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3.1089 \(\int \frac{(a+b x)^{10} (A+B x)}{d+e x} \, dx\)

Optimal. Leaf size=348 \[ -\frac{(a+b x)^{10} (B d-A e)}{10 e^2}+\frac{(a+b x)^9 (b d-a e) (B d-A e)}{9 e^3}-\frac{(a+b x)^8 (b d-a e)^2 (B d-A e)}{8 e^4}+\frac{(a+b x)^7 (b d-a e)^3 (B d-A e)}{7 e^5}-\frac{(a+b x)^6 (b d-a e)^4 (B d-A e)}{6 e^6}+\frac{(a+b x)^5 (b d-a e)^5 (B d-A e)}{5 e^7}-\frac{(a+b x)^4 (b d-a e)^6 (B d-A e)}{4 e^8}+\frac{(a+b x)^3 (b d-a e)^7 (B d-A e)}{3 e^9}-\frac{(a+b x)^2 (b d-a e)^8 (B d-A e)}{2 e^{10}}+\frac{b x (b d-a e)^9 (B d-A e)}{e^{11}}-\frac{(b d-a e)^{10} (B d-A e) \log (d+e x)}{e^{12}}+\frac{B (a+b x)^{11}}{11 b e} \]

[Out]

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

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Rubi [A]  time = 0.357606, antiderivative size = 348, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ -\frac{(a+b x)^{10} (B d-A e)}{10 e^2}+\frac{(a+b x)^9 (b d-a e) (B d-A e)}{9 e^3}-\frac{(a+b x)^8 (b d-a e)^2 (B d-A e)}{8 e^4}+\frac{(a+b x)^7 (b d-a e)^3 (B d-A e)}{7 e^5}-\frac{(a+b x)^6 (b d-a e)^4 (B d-A e)}{6 e^6}+\frac{(a+b x)^5 (b d-a e)^5 (B d-A e)}{5 e^7}-\frac{(a+b x)^4 (b d-a e)^6 (B d-A e)}{4 e^8}+\frac{(a+b x)^3 (b d-a e)^7 (B d-A e)}{3 e^9}-\frac{(a+b x)^2 (b d-a e)^8 (B d-A e)}{2 e^{10}}+\frac{b x (b d-a e)^9 (B d-A e)}{e^{11}}-\frac{(b d-a e)^{10} (B d-A e) \log (d+e x)}{e^{12}}+\frac{B (a+b x)^{11}}{11 b e} \]

Antiderivative was successfully verified.

[In]

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

[Out]

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

Rule 77

Int[((a_.) + (b_.)*(x_))*((c_) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandIntegran
d[(a + b*x)*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, n}, x] && NeQ[b*c - a*d, 0] && ((ILtQ[
n, 0] && ILtQ[p, 0]) || EqQ[p, 1] || (IGtQ[p, 0] && ( !IntegerQ[n] || LeQ[9*p + 5*(n + 2), 0] || GeQ[n + p + 1
, 0] || (GeQ[n + p + 2, 0] && RationalQ[a, b, c, d, e, f]))))

Rubi steps

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

Mathematica [B]  time = 0.945206, size = 1252, normalized size = 3.6 \[ \frac{(A e-B d) \log (d+e x) (b d-a e)^{10}}{e^{12}}+\frac{x \left (\left (11 A e \left (-2520 d^9+1260 e x d^8-840 e^2 x^2 d^7+630 e^3 x^3 d^6-504 e^4 x^4 d^5+420 e^5 x^5 d^4-360 e^6 x^6 d^3+315 e^7 x^7 d^2-280 e^8 x^8 d+252 e^9 x^9\right )+B \left (27720 d^{10}-13860 e x d^9+9240 e^2 x^2 d^8-6930 e^3 x^3 d^7+5544 e^4 x^4 d^6-4620 e^5 x^5 d^5+3960 e^6 x^6 d^4-3465 e^7 x^7 d^3+3080 e^8 x^8 d^2-2772 e^9 x^9 d+2520 e^{10} x^{10}\right )\right ) b^{10}+110 a e \left (A e \left (2520 d^8-1260 e x d^7+840 e^2 x^2 d^6-630 e^3 x^3 d^5+504 e^4 x^4 d^4-420 e^5 x^5 d^3+360 e^6 x^6 d^2-315 e^7 x^7 d+280 e^8 x^8\right )+B \left (-2520 d^9+1260 e x d^8-840 e^2 x^2 d^7+630 e^3 x^3 d^6-504 e^4 x^4 d^5+420 e^5 x^5 d^4-360 e^6 x^6 d^3+315 e^7 x^7 d^2-280 e^8 x^8 d+252 e^9 x^9\right )\right ) b^9+495 a^2 e^2 \left (3 A e \left (-840 d^7+420 e x d^6-280 e^2 x^2 d^5+210 e^3 x^3 d^4-168 e^4 x^4 d^3+140 e^5 x^5 d^2-120 e^6 x^6 d+105 e^7 x^7\right )+B \left (2520 d^8-1260 e x d^7+840 e^2 x^2 d^6-630 e^3 x^3 d^5+504 e^4 x^4 d^4-420 e^5 x^5 d^3+360 e^6 x^6 d^2-315 e^7 x^7 d+280 e^8 x^8\right )\right ) b^8+3960 a^3 e^3 \left (2 A e \left (420 d^6-210 e x d^5+140 e^2 x^2 d^4-105 e^3 x^3 d^3+84 e^4 x^4 d^2-70 e^5 x^5 d+60 e^6 x^6\right )+B \left (-840 d^7+420 e x d^6-280 e^2 x^2 d^5+210 e^3 x^3 d^4-168 e^4 x^4 d^3+140 e^5 x^5 d^2-120 e^6 x^6 d+105 e^7 x^7\right )\right ) b^7+13860 a^4 e^4 \left (7 A e \left (-60 d^5+30 e x d^4-20 e^2 x^2 d^3+15 e^3 x^3 d^2-12 e^4 x^4 d+10 e^5 x^5\right )+B \left (420 d^6-210 e x d^5+140 e^2 x^2 d^4-105 e^3 x^3 d^3+84 e^4 x^4 d^2-70 e^5 x^5 d+60 e^6 x^6\right )\right ) b^6+116424 a^5 e^5 \left (A e \left (60 d^4-30 e x d^3+20 e^2 x^2 d^2-15 e^3 x^3 d+12 e^4 x^4\right )+B \left (-60 d^5+30 e x d^4-20 e^2 x^2 d^3+15 e^3 x^3 d^2-12 e^4 x^4 d+10 e^5 x^5\right )\right ) b^5+97020 a^6 e^6 \left (5 A e \left (-12 d^3+6 e x d^2-4 e^2 x^2 d+3 e^3 x^3\right )+B \left (60 d^4-30 e x d^3+20 e^2 x^2 d^2-15 e^3 x^3 d+12 e^4 x^4\right )\right ) b^4+277200 a^7 e^7 \left (2 A e \left (6 d^2-3 e x d+2 e^2 x^2\right )+B \left (-12 d^3+6 e x d^2-4 e^2 x^2 d+3 e^3 x^3\right )\right ) b^3+207900 a^8 e^8 \left (3 A e (e x-2 d)+B \left (6 d^2-3 e x d+2 e^2 x^2\right )\right ) b^2+138600 a^9 e^9 (-2 B d+2 A e+B e x) b+27720 a^{10} B e^{10}\right )}{27720 e^{11}} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(x*(27720*a^10*B*e^10 + 138600*a^9*b*e^9*(-2*B*d + 2*A*e + B*e*x) + 207900*a^8*b^2*e^8*(3*A*e*(-2*d + e*x) + B
*(6*d^2 - 3*d*e*x + 2*e^2*x^2)) + 277200*a^7*b^3*e^7*(2*A*e*(6*d^2 - 3*d*e*x + 2*e^2*x^2) + B*(-12*d^3 + 6*d^2
*e*x - 4*d*e^2*x^2 + 3*e^3*x^3)) + 97020*a^6*b^4*e^6*(5*A*e*(-12*d^3 + 6*d^2*e*x - 4*d*e^2*x^2 + 3*e^3*x^3) +
B*(60*d^4 - 30*d^3*e*x + 20*d^2*e^2*x^2 - 15*d*e^3*x^3 + 12*e^4*x^4)) + 116424*a^5*b^5*e^5*(A*e*(60*d^4 - 30*d
^3*e*x + 20*d^2*e^2*x^2 - 15*d*e^3*x^3 + 12*e^4*x^4) + B*(-60*d^5 + 30*d^4*e*x - 20*d^3*e^2*x^2 + 15*d^2*e^3*x
^3 - 12*d*e^4*x^4 + 10*e^5*x^5)) + 13860*a^4*b^6*e^4*(7*A*e*(-60*d^5 + 30*d^4*e*x - 20*d^3*e^2*x^2 + 15*d^2*e^
3*x^3 - 12*d*e^4*x^4 + 10*e^5*x^5) + B*(420*d^6 - 210*d^5*e*x + 140*d^4*e^2*x^2 - 105*d^3*e^3*x^3 + 84*d^2*e^4
*x^4 - 70*d*e^5*x^5 + 60*e^6*x^6)) + 3960*a^3*b^7*e^3*(2*A*e*(420*d^6 - 210*d^5*e*x + 140*d^4*e^2*x^2 - 105*d^
3*e^3*x^3 + 84*d^2*e^4*x^4 - 70*d*e^5*x^5 + 60*e^6*x^6) + B*(-840*d^7 + 420*d^6*e*x - 280*d^5*e^2*x^2 + 210*d^
4*e^3*x^3 - 168*d^3*e^4*x^4 + 140*d^2*e^5*x^5 - 120*d*e^6*x^6 + 105*e^7*x^7)) + 495*a^2*b^8*e^2*(3*A*e*(-840*d
^7 + 420*d^6*e*x - 280*d^5*e^2*x^2 + 210*d^4*e^3*x^3 - 168*d^3*e^4*x^4 + 140*d^2*e^5*x^5 - 120*d*e^6*x^6 + 105
*e^7*x^7) + B*(2520*d^8 - 1260*d^7*e*x + 840*d^6*e^2*x^2 - 630*d^5*e^3*x^3 + 504*d^4*e^4*x^4 - 420*d^3*e^5*x^5
 + 360*d^2*e^6*x^6 - 315*d*e^7*x^7 + 280*e^8*x^8)) + 110*a*b^9*e*(A*e*(2520*d^8 - 1260*d^7*e*x + 840*d^6*e^2*x
^2 - 630*d^5*e^3*x^3 + 504*d^4*e^4*x^4 - 420*d^3*e^5*x^5 + 360*d^2*e^6*x^6 - 315*d*e^7*x^7 + 280*e^8*x^8) + B*
(-2520*d^9 + 1260*d^8*e*x - 840*d^7*e^2*x^2 + 630*d^6*e^3*x^3 - 504*d^5*e^4*x^4 + 420*d^4*e^5*x^5 - 360*d^3*e^
6*x^6 + 315*d^2*e^7*x^7 - 280*d*e^8*x^8 + 252*e^9*x^9)) + b^10*(11*A*e*(-2520*d^9 + 1260*d^8*e*x - 840*d^7*e^2
*x^2 + 630*d^6*e^3*x^3 - 504*d^5*e^4*x^4 + 420*d^4*e^5*x^5 - 360*d^3*e^6*x^6 + 315*d^2*e^7*x^7 - 280*d*e^8*x^8
 + 252*e^9*x^9) + B*(27720*d^10 - 13860*d^9*e*x + 9240*d^8*e^2*x^2 - 6930*d^7*e^3*x^3 + 5544*d^6*e^4*x^4 - 462
0*d^5*e^5*x^5 + 3960*d^4*e^6*x^6 - 3465*d^3*e^7*x^7 + 3080*d^2*e^8*x^8 - 2772*d*e^9*x^9 + 2520*e^10*x^10))))/(
27720*e^11) + ((b*d - a*e)^10*(-(B*d) + A*e)*Log[d + e*x])/e^12

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Maple [B]  time = 0.014, size = 2357, normalized size = 6.8 \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),x)

[Out]

-1/4/e^8*B*x^4*b^10*d^7+30/e^5*B*x^4*a^3*b^7*d^4-45/4/e^6*B*x^4*a^2*b^8*d^5+5/2/e^7*B*x^4*a*b^9*d^6-70/e^2*A*x
^3*a^6*b^4*d+84/e^3*A*x^3*a^5*b^5*d^2-70/e^4*A*x^3*a^4*b^6*d^3+40/e*A*x^3*a^7*b^3-1/3/e^8*A*x^3*b^10*d^7+1/11/
e*B*b^10*x^11+1/10/e*A*x^10*b^10+1/e*a^10*B*x+1/e*ln(e*x+d)*a^10*A-1/5/e^6*A*x^5*b^10*d^5+10/9/e*A*x^9*a*b^9-1
/e^2*ln(e*x+d)*B*a^10*d-1/e^12*ln(e*x+d)*b^10*B*d^11+210/e^5*ln(e*x+d)*A*a^6*b^4*d^4-252/e^6*ln(e*x+d)*A*a^5*b
^5*d^5+210/e^7*ln(e*x+d)*A*a^4*b^6*d^6-120/e^8*ln(e*x+d)*A*a^3*b^7*d^7+45/e^9*ln(e*x+d)*A*a^2*b^8*d^8-10/e^10*
ln(e*x+d)*A*a*b^9*d^9+10/e^3*ln(e*x+d)*B*a^9*b*d^2-120/7/e^2*B*x^7*a^3*b^7*d-10/9/e^2*B*x^9*a*b^9*d-5/4/e^2*A*
x^8*a*b^9*d+1/9/e^3*B*x^9*b^10*d^2-1/e^10*A*b^10*d^9*x-1/10/e^2*B*x^10*b^10*d+1/e^11*ln(e*x+d)*A*b^10*d^10+5/e
*B*x^9*a^2*b^8+45/8/e*A*x^8*a^2*b^8+1/8/e^3*A*x^8*b^10*d^2+1/e^11*b^10*B*d^10*x-1/9/e^2*A*x^9*b^10*d-126/e^4*A
*x^2*a^5*b^5*d^3+105/e^5*A*x^2*a^4*b^6*d^4-45/e^4*ln(e*x+d)*B*a^8*b^2*d^3+120/e^5*ln(e*x+d)*B*a^7*b^3*d^4-210/
e^6*ln(e*x+d)*B*a^6*b^4*d^5+252/e^7*ln(e*x+d)*B*a^5*b^5*d^6-210/e^8*ln(e*x+d)*B*a^4*b^6*d^7+120/e^9*ln(e*x+d)*
B*a^3*b^7*d^8-45/e^10*ln(e*x+d)*B*a^2*b^8*d^9+10/e^11*ln(e*x+d)*B*a*b^9*d^10-105/e^4*B*x^2*a^6*b^4*d^3+126/e^5
*B*x^2*a^5*b^5*d^4-105/e^6*B*x^2*a^4*b^6*d^5-24/e^4*B*x^5*a^3*b^7*d^3+9/e^5*B*x^5*a^2*b^8*d^4-2/e^6*B*x^5*a*b^
9*d^5+252/e^5*A*a^5*b^5*d^4*x-15/2/e^4*B*x^6*a^2*b^8*d^3-45/2/e^8*B*x^2*a^2*b^8*d^7+5/e^9*B*x^2*a*b^9*d^8-60/e
^6*A*x^2*a^3*b^7*d^5+45/2/e^7*A*x^2*a^2*b^8*d^6-5/e^8*A*x^2*a*b^9*d^7-45/2/e^2*B*x^2*a^8*b^2*d+60/e^3*B*x^2*a^
7*b^3*d^2-1/2/e^10*B*x^2*b^10*d^9-45/8/e^2*B*x^8*a^2*b^8*d+5/4/e^3*B*x^8*a*b^9*d^2-45/e^2*A*a^8*b^2*d*x+120/e^
3*A*a^7*b^3*d^2*x-210/e^4*A*a^6*b^4*d^3*x+24/e^3*A*x^5*a^3*b^7*d^2-9/e^4*A*x^5*a^2*b^8*d^3+2/e^5*A*x^5*a*b^9*d
^4+5/3/e^5*B*x^6*a*b^9*d^4+20/e^3*B*x^6*a^3*b^7*d^2+45/7/e^3*B*x^7*a^2*b^8*d^2-10/7/e^4*B*x^7*a*b^9*d^3-20/e^2
*A*x^6*a^3*b^7*d+15/2/e^3*A*x^6*a^2*b^8*d^2-5/3/e^4*A*x^6*a*b^9*d^3-35/e^2*B*x^6*a^4*b^6*d-45/7/e^2*A*x^7*a^2*
b^8*d+10/7/e^3*A*x^7*a*b^9*d^2-42/e^2*A*x^5*a^4*b^6*d+15/e*B*x^3*a^8*b^2+10/e*a^9*b*A*x+1/6/e^5*A*x^6*b^10*d^4
+105/2/e*A*x^4*a^6*b^4+1/4/e^7*A*x^4*b^10*d^6+30/e*B*x^4*a^7*b^3+42/e*B*x^6*a^5*b^5-1/6/e^6*B*x^6*b^10*d^5+252
/5/e*A*x^5*a^5*b^5+1/e*B*x^10*a*b^9+42/e*B*x^5*a^6*b^4+15/e*B*x^8*a^3*b^7-1/8/e^4*B*x^8*b^10*d^3+120/7/e*A*x^7
*a^3*b^7-1/7/e^4*A*x^7*b^10*d^3+30/e*B*x^7*a^4*b^6+1/7/e^5*B*x^7*b^10*d^4+35/e*A*x^6*a^4*b^6+45/2/e*A*x^2*a^8*
b^2+1/2/e^9*A*x^2*b^10*d^8+5/e*B*x^2*a^9*b+1/5/e^7*B*x^5*b^10*d^6+1/3/e^9*B*x^3*b^10*d^8+40/e^5*A*x^3*a^3*b^7*
d^4-15/e^6*A*x^3*a^2*b^8*d^5+10/3/e^7*A*x^3*a*b^9*d^6-40/e^2*B*x^3*a^7*b^3*d+70/e^3*B*x^3*a^6*b^4*d^2-84/e^4*B
*x^3*a^5*b^5*d^3+70/e^5*B*x^3*a^4*b^6*d^4-40/e^6*B*x^3*a^3*b^7*d^5+15/e^7*B*x^3*a^2*b^8*d^6-10/3/e^8*B*x^3*a*b
^9*d^7-60/e^2*A*x^2*a^7*b^3*d+105/e^3*A*x^2*a^6*b^4*d^2-10/e^2*ln(e*x+d)*A*a^9*b*d+45/e^3*ln(e*x+d)*A*a^8*b^2*
d^2-120/e^4*ln(e*x+d)*A*a^7*b^3*d^3-210/e^6*A*a^4*b^6*d^5*x+120/e^7*A*a^3*b^7*d^6*x-45/e^8*A*a^2*b^8*d^7*x+10/
e^9*A*a*b^9*d^8*x-10/e^2*B*a^9*b*d*x+45/e^3*B*a^8*b^2*d^2*x-120/e^4*B*a^7*b^3*d^3*x+210/e^5*B*a^6*b^4*d^4*x-25
2/e^6*B*a^5*b^5*d^5*x+210/e^7*B*a^4*b^6*d^6*x-120/e^8*B*a^3*b^7*d^7*x+45/e^9*B*a^2*b^8*d^8*x-10/e^10*B*a*b^9*d
^9*x+60/e^7*B*x^2*a^3*b^7*d^6-252/5/e^2*B*x^5*a^5*b^5*d+42/e^3*B*x^5*a^4*b^6*d^2-63/e^2*A*x^4*a^5*b^5*d+105/2/
e^3*A*x^4*a^4*b^6*d^2-30/e^4*A*x^4*a^3*b^7*d^3+45/4/e^5*A*x^4*a^2*b^8*d^4-5/2/e^6*A*x^4*a*b^9*d^5-105/2/e^2*B*
x^4*a^6*b^4*d+63/e^3*B*x^4*a^5*b^5*d^2-105/2/e^4*B*x^4*a^4*b^6*d^3

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Maxima [B]  time = 1.16919, size = 2435, normalized size = 7. \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),x, algorithm="maxima")

[Out]

1/27720*(2520*B*b^10*e^10*x^11 - 2772*(B*b^10*d*e^9 - (10*B*a*b^9 + A*b^10)*e^10)*x^10 + 3080*(B*b^10*d^2*e^8
- (10*B*a*b^9 + A*b^10)*d*e^9 + 5*(9*B*a^2*b^8 + 2*A*a*b^9)*e^10)*x^9 - 3465*(B*b^10*d^3*e^7 - (10*B*a*b^9 + A
*b^10)*d^2*e^8 + 5*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^9 - 15*(8*B*a^3*b^7 + 3*A*a^2*b^8)*e^10)*x^8 + 3960*(B*b^10*d
^4*e^6 - (10*B*a*b^9 + A*b^10)*d^3*e^7 + 5*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^8 - 15*(8*B*a^3*b^7 + 3*A*a^2*b^8)*
d*e^9 + 30*(7*B*a^4*b^6 + 4*A*a^3*b^7)*e^10)*x^7 - 4620*(B*b^10*d^5*e^5 - (10*B*a*b^9 + A*b^10)*d^4*e^6 + 5*(9
*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^7 - 15*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^8 + 30*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^
9 - 42*(6*B*a^5*b^5 + 5*A*a^4*b^6)*e^10)*x^6 + 5544*(B*b^10*d^6*e^4 - (10*B*a*b^9 + A*b^10)*d^5*e^5 + 5*(9*B*a
^2*b^8 + 2*A*a*b^9)*d^4*e^6 - 15*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^7 + 30*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^8
- 42*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^9 + 42*(5*B*a^6*b^4 + 6*A*a^5*b^5)*e^10)*x^5 - 6930*(B*b^10*d^7*e^3 - (10
*B*a*b^9 + A*b^10)*d^6*e^4 + 5*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^5 - 15*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^6 + 30
*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^7 - 42*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^8 + 42*(5*B*a^6*b^4 + 6*A*a^5*b^5)
*d*e^9 - 30*(4*B*a^7*b^3 + 7*A*a^6*b^4)*e^10)*x^4 + 9240*(B*b^10*d^8*e^2 - (10*B*a*b^9 + A*b^10)*d^7*e^3 + 5*(
9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^4 - 15*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^5 + 30*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4
*e^6 - 42*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^7 + 42*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^8 - 30*(4*B*a^7*b^3 + 7*A
*a^6*b^4)*d*e^9 + 15*(3*B*a^8*b^2 + 8*A*a^7*b^3)*e^10)*x^3 - 13860*(B*b^10*d^9*e - (10*B*a*b^9 + A*b^10)*d^8*e
^2 + 5*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^3 - 15*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^4 + 30*(7*B*a^4*b^6 + 4*A*a^3*
b^7)*d^5*e^5 - 42*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^6 + 42*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^7 - 30*(4*B*a^7*b
^3 + 7*A*a^6*b^4)*d^2*e^8 + 15*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^9 - 5*(2*B*a^9*b + 9*A*a^8*b^2)*e^10)*x^2 + 277
20*(B*b^10*d^10 - (10*B*a*b^9 + A*b^10)*d^9*e + 5*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^2 - 15*(8*B*a^3*b^7 + 3*A*a^
2*b^8)*d^7*e^3 + 30*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^4 - 42*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^5 + 42*(5*B*a^6
*b^4 + 6*A*a^5*b^5)*d^4*e^6 - 30*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^7 + 15*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^8
- 5*(2*B*a^9*b + 9*A*a^8*b^2)*d*e^9 + (B*a^10 + 10*A*a^9*b)*e^10)*x)/e^11 - (B*b^10*d^11 - A*a^10*e^11 - (10*B
*a*b^9 + A*b^10)*d^10*e + 5*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 - 15*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 + 30*(7
*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 - 42*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 + 42*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^
5*e^6 - 30*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 + 15*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^8 - 5*(2*B*a^9*b + 9*A*a
^8*b^2)*d^2*e^9 + (B*a^10 + 10*A*a^9*b)*d*e^10)*log(e*x + d)/e^12

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Fricas [B]  time = 1.9421, size = 3826, normalized size = 10.99 \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),x, algorithm="fricas")

[Out]

1/27720*(2520*B*b^10*e^11*x^11 - 2772*(B*b^10*d*e^10 - (10*B*a*b^9 + A*b^10)*e^11)*x^10 + 3080*(B*b^10*d^2*e^9
 - (10*B*a*b^9 + A*b^10)*d*e^10 + 5*(9*B*a^2*b^8 + 2*A*a*b^9)*e^11)*x^9 - 3465*(B*b^10*d^3*e^8 - (10*B*a*b^9 +
 A*b^10)*d^2*e^9 + 5*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^10 - 15*(8*B*a^3*b^7 + 3*A*a^2*b^8)*e^11)*x^8 + 3960*(B*b^1
0*d^4*e^7 - (10*B*a*b^9 + A*b^10)*d^3*e^8 + 5*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9 - 15*(8*B*a^3*b^7 + 3*A*a^2*b^
8)*d*e^10 + 30*(7*B*a^4*b^6 + 4*A*a^3*b^7)*e^11)*x^7 - 4620*(B*b^10*d^5*e^6 - (10*B*a*b^9 + A*b^10)*d^4*e^7 +
5*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8 - 15*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^9 + 30*(7*B*a^4*b^6 + 4*A*a^3*b^7)*
d*e^10 - 42*(6*B*a^5*b^5 + 5*A*a^4*b^6)*e^11)*x^6 + 5544*(B*b^10*d^6*e^5 - (10*B*a*b^9 + A*b^10)*d^5*e^6 + 5*(
9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 - 15*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^8 + 30*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2
*e^9 - 42*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^10 + 42*(5*B*a^6*b^4 + 6*A*a^5*b^5)*e^11)*x^5 - 6930*(B*b^10*d^7*e^4
 - (10*B*a*b^9 + A*b^10)*d^6*e^5 + 5*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^6 - 15*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^
7 + 30*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^8 - 42*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^9 + 42*(5*B*a^6*b^4 + 6*A*a^
5*b^5)*d*e^10 - 30*(4*B*a^7*b^3 + 7*A*a^6*b^4)*e^11)*x^4 + 9240*(B*b^10*d^8*e^3 - (10*B*a*b^9 + A*b^10)*d^7*e^
4 + 5*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 - 15*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 + 30*(7*B*a^4*b^6 + 4*A*a^3*b
^7)*d^4*e^7 - 42*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^8 + 42*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^9 - 30*(4*B*a^7*b^
3 + 7*A*a^6*b^4)*d*e^10 + 15*(3*B*a^8*b^2 + 8*A*a^7*b^3)*e^11)*x^3 - 13860*(B*b^10*d^9*e^2 - (10*B*a*b^9 + A*b
^10)*d^8*e^3 + 5*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4 - 15*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 + 30*(7*B*a^4*b^6
+ 4*A*a^3*b^7)*d^5*e^6 - 42*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^7 + 42*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^8 - 30*
(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^9 + 15*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^10 - 5*(2*B*a^9*b + 9*A*a^8*b^2)*e^11
)*x^2 + 27720*(B*b^10*d^10*e - (10*B*a*b^9 + A*b^10)*d^9*e^2 + 5*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 - 15*(8*B*a
^3*b^7 + 3*A*a^2*b^8)*d^7*e^4 + 30*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5 - 42*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^
6 + 42*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^7 - 30*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^8 + 15*(3*B*a^8*b^2 + 8*A*a^
7*b^3)*d^2*e^9 - 5*(2*B*a^9*b + 9*A*a^8*b^2)*d*e^10 + (B*a^10 + 10*A*a^9*b)*e^11)*x - 27720*(B*b^10*d^11 - A*a
^10*e^11 - (10*B*a*b^9 + A*b^10)*d^10*e + 5*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 - 15*(8*B*a^3*b^7 + 3*A*a^2*b^8)
*d^8*e^3 + 30*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 - 42*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 + 42*(5*B*a^6*b^4 +
 6*A*a^5*b^5)*d^5*e^6 - 30*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 + 15*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^8 - 5*(2
*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 + (B*a^10 + 10*A*a^9*b)*d*e^10)*log(e*x + d))/e^12

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Sympy [B]  time = 5.34694, size = 1844, normalized size = 5.3 \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),x)

[Out]

B*b**10*x**11/(11*e) + x**10*(A*b**10*e + 10*B*a*b**9*e - B*b**10*d)/(10*e**2) + x**9*(10*A*a*b**9*e**2 - A*b*
*10*d*e + 45*B*a**2*b**8*e**2 - 10*B*a*b**9*d*e + B*b**10*d**2)/(9*e**3) + x**8*(45*A*a**2*b**8*e**3 - 10*A*a*
b**9*d*e**2 + A*b**10*d**2*e + 120*B*a**3*b**7*e**3 - 45*B*a**2*b**8*d*e**2 + 10*B*a*b**9*d**2*e - B*b**10*d**
3)/(8*e**4) + x**7*(120*A*a**3*b**7*e**4 - 45*A*a**2*b**8*d*e**3 + 10*A*a*b**9*d**2*e**2 - A*b**10*d**3*e + 21
0*B*a**4*b**6*e**4 - 120*B*a**3*b**7*d*e**3 + 45*B*a**2*b**8*d**2*e**2 - 10*B*a*b**9*d**3*e + B*b**10*d**4)/(7
*e**5) + x**6*(210*A*a**4*b**6*e**5 - 120*A*a**3*b**7*d*e**4 + 45*A*a**2*b**8*d**2*e**3 - 10*A*a*b**9*d**3*e**
2 + A*b**10*d**4*e + 252*B*a**5*b**5*e**5 - 210*B*a**4*b**6*d*e**4 + 120*B*a**3*b**7*d**2*e**3 - 45*B*a**2*b**
8*d**3*e**2 + 10*B*a*b**9*d**4*e - B*b**10*d**5)/(6*e**6) + x**5*(252*A*a**5*b**5*e**6 - 210*A*a**4*b**6*d*e**
5 + 120*A*a**3*b**7*d**2*e**4 - 45*A*a**2*b**8*d**3*e**3 + 10*A*a*b**9*d**4*e**2 - A*b**10*d**5*e + 210*B*a**6
*b**4*e**6 - 252*B*a**5*b**5*d*e**5 + 210*B*a**4*b**6*d**2*e**4 - 120*B*a**3*b**7*d**3*e**3 + 45*B*a**2*b**8*d
**4*e**2 - 10*B*a*b**9*d**5*e + B*b**10*d**6)/(5*e**7) + x**4*(210*A*a**6*b**4*e**7 - 252*A*a**5*b**5*d*e**6 +
 210*A*a**4*b**6*d**2*e**5 - 120*A*a**3*b**7*d**3*e**4 + 45*A*a**2*b**8*d**4*e**3 - 10*A*a*b**9*d**5*e**2 + A*
b**10*d**6*e + 120*B*a**7*b**3*e**7 - 210*B*a**6*b**4*d*e**6 + 252*B*a**5*b**5*d**2*e**5 - 210*B*a**4*b**6*d**
3*e**4 + 120*B*a**3*b**7*d**4*e**3 - 45*B*a**2*b**8*d**5*e**2 + 10*B*a*b**9*d**6*e - B*b**10*d**7)/(4*e**8) +
x**3*(120*A*a**7*b**3*e**8 - 210*A*a**6*b**4*d*e**7 + 252*A*a**5*b**5*d**2*e**6 - 210*A*a**4*b**6*d**3*e**5 +
120*A*a**3*b**7*d**4*e**4 - 45*A*a**2*b**8*d**5*e**3 + 10*A*a*b**9*d**6*e**2 - A*b**10*d**7*e + 45*B*a**8*b**2
*e**8 - 120*B*a**7*b**3*d*e**7 + 210*B*a**6*b**4*d**2*e**6 - 252*B*a**5*b**5*d**3*e**5 + 210*B*a**4*b**6*d**4*
e**4 - 120*B*a**3*b**7*d**5*e**3 + 45*B*a**2*b**8*d**6*e**2 - 10*B*a*b**9*d**7*e + B*b**10*d**8)/(3*e**9) + x*
*2*(45*A*a**8*b**2*e**9 - 120*A*a**7*b**3*d*e**8 + 210*A*a**6*b**4*d**2*e**7 - 252*A*a**5*b**5*d**3*e**6 + 210
*A*a**4*b**6*d**4*e**5 - 120*A*a**3*b**7*d**5*e**4 + 45*A*a**2*b**8*d**6*e**3 - 10*A*a*b**9*d**7*e**2 + A*b**1
0*d**8*e + 10*B*a**9*b*e**9 - 45*B*a**8*b**2*d*e**8 + 120*B*a**7*b**3*d**2*e**7 - 210*B*a**6*b**4*d**3*e**6 +
252*B*a**5*b**5*d**4*e**5 - 210*B*a**4*b**6*d**5*e**4 + 120*B*a**3*b**7*d**6*e**3 - 45*B*a**2*b**8*d**7*e**2 +
 10*B*a*b**9*d**8*e - B*b**10*d**9)/(2*e**10) + x*(10*A*a**9*b*e**10 - 45*A*a**8*b**2*d*e**9 + 120*A*a**7*b**3
*d**2*e**8 - 210*A*a**6*b**4*d**3*e**7 + 252*A*a**5*b**5*d**4*e**6 - 210*A*a**4*b**6*d**5*e**5 + 120*A*a**3*b*
*7*d**6*e**4 - 45*A*a**2*b**8*d**7*e**3 + 10*A*a*b**9*d**8*e**2 - A*b**10*d**9*e + B*a**10*e**10 - 10*B*a**9*b
*d*e**9 + 45*B*a**8*b**2*d**2*e**8 - 120*B*a**7*b**3*d**3*e**7 + 210*B*a**6*b**4*d**4*e**6 - 252*B*a**5*b**5*d
**5*e**5 + 210*B*a**4*b**6*d**6*e**4 - 120*B*a**3*b**7*d**7*e**3 + 45*B*a**2*b**8*d**8*e**2 - 10*B*a*b**9*d**9
*e + B*b**10*d**10)/e**11 - (-A*e + B*d)*(a*e - b*d)**10*log(d + e*x)/e**12

________________________________________________________________________________________

Giac [B]  time = 2.13872, size = 2832, normalized size = 8.14 \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),x, algorithm="giac")

[Out]

-(B*b^10*d^11 - 10*B*a*b^9*d^10*e - A*b^10*d^10*e + 45*B*a^2*b^8*d^9*e^2 + 10*A*a*b^9*d^9*e^2 - 120*B*a^3*b^7*
d^8*e^3 - 45*A*a^2*b^8*d^8*e^3 + 210*B*a^4*b^6*d^7*e^4 + 120*A*a^3*b^7*d^7*e^4 - 252*B*a^5*b^5*d^6*e^5 - 210*A
*a^4*b^6*d^6*e^5 + 210*B*a^6*b^4*d^5*e^6 + 252*A*a^5*b^5*d^5*e^6 - 120*B*a^7*b^3*d^4*e^7 - 210*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 + B*a^10*d*e^10
+ 10*A*a^9*b*d*e^10 - A*a^10*e^11)*e^(-12)*log(abs(x*e + d)) + 1/27720*(2520*B*b^10*x^11*e^10 - 2772*B*b^10*d*
x^10*e^9 + 3080*B*b^10*d^2*x^9*e^8 - 3465*B*b^10*d^3*x^8*e^7 + 3960*B*b^10*d^4*x^7*e^6 - 4620*B*b^10*d^5*x^6*e
^5 + 5544*B*b^10*d^6*x^5*e^4 - 6930*B*b^10*d^7*x^4*e^3 + 9240*B*b^10*d^8*x^3*e^2 - 13860*B*b^10*d^9*x^2*e + 27
720*B*b^10*d^10*x + 27720*B*a*b^9*x^10*e^10 + 2772*A*b^10*x^10*e^10 - 30800*B*a*b^9*d*x^9*e^9 - 3080*A*b^10*d*
x^9*e^9 + 34650*B*a*b^9*d^2*x^8*e^8 + 3465*A*b^10*d^2*x^8*e^8 - 39600*B*a*b^9*d^3*x^7*e^7 - 3960*A*b^10*d^3*x^
7*e^7 + 46200*B*a*b^9*d^4*x^6*e^6 + 4620*A*b^10*d^4*x^6*e^6 - 55440*B*a*b^9*d^5*x^5*e^5 - 5544*A*b^10*d^5*x^5*
e^5 + 69300*B*a*b^9*d^6*x^4*e^4 + 6930*A*b^10*d^6*x^4*e^4 - 92400*B*a*b^9*d^7*x^3*e^3 - 9240*A*b^10*d^7*x^3*e^
3 + 138600*B*a*b^9*d^8*x^2*e^2 + 13860*A*b^10*d^8*x^2*e^2 - 277200*B*a*b^9*d^9*x*e - 27720*A*b^10*d^9*x*e + 13
8600*B*a^2*b^8*x^9*e^10 + 30800*A*a*b^9*x^9*e^10 - 155925*B*a^2*b^8*d*x^8*e^9 - 34650*A*a*b^9*d*x^8*e^9 + 1782
00*B*a^2*b^8*d^2*x^7*e^8 + 39600*A*a*b^9*d^2*x^7*e^8 - 207900*B*a^2*b^8*d^3*x^6*e^7 - 46200*A*a*b^9*d^3*x^6*e^
7 + 249480*B*a^2*b^8*d^4*x^5*e^6 + 55440*A*a*b^9*d^4*x^5*e^6 - 311850*B*a^2*b^8*d^5*x^4*e^5 - 69300*A*a*b^9*d^
5*x^4*e^5 + 415800*B*a^2*b^8*d^6*x^3*e^4 + 92400*A*a*b^9*d^6*x^3*e^4 - 623700*B*a^2*b^8*d^7*x^2*e^3 - 138600*A
*a*b^9*d^7*x^2*e^3 + 1247400*B*a^2*b^8*d^8*x*e^2 + 277200*A*a*b^9*d^8*x*e^2 + 415800*B*a^3*b^7*x^8*e^10 + 1559
25*A*a^2*b^8*x^8*e^10 - 475200*B*a^3*b^7*d*x^7*e^9 - 178200*A*a^2*b^8*d*x^7*e^9 + 554400*B*a^3*b^7*d^2*x^6*e^8
 + 207900*A*a^2*b^8*d^2*x^6*e^8 - 665280*B*a^3*b^7*d^3*x^5*e^7 - 249480*A*a^2*b^8*d^3*x^5*e^7 + 831600*B*a^3*b
^7*d^4*x^4*e^6 + 311850*A*a^2*b^8*d^4*x^4*e^6 - 1108800*B*a^3*b^7*d^5*x^3*e^5 - 415800*A*a^2*b^8*d^5*x^3*e^5 +
 1663200*B*a^3*b^7*d^6*x^2*e^4 + 623700*A*a^2*b^8*d^6*x^2*e^4 - 3326400*B*a^3*b^7*d^7*x*e^3 - 1247400*A*a^2*b^
8*d^7*x*e^3 + 831600*B*a^4*b^6*x^7*e^10 + 475200*A*a^3*b^7*x^7*e^10 - 970200*B*a^4*b^6*d*x^6*e^9 - 554400*A*a^
3*b^7*d*x^6*e^9 + 1164240*B*a^4*b^6*d^2*x^5*e^8 + 665280*A*a^3*b^7*d^2*x^5*e^8 - 1455300*B*a^4*b^6*d^3*x^4*e^7
 - 831600*A*a^3*b^7*d^3*x^4*e^7 + 1940400*B*a^4*b^6*d^4*x^3*e^6 + 1108800*A*a^3*b^7*d^4*x^3*e^6 - 2910600*B*a^
4*b^6*d^5*x^2*e^5 - 1663200*A*a^3*b^7*d^5*x^2*e^5 + 5821200*B*a^4*b^6*d^6*x*e^4 + 3326400*A*a^3*b^7*d^6*x*e^4
+ 1164240*B*a^5*b^5*x^6*e^10 + 970200*A*a^4*b^6*x^6*e^10 - 1397088*B*a^5*b^5*d*x^5*e^9 - 1164240*A*a^4*b^6*d*x
^5*e^9 + 1746360*B*a^5*b^5*d^2*x^4*e^8 + 1455300*A*a^4*b^6*d^2*x^4*e^8 - 2328480*B*a^5*b^5*d^3*x^3*e^7 - 19404
00*A*a^4*b^6*d^3*x^3*e^7 + 3492720*B*a^5*b^5*d^4*x^2*e^6 + 2910600*A*a^4*b^6*d^4*x^2*e^6 - 6985440*B*a^5*b^5*d
^5*x*e^5 - 5821200*A*a^4*b^6*d^5*x*e^5 + 1164240*B*a^6*b^4*x^5*e^10 + 1397088*A*a^5*b^5*x^5*e^10 - 1455300*B*a
^6*b^4*d*x^4*e^9 - 1746360*A*a^5*b^5*d*x^4*e^9 + 1940400*B*a^6*b^4*d^2*x^3*e^8 + 2328480*A*a^5*b^5*d^2*x^3*e^8
 - 2910600*B*a^6*b^4*d^3*x^2*e^7 - 3492720*A*a^5*b^5*d^3*x^2*e^7 + 5821200*B*a^6*b^4*d^4*x*e^6 + 6985440*A*a^5
*b^5*d^4*x*e^6 + 831600*B*a^7*b^3*x^4*e^10 + 1455300*A*a^6*b^4*x^4*e^10 - 1108800*B*a^7*b^3*d*x^3*e^9 - 194040
0*A*a^6*b^4*d*x^3*e^9 + 1663200*B*a^7*b^3*d^2*x^2*e^8 + 2910600*A*a^6*b^4*d^2*x^2*e^8 - 3326400*B*a^7*b^3*d^3*
x*e^7 - 5821200*A*a^6*b^4*d^3*x*e^7 + 415800*B*a^8*b^2*x^3*e^10 + 1108800*A*a^7*b^3*x^3*e^10 - 623700*B*a^8*b^
2*d*x^2*e^9 - 1663200*A*a^7*b^3*d*x^2*e^9 + 1247400*B*a^8*b^2*d^2*x*e^8 + 3326400*A*a^7*b^3*d^2*x*e^8 + 138600
*B*a^9*b*x^2*e^10 + 623700*A*a^8*b^2*x^2*e^10 - 277200*B*a^9*b*d*x*e^9 - 1247400*A*a^8*b^2*d*x*e^9 + 27720*B*a
^10*x*e^10 + 277200*A*a^9*b*x*e^10)*e^(-11)

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