3.11.95 \(\int \frac {(a+b x)^{10} (A+B x)}{(d+e x)^7} \, dx\) [1095]
Optimal. Leaf size=447 \[ \frac {30 b^6 (b d-a e)^3 (11 b B d-4 A b e-7 a B e) x}{e^{11}}+\frac {(b d-a e)^{10} (B d-A e)}{6 e^{12} (d+e x)^6}-\frac {(b d-a e)^9 (11 b B d-10 A b e-a B e)}{5 e^{12} (d+e x)^5}+\frac {5 b (b d-a e)^8 (11 b B d-9 A b e-2 a B e)}{4 e^{12} (d+e x)^4}-\frac {5 b^2 (b d-a e)^7 (11 b B d-8 A b e-3 a B e)}{e^{12} (d+e x)^3}+\frac {15 b^3 (b d-a e)^6 (11 b B d-7 A b e-4 a B e)}{e^{12} (d+e x)^2}-\frac {42 b^4 (b d-a e)^5 (11 b B d-6 A b e-5 a B e)}{e^{12} (d+e x)}-\frac {15 b^7 (b d-a e)^2 (11 b B d-3 A b e-8 a B e) (d+e x)^2}{2 e^{12}}+\frac {5 b^8 (b d-a e) (11 b B d-2 A b e-9 a B e) (d+e x)^3}{3 e^{12}}-\frac {b^9 (11 b B d-A b e-10 a B e) (d+e x)^4}{4 e^{12}}+\frac {b^{10} B (d+e x)^5}{5 e^{12}}-\frac {42 b^5 (b d-a e)^4 (11 b B d-5 A b e-6 a B e) \log (d+e x)}{e^{12}} \]
[Out]
30*b^6*(-a*e+b*d)^3*(-4*A*b*e-7*B*a*e+11*B*b*d)*x/e^11+1/6*(-a*e+b*d)^10*(-A*e+B*d)/e^12/(e*x+d)^6-1/5*(-a*e+b
*d)^9*(-10*A*b*e-B*a*e+11*B*b*d)/e^12/(e*x+d)^5+5/4*b*(-a*e+b*d)^8*(-9*A*b*e-2*B*a*e+11*B*b*d)/e^12/(e*x+d)^4-
5*b^2*(-a*e+b*d)^7*(-8*A*b*e-3*B*a*e+11*B*b*d)/e^12/(e*x+d)^3+15*b^3*(-a*e+b*d)^6*(-7*A*b*e-4*B*a*e+11*B*b*d)/
e^12/(e*x+d)^2-42*b^4*(-a*e+b*d)^5*(-6*A*b*e-5*B*a*e+11*B*b*d)/e^12/(e*x+d)-15/2*b^7*(-a*e+b*d)^2*(-3*A*b*e-8*
B*a*e+11*B*b*d)*(e*x+d)^2/e^12+5/3*b^8*(-a*e+b*d)*(-2*A*b*e-9*B*a*e+11*B*b*d)*(e*x+d)^3/e^12-1/4*b^9*(-A*b*e-1
0*B*a*e+11*B*b*d)*(e*x+d)^4/e^12+1/5*b^10*B*(e*x+d)^5/e^12-42*b^5*(-a*e+b*d)^4*(-5*A*b*e-6*B*a*e+11*B*b*d)*ln(
e*x+d)/e^12
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Rubi [A]
time = 0.74, 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)^4 (-10 a B e-A b e+11 b B d)}{4 e^{12}}+\frac {5 b^8 (d+e x)^3 (b d-a e) (-9 a B e-2 A b e+11 b B d)}{3 e^{12}}-\frac {15 b^7 (d+e x)^2 (b d-a e)^2 (-8 a B e-3 A b e+11 b B d)}{2 e^{12}}+\frac {30 b^6 x (b d-a e)^3 (-7 a B e-4 A b e+11 b B d)}{e^{11}}-\frac {42 b^5 (b d-a e)^4 \log (d+e x) (-6 a B e-5 A b e+11 b B d)}{e^{12}}-\frac {42 b^4 (b d-a e)^5 (-5 a B e-6 A b e+11 b B d)}{e^{12} (d+e x)}+\frac {15 b^3 (b d-a e)^6 (-4 a B e-7 A b e+11 b B d)}{e^{12} (d+e x)^2}-\frac {5 b^2 (b d-a e)^7 (-3 a B e-8 A b e+11 b B d)}{e^{12} (d+e x)^3}+\frac {5 b (b d-a e)^8 (-2 a B e-9 A b e+11 b B d)}{4 e^{12} (d+e x)^4}-\frac {(b d-a e)^9 (-a B e-10 A b e+11 b B d)}{5 e^{12} (d+e x)^5}+\frac {(b d-a e)^{10} (B d-A e)}{6 e^{12} (d+e x)^6}+\frac {b^{10} B (d+e x)^5}{5 e^{12}} \end {gather*}
Antiderivative was successfully verified.
[In]
Int[((a + b*x)^10*(A + B*x))/(d + e*x)^7,x]
[Out]
(30*b^6*(b*d - a*e)^3*(11*b*B*d - 4*A*b*e - 7*a*B*e)*x)/e^11 + ((b*d - a*e)^10*(B*d - A*e))/(6*e^12*(d + e*x)^
6) - ((b*d - a*e)^9*(11*b*B*d - 10*A*b*e - a*B*e))/(5*e^12*(d + e*x)^5) + (5*b*(b*d - a*e)^8*(11*b*B*d - 9*A*b
*e - 2*a*B*e))/(4*e^12*(d + e*x)^4) - (5*b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b*e - 3*a*B*e))/(e^12*(d + e*x)^3)
+ (15*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*e - 4*a*B*e))/(e^12*(d + e*x)^2) - (42*b^4*(b*d - a*e)^5*(11*b*B*d -
6*A*b*e - 5*a*B*e))/(e^12*(d + e*x)) - (15*b^7*(b*d - a*e)^2*(11*b*B*d - 3*A*b*e - 8*a*B*e)*(d + e*x)^2)/(2*e
^12) + (5*b^8*(b*d - a*e)*(11*b*B*d - 2*A*b*e - 9*a*B*e)*(d + e*x)^3)/(3*e^12) - (b^9*(11*b*B*d - A*b*e - 10*a
*B*e)*(d + e*x)^4)/(4*e^12) + (b^10*B*(d + e*x)^5)/(5*e^12) - (42*b^5*(b*d - a*e)^4*(11*b*B*d - 5*A*b*e - 6*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)^7} \, dx &=\int \left (-\frac {30 b^6 (b d-a e)^3 (-11 b B d+4 A b e+7 a B e)}{e^{11}}+\frac {(-b d+a e)^{10} (-B d+A e)}{e^{11} (d+e x)^7}+\frac {(-b d+a e)^9 (-11 b B d+10 A b e+a B e)}{e^{11} (d+e x)^6}+\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)^5}-\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)^4}+\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)^3}-\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)^2}+\frac {42 b^5 (b d-a e)^4 (-11 b B d+5 A b e+6 a B e)}{e^{11} (d+e x)}+\frac {15 b^7 (b d-a e)^2 (-11 b B d+3 A b e+8 a B e) (d+e x)}{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)^2}{e^{11}}+\frac {b^9 (-11 b B d+A b e+10 a B e) (d+e x)^3}{e^{11}}+\frac {b^{10} B (d+e x)^4}{e^{11}}\right ) \, dx\\ &=\frac {30 b^6 (b d-a e)^3 (11 b B d-4 A b e-7 a B e) x}{e^{11}}+\frac {(b d-a e)^{10} (B d-A e)}{6 e^{12} (d+e x)^6}-\frac {(b d-a e)^9 (11 b B d-10 A b e-a B e)}{5 e^{12} (d+e x)^5}+\frac {5 b (b d-a e)^8 (11 b B d-9 A b e-2 a B e)}{4 e^{12} (d+e x)^4}-\frac {5 b^2 (b d-a e)^7 (11 b B d-8 A b e-3 a B e)}{e^{12} (d+e x)^3}+\frac {15 b^3 (b d-a e)^6 (11 b B d-7 A b e-4 a B e)}{e^{12} (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^{12} (d+e x)}-\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}{2 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)^3}{3 e^{12}}-\frac {b^9 (11 b B d-A b e-10 a B e) (d+e x)^4}{4 e^{12}}+\frac {b^{10} B (d+e x)^5}{5 e^{12}}-\frac {42 b^5 (b d-a e)^4 (11 b B d-5 A b e-6 a B e) \log (d+e x)}{e^{12}}\\ \end {align*}
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Mathematica [A]
time = 0.32, size = 505, normalized size = 1.13 \begin {gather*} \frac {-60 b^6 e \left (-210 a^4 B e^4-42 b^4 d^3 (5 B d-2 A e)+280 a b^3 d^2 e (3 B d-A e)-315 a^2 b^2 d e^2 (4 B d-A e)-120 a^3 b e^3 (-7 B d+A e)\right ) x+30 b^7 e^2 \left (120 a^3 B e^3+70 a b^2 d e (4 B d-A e)+45 a^2 b e^2 (-7 B d+A e)+28 b^3 d^2 (-3 B d+A e)\right ) x^2-20 b^8 e^3 \left (-45 a^2 B e^2-10 a b e (-7 B d+A e)+7 b^2 d (-4 B d+A e)\right ) x^3+15 b^9 e^4 (-7 b B d+A b e+10 a B e) x^4+12 b^{10} B e^5 x^5+\frac {10 (b d-a e)^{10} (B d-A e)}{(d+e x)^6}-\frac {12 (b d-a e)^9 (11 b B d-10 A b e-a B e)}{(d+e x)^5}+\frac {75 b (b d-a e)^8 (11 b B d-9 A b e-2 a B e)}{(d+e x)^4}-\frac {300 b^2 (b d-a e)^7 (11 b B d-8 A b e-3 a B e)}{(d+e x)^3}+\frac {900 b^3 (b d-a e)^6 (11 b B d-7 A b e-4 a B e)}{(d+e x)^2}-\frac {2520 b^4 (b d-a e)^5 (11 b B d-6 A b e-5 a B e)}{d+e x}-2520 b^5 (b d-a e)^4 (11 b B d-5 A b e-6 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)^7,x]
[Out]
(-60*b^6*e*(-210*a^4*B*e^4 - 42*b^4*d^3*(5*B*d - 2*A*e) + 280*a*b^3*d^2*e*(3*B*d - A*e) - 315*a^2*b^2*d*e^2*(4
*B*d - A*e) - 120*a^3*b*e^3*(-7*B*d + A*e))*x + 30*b^7*e^2*(120*a^3*B*e^3 + 70*a*b^2*d*e*(4*B*d - A*e) + 45*a^
2*b*e^2*(-7*B*d + A*e) + 28*b^3*d^2*(-3*B*d + A*e))*x^2 - 20*b^8*e^3*(-45*a^2*B*e^2 - 10*a*b*e*(-7*B*d + A*e)
+ 7*b^2*d*(-4*B*d + A*e))*x^3 + 15*b^9*e^4*(-7*b*B*d + A*b*e + 10*a*B*e)*x^4 + 12*b^10*B*e^5*x^5 + (10*(b*d -
a*e)^10*(B*d - A*e))/(d + e*x)^6 - (12*(b*d - a*e)^9*(11*b*B*d - 10*A*b*e - a*B*e))/(d + e*x)^5 + (75*b*(b*d -
a*e)^8*(11*b*B*d - 9*A*b*e - 2*a*B*e))/(d + e*x)^4 - (300*b^2*(b*d - a*e)^7*(11*b*B*d - 8*A*b*e - 3*a*B*e))/(
d + e*x)^3 + (900*b^3*(b*d - a*e)^6*(11*b*B*d - 7*A*b*e - 4*a*B*e))/(d + e*x)^2 - (2520*b^4*(b*d - a*e)^5*(11*
b*B*d - 6*A*b*e - 5*a*B*e))/(d + e*x) - 2520*b^5*(b*d - a*e)^4*(11*b*B*d - 5*A*b*e - 6*a*B*e)*Log[d + e*x])/(6
0*e^12)
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(1973\) vs.
\(2(433)=866\).
time = 0.09, size = 1974, normalized size = 4.42
| | |
| method |
result |
size |
| | |
| norman |
\(\text {Expression too large to display}\) |
\(1921\) |
| default |
\(\text {Expression too large to display}\) |
\(1974\) |
| risch |
\(\text {Expression too large to display}\) |
\(2036\) |
| | |
|
|
|
|
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((b*x+a)^10*(B*x+A)/(e*x+d)^7,x,method=_RETURNVERBOSE)
[Out]
b^6/e^11*(-315*A*a^2*b^2*d*e^3*x+280*A*a*b^3*d^2*e^2*x-840*B*a^3*b*d*e^3*x+1260*B*a^2*b^2*d^2*e^2*x-840*B*a*b^
3*d^3*e*x-315/2*B*a^2*b^2*d*e^3*x^2+140*B*a*b^3*d^2*e^2*x^2-35*A*a*b^3*d*e^3*x^2-70/3*B*a*b^3*d*e^3*x^3+1/5*b^
4*B*x^5*e^4+1/4*A*b^4*e^4*x^4+210*B*a^4*e^4*x+210*B*b^4*d^4*x+14*A*b^4*d^2*e^2*x^2+60*B*a^3*b*e^4*x^2+5/2*B*a*
b^3*e^4*x^4-7/4*B*b^4*d*e^3*x^4+10/3*A*a*b^3*e^4*x^3-7/3*A*b^4*d*e^3*x^3+15*B*a^2*b^2*e^4*x^3+28/3*B*b^4*d^2*e
^2*x^3+45/2*A*a^2*b^2*e^4*x^2-42*B*b^4*d^3*e*x^2+120*A*a^3*b*e^4*x-84*A*b^4*d^3*e*x)-15*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)^2-5/4*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)^4-42*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)/(e*x+d)-1/6*(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)^6-1/5/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)^5-5*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)^3+42*b^5/e^12*(5*A*a^4*b*e^5-20*A*a^3*
b^2*d*e^4+30*A*a^2*b^3*d^2*e^3-20*A*a*b^4*d^3*e^2+5*A*b^5*d^4*e+6*B*a^5*e^5-35*B*a^4*b*d*e^4+80*B*a^3*b^2*d^2*
e^3-90*B*a^2*b^3*d^3*e^2+50*B*a*b^4*d^4*e-11*B*b^5*d^5)*ln(e*x+d)
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 1902 vs.
\(2 (463) = 926\).
time = 0.59, size = 1902, normalized size = 4.26 \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)^7,x, algorithm="maxima")
[Out]
-42*(11*B*b^10*d^5 - 6*B*a^5*b^5*e^5 - 5*A*a^4*b^6*e^5 - 5*(10*B*a*b^9*e + A*b^10*e)*d^4 + 10*(9*B*a^2*b^8*e^2
+ 2*A*a*b^9*e^2)*d^3 - 10*(8*B*a^3*b^7*e^3 + 3*A*a^2*b^8*e^3)*d^2 + 5*(7*B*a^4*b^6*e^4 + 4*A*a^3*b^7*e^4)*d)*
e^(-12)*log(x*e + d) + 1/60*(12*B*b^10*x^5*e^4 - 15*(7*B*b^10*d*e^3 - 10*B*a*b^9*e^4 - A*b^10*e^4)*x^4 + 20*(2
8*B*b^10*d^2*e^2 + 45*B*a^2*b^8*e^4 + 10*A*a*b^9*e^4 - 7*(10*B*a*b^9*e^3 + A*b^10*e^3)*d)*x^3 - 30*(84*B*b^10*
d^3*e - 120*B*a^3*b^7*e^4 - 45*A*a^2*b^8*e^4 - 28*(10*B*a*b^9*e^2 + A*b^10*e^2)*d^2 + 35*(9*B*a^2*b^8*e^3 + 2*
A*a*b^9*e^3)*d)*x^2 + 60*(210*B*b^10*d^4 + 210*B*a^4*b^6*e^4 + 120*A*a^3*b^7*e^4 - 84*(10*B*a*b^9*e + A*b^10*e
)*d^3 + 140*(9*B*a^2*b^8*e^2 + 2*A*a*b^9*e^2)*d^2 - 105*(8*B*a^3*b^7*e^3 + 3*A*a^2*b^8*e^3)*d)*x)*e^(-11) - 1/
60*(20417*B*b^10*d^11 + 10*A*a^10*e^11 - 10655*(10*B*a*b^9*e + A*b^10*e)*d^10 + 25090*(9*B*a^2*b^8*e^2 + 2*A*a
*b^9*e^2)*d^9 - 30690*(8*B*a^3*b^7*e^3 + 3*A*a^2*b^8*e^3)*d^8 + 20070*(7*B*a^4*b^6*e^4 + 4*A*a^3*b^7*e^4)*d^7
- 6174*(6*B*a^5*b^5*e^5 + 5*A*a^4*b^6*e^5)*d^6 + 420*(5*B*a^6*b^4*e^6 + 6*A*a^5*b^5*e^6)*d^5 + 2520*(11*B*b^10
*d^6*e^5 + 5*B*a^6*b^4*e^11 + 6*A*a^5*b^5*e^11 - 6*(10*B*a*b^9*e^6 + A*b^10*e^6)*d^5 + 15*(9*B*a^2*b^8*e^7 + 2
*A*a*b^9*e^7)*d^4 - 20*(8*B*a^3*b^7*e^8 + 3*A*a^2*b^8*e^8)*d^3 + 15*(7*B*a^4*b^6*e^9 + 4*A*a^3*b^7*e^9)*d^2 -
6*(6*B*a^5*b^5*e^10 + 5*A*a^4*b^6*e^10)*d)*x^5 + 60*(4*B*a^7*b^3*e^7 + 7*A*a^6*b^4*e^7)*d^4 + 900*(143*B*b^10*
d^7*e^4 + 4*B*a^7*b^3*e^11 + 7*A*a^6*b^4*e^11 - 77*(10*B*a*b^9*e^5 + A*b^10*e^5)*d^6 + 189*(9*B*a^2*b^8*e^6 +
2*A*a*b^9*e^6)*d^5 - 245*(8*B*a^3*b^7*e^7 + 3*A*a^2*b^8*e^7)*d^4 + 175*(7*B*a^4*b^6*e^8 + 4*A*a^3*b^7*e^8)*d^3
- 63*(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 + 15*(3*B*a^8*b
^2*e^8 + 8*A*a^7*b^3*e^8)*d^3 + 300*(803*B*b^10*d^8*e^3 + 3*B*a^8*b^2*e^11 + 8*A*a^7*b^3*e^11 - 428*(10*B*a*b^
9*e^4 + A*b^10*e^4)*d^7 + 1036*(9*B*a^2*b^8*e^5 + 2*A*a*b^9*e^5)*d^6 - 1316*(8*B*a^3*b^7*e^6 + 3*A*a^2*b^8*e^6
)*d^5 + 910*(7*B*a^4*b^6*e^7 + 4*A*a^3*b^7*e^7)*d^4 - 308*(6*B*a^5*b^5*e^8 + 5*A*a^4*b^6*e^8)*d^3 + 28*(5*B*a^
6*b^4*e^9 + 6*A*a^5*b^5*e^9)*d^2 + 4*(4*B*a^7*b^3*e^10 + 7*A*a^6*b^4*e^10)*d)*x^3 + 5*(2*B*a^9*b*e^9 + 9*A*a^8
*b^2*e^9)*d^2 + 75*(3025*B*b^10*d^9*e^2 + 2*B*a^9*b*e^11 + 9*A*a^8*b^2*e^11 - 1599*(10*B*a*b^9*e^3 + A*b^10*e^
3)*d^8 + 3828*(9*B*a^2*b^8*e^4 + 2*A*a*b^9*e^4)*d^7 - 4788*(8*B*a^3*b^7*e^5 + 3*A*a^2*b^8*e^5)*d^6 + 3234*(7*B
*a^4*b^6*e^6 + 4*A*a^3*b^7*e^6)*d^5 - 1050*(6*B*a^5*b^5*e^7 + 5*A*a^4*b^6*e^7)*d^4 + 84*(5*B*a^6*b^4*e^8 + 6*A
*a^5*b^5*e^8)*d^3 + 12*(4*B*a^7*b^3*e^9 + 7*A*a^6*b^4*e^9)*d^2 + 3*(3*B*a^8*b^2*e^10 + 8*A*a^7*b^3*e^10)*d)*x^
2 + 2*(B*a^10*e^10 + 10*A*a^9*b*e^10)*d + 6*(17897*B*b^10*d^10*e + 2*B*a^10*e^11 + 20*A*a^9*b*e^11 - 9395*(10*
B*a*b^9*e^2 + A*b^10*e^2)*d^9 + 22290*(9*B*a^2*b^8*e^3 + 2*A*a*b^9*e^3)*d^8 - 27540*(8*B*a^3*b^7*e^4 + 3*A*a^2
*b^8*e^4)*d^7 + 18270*(7*B*a^4*b^6*e^5 + 4*A*a^3*b^7*e^5)*d^6 - 5754*(6*B*a^5*b^5*e^6 + 5*A*a^4*b^6*e^6)*d^5 +
420*(5*B*a^6*b^4*e^7 + 6*A*a^5*b^5*e^7)*d^4 + 60*(4*B*a^7*b^3*e^8 + 7*A*a^6*b^4*e^8)*d^3 + 15*(3*B*a^8*b^2*e^
9 + 8*A*a^7*b^3*e^9)*d^2 + 5*(2*B*a^9*b*e^10 + 9*A*a^8*b^2*e^10)*d)*x)/(x^6*e^18 + 6*d*x^5*e^17 + 15*d^2*x^4*e
^16 + 20*d^3*x^3*e^15 + 15*d^4*x^2*e^14 + 6*d^5*x*e^13 + d^6*e^12)
________________________________________________________________________________________
Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 2776 vs.
\(2 (463) = 926\).
time = 0.90, size = 2776, normalized size = 6.21 \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)^7,x, algorithm="fricas")
[Out]
-1/60*(20417*B*b^10*d^11 - (12*B*b^10*x^11 - 10*A*a^10 + 15*(10*B*a*b^9 + A*b^10)*x^10 + 100*(9*B*a^2*b^8 + 2*
A*a*b^9)*x^9 + 450*(8*B*a^3*b^7 + 3*A*a^2*b^8)*x^8 + 1800*(7*B*a^4*b^6 + 4*A*a^3*b^7)*x^7 - 2520*(5*B*a^6*b^4
+ 6*A*a^5*b^5)*x^5 - 900*(4*B*a^7*b^3 + 7*A*a^6*b^4)*x^4 - 300*(3*B*a^8*b^2 + 8*A*a^7*b^3)*x^3 - 75*(2*B*a^9*b
+ 9*A*a^8*b^2)*x^2 - 12*(B*a^10 + 10*A*a^9*b)*x)*e^11 + (33*B*b^10*d*x^10 + 50*(10*B*a*b^9 + A*b^10)*d*x^9 +
450*(9*B*a^2*b^8 + 2*A*a*b^9)*d*x^8 + 3600*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*x^7 - 10800*(7*B*a^4*b^6 + 4*A*a^3*b^
7)*d*x^6 - 15120*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*x^5 + 6300*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*x^4 + 1200*(4*B*a^7*b^
3 + 7*A*a^6*b^4)*d*x^3 + 225*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*x^2 + 30*(2*B*a^9*b + 9*A*a^8*b^2)*d*x + 2*(B*a^10
+ 10*A*a^9*b)*d)*e^10 - 5*(22*B*b^10*d^2*x^9 + 45*(10*B*a*b^9 + A*b^10)*d^2*x^8 + 720*(9*B*a^2*b^8 + 2*A*a*b^9
)*d^2*x^7 - 6210*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*x^6 - 2160*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*x^5 + 11340*(6*B*a
^5*b^5 + 5*A*a^4*b^6)*d^2*x^4 - 1680*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*x^3 - 180*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2
*x^2 - 18*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*x - (2*B*a^9*b + 9*A*a^8*b^2)*d^2)*e^9 + 5*(99*B*b^10*d^3*x^8 + 360*
(10*B*a*b^9 + A*b^10)*d^3*x^7 - 7330*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*x^6 + 7020*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*
x^5 + 24300*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*x^4 - 18480*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*x^3 + 1260*(5*B*a^6*b^
4 + 6*A*a^5*b^5)*d^3*x^2 + 72*(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 - 5*(
792*B*b^10*d^4*x^7 - 4043*(10*B*a*b^9 + A*b^10)*d^4*x^6 + 13740*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*x^5 + 20250*(8*B
*a^3*b^7 + 3*A*a^2*b^8)*d^4*x^4 - 49200*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*x^3 + 15750*(6*B*a^5*b^5 + 5*A*a^4*b^6
)*d^4*x^2 - 504*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*x - 12*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4)*e^7 - (47497*B*b^10*d^
5*x^6 - 45690*(10*B*a*b^9 + A*b^10)*d^5*x^5 - 17250*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*x^4 + 303000*(8*B*a^3*b^7 +
3*A*a^2*b^8)*d^5*x^3 - 231750*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*x^2 + 34524*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*x -
420*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5)*e^6 - (118662*B*b^10*d^6*x^5 - 19725*(10*B*a*b^9 + A*b^10)*d^6*x^4 - 1910
00*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*x^3 + 321750*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*x^2 - 107820*(7*B*a^4*b^6 + 4*A*
a^3*b^7)*d^6*x + 6174*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6)*e^5 - 5*(17751*B*b^10*d^7*x^4 + 11540*(10*B*a*b^9 + A*b
^10)*d^7*x^3 - 47550*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*x^2 + 31788*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*x - 4014*(7*B*a
^4*b^6 + 4*A*a^3*b^7)*d^7)*e^4 + 5*(13292*B*b^10*d^8*x^3 - 18105*(10*B*a*b^9 + A*b^10)*d^8*x^2 + 25068*(9*B*a^
2*b^8 + 2*A*a*b^9)*d^8*x - 6138*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8)*e^3 + 5*(30759*B*b^10*d^9*x^2 - 10266*(10*B*a
*b^9 + A*b^10)*d^9*x + 5018*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9)*e^2 + (94782*B*b^10*d^10*x - 10655*(10*B*a*b^9 + A*
b^10)*d^10)*e + 2520*(11*B*b^10*d^11 - (6*B*a^5*b^5 + 5*A*a^4*b^6)*x^6*e^11 + (5*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d
*x^6 - 6*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*x^5)*e^10 - 5*(2*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*x^6 - 6*(7*B*a^4*b^6 +
4*A*a^3*b^7)*d^2*x^5 + 3*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*x^4)*e^9 + 5*(2*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*x^6 -
12*(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 - 4*(6*B*a^5*b^5 + 5*A*a^4*b^6
)*d^3*x^3)*e^8 - 5*((10*B*a*b^9 + A*b^10)*d^4*x^6 - 12*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*x^5 + 30*(8*B*a^3*b^7 + 3
*A*a^2*b^8)*d^4*x^4 - 20*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*x^3 + 3*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*x^2)*e^7 + (1
1*B*b^10*d^5*x^6 - 30*(10*B*a*b^9 + A*b^10)*d^5*x^5 + 150*(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 + 75*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*x^2 - 6*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*x)*e^6 +
(66*B*b^10*d^6*x^5 - 75*(10*B*a*b^9 + A*b^10)*d^6*x^4 + 200*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*x^3 - 150*(8*B*a^3*b
^7 + 3*A*a^2*b^8)*d^6*x^2 + 30*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*x - (6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6)*e^5 + 5*(3
3*B*b^10*d^7*x^4 - 20*(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 - 12*(8*B*a^3*b^7 +
3*A*a^2*b^8)*d^7*x + (7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7)*e^4 + 5*(44*B*b^10*d^8*x^3 - 15*(10*B*a*b^9 + A*b^10)*d
^8*x^2 + 12*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*x - 2*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8)*e^3 + 5*(33*B*b^10*d^9*x^2 -
6*(10*B*a*b^9 + A*b^10)*d^9*x + 2*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9)*e^2 + (66*B*b^10*d^10*x - 5*(10*B*a*b^9 + A*b
^10)*d^10)*e)*log(x*e + d))/(x^6*e^18 + 6*d*x^5*e^17 + 15*d^2*x^4*e^16 + 20*d^3*x^3*e^15 + 15*d^4*x^2*e^14 + 6
*d^5*x*e^13 + d^6*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)**7,x)
[Out]
Timed out
________________________________________________________________________________________
Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 1877 vs.
\(2 (463) = 926\).
time = 1.13, size = 1877, normalized size = 4.20 \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)^7,x, algorithm="giac")
[Out]
-42*(11*B*b^10*d^5 - 50*B*a*b^9*d^4*e - 5*A*b^10*d^4*e + 90*B*a^2*b^8*d^3*e^2 + 20*A*a*b^9*d^3*e^2 - 80*B*a^3*
b^7*d^2*e^3 - 30*A*a^2*b^8*d^2*e^3 + 35*B*a^4*b^6*d*e^4 + 20*A*a^3*b^7*d*e^4 - 6*B*a^5*b^5*e^5 - 5*A*a^4*b^6*e
^5)*e^(-12)*log(abs(x*e + d)) + 1/60*(12*B*b^10*x^5*e^28 - 105*B*b^10*d*x^4*e^27 + 560*B*b^10*d^2*x^3*e^26 - 2
520*B*b^10*d^3*x^2*e^25 + 12600*B*b^10*d^4*x*e^24 + 150*B*a*b^9*x^4*e^28 + 15*A*b^10*x^4*e^28 - 1400*B*a*b^9*d
*x^3*e^27 - 140*A*b^10*d*x^3*e^27 + 8400*B*a*b^9*d^2*x^2*e^26 + 840*A*b^10*d^2*x^2*e^26 - 50400*B*a*b^9*d^3*x*
e^25 - 5040*A*b^10*d^3*x*e^25 + 900*B*a^2*b^8*x^3*e^28 + 200*A*a*b^9*x^3*e^28 - 9450*B*a^2*b^8*d*x^2*e^27 - 21
00*A*a*b^9*d*x^2*e^27 + 75600*B*a^2*b^8*d^2*x*e^26 + 16800*A*a*b^9*d^2*x*e^26 + 3600*B*a^3*b^7*x^2*e^28 + 1350
*A*a^2*b^8*x^2*e^28 - 50400*B*a^3*b^7*d*x*e^27 - 18900*A*a^2*b^8*d*x*e^27 + 12600*B*a^4*b^6*x*e^28 + 7200*A*a^
3*b^7*x*e^28)*e^(-35) - 1/60*(20417*B*b^10*d^11 - 106550*B*a*b^9*d^10*e - 10655*A*b^10*d^10*e + 225810*B*a^2*b
^8*d^9*e^2 + 50180*A*a*b^9*d^9*e^2 - 245520*B*a^3*b^7*d^8*e^3 - 92070*A*a^2*b^8*d^8*e^3 + 140490*B*a^4*b^6*d^7
*e^4 + 80280*A*a^3*b^7*d^7*e^4 - 37044*B*a^5*b^5*d^6*e^5 - 30870*A*a^4*b^6*d^6*e^5 + 2100*B*a^6*b^4*d^5*e^6 +
2520*A*a^5*b^5*d^5*e^6 + 240*B*a^7*b^3*d^4*e^7 + 420*A*a^6*b^4*d^4*e^7 + 45*B*a^8*b^2*d^3*e^8 + 120*A*a^7*b^3*
d^3*e^8 + 10*B*a^9*b*d^2*e^9 + 45*A*a^8*b^2*d^2*e^9 + 2*B*a^10*d*e^10 + 20*A*a^9*b*d*e^10 + 10*A*a^10*e^11 + 2
520*(11*B*b^10*d^6*e^5 - 60*B*a*b^9*d^5*e^6 - 6*A*b^10*d^5*e^6 + 135*B*a^2*b^8*d^4*e^7 + 30*A*a*b^9*d^4*e^7 -
160*B*a^3*b^7*d^3*e^8 - 60*A*a^2*b^8*d^3*e^8 + 105*B*a^4*b^6*d^2*e^9 + 60*A*a^3*b^7*d^2*e^9 - 36*B*a^5*b^5*d*e
^10 - 30*A*a^4*b^6*d*e^10 + 5*B*a^6*b^4*e^11 + 6*A*a^5*b^5*e^11)*x^5 + 900*(143*B*b^10*d^7*e^4 - 770*B*a*b^9*d
^6*e^5 - 77*A*b^10*d^6*e^5 + 1701*B*a^2*b^8*d^5*e^6 + 378*A*a*b^9*d^5*e^6 - 1960*B*a^3*b^7*d^4*e^7 - 735*A*a^2
*b^8*d^4*e^7 + 1225*B*a^4*b^6*d^3*e^8 + 700*A*a^3*b^7*d^3*e^8 - 378*B*a^5*b^5*d^2*e^9 - 315*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 + 300*(803*B*b^10*d^8*e
^3 - 4280*B*a*b^9*d^7*e^4 - 428*A*b^10*d^7*e^4 + 9324*B*a^2*b^8*d^6*e^5 + 2072*A*a*b^9*d^6*e^5 - 10528*B*a^3*b
^7*d^5*e^6 - 3948*A*a^2*b^8*d^5*e^6 + 6370*B*a^4*b^6*d^4*e^7 + 3640*A*a^3*b^7*d^4*e^7 - 1848*B*a^5*b^5*d^3*e^8
- 1540*A*a^4*b^6*d^3*e^8 + 140*B*a^6*b^4*d^2*e^9 + 168*A*a^5*b^5*d^2*e^9 + 16*B*a^7*b^3*d*e^10 + 28*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 + 75*(3025*B*b^10*d^9*e^2 - 15990*B*a*b^9*d^8*e^3 - 1599*A*
b^10*d^8*e^3 + 34452*B*a^2*b^8*d^7*e^4 + 7656*A*a*b^9*d^7*e^4 - 38304*B*a^3*b^7*d^6*e^5 - 14364*A*a^2*b^8*d^6*
e^5 + 22638*B*a^4*b^6*d^5*e^6 + 12936*A*a^3*b^7*d^5*e^6 - 6300*B*a^5*b^5*d^4*e^7 - 5250*A*a^4*b^6*d^4*e^7 + 42
0*B*a^6*b^4*d^3*e^8 + 504*A*a^5*b^5*d^3*e^8 + 48*B*a^7*b^3*d^2*e^9 + 84*A*a^6*b^4*d^2*e^9 + 9*B*a^8*b^2*d*e^10
+ 24*A*a^7*b^3*d*e^10 + 2*B*a^9*b*e^11 + 9*A*a^8*b^2*e^11)*x^2 + 6*(17897*B*b^10*d^10*e - 93950*B*a*b^9*d^9*e
^2 - 9395*A*b^10*d^9*e^2 + 200610*B*a^2*b^8*d^8*e^3 + 44580*A*a*b^9*d^8*e^3 - 220320*B*a^3*b^7*d^7*e^4 - 82620
*A*a^2*b^8*d^7*e^4 + 127890*B*a^4*b^6*d^6*e^5 + 73080*A*a^3*b^7*d^6*e^5 - 34524*B*a^5*b^5*d^5*e^6 - 28770*A*a^
4*b^6*d^5*e^6 + 2100*B*a^6*b^4*d^4*e^7 + 2520*A*a^5*b^5*d^4*e^7 + 240*B*a^7*b^3*d^3*e^8 + 420*A*a^6*b^4*d^3*e^
8 + 45*B*a^8*b^2*d^2*e^9 + 120*A*a^7*b^3*d^2*e^9 + 10*B*a^9*b*d*e^10 + 45*A*a^8*b^2*d*e^10 + 2*B*a^10*e^11 + 2
0*A*a^9*b*e^11)*x)*e^(-12)/(x*e + d)^6
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Mupad [B]
time = 1.49, size = 2252, normalized size = 5.04 \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)^7,x)
[Out]
x*((7*d*((21*d^2*((A*b^10 + 10*B*a*b^9)/e^7 - (7*B*b^10*d)/e^8))/e^2 - (7*d*((7*d*((A*b^10 + 10*B*a*b^9)/e^7 -
(7*B*b^10*d)/e^8))/e - (5*a*b^8*(2*A*b + 9*B*a))/e^7 + (21*B*b^10*d^2)/e^9))/e - (15*a^2*b^7*(3*A*b + 8*B*a))
/e^7 + (35*B*b^10*d^3)/e^10))/e - (35*d^3*((A*b^10 + 10*B*a*b^9)/e^7 - (7*B*b^10*d)/e^8))/e^3 + (21*d^2*((7*d*
((A*b^10 + 10*B*a*b^9)/e^7 - (7*B*b^10*d)/e^8))/e - (5*a*b^8*(2*A*b + 9*B*a))/e^7 + (21*B*b^10*d^2)/e^9))/e^2
+ (30*a^3*b^6*(4*A*b + 7*B*a))/e^7 - (35*B*b^10*d^4)/e^11) - x^3*((7*d*((A*b^10 + 10*B*a*b^9)/e^7 - (7*B*b^10*
d)/e^8))/(3*e) - (5*a*b^8*(2*A*b + 9*B*a))/(3*e^7) + (7*B*b^10*d^2)/e^9) - x^2*((21*d^2*((A*b^10 + 10*B*a*b^9)
/e^7 - (7*B*b^10*d)/e^8))/(2*e^2) - (7*d*((7*d*((A*b^10 + 10*B*a*b^9)/e^7 - (7*B*b^10*d)/e^8))/e - (5*a*b^8*(2
*A*b + 9*B*a))/e^7 + (21*B*b^10*d^2)/e^9))/(2*e) - (15*a^2*b^7*(3*A*b + 8*B*a))/(2*e^7) + (35*B*b^10*d^3)/(2*e
^10)) + x^4*((A*b^10 + 10*B*a*b^9)/(4*e^7) - (7*B*b^10*d)/(4*e^8)) - (x^4*(105*A*a^6*b^4*e^10 + 60*B*a^7*b^3*e
^10 - 1155*A*b^10*d^6*e^4 + 2145*B*b^10*d^7*e^3 + 5670*A*a*b^9*d^5*e^5 + 630*A*a^5*b^5*d*e^9 - 11550*B*a*b^9*d
^6*e^4 + 525*B*a^6*b^4*d*e^9 - 11025*A*a^2*b^8*d^4*e^6 + 10500*A*a^3*b^7*d^3*e^7 - 4725*A*a^4*b^6*d^2*e^8 + 25
515*B*a^2*b^8*d^5*e^5 - 29400*B*a^3*b^7*d^4*e^6 + 18375*B*a^4*b^6*d^3*e^7 - 5670*B*a^5*b^5*d^2*e^8) + x^3*(40*
A*a^7*b^3*e^10 + 15*B*a^8*b^2*e^10 - 2140*A*b^10*d^7*e^3 + 4015*B*b^10*d^8*e^2 + 10360*A*a*b^9*d^6*e^4 + 140*A
*a^6*b^4*d*e^9 - 21400*B*a*b^9*d^7*e^3 + 80*B*a^7*b^3*d*e^9 - 19740*A*a^2*b^8*d^5*e^5 + 18200*A*a^3*b^7*d^4*e^
6 - 7700*A*a^4*b^6*d^3*e^7 + 840*A*a^5*b^5*d^2*e^8 + 46620*B*a^2*b^8*d^6*e^4 - 52640*B*a^3*b^7*d^5*e^5 + 31850
*B*a^4*b^6*d^4*e^6 - 9240*B*a^5*b^5*d^3*e^7 + 700*B*a^6*b^4*d^2*e^8) + (10*A*a^10*e^11 + 20417*B*b^10*d^11 - 1
0655*A*b^10*d^10*e + 2*B*a^10*d*e^10 + 50180*A*a*b^9*d^9*e^2 + 10*B*a^9*b*d^2*e^9 - 92070*A*a^2*b^8*d^8*e^3 +
80280*A*a^3*b^7*d^7*e^4 - 30870*A*a^4*b^6*d^6*e^5 + 2520*A*a^5*b^5*d^5*e^6 + 420*A*a^6*b^4*d^4*e^7 + 120*A*a^7
*b^3*d^3*e^8 + 45*A*a^8*b^2*d^2*e^9 + 225810*B*a^2*b^8*d^9*e^2 - 245520*B*a^3*b^7*d^8*e^3 + 140490*B*a^4*b^6*d
^7*e^4 - 37044*B*a^5*b^5*d^6*e^5 + 2100*B*a^6*b^4*d^5*e^6 + 240*B*a^7*b^3*d^4*e^7 + 45*B*a^8*b^2*d^3*e^8 + 20*
A*a^9*b*d*e^10 - 106550*B*a*b^9*d^10*e)/(60*e) + x*((B*a^10*e^10)/5 + (17897*B*b^10*d^10)/10 + 2*A*a^9*b*e^10
- (1879*A*b^10*d^9*e)/2 + 4458*A*a*b^9*d^8*e^2 + (9*A*a^8*b^2*d*e^9)/2 - 8262*A*a^2*b^8*d^7*e^3 + 7308*A*a^3*b
^7*d^6*e^4 - 2877*A*a^4*b^6*d^5*e^5 + 252*A*a^5*b^5*d^4*e^6 + 42*A*a^6*b^4*d^3*e^7 + 12*A*a^7*b^3*d^2*e^8 + 20
061*B*a^2*b^8*d^8*e^2 - 22032*B*a^3*b^7*d^7*e^3 + 12789*B*a^4*b^6*d^6*e^4 - (17262*B*a^5*b^5*d^5*e^5)/5 + 210*
B*a^6*b^4*d^4*e^6 + 24*B*a^7*b^3*d^3*e^7 + (9*B*a^8*b^2*d^2*e^8)/2 - 9395*B*a*b^9*d^9*e + B*a^9*b*d*e^9) + x^5
*(252*A*a^5*b^5*e^10 + 210*B*a^6*b^4*e^10 - 252*A*b^10*d^5*e^5 + 462*B*b^10*d^6*e^4 + 1260*A*a*b^9*d^4*e^6 - 1
260*A*a^4*b^6*d*e^9 - 2520*B*a*b^9*d^5*e^5 - 1512*B*a^5*b^5*d*e^9 - 2520*A*a^2*b^8*d^3*e^7 + 2520*A*a^3*b^7*d^
2*e^8 + 5670*B*a^2*b^8*d^4*e^6 - 6720*B*a^3*b^7*d^3*e^7 + 4410*B*a^4*b^6*d^2*e^8) + x^2*((5*B*a^9*b*e^10)/2 +
(15125*B*b^10*d^9*e)/4 + (45*A*a^8*b^2*e^10)/4 - (7995*A*b^10*d^8*e^2)/4 + 9570*A*a*b^9*d^7*e^3 + 30*A*a^7*b^3
*d*e^9 - (39975*B*a*b^9*d^8*e^2)/2 + (45*B*a^8*b^2*d*e^9)/4 - 17955*A*a^2*b^8*d^6*e^4 + 16170*A*a^3*b^7*d^5*e^
5 - (13125*A*a^4*b^6*d^4*e^6)/2 + 630*A*a^5*b^5*d^3*e^7 + 105*A*a^6*b^4*d^2*e^8 + 43065*B*a^2*b^8*d^7*e^3 - 47
880*B*a^3*b^7*d^6*e^4 + (56595*B*a^4*b^6*d^5*e^5)/2 - 7875*B*a^5*b^5*d^4*e^6 + 525*B*a^6*b^4*d^3*e^7 + 60*B*a^
7*b^3*d^2*e^8))/(d^6*e^11 + e^17*x^6 + 6*d^5*e^12*x + 6*d*e^16*x^5 + 15*d^4*e^13*x^2 + 20*d^3*e^14*x^3 + 15*d^
2*e^15*x^4) + (log(d + e*x)*(210*A*b^10*d^4*e - 462*B*b^10*d^5 + 210*A*a^4*b^6*e^5 + 252*B*a^5*b^5*e^5 - 840*A
*a*b^9*d^3*e^2 - 840*A*a^3*b^7*d*e^4 - 1470*B*a^4*b^6*d*e^4 + 1260*A*a^2*b^8*d^2*e^3 - 3780*B*a^2*b^8*d^3*e^2
+ 3360*B*a^3*b^7*d^2*e^3 + 2100*B*a*b^9*d^4*e))/e^12 + (B*b^10*x^5)/(5*e^7)
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