*(2*A*b + 9*B*a))/e^6 + (15*B*b^10*d^2)/e^8))/(2*e^2) +
(15*a^3*b^6*(4*A*b + 7*B*a))/e^6 - (15*B*b^10*d^4)/(2*e^10)) + (log(d + e*x)*(462*B*b^10*d^6 - 252*A*b^10*d^5*
e + 252*A*a^5*b^5*e^6 + 210*B*a^6*b^4*e^6 + 1260*A*a*b^9*d^4*e^2 - 1260*A*a^4*b^6*d*e^5 - 1512*B*a^5*b^5*d*e^5
- 2520*A*a^2*b^8*d^3*e^3 + 2520*A*a^3*b^7*d^2*e^4 + 5670*B*a^2*b^8*d^4*e^2 - 6720*B*a^3*b^7*d^3*e^3 + 4410*B*
a^4*b^6*d^2*e^4 - 2520*B*a*b^9*d^5*e))/e^12 + (B*b^10*x^6)/(6*e^6)

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