3.1106 \(\int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^{18}} \, dx\)

Optimal. Leaf size=335 \[ \frac{b^5 (a+b x)^{11} (-17 a B e+6 A b e+11 b B d)}{816816 e (d+e x)^{11} (b d-a e)^7}+\frac{b^4 (a+b x)^{11} (-17 a B e+6 A b e+11 b B d)}{74256 e (d+e x)^{12} (b d-a e)^6}+\frac{b^3 (a+b x)^{11} (-17 a B e+6 A b e+11 b B d)}{12376 e (d+e x)^{13} (b d-a e)^5}+\frac{b^2 (a+b x)^{11} (-17 a B e+6 A b e+11 b B d)}{2856 e (d+e x)^{14} (b d-a e)^4}+\frac{b (a+b x)^{11} (-17 a B e+6 A b e+11 b B d)}{816 e (d+e x)^{15} (b d-a e)^3}+\frac{(a+b x)^{11} (-17 a B e+6 A b e+11 b B d)}{272 e (d+e x)^{16} (b d-a e)^2}-\frac{(a+b x)^{11} (B d-A e)}{17 e (d+e x)^{17} (b d-a e)} \]

[Out]

-((B*d - A*e)*(a + b*x)^11)/(17*e*(b*d - a*e)*(d + e*x)^17) + ((11*b*B*d + 6*A*b*e - 17*a*B*e)*(a + b*x)^11)/(
272*e*(b*d - a*e)^2*(d + e*x)^16) + (b*(11*b*B*d + 6*A*b*e - 17*a*B*e)*(a + b*x)^11)/(816*e*(b*d - a*e)^3*(d +
e*x)^15) + (b^2*(11*b*B*d + 6*A*b*e - 17*a*B*e)*(a + b*x)^11)/(2856*e*(b*d - a*e)^4*(d + e*x)^14) + (b^3*(11*
b*B*d + 6*A*b*e - 17*a*B*e)*(a + b*x)^11)/(12376*e*(b*d - a*e)^5*(d + e*x)^13) + (b^4*(11*b*B*d + 6*A*b*e - 17
*a*B*e)*(a + b*x)^11)/(74256*e*(b*d - a*e)^6*(d + e*x)^12) + (b^5*(11*b*B*d + 6*A*b*e - 17*a*B*e)*(a + b*x)^11
)/(816816*e*(b*d - a*e)^7*(d + e*x)^11)

________________________________________________________________________________________

Rubi [A]  time = 0.182601, antiderivative size = 335, normalized size of antiderivative = 1., number of steps used = 7, number of rules used = 3, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.15, Rules used = {78, 45, 37} \[ \frac{b^5 (a+b x)^{11} (-17 a B e+6 A b e+11 b B d)}{816816 e (d+e x)^{11} (b d-a e)^7}+\frac{b^4 (a+b x)^{11} (-17 a B e+6 A b e+11 b B d)}{74256 e (d+e x)^{12} (b d-a e)^6}+\frac{b^3 (a+b x)^{11} (-17 a B e+6 A b e+11 b B d)}{12376 e (d+e x)^{13} (b d-a e)^5}+\frac{b^2 (a+b x)^{11} (-17 a B e+6 A b e+11 b B d)}{2856 e (d+e x)^{14} (b d-a e)^4}+\frac{b (a+b x)^{11} (-17 a B e+6 A b e+11 b B d)}{816 e (d+e x)^{15} (b d-a e)^3}+\frac{(a+b x)^{11} (-17 a B e+6 A b e+11 b B d)}{272 e (d+e x)^{16} (b d-a e)^2}-\frac{(a+b x)^{11} (B d-A e)}{17 e (d+e x)^{17} (b d-a e)} \]

Antiderivative was successfully verified.

[In]

Int[((a + b*x)^10*(A + B*x))/(d + e*x)^18,x]

[Out]

-((B*d - A*e)*(a + b*x)^11)/(17*e*(b*d - a*e)*(d + e*x)^17) + ((11*b*B*d + 6*A*b*e - 17*a*B*e)*(a + b*x)^11)/(
272*e*(b*d - a*e)^2*(d + e*x)^16) + (b*(11*b*B*d + 6*A*b*e - 17*a*B*e)*(a + b*x)^11)/(816*e*(b*d - a*e)^3*(d +
e*x)^15) + (b^2*(11*b*B*d + 6*A*b*e - 17*a*B*e)*(a + b*x)^11)/(2856*e*(b*d - a*e)^4*(d + e*x)^14) + (b^3*(11*
b*B*d + 6*A*b*e - 17*a*B*e)*(a + b*x)^11)/(12376*e*(b*d - a*e)^5*(d + e*x)^13) + (b^4*(11*b*B*d + 6*A*b*e - 17
*a*B*e)*(a + b*x)^11)/(74256*e*(b*d - a*e)^6*(d + e*x)^12) + (b^5*(11*b*B*d + 6*A*b*e - 17*a*B*e)*(a + b*x)^11
)/(816816*e*(b*d - a*e)^7*(d + e*x)^11)

Rule 78

Int[((a_.) + (b_.)*(x_))*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> -Simp[((b*e - a*f
)*(c + d*x)^(n + 1)*(e + f*x)^(p + 1))/(f*(p + 1)*(c*f - d*e)), x] - Dist[(a*d*f*(n + p + 2) - b*(d*e*(n + 1)
+ c*f*(p + 1)))/(f*(p + 1)*(c*f - d*e)), Int[(c + d*x)^n*(e + f*x)^(p + 1), x], x] /; FreeQ[{a, b, c, d, e, f,
n}, x] && LtQ[p, -1] && ( !LtQ[n, -1] || IntegerQ[p] ||  !(IntegerQ[n] ||  !(EqQ[e, 0] ||  !(EqQ[c, 0] || LtQ
[p, n]))))

Rule 45

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> Simp[((a + b*x)^(m + 1)*(c + d*x)^(n + 1
))/((b*c - a*d)*(m + 1)), x] - Dist[(d*Simplify[m + n + 2])/((b*c - a*d)*(m + 1)), Int[(a + b*x)^Simplify[m +
1]*(c + d*x)^n, x], x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[b*c - a*d, 0] && ILtQ[Simplify[m + n + 2], 0] &&
NeQ[m, -1] &&  !(LtQ[m, -1] && LtQ[n, -1] && (EqQ[a, 0] || (NeQ[c, 0] && LtQ[m - n, 0] && IntegerQ[n]))) && (
SumSimplerQ[m, 1] ||  !SumSimplerQ[n, 1])

Rule 37

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> Simp[((a + b*x)^(m + 1)*(c + d*x)^(n +
1))/((b*c - a*d)*(m + 1)), x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[b*c - a*d, 0] && EqQ[m + n + 2, 0] && NeQ
[m, -1]

Rubi steps

\begin{align*} \int \frac{(a+b x)^{10} (A+B x)}{(d+e x)^{18}} \, dx &=-\frac{(B d-A e) (a+b x)^{11}}{17 e (b d-a e) (d+e x)^{17}}+\frac{(11 b B d+6 A b e-17 a B e) \int \frac{(a+b x)^{10}}{(d+e x)^{17}} \, dx}{17 e (b d-a e)}\\ &=-\frac{(B d-A e) (a+b x)^{11}}{17 e (b d-a e) (d+e x)^{17}}+\frac{(11 b B d+6 A b e-17 a B e) (a+b x)^{11}}{272 e (b d-a e)^2 (d+e x)^{16}}+\frac{(5 b (11 b B d+6 A b e-17 a B e)) \int \frac{(a+b x)^{10}}{(d+e x)^{16}} \, dx}{272 e (b d-a e)^2}\\ &=-\frac{(B d-A e) (a+b x)^{11}}{17 e (b d-a e) (d+e x)^{17}}+\frac{(11 b B d+6 A b e-17 a B e) (a+b x)^{11}}{272 e (b d-a e)^2 (d+e x)^{16}}+\frac{b (11 b B d+6 A b e-17 a B e) (a+b x)^{11}}{816 e (b d-a e)^3 (d+e x)^{15}}+\frac{\left (b^2 (11 b B d+6 A b e-17 a B e)\right ) \int \frac{(a+b x)^{10}}{(d+e x)^{15}} \, dx}{204 e (b d-a e)^3}\\ &=-\frac{(B d-A e) (a+b x)^{11}}{17 e (b d-a e) (d+e x)^{17}}+\frac{(11 b B d+6 A b e-17 a B e) (a+b x)^{11}}{272 e (b d-a e)^2 (d+e x)^{16}}+\frac{b (11 b B d+6 A b e-17 a B e) (a+b x)^{11}}{816 e (b d-a e)^3 (d+e x)^{15}}+\frac{b^2 (11 b B d+6 A b e-17 a B e) (a+b x)^{11}}{2856 e (b d-a e)^4 (d+e x)^{14}}+\frac{\left (b^3 (11 b B d+6 A b e-17 a B e)\right ) \int \frac{(a+b x)^{10}}{(d+e x)^{14}} \, dx}{952 e (b d-a e)^4}\\ &=-\frac{(B d-A e) (a+b x)^{11}}{17 e (b d-a e) (d+e x)^{17}}+\frac{(11 b B d+6 A b e-17 a B e) (a+b x)^{11}}{272 e (b d-a e)^2 (d+e x)^{16}}+\frac{b (11 b B d+6 A b e-17 a B e) (a+b x)^{11}}{816 e (b d-a e)^3 (d+e x)^{15}}+\frac{b^2 (11 b B d+6 A b e-17 a B e) (a+b x)^{11}}{2856 e (b d-a e)^4 (d+e x)^{14}}+\frac{b^3 (11 b B d+6 A b e-17 a B e) (a+b x)^{11}}{12376 e (b d-a e)^5 (d+e x)^{13}}+\frac{\left (b^4 (11 b B d+6 A b e-17 a B e)\right ) \int \frac{(a+b x)^{10}}{(d+e x)^{13}} \, dx}{6188 e (b d-a e)^5}\\ &=-\frac{(B d-A e) (a+b x)^{11}}{17 e (b d-a e) (d+e x)^{17}}+\frac{(11 b B d+6 A b e-17 a B e) (a+b x)^{11}}{272 e (b d-a e)^2 (d+e x)^{16}}+\frac{b (11 b B d+6 A b e-17 a B e) (a+b x)^{11}}{816 e (b d-a e)^3 (d+e x)^{15}}+\frac{b^2 (11 b B d+6 A b e-17 a B e) (a+b x)^{11}}{2856 e (b d-a e)^4 (d+e x)^{14}}+\frac{b^3 (11 b B d+6 A b e-17 a B e) (a+b x)^{11}}{12376 e (b d-a e)^5 (d+e x)^{13}}+\frac{b^4 (11 b B d+6 A b e-17 a B e) (a+b x)^{11}}{74256 e (b d-a e)^6 (d+e x)^{12}}+\frac{\left (b^5 (11 b B d+6 A b e-17 a B e)\right ) \int \frac{(a+b x)^{10}}{(d+e x)^{12}} \, dx}{74256 e (b d-a e)^6}\\ &=-\frac{(B d-A e) (a+b x)^{11}}{17 e (b d-a e) (d+e x)^{17}}+\frac{(11 b B d+6 A b e-17 a B e) (a+b x)^{11}}{272 e (b d-a e)^2 (d+e x)^{16}}+\frac{b (11 b B d+6 A b e-17 a B e) (a+b x)^{11}}{816 e (b d-a e)^3 (d+e x)^{15}}+\frac{b^2 (11 b B d+6 A b e-17 a B e) (a+b x)^{11}}{2856 e (b d-a e)^4 (d+e x)^{14}}+\frac{b^3 (11 b B d+6 A b e-17 a B e) (a+b x)^{11}}{12376 e (b d-a e)^5 (d+e x)^{13}}+\frac{b^4 (11 b B d+6 A b e-17 a B e) (a+b x)^{11}}{74256 e (b d-a e)^6 (d+e x)^{12}}+\frac{b^5 (11 b B d+6 A b e-17 a B e) (a+b x)^{11}}{816816 e (b d-a e)^7 (d+e x)^{11}}\\ \end{align*}

Mathematica [B]  time = 0.77208, size = 1433, normalized size = 4.28 \[ -\frac{\left (6 A e \left (d^{10}+17 e x d^9+136 e^2 x^2 d^8+680 e^3 x^3 d^7+2380 e^4 x^4 d^6+6188 e^5 x^5 d^5+12376 e^6 x^6 d^4+19448 e^7 x^7 d^3+24310 e^8 x^8 d^2+24310 e^9 x^9 d+19448 e^{10} x^{10}\right )+11 B \left (d^{11}+17 e x d^{10}+136 e^2 x^2 d^9+680 e^3 x^3 d^8+2380 e^4 x^4 d^7+6188 e^5 x^5 d^6+12376 e^6 x^6 d^5+19448 e^7 x^7 d^4+24310 e^8 x^8 d^3+24310 e^9 x^9 d^2+19448 e^{10} x^{10} d+12376 e^{11} x^{11}\right )\right ) b^{10}+6 a e \left (7 A e \left (d^9+17 e x d^8+136 e^2 x^2 d^7+680 e^3 x^3 d^6+2380 e^4 x^4 d^5+6188 e^5 x^5 d^4+12376 e^6 x^6 d^3+19448 e^7 x^7 d^2+24310 e^8 x^8 d+24310 e^9 x^9\right )+10 B \left (d^{10}+17 e x d^9+136 e^2 x^2 d^8+680 e^3 x^3 d^7+2380 e^4 x^4 d^6+6188 e^5 x^5 d^5+12376 e^6 x^6 d^4+19448 e^7 x^7 d^3+24310 e^8 x^8 d^2+24310 e^9 x^9 d+19448 e^{10} x^{10}\right )\right ) b^9+21 a^2 e^2 \left (8 A e \left (d^8+17 e x d^7+136 e^2 x^2 d^6+680 e^3 x^3 d^5+2380 e^4 x^4 d^4+6188 e^5 x^5 d^3+12376 e^6 x^6 d^2+19448 e^7 x^7 d+24310 e^8 x^8\right )+9 B \left (d^9+17 e x d^8+136 e^2 x^2 d^7+680 e^3 x^3 d^6+2380 e^4 x^4 d^5+6188 e^5 x^5 d^4+12376 e^6 x^6 d^3+19448 e^7 x^7 d^2+24310 e^8 x^8 d+24310 e^9 x^9\right )\right ) b^8+56 a^3 e^3 \left (9 A e \left (d^7+17 e x d^6+136 e^2 x^2 d^5+680 e^3 x^3 d^4+2380 e^4 x^4 d^3+6188 e^5 x^5 d^2+12376 e^6 x^6 d+19448 e^7 x^7\right )+8 B \left (d^8+17 e x d^7+136 e^2 x^2 d^6+680 e^3 x^3 d^5+2380 e^4 x^4 d^4+6188 e^5 x^5 d^3+12376 e^6 x^6 d^2+19448 e^7 x^7 d+24310 e^8 x^8\right )\right ) b^7+126 a^4 e^4 \left (10 A e \left (d^6+17 e x d^5+136 e^2 x^2 d^4+680 e^3 x^3 d^3+2380 e^4 x^4 d^2+6188 e^5 x^5 d+12376 e^6 x^6\right )+7 B \left (d^7+17 e x d^6+136 e^2 x^2 d^5+680 e^3 x^3 d^4+2380 e^4 x^4 d^3+6188 e^5 x^5 d^2+12376 e^6 x^6 d+19448 e^7 x^7\right )\right ) b^6+252 a^5 e^5 \left (11 A e \left (d^5+17 e x d^4+136 e^2 x^2 d^3+680 e^3 x^3 d^2+2380 e^4 x^4 d+6188 e^5 x^5\right )+6 B \left (d^6+17 e x d^5+136 e^2 x^2 d^4+680 e^3 x^3 d^3+2380 e^4 x^4 d^2+6188 e^5 x^5 d+12376 e^6 x^6\right )\right ) b^5+462 a^6 e^6 \left (12 A e \left (d^4+17 e x d^3+136 e^2 x^2 d^2+680 e^3 x^3 d+2380 e^4 x^4\right )+5 B \left (d^5+17 e x d^4+136 e^2 x^2 d^3+680 e^3 x^3 d^2+2380 e^4 x^4 d+6188 e^5 x^5\right )\right ) b^4+792 a^7 e^7 \left (13 A e \left (d^3+17 e x d^2+136 e^2 x^2 d+680 e^3 x^3\right )+4 B \left (d^4+17 e x d^3+136 e^2 x^2 d^2+680 e^3 x^3 d+2380 e^4 x^4\right )\right ) b^3+1287 a^8 e^8 \left (14 A e \left (d^2+17 e x d+136 e^2 x^2\right )+3 B \left (d^3+17 e x d^2+136 e^2 x^2 d+680 e^3 x^3\right )\right ) b^2+2002 a^9 e^9 \left (15 A e (d+17 e x)+2 B \left (d^2+17 e x d+136 e^2 x^2\right )\right ) b+3003 a^{10} e^{10} (16 A e+B (d+17 e x))}{816816 e^{12} (d+e x)^{17}} \]

Antiderivative was successfully verified.

[In]

Integrate[((a + b*x)^10*(A + B*x))/(d + e*x)^18,x]

[Out]

-(3003*a^10*e^10*(16*A*e + B*(d + 17*e*x)) + 2002*a^9*b*e^9*(15*A*e*(d + 17*e*x) + 2*B*(d^2 + 17*d*e*x + 136*e
^2*x^2)) + 1287*a^8*b^2*e^8*(14*A*e*(d^2 + 17*d*e*x + 136*e^2*x^2) + 3*B*(d^3 + 17*d^2*e*x + 136*d*e^2*x^2 + 6
80*e^3*x^3)) + 792*a^7*b^3*e^7*(13*A*e*(d^3 + 17*d^2*e*x + 136*d*e^2*x^2 + 680*e^3*x^3) + 4*B*(d^4 + 17*d^3*e*
x + 136*d^2*e^2*x^2 + 680*d*e^3*x^3 + 2380*e^4*x^4)) + 462*a^6*b^4*e^6*(12*A*e*(d^4 + 17*d^3*e*x + 136*d^2*e^2
*x^2 + 680*d*e^3*x^3 + 2380*e^4*x^4) + 5*B*(d^5 + 17*d^4*e*x + 136*d^3*e^2*x^2 + 680*d^2*e^3*x^3 + 2380*d*e^4*
x^4 + 6188*e^5*x^5)) + 252*a^5*b^5*e^5*(11*A*e*(d^5 + 17*d^4*e*x + 136*d^3*e^2*x^2 + 680*d^2*e^3*x^3 + 2380*d*
e^4*x^4 + 6188*e^5*x^5) + 6*B*(d^6 + 17*d^5*e*x + 136*d^4*e^2*x^2 + 680*d^3*e^3*x^3 + 2380*d^2*e^4*x^4 + 6188*
d*e^5*x^5 + 12376*e^6*x^6)) + 126*a^4*b^6*e^4*(10*A*e*(d^6 + 17*d^5*e*x + 136*d^4*e^2*x^2 + 680*d^3*e^3*x^3 +
2380*d^2*e^4*x^4 + 6188*d*e^5*x^5 + 12376*e^6*x^6) + 7*B*(d^7 + 17*d^6*e*x + 136*d^5*e^2*x^2 + 680*d^4*e^3*x^3
+ 2380*d^3*e^4*x^4 + 6188*d^2*e^5*x^5 + 12376*d*e^6*x^6 + 19448*e^7*x^7)) + 56*a^3*b^7*e^3*(9*A*e*(d^7 + 17*d
^6*e*x + 136*d^5*e^2*x^2 + 680*d^4*e^3*x^3 + 2380*d^3*e^4*x^4 + 6188*d^2*e^5*x^5 + 12376*d*e^6*x^6 + 19448*e^7
*x^7) + 8*B*(d^8 + 17*d^7*e*x + 136*d^6*e^2*x^2 + 680*d^5*e^3*x^3 + 2380*d^4*e^4*x^4 + 6188*d^3*e^5*x^5 + 1237
6*d^2*e^6*x^6 + 19448*d*e^7*x^7 + 24310*e^8*x^8)) + 21*a^2*b^8*e^2*(8*A*e*(d^8 + 17*d^7*e*x + 136*d^6*e^2*x^2
+ 680*d^5*e^3*x^3 + 2380*d^4*e^4*x^4 + 6188*d^3*e^5*x^5 + 12376*d^2*e^6*x^6 + 19448*d*e^7*x^7 + 24310*e^8*x^8)
+ 9*B*(d^9 + 17*d^8*e*x + 136*d^7*e^2*x^2 + 680*d^6*e^3*x^3 + 2380*d^5*e^4*x^4 + 6188*d^4*e^5*x^5 + 12376*d^3
*e^6*x^6 + 19448*d^2*e^7*x^7 + 24310*d*e^8*x^8 + 24310*e^9*x^9)) + 6*a*b^9*e*(7*A*e*(d^9 + 17*d^8*e*x + 136*d^
7*e^2*x^2 + 680*d^6*e^3*x^3 + 2380*d^5*e^4*x^4 + 6188*d^4*e^5*x^5 + 12376*d^3*e^6*x^6 + 19448*d^2*e^7*x^7 + 24
310*d*e^8*x^8 + 24310*e^9*x^9) + 10*B*(d^10 + 17*d^9*e*x + 136*d^8*e^2*x^2 + 680*d^7*e^3*x^3 + 2380*d^6*e^4*x^
4 + 6188*d^5*e^5*x^5 + 12376*d^4*e^6*x^6 + 19448*d^3*e^7*x^7 + 24310*d^2*e^8*x^8 + 24310*d*e^9*x^9 + 19448*e^1
0*x^10)) + b^10*(6*A*e*(d^10 + 17*d^9*e*x + 136*d^8*e^2*x^2 + 680*d^7*e^3*x^3 + 2380*d^6*e^4*x^4 + 6188*d^5*e^
5*x^5 + 12376*d^4*e^6*x^6 + 19448*d^3*e^7*x^7 + 24310*d^2*e^8*x^8 + 24310*d*e^9*x^9 + 19448*e^10*x^10) + 11*B*
(d^11 + 17*d^10*e*x + 136*d^9*e^2*x^2 + 680*d^8*e^3*x^3 + 2380*d^7*e^4*x^4 + 6188*d^6*e^5*x^5 + 12376*d^5*e^6*
x^6 + 19448*d^4*e^7*x^7 + 24310*d^3*e^8*x^8 + 24310*d^2*e^9*x^9 + 19448*d*e^10*x^10 + 12376*e^11*x^11)))/(8168
16*e^12*(d + e*x)^17)

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Maple [B]  time = 0.013, size = 1942, normalized size = 5.8 \begin{align*} \text{result too large to display} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((b*x+a)^10*(B*x+A)/(e*x+d)^18,x)

[Out]

-1/6*B*b^10/e^12/(e*x+d)^6-30/13*b^3*(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^12/(e*x+d)
^13-1/7*b^9*(A*b*e+10*B*a*e-11*B*b*d)/e^12/(e*x+d)^7-5/3*b^7*(3*A*a^2*b*e^3-6*A*a*b^2*d*e^2+3*A*b^3*d^2*e+8*B*
a^3*e^3-27*B*a^2*b*d*e^2+30*B*a*b^2*d^2*e-11*B*b^3*d^3)/e^12/(e*x+d)^9-15/14*b^2*(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^12/(e*x+d)^14-1/16*(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^12/(e*x+d)^16-7/2*b^4*(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^12/(e*x+d)^12-1/17*(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)^17-5/8*b^8*(2*A*a*b*e^2-2*A*b^2*d*e+9*B*a^2*e^2-20*B*a*b*d*e+11*B*b^2*d^2
)/e^12/(e*x+d)^8-3*b^6*(4*A*a^3*b*e^4-12*A*a^2*b^2*d*e^3+12*A*a*b^3*d^2*e^2-4*A*b^4*d^3*e+7*B*a^4*e^4-32*B*a^3
*b*d*e^3+54*B*a^2*b^2*d^2*e^2-40*B*a*b^3*d^3*e+11*B*b^4*d^4)/e^12/(e*x+d)^10-42/11*b^5*(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)/e^12/(e*x+d)^11-1/3*b*(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+7
56*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^12/(e*x+d)^15

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Maxima [B]  time = 1.83216, size = 2693, normalized size = 8.04 \begin{align*} \text{result too large to display} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)^10*(B*x+A)/(e*x+d)^18,x, algorithm="maxima")

[Out]

-1/816816*(136136*B*b^10*e^11*x^11 + 11*B*b^10*d^11 + 48048*A*a^10*e^11 + 6*(10*B*a*b^9 + A*b^10)*d^10*e + 21*
(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 + 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d
^7*e^4 + 252*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 + 462*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 + 792*(4*B*a^7*b^3
+ 7*A*a^6*b^4)*d^4*e^7 + 1287*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^8 + 2002*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 + 3
003*(B*a^10 + 10*A*a^9*b)*d*e^10 + 19448*(11*B*b^10*d*e^10 + 6*(10*B*a*b^9 + A*b^10)*e^11)*x^10 + 24310*(11*B*
b^10*d^2*e^9 + 6*(10*B*a*b^9 + A*b^10)*d*e^10 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*e^11)*x^9 + 24310*(11*B*b^10*d^3*
e^8 + 6*(10*B*a*b^9 + A*b^10)*d^2*e^9 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^10 + 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*e
^11)*x^8 + 19448*(11*B*b^10*d^4*e^7 + 6*(10*B*a*b^9 + A*b^10)*d^3*e^8 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9 +
56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^10 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*e^11)*x^7 + 12376*(11*B*b^10*d^5*e^6
+ 6*(10*B*a*b^9 + A*b^10)*d^4*e^7 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8 + 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*
e^9 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^10 + 252*(6*B*a^5*b^5 + 5*A*a^4*b^6)*e^11)*x^6 + 6188*(11*B*b^10*d^6
*e^5 + 6*(10*B*a*b^9 + A*b^10)*d^5*e^6 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 + 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)
*d^3*e^8 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9 + 252*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^10 + 462*(5*B*a^6*b^4
+ 6*A*a^5*b^5)*e^11)*x^5 + 2380*(11*B*b^10*d^7*e^4 + 6*(10*B*a*b^9 + A*b^10)*d^6*e^5 + 21*(9*B*a^2*b^8 + 2*A*
a*b^9)*d^5*e^6 + 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^7 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^8 + 252*(6*B*a
^5*b^5 + 5*A*a^4*b^6)*d^2*e^9 + 462*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*e^10 + 792*(4*B*a^7*b^3 + 7*A*a^6*b^4)*e^11)
*x^4 + 680*(11*B*b^10*d^8*e^3 + 6*(10*B*a*b^9 + A*b^10)*d^7*e^4 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 + 56*(8
*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^7 + 252*(6*B*a^5*b^5 + 5*A*a^4*b^6)*
d^3*e^8 + 462*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^9 + 792*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*e^10 + 1287*(3*B*a^8*b^2
+ 8*A*a^7*b^3)*e^11)*x^3 + 136*(11*B*b^10*d^9*e^2 + 6*(10*B*a*b^9 + A*b^10)*d^8*e^3 + 21*(9*B*a^2*b^8 + 2*A*a
*b^9)*d^7*e^4 + 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^6 + 252*(6*B*a^
5*b^5 + 5*A*a^4*b^6)*d^4*e^7 + 462*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^8 + 792*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e
^9 + 1287*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^10 + 2002*(2*B*a^9*b + 9*A*a^8*b^2)*e^11)*x^2 + 17*(11*B*b^10*d^10*e
+ 6*(10*B*a*b^9 + A*b^10)*d^9*e^2 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 + 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7
*e^4 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5 + 252*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^6 + 462*(5*B*a^6*b^4 +
6*A*a^5*b^5)*d^4*e^7 + 792*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^8 + 1287*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^9 + 20
02*(2*B*a^9*b + 9*A*a^8*b^2)*d*e^10 + 3003*(B*a^10 + 10*A*a^9*b)*e^11)*x)/(e^29*x^17 + 17*d*e^28*x^16 + 136*d^
2*e^27*x^15 + 680*d^3*e^26*x^14 + 2380*d^4*e^25*x^13 + 6188*d^5*e^24*x^12 + 12376*d^6*e^23*x^11 + 19448*d^7*e^
22*x^10 + 24310*d^8*e^21*x^9 + 24310*d^9*e^20*x^8 + 19448*d^10*e^19*x^7 + 12376*d^11*e^18*x^6 + 6188*d^12*e^17
*x^5 + 2380*d^13*e^16*x^4 + 680*d^14*e^15*x^3 + 136*d^15*e^14*x^2 + 17*d^16*e^13*x + d^17*e^12)

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Fricas [B]  time = 1.72207, size = 4437, normalized size = 13.24 \begin{align*} \text{result too large to display} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)^10*(B*x+A)/(e*x+d)^18,x, algorithm="fricas")

[Out]

-1/816816*(136136*B*b^10*e^11*x^11 + 11*B*b^10*d^11 + 48048*A*a^10*e^11 + 6*(10*B*a*b^9 + A*b^10)*d^10*e + 21*
(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 + 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d
^7*e^4 + 252*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 + 462*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 + 792*(4*B*a^7*b^3
+ 7*A*a^6*b^4)*d^4*e^7 + 1287*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^8 + 2002*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 + 3
003*(B*a^10 + 10*A*a^9*b)*d*e^10 + 19448*(11*B*b^10*d*e^10 + 6*(10*B*a*b^9 + A*b^10)*e^11)*x^10 + 24310*(11*B*
b^10*d^2*e^9 + 6*(10*B*a*b^9 + A*b^10)*d*e^10 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*e^11)*x^9 + 24310*(11*B*b^10*d^3*
e^8 + 6*(10*B*a*b^9 + A*b^10)*d^2*e^9 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^10 + 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*e
^11)*x^8 + 19448*(11*B*b^10*d^4*e^7 + 6*(10*B*a*b^9 + A*b^10)*d^3*e^8 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9 +
56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^10 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*e^11)*x^7 + 12376*(11*B*b^10*d^5*e^6
+ 6*(10*B*a*b^9 + A*b^10)*d^4*e^7 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8 + 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*
e^9 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^10 + 252*(6*B*a^5*b^5 + 5*A*a^4*b^6)*e^11)*x^6 + 6188*(11*B*b^10*d^6
*e^5 + 6*(10*B*a*b^9 + A*b^10)*d^5*e^6 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 + 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)
*d^3*e^8 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9 + 252*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^10 + 462*(5*B*a^6*b^4
+ 6*A*a^5*b^5)*e^11)*x^5 + 2380*(11*B*b^10*d^7*e^4 + 6*(10*B*a*b^9 + A*b^10)*d^6*e^5 + 21*(9*B*a^2*b^8 + 2*A*
a*b^9)*d^5*e^6 + 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^7 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^8 + 252*(6*B*a
^5*b^5 + 5*A*a^4*b^6)*d^2*e^9 + 462*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*e^10 + 792*(4*B*a^7*b^3 + 7*A*a^6*b^4)*e^11)
*x^4 + 680*(11*B*b^10*d^8*e^3 + 6*(10*B*a*b^9 + A*b^10)*d^7*e^4 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 + 56*(8
*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^7 + 252*(6*B*a^5*b^5 + 5*A*a^4*b^6)*
d^3*e^8 + 462*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^9 + 792*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*e^10 + 1287*(3*B*a^8*b^2
+ 8*A*a^7*b^3)*e^11)*x^3 + 136*(11*B*b^10*d^9*e^2 + 6*(10*B*a*b^9 + A*b^10)*d^8*e^3 + 21*(9*B*a^2*b^8 + 2*A*a
*b^9)*d^7*e^4 + 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^6 + 252*(6*B*a^
5*b^5 + 5*A*a^4*b^6)*d^4*e^7 + 462*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^8 + 792*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e
^9 + 1287*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^10 + 2002*(2*B*a^9*b + 9*A*a^8*b^2)*e^11)*x^2 + 17*(11*B*b^10*d^10*e
+ 6*(10*B*a*b^9 + A*b^10)*d^9*e^2 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 + 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7
*e^4 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5 + 252*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^6 + 462*(5*B*a^6*b^4 +
6*A*a^5*b^5)*d^4*e^7 + 792*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^8 + 1287*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^9 + 20
02*(2*B*a^9*b + 9*A*a^8*b^2)*d*e^10 + 3003*(B*a^10 + 10*A*a^9*b)*e^11)*x)/(e^29*x^17 + 17*d*e^28*x^16 + 136*d^
2*e^27*x^15 + 680*d^3*e^26*x^14 + 2380*d^4*e^25*x^13 + 6188*d^5*e^24*x^12 + 12376*d^6*e^23*x^11 + 19448*d^7*e^
22*x^10 + 24310*d^8*e^21*x^9 + 24310*d^9*e^20*x^8 + 19448*d^10*e^19*x^7 + 12376*d^11*e^18*x^6 + 6188*d^12*e^17
*x^5 + 2380*d^13*e^16*x^4 + 680*d^14*e^15*x^3 + 136*d^15*e^14*x^2 + 17*d^16*e^13*x + d^17*e^12)

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)**10*(B*x+A)/(e*x+d)**18,x)

[Out]

Timed out

________________________________________________________________________________________

Giac [B]  time = 2.46714, size = 2830, normalized size = 8.45 \begin{align*} \text{result too large to display} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)^10*(B*x+A)/(e*x+d)^18,x, algorithm="giac")

[Out]

-1/816816*(136136*B*b^10*x^11*e^11 + 213928*B*b^10*d*x^10*e^10 + 267410*B*b^10*d^2*x^9*e^9 + 267410*B*b^10*d^3
*x^8*e^8 + 213928*B*b^10*d^4*x^7*e^7 + 136136*B*b^10*d^5*x^6*e^6 + 68068*B*b^10*d^6*x^5*e^5 + 26180*B*b^10*d^7
*x^4*e^4 + 7480*B*b^10*d^8*x^3*e^3 + 1496*B*b^10*d^9*x^2*e^2 + 187*B*b^10*d^10*x*e + 11*B*b^10*d^11 + 1166880*
B*a*b^9*x^10*e^11 + 116688*A*b^10*x^10*e^11 + 1458600*B*a*b^9*d*x^9*e^10 + 145860*A*b^10*d*x^9*e^10 + 1458600*
B*a*b^9*d^2*x^8*e^9 + 145860*A*b^10*d^2*x^8*e^9 + 1166880*B*a*b^9*d^3*x^7*e^8 + 116688*A*b^10*d^3*x^7*e^8 + 74
2560*B*a*b^9*d^4*x^6*e^7 + 74256*A*b^10*d^4*x^6*e^7 + 371280*B*a*b^9*d^5*x^5*e^6 + 37128*A*b^10*d^5*x^5*e^6 +
142800*B*a*b^9*d^6*x^4*e^5 + 14280*A*b^10*d^6*x^4*e^5 + 40800*B*a*b^9*d^7*x^3*e^4 + 4080*A*b^10*d^7*x^3*e^4 +
8160*B*a*b^9*d^8*x^2*e^3 + 816*A*b^10*d^8*x^2*e^3 + 1020*B*a*b^9*d^9*x*e^2 + 102*A*b^10*d^9*x*e^2 + 60*B*a*b^9
*d^10*e + 6*A*b^10*d^10*e + 4594590*B*a^2*b^8*x^9*e^11 + 1021020*A*a*b^9*x^9*e^11 + 4594590*B*a^2*b^8*d*x^8*e^
10 + 1021020*A*a*b^9*d*x^8*e^10 + 3675672*B*a^2*b^8*d^2*x^7*e^9 + 816816*A*a*b^9*d^2*x^7*e^9 + 2339064*B*a^2*b
^8*d^3*x^6*e^8 + 519792*A*a*b^9*d^3*x^6*e^8 + 1169532*B*a^2*b^8*d^4*x^5*e^7 + 259896*A*a*b^9*d^4*x^5*e^7 + 449
820*B*a^2*b^8*d^5*x^4*e^6 + 99960*A*a*b^9*d^5*x^4*e^6 + 128520*B*a^2*b^8*d^6*x^3*e^5 + 28560*A*a*b^9*d^6*x^3*e
^5 + 25704*B*a^2*b^8*d^7*x^2*e^4 + 5712*A*a*b^9*d^7*x^2*e^4 + 3213*B*a^2*b^8*d^8*x*e^3 + 714*A*a*b^9*d^8*x*e^3
+ 189*B*a^2*b^8*d^9*e^2 + 42*A*a*b^9*d^9*e^2 + 10890880*B*a^3*b^7*x^8*e^11 + 4084080*A*a^2*b^8*x^8*e^11 + 871
2704*B*a^3*b^7*d*x^7*e^10 + 3267264*A*a^2*b^8*d*x^7*e^10 + 5544448*B*a^3*b^7*d^2*x^6*e^9 + 2079168*A*a^2*b^8*d
^2*x^6*e^9 + 2772224*B*a^3*b^7*d^3*x^5*e^8 + 1039584*A*a^2*b^8*d^3*x^5*e^8 + 1066240*B*a^3*b^7*d^4*x^4*e^7 + 3
99840*A*a^2*b^8*d^4*x^4*e^7 + 304640*B*a^3*b^7*d^5*x^3*e^6 + 114240*A*a^2*b^8*d^5*x^3*e^6 + 60928*B*a^3*b^7*d^
6*x^2*e^5 + 22848*A*a^2*b^8*d^6*x^2*e^5 + 7616*B*a^3*b^7*d^7*x*e^4 + 2856*A*a^2*b^8*d^7*x*e^4 + 448*B*a^3*b^7*
d^8*e^3 + 168*A*a^2*b^8*d^8*e^3 + 17153136*B*a^4*b^6*x^7*e^11 + 9801792*A*a^3*b^7*x^7*e^11 + 10915632*B*a^4*b^
6*d*x^6*e^10 + 6237504*A*a^3*b^7*d*x^6*e^10 + 5457816*B*a^4*b^6*d^2*x^5*e^9 + 3118752*A*a^3*b^7*d^2*x^5*e^9 +
2099160*B*a^4*b^6*d^3*x^4*e^8 + 1199520*A*a^3*b^7*d^3*x^4*e^8 + 599760*B*a^4*b^6*d^4*x^3*e^7 + 342720*A*a^3*b^
7*d^4*x^3*e^7 + 119952*B*a^4*b^6*d^5*x^2*e^6 + 68544*A*a^3*b^7*d^5*x^2*e^6 + 14994*B*a^4*b^6*d^6*x*e^5 + 8568*
A*a^3*b^7*d^6*x*e^5 + 882*B*a^4*b^6*d^7*e^4 + 504*A*a^3*b^7*d^7*e^4 + 18712512*B*a^5*b^5*x^6*e^11 + 15593760*A
*a^4*b^6*x^6*e^11 + 9356256*B*a^5*b^5*d*x^5*e^10 + 7796880*A*a^4*b^6*d*x^5*e^10 + 3598560*B*a^5*b^5*d^2*x^4*e^
9 + 2998800*A*a^4*b^6*d^2*x^4*e^9 + 1028160*B*a^5*b^5*d^3*x^3*e^8 + 856800*A*a^4*b^6*d^3*x^3*e^8 + 205632*B*a^
5*b^5*d^4*x^2*e^7 + 171360*A*a^4*b^6*d^4*x^2*e^7 + 25704*B*a^5*b^5*d^5*x*e^6 + 21420*A*a^4*b^6*d^5*x*e^6 + 151
2*B*a^5*b^5*d^6*e^5 + 1260*A*a^4*b^6*d^6*e^5 + 14294280*B*a^6*b^4*x^5*e^11 + 17153136*A*a^5*b^5*x^5*e^11 + 549
7800*B*a^6*b^4*d*x^4*e^10 + 6597360*A*a^5*b^5*d*x^4*e^10 + 1570800*B*a^6*b^4*d^2*x^3*e^9 + 1884960*A*a^5*b^5*d
^2*x^3*e^9 + 314160*B*a^6*b^4*d^3*x^2*e^8 + 376992*A*a^5*b^5*d^3*x^2*e^8 + 39270*B*a^6*b^4*d^4*x*e^7 + 47124*A
*a^5*b^5*d^4*x*e^7 + 2310*B*a^6*b^4*d^5*e^6 + 2772*A*a^5*b^5*d^5*e^6 + 7539840*B*a^7*b^3*x^4*e^11 + 13194720*A
*a^6*b^4*x^4*e^11 + 2154240*B*a^7*b^3*d*x^3*e^10 + 3769920*A*a^6*b^4*d*x^3*e^10 + 430848*B*a^7*b^3*d^2*x^2*e^9
+ 753984*A*a^6*b^4*d^2*x^2*e^9 + 53856*B*a^7*b^3*d^3*x*e^8 + 94248*A*a^6*b^4*d^3*x*e^8 + 3168*B*a^7*b^3*d^4*e
^7 + 5544*A*a^6*b^4*d^4*e^7 + 2625480*B*a^8*b^2*x^3*e^11 + 7001280*A*a^7*b^3*x^3*e^11 + 525096*B*a^8*b^2*d*x^2
*e^10 + 1400256*A*a^7*b^3*d*x^2*e^10 + 65637*B*a^8*b^2*d^2*x*e^9 + 175032*A*a^7*b^3*d^2*x*e^9 + 3861*B*a^8*b^2
*d^3*e^8 + 10296*A*a^7*b^3*d^3*e^8 + 544544*B*a^9*b*x^2*e^11 + 2450448*A*a^8*b^2*x^2*e^11 + 68068*B*a^9*b*d*x*
e^10 + 306306*A*a^8*b^2*d*x*e^10 + 4004*B*a^9*b*d^2*e^9 + 18018*A*a^8*b^2*d^2*e^9 + 51051*B*a^10*x*e^11 + 5105
10*A*a^9*b*x*e^11 + 3003*B*a^10*d*e^10 + 30030*A*a^9*b*d*e^10 + 48048*A*a^10*e^11)*e^(-12)/(x*e + d)^17