3.46.43 \(\int \frac {e^{10} (5+e^4 (-3 x+4 x^2))+e^5 (-5 x^2+e^4 (4 x^2-5 x^3))}{3125 x^2-6250 x^3+3125 x^4+e^4 (3125 x^3-6250 x^4+3125 x^5)+e^8 (1250 x^4-2500 x^5+1250 x^6)+e^{12} (250 x^5-500 x^6+250 x^7)+e^{16} (25 x^6-50 x^7+25 x^8)+e^{20} (x^7-2 x^8+x^9)+e^{10} (3125-6250 x+3125 x^2+e^4 (3125 x-6250 x^2+3125 x^3)+e^8 (1250 x^2-2500 x^3+1250 x^4)+e^{12} (250 x^3-500 x^4+250 x^5)+e^{16} (25 x^4-50 x^5+25 x^6)+e^{20} (x^5-2 x^6+x^7))+e^5 (-6250 x+12500 x^2-6250 x^3+e^4 (-6250 x^2+12500 x^3-6250 x^4)+e^8 (-2500 x^3+5000 x^4-2500 x^5)+e^{12} (-500 x^4+1000 x^5-500 x^6)+e^{16} (-50 x^5+100 x^6-50 x^7)+e^{20} (-2 x^6+4 x^7-2 x^8))} \, dx\)
Optimal. Leaf size=30 \[ \frac {x}{\left (5+e^4 x\right )^4 \left (1-x-\frac {x-x^2}{e^5}\right )} \]
________________________________________________________________________________________
Rubi [B] time = 1.05, antiderivative size = 226, normalized size of antiderivative = 7.53,
number of steps used = 2, number of rules used = 1, integrand size = 386, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.003, Rules used
= {2074} \begin {gather*} \frac {e^{10}}{\left (1-e^5\right ) \left (5+e^9\right )^4 \left (e^5-x\right )}-\frac {e^9 \left (625-150 e^{13}-20 e^{17}-e^{21}-20 e^{22}-e^{26}-e^{31}\right )}{\left (5+e^4\right )^4 \left (5+e^9\right )^4 \left (e^4 x+5\right )}-\frac {e^9 \left (125-15 e^{13}-e^{17}-e^{22}\right )}{\left (5+e^4\right )^3 \left (5+e^9\right )^3 \left (e^4 x+5\right )^2}-\frac {e^9 \left (25-e^{13}\right )}{\left (5+e^4\right )^2 \left (5+e^9\right )^2 \left (e^4 x+5\right )^3}-\frac {5 e^9}{\left (5+e^4\right ) \left (5+e^9\right ) \left (e^4 x+5\right )^4}-\frac {e^5}{\left (5+e^4\right )^4 \left (1-e^5\right ) (1-x)} \end {gather*}
Antiderivative was successfully verified.
[In]
Int[(E^10*(5 + E^4*(-3*x + 4*x^2)) + E^5*(-5*x^2 + E^4*(4*x^2 - 5*x^3)))/(3125*x^2 - 6250*x^3 + 3125*x^4 + E^4
*(3125*x^3 - 6250*x^4 + 3125*x^5) + E^8*(1250*x^4 - 2500*x^5 + 1250*x^6) + E^12*(250*x^5 - 500*x^6 + 250*x^7)
+ E^16*(25*x^6 - 50*x^7 + 25*x^8) + E^20*(x^7 - 2*x^8 + x^9) + E^10*(3125 - 6250*x + 3125*x^2 + E^4*(3125*x -
6250*x^2 + 3125*x^3) + E^8*(1250*x^2 - 2500*x^3 + 1250*x^4) + E^12*(250*x^3 - 500*x^4 + 250*x^5) + E^16*(25*x^
4 - 50*x^5 + 25*x^6) + E^20*(x^5 - 2*x^6 + x^7)) + E^5*(-6250*x + 12500*x^2 - 6250*x^3 + E^4*(-6250*x^2 + 1250
0*x^3 - 6250*x^4) + E^8*(-2500*x^3 + 5000*x^4 - 2500*x^5) + E^12*(-500*x^4 + 1000*x^5 - 500*x^6) + E^16*(-50*x
^5 + 100*x^6 - 50*x^7) + E^20*(-2*x^6 + 4*x^7 - 2*x^8))),x]
[Out]
-(E^5/((5 + E^4)^4*(1 - E^5)*(1 - x))) + E^10/((1 - E^5)*(5 + E^9)^4*(E^5 - x)) - (5*E^9)/((5 + E^4)*(5 + E^9)
*(5 + E^4*x)^4) - (E^9*(25 - E^13))/((5 + E^4)^2*(5 + E^9)^2*(5 + E^4*x)^3) - (E^9*(125 - 15*E^13 - E^17 - E^2
2))/((5 + E^4)^3*(5 + E^9)^3*(5 + E^4*x)^2) - (E^9*(625 - 150*E^13 - 20*E^17 - E^21 - 20*E^22 - E^26 - E^31))/
((5 + E^4)^4*(5 + E^9)^4*(5 + E^4*x))
Rule 2074
Int[(P_)^(p_)*(Q_)^(q_.), x_Symbol] :> With[{PP = Factor[P]}, Int[ExpandIntegrand[PP^p*Q^q, x], x] /; !SumQ[N
onfreeFactors[PP, x]]] /; FreeQ[q, x] && PolyQ[P, x] && PolyQ[Q, x] && IntegerQ[p] && NeQ[P, x]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {e^{10}}{\left (-1+e^5\right ) \left (5+e^9\right )^4 \left (e^5-x\right )^2}+\frac {e^5}{\left (5+e^4\right )^4 \left (-1+e^5\right ) (-1+x)^2}+\frac {20 e^{13}}{\left (5+e^4\right ) \left (5+e^9\right ) \left (5+e^4 x\right )^5}+\frac {3 e^{13} \left (25-e^{13}\right )}{\left (5+e^4\right )^2 \left (5+e^9\right )^2 \left (5+e^4 x\right )^4}+\frac {2 e^{13} \left (125-15 e^{13}-e^{17}-e^{22}\right )}{\left (5+e^4\right )^3 \left (5+e^9\right )^3 \left (5+e^4 x\right )^3}+\frac {e^{13} \left (625-150 e^{13}-20 e^{17}-e^{21}-20 e^{22}-e^{26}-e^{31}\right )}{\left (5+e^4\right )^4 \left (5+e^9\right )^4 \left (5+e^4 x\right )^2}\right ) \, dx\\ &=-\frac {e^5}{\left (5+e^4\right )^4 \left (1-e^5\right ) (1-x)}+\frac {e^{10}}{\left (1-e^5\right ) \left (5+e^9\right )^4 \left (e^5-x\right )}-\frac {5 e^9}{\left (5+e^4\right ) \left (5+e^9\right ) \left (5+e^4 x\right )^4}-\frac {e^9 \left (25-e^{13}\right )}{\left (5+e^4\right )^2 \left (5+e^9\right )^2 \left (5+e^4 x\right )^3}-\frac {e^9 \left (125-15 e^{13}-e^{17}-e^{22}\right )}{\left (5+e^4\right )^3 \left (5+e^9\right )^3 \left (5+e^4 x\right )^2}-\frac {e^9 \left (625-150 e^{13}-20 e^{17}-e^{21}-20 e^{22}-e^{26}-e^{31}\right )}{\left (5+e^4\right )^4 \left (5+e^9\right )^4 \left (5+e^4 x\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.28, size = 29, normalized size = 0.97 \begin {gather*} -\frac {e^5 x}{\left (e^5-x\right ) (-1+x) \left (5+e^4 x\right )^4} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(E^10*(5 + E^4*(-3*x + 4*x^2)) + E^5*(-5*x^2 + E^4*(4*x^2 - 5*x^3)))/(3125*x^2 - 6250*x^3 + 3125*x^4
+ E^4*(3125*x^3 - 6250*x^4 + 3125*x^5) + E^8*(1250*x^4 - 2500*x^5 + 1250*x^6) + E^12*(250*x^5 - 500*x^6 + 250
*x^7) + E^16*(25*x^6 - 50*x^7 + 25*x^8) + E^20*(x^7 - 2*x^8 + x^9) + E^10*(3125 - 6250*x + 3125*x^2 + E^4*(312
5*x - 6250*x^2 + 3125*x^3) + E^8*(1250*x^2 - 2500*x^3 + 1250*x^4) + E^12*(250*x^3 - 500*x^4 + 250*x^5) + E^16*
(25*x^4 - 50*x^5 + 25*x^6) + E^20*(x^5 - 2*x^6 + x^7)) + E^5*(-6250*x + 12500*x^2 - 6250*x^3 + E^4*(-6250*x^2
+ 12500*x^3 - 6250*x^4) + E^8*(-2500*x^3 + 5000*x^4 - 2500*x^5) + E^12*(-500*x^4 + 1000*x^5 - 500*x^6) + E^16*
(-50*x^5 + 100*x^6 - 50*x^7) + E^20*(-2*x^6 + 4*x^7 - 2*x^8))),x]
[Out]
-((E^5*x)/((E^5 - x)*(-1 + x)*(5 + E^4*x)^4))
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fricas [B] time = 0.60, size = 123, normalized size = 4.10 \begin {gather*} \frac {x e^{5}}{625 \, x^{2} - {\left (x^{5} - x^{4}\right )} e^{21} - 20 \, {\left (x^{4} - x^{3}\right )} e^{17} + {\left (x^{6} - x^{5}\right )} e^{16} - 150 \, {\left (x^{3} - x^{2}\right )} e^{13} + 20 \, {\left (x^{5} - x^{4}\right )} e^{12} - 500 \, {\left (x^{2} - x\right )} e^{9} + 150 \, {\left (x^{4} - x^{3}\right )} e^{8} - 625 \, {\left (x - 1\right )} e^{5} + 500 \, {\left (x^{3} - x^{2}\right )} e^{4} - 625 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((4*x^2-3*x)*exp(4)+5)*exp(5)^2+((-5*x^3+4*x^2)*exp(4)-5*x^2)*exp(5))/(((x^7-2*x^6+x^5)*exp(4)^5+(2
5*x^6-50*x^5+25*x^4)*exp(4)^4+(250*x^5-500*x^4+250*x^3)*exp(4)^3+(1250*x^4-2500*x^3+1250*x^2)*exp(4)^2+(3125*x
^3-6250*x^2+3125*x)*exp(4)+3125*x^2-6250*x+3125)*exp(5)^2+((-2*x^8+4*x^7-2*x^6)*exp(4)^5+(-50*x^7+100*x^6-50*x
^5)*exp(4)^4+(-500*x^6+1000*x^5-500*x^4)*exp(4)^3+(-2500*x^5+5000*x^4-2500*x^3)*exp(4)^2+(-6250*x^4+12500*x^3-
6250*x^2)*exp(4)-6250*x^3+12500*x^2-6250*x)*exp(5)+(x^9-2*x^8+x^7)*exp(4)^5+(25*x^8-50*x^7+25*x^6)*exp(4)^4+(2
50*x^7-500*x^6+250*x^5)*exp(4)^3+(1250*x^6-2500*x^5+1250*x^4)*exp(4)^2+(3125*x^5-6250*x^4+3125*x^3)*exp(4)+312
5*x^4-6250*x^3+3125*x^2),x, algorithm="fricas")
[Out]
x*e^5/(625*x^2 - (x^5 - x^4)*e^21 - 20*(x^4 - x^3)*e^17 + (x^6 - x^5)*e^16 - 150*(x^3 - x^2)*e^13 + 20*(x^5 -
x^4)*e^12 - 500*(x^2 - x)*e^9 + 150*(x^4 - x^3)*e^8 - 625*(x - 1)*e^5 + 500*(x^3 - x^2)*e^4 - 625*x)
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giac [F(-1)] 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((((4*x^2-3*x)*exp(4)+5)*exp(5)^2+((-5*x^3+4*x^2)*exp(4)-5*x^2)*exp(5))/(((x^7-2*x^6+x^5)*exp(4)^5+(2
5*x^6-50*x^5+25*x^4)*exp(4)^4+(250*x^5-500*x^4+250*x^3)*exp(4)^3+(1250*x^4-2500*x^3+1250*x^2)*exp(4)^2+(3125*x
^3-6250*x^2+3125*x)*exp(4)+3125*x^2-6250*x+3125)*exp(5)^2+((-2*x^8+4*x^7-2*x^6)*exp(4)^5+(-50*x^7+100*x^6-50*x
^5)*exp(4)^4+(-500*x^6+1000*x^5-500*x^4)*exp(4)^3+(-2500*x^5+5000*x^4-2500*x^3)*exp(4)^2+(-6250*x^4+12500*x^3-
6250*x^2)*exp(4)-6250*x^3+12500*x^2-6250*x)*exp(5)+(x^9-2*x^8+x^7)*exp(4)^5+(25*x^8-50*x^7+25*x^6)*exp(4)^4+(2
50*x^7-500*x^6+250*x^5)*exp(4)^3+(1250*x^6-2500*x^5+1250*x^4)*exp(4)^2+(3125*x^5-6250*x^4+3125*x^3)*exp(4)+312
5*x^4-6250*x^3+3125*x^2),x, algorithm="giac")
[Out]
Timed out
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maple [A] time = 1.42, size = 27, normalized size = 0.90
|
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| method |
result |
size |
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| norman |
\(-\frac {x \,{\mathrm e}^{5}}{\left (x -1\right ) \left (5+x \,{\mathrm e}^{4}\right )^{4} \left ({\mathrm e}^{5}-x \right )}\) |
\(27\) |
| risch |
\(-\frac {{\mathrm e}^{5} x}{x^{5} {\mathrm e}^{21}-x^{4} {\mathrm e}^{21}-{\mathrm e}^{16} x^{6}+20 x^{4} {\mathrm e}^{17}+x^{5} {\mathrm e}^{16}-20 x^{3} {\mathrm e}^{17}-20 \,{\mathrm e}^{12} x^{5}+150 x^{3} {\mathrm e}^{13}+20 \,{\mathrm e}^{12} x^{4}-150 x^{2} {\mathrm e}^{13}-150 \,{\mathrm e}^{8} x^{4}+500 x^{2} {\mathrm e}^{9}+150 \,{\mathrm e}^{8} x^{3}-500 x \,{\mathrm e}^{9}-500 x^{3} {\mathrm e}^{4}+625 x \,{\mathrm e}^{5}+500 x^{2} {\mathrm e}^{4}-625 \,{\mathrm e}^{5}-625 x^{2}+625 x}\) |
\(134\) |
| gosper |
\(-\frac {x \,{\mathrm e}^{5}}{{\mathrm e}^{5} {\mathrm e}^{16} x^{5}-{\mathrm e}^{16} x^{6}-{\mathrm e}^{5} {\mathrm e}^{16} x^{4}+x^{5} {\mathrm e}^{16}+20 \,{\mathrm e}^{5} {\mathrm e}^{12} x^{4}-20 \,{\mathrm e}^{12} x^{5}-20 \,{\mathrm e}^{5} {\mathrm e}^{12} x^{3}+20 \,{\mathrm e}^{12} x^{4}+150 \,{\mathrm e}^{5} {\mathrm e}^{8} x^{3}-150 \,{\mathrm e}^{8} x^{4}-150 \,{\mathrm e}^{5} {\mathrm e}^{8} x^{2}+150 \,{\mathrm e}^{8} x^{3}+500 x^{2} {\mathrm e}^{4} {\mathrm e}^{5}-500 x^{3} {\mathrm e}^{4}-500 x \,{\mathrm e}^{4} {\mathrm e}^{5}+500 x^{2} {\mathrm e}^{4}+625 x \,{\mathrm e}^{5}-625 x^{2}-625 \,{\mathrm e}^{5}+625 x}\) |
\(174\) |
| default |
\(\text {Expression too large to display}\) |
\(1549\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int((((4*x^2-3*x)*exp(4)+5)*exp(5)^2+((-5*x^3+4*x^2)*exp(4)-5*x^2)*exp(5))/(((x^7-2*x^6+x^5)*exp(4)^5+(25*x^6-
50*x^5+25*x^4)*exp(4)^4+(250*x^5-500*x^4+250*x^3)*exp(4)^3+(1250*x^4-2500*x^3+1250*x^2)*exp(4)^2+(3125*x^3-625
0*x^2+3125*x)*exp(4)+3125*x^2-6250*x+3125)*exp(5)^2+((-2*x^8+4*x^7-2*x^6)*exp(4)^5+(-50*x^7+100*x^6-50*x^5)*ex
p(4)^4+(-500*x^6+1000*x^5-500*x^4)*exp(4)^3+(-2500*x^5+5000*x^4-2500*x^3)*exp(4)^2+(-6250*x^4+12500*x^3-6250*x
^2)*exp(4)-6250*x^3+12500*x^2-6250*x)*exp(5)+(x^9-2*x^8+x^7)*exp(4)^5+(25*x^8-50*x^7+25*x^6)*exp(4)^4+(250*x^7
-500*x^6+250*x^5)*exp(4)^3+(1250*x^6-2500*x^5+1250*x^4)*exp(4)^2+(3125*x^5-6250*x^4+3125*x^3)*exp(4)+3125*x^4-
6250*x^3+3125*x^2),x,method=_RETURNVERBOSE)
[Out]
-x*exp(5)/(x-1)/(5+x*exp(4))^4/(exp(5)-x)
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maxima [B] time = 0.55, size = 104, normalized size = 3.47 \begin {gather*} \frac {x e^{5}}{x^{6} e^{16} - x^{5} {\left (e^{21} + e^{16} - 20 \, e^{12}\right )} + x^{4} {\left (e^{21} - 20 \, e^{17} - 20 \, e^{12} + 150 \, e^{8}\right )} + 10 \, x^{3} {\left (2 \, e^{17} - 15 \, e^{13} - 15 \, e^{8} + 50 \, e^{4}\right )} + 25 \, x^{2} {\left (6 \, e^{13} - 20 \, e^{9} - 20 \, e^{4} + 25\right )} + 125 \, x {\left (4 \, e^{9} - 5 \, e^{5} - 5\right )} + 625 \, e^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((4*x^2-3*x)*exp(4)+5)*exp(5)^2+((-5*x^3+4*x^2)*exp(4)-5*x^2)*exp(5))/(((x^7-2*x^6+x^5)*exp(4)^5+(2
5*x^6-50*x^5+25*x^4)*exp(4)^4+(250*x^5-500*x^4+250*x^3)*exp(4)^3+(1250*x^4-2500*x^3+1250*x^2)*exp(4)^2+(3125*x
^3-6250*x^2+3125*x)*exp(4)+3125*x^2-6250*x+3125)*exp(5)^2+((-2*x^8+4*x^7-2*x^6)*exp(4)^5+(-50*x^7+100*x^6-50*x
^5)*exp(4)^4+(-500*x^6+1000*x^5-500*x^4)*exp(4)^3+(-2500*x^5+5000*x^4-2500*x^3)*exp(4)^2+(-6250*x^4+12500*x^3-
6250*x^2)*exp(4)-6250*x^3+12500*x^2-6250*x)*exp(5)+(x^9-2*x^8+x^7)*exp(4)^5+(25*x^8-50*x^7+25*x^6)*exp(4)^4+(2
50*x^7-500*x^6+250*x^5)*exp(4)^3+(1250*x^6-2500*x^5+1250*x^4)*exp(4)^2+(3125*x^5-6250*x^4+3125*x^3)*exp(4)+312
5*x^4-6250*x^3+3125*x^2),x, algorithm="maxima")
[Out]
x*e^5/(x^6*e^16 - x^5*(e^21 + e^16 - 20*e^12) + x^4*(e^21 - 20*e^17 - 20*e^12 + 150*e^8) + 10*x^3*(2*e^17 - 15
*e^13 - 15*e^8 + 50*e^4) + 25*x^2*(6*e^13 - 20*e^9 - 20*e^4 + 25) + 125*x*(4*e^9 - 5*e^5 - 5) + 625*e^5)
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mupad [B] time = 0.99, size = 25, normalized size = 0.83 \begin {gather*} \frac {x\,{\mathrm {e}}^5}{\left (x-{\mathrm {e}}^5\right )\,{\left (x\,{\mathrm {e}}^4+5\right )}^4\,\left (x-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(-(exp(10)*(exp(4)*(3*x - 4*x^2) - 5) - exp(5)*(exp(4)*(4*x^2 - 5*x^3) - 5*x^2))/(exp(10)*(exp(20)*(x^5 - 2
*x^6 + x^7) - 6250*x + exp(4)*(3125*x - 6250*x^2 + 3125*x^3) + exp(16)*(25*x^4 - 50*x^5 + 25*x^6) + exp(12)*(2
50*x^3 - 500*x^4 + 250*x^5) + exp(8)*(1250*x^2 - 2500*x^3 + 1250*x^4) + 3125*x^2 + 3125) + exp(20)*(x^7 - 2*x^
8 + x^9) - exp(5)*(6250*x + exp(20)*(2*x^6 - 4*x^7 + 2*x^8) + exp(16)*(50*x^5 - 100*x^6 + 50*x^7) + exp(12)*(5
00*x^4 - 1000*x^5 + 500*x^6) + exp(8)*(2500*x^3 - 5000*x^4 + 2500*x^5) + exp(4)*(6250*x^2 - 12500*x^3 + 6250*x
^4) - 12500*x^2 + 6250*x^3) + exp(16)*(25*x^6 - 50*x^7 + 25*x^8) + exp(12)*(250*x^5 - 500*x^6 + 250*x^7) + exp
(8)*(1250*x^4 - 2500*x^5 + 1250*x^6) + exp(4)*(3125*x^3 - 6250*x^4 + 3125*x^5) + 3125*x^2 - 6250*x^3 + 3125*x^
4),x)
[Out]
(x*exp(5))/((x - exp(5))*(x*exp(4) + 5)^4*(x - 1))
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sympy [B] time = 25.33, size = 110, normalized size = 3.67 \begin {gather*} \frac {x e^{5}}{x^{6} e^{16} + x^{5} \left (- e^{21} - e^{16} + 20 e^{12}\right ) + x^{4} \left (- 20 e^{17} - 20 e^{12} + 150 e^{8} + e^{21}\right ) + x^{3} \left (- 150 e^{13} - 150 e^{8} + 500 e^{4} + 20 e^{17}\right ) + x^{2} \left (- 500 e^{9} - 500 e^{4} + 625 + 150 e^{13}\right ) + x \left (- 625 e^{5} - 625 + 500 e^{9}\right ) + 625 e^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((4*x**2-3*x)*exp(4)+5)*exp(5)**2+((-5*x**3+4*x**2)*exp(4)-5*x**2)*exp(5))/(((x**7-2*x**6+x**5)*exp
(4)**5+(25*x**6-50*x**5+25*x**4)*exp(4)**4+(250*x**5-500*x**4+250*x**3)*exp(4)**3+(1250*x**4-2500*x**3+1250*x*
*2)*exp(4)**2+(3125*x**3-6250*x**2+3125*x)*exp(4)+3125*x**2-6250*x+3125)*exp(5)**2+((-2*x**8+4*x**7-2*x**6)*ex
p(4)**5+(-50*x**7+100*x**6-50*x**5)*exp(4)**4+(-500*x**6+1000*x**5-500*x**4)*exp(4)**3+(-2500*x**5+5000*x**4-2
500*x**3)*exp(4)**2+(-6250*x**4+12500*x**3-6250*x**2)*exp(4)-6250*x**3+12500*x**2-6250*x)*exp(5)+(x**9-2*x**8+
x**7)*exp(4)**5+(25*x**8-50*x**7+25*x**6)*exp(4)**4+(250*x**7-500*x**6+250*x**5)*exp(4)**3+(1250*x**6-2500*x**
5+1250*x**4)*exp(4)**2+(3125*x**5-6250*x**4+3125*x**3)*exp(4)+3125*x**4-6250*x**3+3125*x**2),x)
[Out]
x*exp(5)/(x**6*exp(16) + x**5*(-exp(21) - exp(16) + 20*exp(12)) + x**4*(-20*exp(17) - 20*exp(12) + 150*exp(8)
+ exp(21)) + x**3*(-150*exp(13) - 150*exp(8) + 500*exp(4) + 20*exp(17)) + x**2*(-500*exp(9) - 500*exp(4) + 625
+ 150*exp(13)) + x*(-625*exp(5) - 625 + 500*exp(9)) + 625*exp(5))
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