3.1499 \(\int \frac {(a^2+2 a b x+b^2 x^2)^3}{(d+e x)^{10}} \, dx\)

Optimal. Leaf size=89 \[ \frac {b^2 (a+b x)^7}{252 (d+e x)^7 (b d-a e)^3}+\frac {b (a+b x)^7}{36 (d+e x)^8 (b d-a e)^2}+\frac {(a+b x)^7}{9 (d+e x)^9 (b d-a e)} \]

[Out]

1/9*(b*x+a)^7/(-a*e+b*d)/(e*x+d)^9+1/36*b*(b*x+a)^7/(-a*e+b*d)^2/(e*x+d)^8+1/252*b^2*(b*x+a)^7/(-a*e+b*d)^3/(e
*x+d)^7

________________________________________________________________________________________

Rubi [A]  time = 0.02, antiderivative size = 89, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.115, Rules used = {27, 45, 37} \[ \frac {b^2 (a+b x)^7}{252 (d+e x)^7 (b d-a e)^3}+\frac {b (a+b x)^7}{36 (d+e x)^8 (b d-a e)^2}+\frac {(a+b x)^7}{9 (d+e x)^9 (b d-a e)} \]

Antiderivative was successfully verified.

[In]

Int[(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^10,x]

[Out]

(a + b*x)^7/(9*(b*d - a*e)*(d + e*x)^9) + (b*(a + b*x)^7)/(36*(b*d - a*e)^2*(d + e*x)^8) + (b^2*(a + b*x)^7)/(
252*(b*d - a*e)^3*(d + e*x)^7)

Rule 27

Int[(u_.)*((a_) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> Int[u*Cancel[(b/2 + c*x)^(2*p)/c^p], x] /; Fr
eeQ[{a, b, c}, x] && EqQ[b^2 - 4*a*c, 0] && IntegerQ[p]

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]

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])

Rubi steps

\begin {align*} \int \frac {\left (a^2+2 a b x+b^2 x^2\right )^3}{(d+e x)^{10}} \, dx &=\int \frac {(a+b x)^6}{(d+e x)^{10}} \, dx\\ &=\frac {(a+b x)^7}{9 (b d-a e) (d+e x)^9}+\frac {(2 b) \int \frac {(a+b x)^6}{(d+e x)^9} \, dx}{9 (b d-a e)}\\ &=\frac {(a+b x)^7}{9 (b d-a e) (d+e x)^9}+\frac {b (a+b x)^7}{36 (b d-a e)^2 (d+e x)^8}+\frac {b^2 \int \frac {(a+b x)^6}{(d+e x)^8} \, dx}{36 (b d-a e)^2}\\ &=\frac {(a+b x)^7}{9 (b d-a e) (d+e x)^9}+\frac {b (a+b x)^7}{36 (b d-a e)^2 (d+e x)^8}+\frac {b^2 (a+b x)^7}{252 (b d-a e)^3 (d+e x)^7}\\ \end {align*}

________________________________________________________________________________________

Mathematica [B]  time = 0.09, size = 277, normalized size = 3.11 \[ -\frac {28 a^6 e^6+21 a^5 b e^5 (d+9 e x)+15 a^4 b^2 e^4 \left (d^2+9 d e x+36 e^2 x^2\right )+10 a^3 b^3 e^3 \left (d^3+9 d^2 e x+36 d e^2 x^2+84 e^3 x^3\right )+6 a^2 b^4 e^2 \left (d^4+9 d^3 e x+36 d^2 e^2 x^2+84 d e^3 x^3+126 e^4 x^4\right )+3 a b^5 e \left (d^5+9 d^4 e x+36 d^3 e^2 x^2+84 d^2 e^3 x^3+126 d e^4 x^4+126 e^5 x^5\right )+b^6 \left (d^6+9 d^5 e x+36 d^4 e^2 x^2+84 d^3 e^3 x^3+126 d^2 e^4 x^4+126 d e^5 x^5+84 e^6 x^6\right )}{252 e^7 (d+e x)^9} \]

Antiderivative was successfully verified.

[In]

Integrate[(a^2 + 2*a*b*x + b^2*x^2)^3/(d + e*x)^10,x]

[Out]

-1/252*(28*a^6*e^6 + 21*a^5*b*e^5*(d + 9*e*x) + 15*a^4*b^2*e^4*(d^2 + 9*d*e*x + 36*e^2*x^2) + 10*a^3*b^3*e^3*(
d^3 + 9*d^2*e*x + 36*d*e^2*x^2 + 84*e^3*x^3) + 6*a^2*b^4*e^2*(d^4 + 9*d^3*e*x + 36*d^2*e^2*x^2 + 84*d*e^3*x^3
+ 126*e^4*x^4) + 3*a*b^5*e*(d^5 + 9*d^4*e*x + 36*d^3*e^2*x^2 + 84*d^2*e^3*x^3 + 126*d*e^4*x^4 + 126*e^5*x^5) +
b^6*(d^6 + 9*d^5*e*x + 36*d^4*e^2*x^2 + 84*d^3*e^3*x^3 + 126*d^2*e^4*x^4 + 126*d*e^5*x^5 + 84*e^6*x^6))/(e^7*
(d + e*x)^9)

________________________________________________________________________________________

fricas [B]  time = 0.74, size = 441, normalized size = 4.96 \[ -\frac {84 \, b^{6} e^{6} x^{6} + b^{6} d^{6} + 3 \, a b^{5} d^{5} e + 6 \, a^{2} b^{4} d^{4} e^{2} + 10 \, a^{3} b^{3} d^{3} e^{3} + 15 \, a^{4} b^{2} d^{2} e^{4} + 21 \, a^{5} b d e^{5} + 28 \, a^{6} e^{6} + 126 \, {\left (b^{6} d e^{5} + 3 \, a b^{5} e^{6}\right )} x^{5} + 126 \, {\left (b^{6} d^{2} e^{4} + 3 \, a b^{5} d e^{5} + 6 \, a^{2} b^{4} e^{6}\right )} x^{4} + 84 \, {\left (b^{6} d^{3} e^{3} + 3 \, a b^{5} d^{2} e^{4} + 6 \, a^{2} b^{4} d e^{5} + 10 \, a^{3} b^{3} e^{6}\right )} x^{3} + 36 \, {\left (b^{6} d^{4} e^{2} + 3 \, a b^{5} d^{3} e^{3} + 6 \, a^{2} b^{4} d^{2} e^{4} + 10 \, a^{3} b^{3} d e^{5} + 15 \, a^{4} b^{2} e^{6}\right )} x^{2} + 9 \, {\left (b^{6} d^{5} e + 3 \, a b^{5} d^{4} e^{2} + 6 \, a^{2} b^{4} d^{3} e^{3} + 10 \, a^{3} b^{3} d^{2} e^{4} + 15 \, a^{4} b^{2} d e^{5} + 21 \, a^{5} b e^{6}\right )} x}{252 \, {\left (e^{16} x^{9} + 9 \, d e^{15} x^{8} + 36 \, d^{2} e^{14} x^{7} + 84 \, d^{3} e^{13} x^{6} + 126 \, d^{4} e^{12} x^{5} + 126 \, d^{5} e^{11} x^{4} + 84 \, d^{6} e^{10} x^{3} + 36 \, d^{7} e^{9} x^{2} + 9 \, d^{8} e^{8} x + d^{9} e^{7}\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^10,x, algorithm="fricas")

[Out]

-1/252*(84*b^6*e^6*x^6 + b^6*d^6 + 3*a*b^5*d^5*e + 6*a^2*b^4*d^4*e^2 + 10*a^3*b^3*d^3*e^3 + 15*a^4*b^2*d^2*e^4
+ 21*a^5*b*d*e^5 + 28*a^6*e^6 + 126*(b^6*d*e^5 + 3*a*b^5*e^6)*x^5 + 126*(b^6*d^2*e^4 + 3*a*b^5*d*e^5 + 6*a^2*
b^4*e^6)*x^4 + 84*(b^6*d^3*e^3 + 3*a*b^5*d^2*e^4 + 6*a^2*b^4*d*e^5 + 10*a^3*b^3*e^6)*x^3 + 36*(b^6*d^4*e^2 + 3
*a*b^5*d^3*e^3 + 6*a^2*b^4*d^2*e^4 + 10*a^3*b^3*d*e^5 + 15*a^4*b^2*e^6)*x^2 + 9*(b^6*d^5*e + 3*a*b^5*d^4*e^2 +
6*a^2*b^4*d^3*e^3 + 10*a^3*b^3*d^2*e^4 + 15*a^4*b^2*d*e^5 + 21*a^5*b*e^6)*x)/(e^16*x^9 + 9*d*e^15*x^8 + 36*d^
2*e^14*x^7 + 84*d^3*e^13*x^6 + 126*d^4*e^12*x^5 + 126*d^5*e^11*x^4 + 84*d^6*e^10*x^3 + 36*d^7*e^9*x^2 + 9*d^8*
e^8*x + d^9*e^7)

________________________________________________________________________________________

giac [B]  time = 0.16, size = 352, normalized size = 3.96 \[ -\frac {{\left (84 \, b^{6} x^{6} e^{6} + 126 \, b^{6} d x^{5} e^{5} + 126 \, b^{6} d^{2} x^{4} e^{4} + 84 \, b^{6} d^{3} x^{3} e^{3} + 36 \, b^{6} d^{4} x^{2} e^{2} + 9 \, b^{6} d^{5} x e + b^{6} d^{6} + 378 \, a b^{5} x^{5} e^{6} + 378 \, a b^{5} d x^{4} e^{5} + 252 \, a b^{5} d^{2} x^{3} e^{4} + 108 \, a b^{5} d^{3} x^{2} e^{3} + 27 \, a b^{5} d^{4} x e^{2} + 3 \, a b^{5} d^{5} e + 756 \, a^{2} b^{4} x^{4} e^{6} + 504 \, a^{2} b^{4} d x^{3} e^{5} + 216 \, a^{2} b^{4} d^{2} x^{2} e^{4} + 54 \, a^{2} b^{4} d^{3} x e^{3} + 6 \, a^{2} b^{4} d^{4} e^{2} + 840 \, a^{3} b^{3} x^{3} e^{6} + 360 \, a^{3} b^{3} d x^{2} e^{5} + 90 \, a^{3} b^{3} d^{2} x e^{4} + 10 \, a^{3} b^{3} d^{3} e^{3} + 540 \, a^{4} b^{2} x^{2} e^{6} + 135 \, a^{4} b^{2} d x e^{5} + 15 \, a^{4} b^{2} d^{2} e^{4} + 189 \, a^{5} b x e^{6} + 21 \, a^{5} b d e^{5} + 28 \, a^{6} e^{6}\right )} e^{\left (-7\right )}}{252 \, {\left (x e + d\right )}^{9}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^10,x, algorithm="giac")

[Out]

-1/252*(84*b^6*x^6*e^6 + 126*b^6*d*x^5*e^5 + 126*b^6*d^2*x^4*e^4 + 84*b^6*d^3*x^3*e^3 + 36*b^6*d^4*x^2*e^2 + 9
*b^6*d^5*x*e + b^6*d^6 + 378*a*b^5*x^5*e^6 + 378*a*b^5*d*x^4*e^5 + 252*a*b^5*d^2*x^3*e^4 + 108*a*b^5*d^3*x^2*e
^3 + 27*a*b^5*d^4*x*e^2 + 3*a*b^5*d^5*e + 756*a^2*b^4*x^4*e^6 + 504*a^2*b^4*d*x^3*e^5 + 216*a^2*b^4*d^2*x^2*e^
4 + 54*a^2*b^4*d^3*x*e^3 + 6*a^2*b^4*d^4*e^2 + 840*a^3*b^3*x^3*e^6 + 360*a^3*b^3*d*x^2*e^5 + 90*a^3*b^3*d^2*x*
e^4 + 10*a^3*b^3*d^3*e^3 + 540*a^4*b^2*x^2*e^6 + 135*a^4*b^2*d*x*e^5 + 15*a^4*b^2*d^2*e^4 + 189*a^5*b*x*e^6 +
21*a^5*b*d*e^5 + 28*a^6*e^6)*e^(-7)/(x*e + d)^9

________________________________________________________________________________________

maple [B]  time = 0.05, size = 357, normalized size = 4.01 \[ -\frac {b^{6}}{3 \left (e x +d \right )^{3} e^{7}}-\frac {3 \left (a e -b d \right ) b^{5}}{2 \left (e x +d \right )^{4} e^{7}}-\frac {3 \left (a^{2} e^{2}-2 a b d e +b^{2} d^{2}\right ) b^{4}}{\left (e x +d \right )^{5} e^{7}}-\frac {10 \left (a^{3} e^{3}-3 a^{2} b d \,e^{2}+3 a \,b^{2} d^{2} e -b^{3} d^{3}\right ) b^{3}}{3 \left (e x +d \right )^{6} e^{7}}-\frac {15 \left (e^{4} a^{4}-4 d \,e^{3} a^{3} b +6 a^{2} b^{2} d^{2} e^{2}-4 a \,b^{3} d^{3} e +b^{4} d^{4}\right ) b^{2}}{7 \left (e x +d \right )^{7} e^{7}}-\frac {3 \left (a^{5} e^{5}-5 a^{4} b d \,e^{4}+10 a^{3} b^{2} d^{2} e^{3}-10 a^{2} b^{3} d^{3} e^{2}+5 a \,b^{4} d^{4} e -b^{5} d^{5}\right ) b}{4 \left (e x +d \right )^{8} e^{7}}-\frac {a^{6} e^{6}-6 d \,e^{5} a^{5} b +15 d^{2} e^{4} a^{4} b^{2}-20 d^{3} e^{3} a^{3} b^{3}+15 d^{4} a^{2} b^{4} e^{2}-6 d^{5} e a \,b^{5}+b^{6} d^{6}}{9 \left (e x +d \right )^{9} e^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^10,x)

[Out]

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

________________________________________________________________________________________

maxima [B]  time = 1.70, size = 441, normalized size = 4.96 \[ -\frac {84 \, b^{6} e^{6} x^{6} + b^{6} d^{6} + 3 \, a b^{5} d^{5} e + 6 \, a^{2} b^{4} d^{4} e^{2} + 10 \, a^{3} b^{3} d^{3} e^{3} + 15 \, a^{4} b^{2} d^{2} e^{4} + 21 \, a^{5} b d e^{5} + 28 \, a^{6} e^{6} + 126 \, {\left (b^{6} d e^{5} + 3 \, a b^{5} e^{6}\right )} x^{5} + 126 \, {\left (b^{6} d^{2} e^{4} + 3 \, a b^{5} d e^{5} + 6 \, a^{2} b^{4} e^{6}\right )} x^{4} + 84 \, {\left (b^{6} d^{3} e^{3} + 3 \, a b^{5} d^{2} e^{4} + 6 \, a^{2} b^{4} d e^{5} + 10 \, a^{3} b^{3} e^{6}\right )} x^{3} + 36 \, {\left (b^{6} d^{4} e^{2} + 3 \, a b^{5} d^{3} e^{3} + 6 \, a^{2} b^{4} d^{2} e^{4} + 10 \, a^{3} b^{3} d e^{5} + 15 \, a^{4} b^{2} e^{6}\right )} x^{2} + 9 \, {\left (b^{6} d^{5} e + 3 \, a b^{5} d^{4} e^{2} + 6 \, a^{2} b^{4} d^{3} e^{3} + 10 \, a^{3} b^{3} d^{2} e^{4} + 15 \, a^{4} b^{2} d e^{5} + 21 \, a^{5} b e^{6}\right )} x}{252 \, {\left (e^{16} x^{9} + 9 \, d e^{15} x^{8} + 36 \, d^{2} e^{14} x^{7} + 84 \, d^{3} e^{13} x^{6} + 126 \, d^{4} e^{12} x^{5} + 126 \, d^{5} e^{11} x^{4} + 84 \, d^{6} e^{10} x^{3} + 36 \, d^{7} e^{9} x^{2} + 9 \, d^{8} e^{8} x + d^{9} e^{7}\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^10,x, algorithm="maxima")

[Out]

-1/252*(84*b^6*e^6*x^6 + b^6*d^6 + 3*a*b^5*d^5*e + 6*a^2*b^4*d^4*e^2 + 10*a^3*b^3*d^3*e^3 + 15*a^4*b^2*d^2*e^4
+ 21*a^5*b*d*e^5 + 28*a^6*e^6 + 126*(b^6*d*e^5 + 3*a*b^5*e^6)*x^5 + 126*(b^6*d^2*e^4 + 3*a*b^5*d*e^5 + 6*a^2*
b^4*e^6)*x^4 + 84*(b^6*d^3*e^3 + 3*a*b^5*d^2*e^4 + 6*a^2*b^4*d*e^5 + 10*a^3*b^3*e^6)*x^3 + 36*(b^6*d^4*e^2 + 3
*a*b^5*d^3*e^3 + 6*a^2*b^4*d^2*e^4 + 10*a^3*b^3*d*e^5 + 15*a^4*b^2*e^6)*x^2 + 9*(b^6*d^5*e + 3*a*b^5*d^4*e^2 +
6*a^2*b^4*d^3*e^3 + 10*a^3*b^3*d^2*e^4 + 15*a^4*b^2*d*e^5 + 21*a^5*b*e^6)*x)/(e^16*x^9 + 9*d*e^15*x^8 + 36*d^
2*e^14*x^7 + 84*d^3*e^13*x^6 + 126*d^4*e^12*x^5 + 126*d^5*e^11*x^4 + 84*d^6*e^10*x^3 + 36*d^7*e^9*x^2 + 9*d^8*
e^8*x + d^9*e^7)

________________________________________________________________________________________

mupad [B]  time = 0.61, size = 423, normalized size = 4.75 \[ -\frac {\frac {28\,a^6\,e^6+21\,a^5\,b\,d\,e^5+15\,a^4\,b^2\,d^2\,e^4+10\,a^3\,b^3\,d^3\,e^3+6\,a^2\,b^4\,d^4\,e^2+3\,a\,b^5\,d^5\,e+b^6\,d^6}{252\,e^7}+\frac {b^6\,x^6}{3\,e}+\frac {b^3\,x^3\,\left (10\,a^3\,e^3+6\,a^2\,b\,d\,e^2+3\,a\,b^2\,d^2\,e+b^3\,d^3\right )}{3\,e^4}+\frac {b\,x\,\left (21\,a^5\,e^5+15\,a^4\,b\,d\,e^4+10\,a^3\,b^2\,d^2\,e^3+6\,a^2\,b^3\,d^3\,e^2+3\,a\,b^4\,d^4\,e+b^5\,d^5\right )}{28\,e^6}+\frac {b^5\,x^5\,\left (3\,a\,e+b\,d\right )}{2\,e^2}+\frac {b^2\,x^2\,\left (15\,a^4\,e^4+10\,a^3\,b\,d\,e^3+6\,a^2\,b^2\,d^2\,e^2+3\,a\,b^3\,d^3\,e+b^4\,d^4\right )}{7\,e^5}+\frac {b^4\,x^4\,\left (6\,a^2\,e^2+3\,a\,b\,d\,e+b^2\,d^2\right )}{2\,e^3}}{d^9+9\,d^8\,e\,x+36\,d^7\,e^2\,x^2+84\,d^6\,e^3\,x^3+126\,d^5\,e^4\,x^4+126\,d^4\,e^5\,x^5+84\,d^3\,e^6\,x^6+36\,d^2\,e^7\,x^7+9\,d\,e^8\,x^8+e^9\,x^9} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a^2 + b^2*x^2 + 2*a*b*x)^3/(d + e*x)^10,x)

[Out]

-((28*a^6*e^6 + b^6*d^6 + 6*a^2*b^4*d^4*e^2 + 10*a^3*b^3*d^3*e^3 + 15*a^4*b^2*d^2*e^4 + 3*a*b^5*d^5*e + 21*a^5
*b*d*e^5)/(252*e^7) + (b^6*x^6)/(3*e) + (b^3*x^3*(10*a^3*e^3 + b^3*d^3 + 3*a*b^2*d^2*e + 6*a^2*b*d*e^2))/(3*e^
4) + (b*x*(21*a^5*e^5 + b^5*d^5 + 6*a^2*b^3*d^3*e^2 + 10*a^3*b^2*d^2*e^3 + 3*a*b^4*d^4*e + 15*a^4*b*d*e^4))/(2
8*e^6) + (b^5*x^5*(3*a*e + b*d))/(2*e^2) + (b^2*x^2*(15*a^4*e^4 + b^4*d^4 + 6*a^2*b^2*d^2*e^2 + 3*a*b^3*d^3*e
+ 10*a^3*b*d*e^3))/(7*e^5) + (b^4*x^4*(6*a^2*e^2 + b^2*d^2 + 3*a*b*d*e))/(2*e^3))/(d^9 + e^9*x^9 + 9*d*e^8*x^8
+ 36*d^7*e^2*x^2 + 84*d^6*e^3*x^3 + 126*d^5*e^4*x^4 + 126*d^4*e^5*x^5 + 84*d^3*e^6*x^6 + 36*d^2*e^7*x^7 + 9*d
^8*e*x)

________________________________________________________________________________________

sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b**2*x**2+2*a*b*x+a**2)**3/(e*x+d)**10,x)

[Out]

Timed out

________________________________________________________________________________________