3.74.51 \(\int \frac {e^{5 x} (e^{2 x} (4+20 x)+e^x (-28 x^2+6 e^3 x^2-12 x^3))}{16 e^{2 x}+25 x^2+e^6 x^2+20 x^3+4 x^4+e^x (-40 x+8 e^3 x-16 x^2)+e^3 (-10 x^2-4 x^3)} \, dx\)

Optimal. Leaf size=31 \[ \frac {e^{5 x}}{\frac {4}{x}-e^{-x} \left (5-e^3+2 x\right )} \]

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Rubi [F]  time = 2.41, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {e^{5 x} \left (e^{2 x} (4+20 x)+e^x \left (-28 x^2+6 e^3 x^2-12 x^3\right )\right )}{16 e^{2 x}+25 x^2+e^6 x^2+20 x^3+4 x^4+e^x \left (-40 x+8 e^3 x-16 x^2\right )+e^3 \left (-10 x^2-4 x^3\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(5*x)*(E^(2*x)*(4 + 20*x) + E^x*(-28*x^2 + 6*E^3*x^2 - 12*x^3)))/(16*E^(2*x) + 25*x^2 + E^6*x^2 + 20*x^
3 + 4*x^4 + E^x*(-40*x + 8*E^3*x - 16*x^2) + E^3*(-10*x^2 - 4*x^3)),x]

[Out]

(5 - E^3)*Defer[Int][(E^(6*x)*x)/(4*E^x - 5*(1 - E^3/5)*x - 2*x^2)^2, x] - (1 - E^3)*Defer[Int][(E^(6*x)*x^2)/
(4*E^x - 5*(1 - E^3/5)*x - 2*x^2)^2, x] - 2*Defer[Int][(E^(6*x)*x^3)/(4*E^x - 5*(1 - E^3/5)*x - 2*x^2)^2, x] +
Defer[Int][E^(6*x)/(4*E^x - 5*(1 - E^3/5)*x - 2*x^2), x] + 5*Defer[Int][(E^(6*x)*x)/(4*E^x - 5*(1 - E^3/5)*x
- 2*x^2), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{5 x} \left (e^{2 x} (4+20 x)+e^x \left (-28 x^2+6 e^3 x^2-12 x^3\right )\right )}{16 e^{2 x}+\left (25+e^6\right ) x^2+20 x^3+4 x^4+e^x \left (-40 x+8 e^3 x-16 x^2\right )+e^3 \left (-10 x^2-4 x^3\right )} \, dx\\ &=\int \frac {2 e^{6 x} \left (3 e^3 x^2-2 x^2 (7+3 x)+2 e^x (1+5 x)\right )}{\left (4 e^x+e^3 x-x (5+2 x)\right )^2} \, dx\\ &=2 \int \frac {e^{6 x} \left (3 e^3 x^2-2 x^2 (7+3 x)+2 e^x (1+5 x)\right )}{\left (4 e^x+e^3 x-x (5+2 x)\right )^2} \, dx\\ &=2 \int \left (\frac {e^{6 x} x \left (5-e^3-\left (1-e^3\right ) x-2 x^2\right )}{2 \left (4 e^x-5 \left (1-\frac {e^3}{5}\right ) x-2 x^2\right )^2}+\frac {e^{6 x} (1+5 x)}{2 \left (4 e^x-5 \left (1-\frac {e^3}{5}\right ) x-2 x^2\right )}\right ) \, dx\\ &=\int \frac {e^{6 x} x \left (5-e^3-\left (1-e^3\right ) x-2 x^2\right )}{\left (4 e^x-5 \left (1-\frac {e^3}{5}\right ) x-2 x^2\right )^2} \, dx+\int \frac {e^{6 x} (1+5 x)}{4 e^x-5 \left (1-\frac {e^3}{5}\right ) x-2 x^2} \, dx\\ &=\int \left (\frac {e^{6 x} \left (5-e^3\right ) x}{\left (4 e^x-5 \left (1-\frac {e^3}{5}\right ) x-2 x^2\right )^2}+\frac {(1-e) e^{6 x} \left (-1-e-e^2\right ) x^2}{\left (4 e^x-5 \left (1-\frac {e^3}{5}\right ) x-2 x^2\right )^2}-\frac {2 e^{6 x} x^3}{\left (4 e^x-5 \left (1-\frac {e^3}{5}\right ) x-2 x^2\right )^2}\right ) \, dx+\int \left (\frac {e^{6 x}}{4 e^x-5 \left (1-\frac {e^3}{5}\right ) x-2 x^2}+\frac {5 e^{6 x} x}{4 e^x-5 \left (1-\frac {e^3}{5}\right ) x-2 x^2}\right ) \, dx\\ &=-\left (2 \int \frac {e^{6 x} x^3}{\left (4 e^x-5 \left (1-\frac {e^3}{5}\right ) x-2 x^2\right )^2} \, dx\right )+5 \int \frac {e^{6 x} x}{4 e^x-5 \left (1-\frac {e^3}{5}\right ) x-2 x^2} \, dx+\left ((1-e) \left (-1-e-e^2\right )\right ) \int \frac {e^{6 x} x^2}{\left (4 e^x-5 \left (1-\frac {e^3}{5}\right ) x-2 x^2\right )^2} \, dx+\left (5-e^3\right ) \int \frac {e^{6 x} x}{\left (4 e^x-5 \left (1-\frac {e^3}{5}\right ) x-2 x^2\right )^2} \, dx+\int \frac {e^{6 x}}{4 e^x-5 \left (1-\frac {e^3}{5}\right ) x-2 x^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.87, size = 30, normalized size = 0.97 \begin {gather*} \frac {2 e^{6 x} x}{8 e^x+2 e^3 x-2 x (5+2 x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(5*x)*(E^(2*x)*(4 + 20*x) + E^x*(-28*x^2 + 6*E^3*x^2 - 12*x^3)))/(16*E^(2*x) + 25*x^2 + E^6*x^2 +
20*x^3 + 4*x^4 + E^x*(-40*x + 8*E^3*x - 16*x^2) + E^3*(-10*x^2 - 4*x^3)),x]

[Out]

(2*E^(6*x)*x)/(8*E^x + 2*E^3*x - 2*x*(5 + 2*x))

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fricas [A]  time = 0.58, size = 27, normalized size = 0.87 \begin {gather*} -\frac {x e^{\left (6 \, x\right )}}{2 \, x^{2} - x e^{3} + 5 \, x - 4 \, e^{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((20*x+4)*exp(x)^2+(6*x^2*exp(3)-12*x^3-28*x^2)*exp(x))*exp(5*x)/(16*exp(x)^2+(8*x*exp(3)-16*x^2-40*
x)*exp(x)+x^2*exp(3)^2+(-4*x^3-10*x^2)*exp(3)+4*x^4+20*x^3+25*x^2),x, algorithm="fricas")

[Out]

-x*e^(6*x)/(2*x^2 - x*e^3 + 5*x - 4*e^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(((20*x+4)*exp(x)^2+(6*x^2*exp(3)-12*x^3-28*x^2)*exp(x))*exp(5*x)/(16*exp(x)^2+(8*x*exp(3)-16*x^2-40*
x)*exp(x)+x^2*exp(3)^2+(-4*x^3-10*x^2)*exp(3)+4*x^4+20*x^3+25*x^2),x, algorithm="giac")

[Out]

Timed out

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maple [B]  time = 0.07, size = 547, normalized size = 17.65

method	result	size
risch	\(\frac {x^{11}}{128}+\frac {3125 x^{7}}{2048}+\frac {625 x^{8}}{512}+\frac {25 x^{10}}{256}+\frac {125 x^{9}}{256}+\frac {3125 x^{6}}{4096}-\frac {625 x^{7} {\mathrm e}^{3}}{512}+\frac {625 x^{6} {\mathrm e}^{6}}{2048}+\frac {x \,{\mathrm e}^{5 x}}{4}+\frac {x^{7} \left (15625+37500 x -12 x \,{\mathrm e}^{15}+9000 x^{2} {\mathrm e}^{6}+2400 x^{3} {\mathrm e}^{6}-2500 \,{\mathrm e}^{9}+9375 \,{\mathrm e}^{6}-18750 \,{\mathrm e}^{3}+64 x^{6}+960 x^{5}+6000 x^{4}+20000 x^{3}+37500 x^{2}-3000 x \,{\mathrm e}^{9}+15000 x \,{\mathrm e}^{6}-2400 x^{4} {\mathrm e}^{3}-37500 x \,{\mathrm e}^{3}-12000 x^{3} {\mathrm e}^{3}-192 x^{5} {\mathrm e}^{3}-30000 x^{2} {\mathrm e}^{3}-1200 x^{2} {\mathrm e}^{9}+{\mathrm e}^{18}+375 \,{\mathrm e}^{12}-30 \,{\mathrm e}^{15}-160 x^{3} {\mathrm e}^{9}+300 x \,{\mathrm e}^{12}+60 x^{2} {\mathrm e}^{12}+240 \,{\mathrm e}^{6} x^{4}\right )}{4096 x \,{\mathrm e}^{3}-8192 x^{2}+16384 \,{\mathrm e}^{x}-20480 x}-\frac {3125 x^{6} {\mathrm e}^{3}}{4096}-\frac {375 \,{\mathrm e}^{3} x^{8}}{512}+\left (\frac {5 x^{2}}{16}-\frac {x^{2} {\mathrm e}^{3}}{16}+\frac {x^{3}}{8}\right ) {\mathrm e}^{4 x}+\left (\frac {25 x^{3}}{64}+\frac {x^{3} {\mathrm e}^{6}}{64}-\frac {5 x^{3} {\mathrm e}^{3}}{32}+\frac {5 x^{4}}{16}-\frac {x^{4} {\mathrm e}^{3}}{16}+\frac {x^{5}}{16}\right ) {\mathrm e}^{3 x}+\left (\frac {125 x^{4}}{256}-\frac {x^{4} {\mathrm e}^{9}}{256}+\frac {15 \,{\mathrm e}^{6} x^{4}}{256}-\frac {75 x^{4} {\mathrm e}^{3}}{256}+\frac {75 x^{5}}{128}+\frac {3 \,{\mathrm e}^{6} x^{5}}{128}-\frac {15 x^{5} {\mathrm e}^{3}}{64}+\frac {15 x^{6}}{64}-\frac {3 x^{6} {\mathrm e}^{3}}{64}+\frac {x^{7}}{32}\right ) {\mathrm e}^{2 x}+\left (\frac {625 x^{5}}{1024}+\frac {{\mathrm e}^{12} x^{5}}{1024}-\frac {5 \,{\mathrm e}^{9} x^{5}}{256}+\frac {75 \,{\mathrm e}^{6} x^{5}}{512}-\frac {125 x^{5} {\mathrm e}^{3}}{256}+\frac {125 x^{6}}{128}-\frac {x^{6} {\mathrm e}^{9}}{128}+\frac {15 x^{6} {\mathrm e}^{6}}{128}-\frac {75 x^{6} {\mathrm e}^{3}}{128}+\frac {75 x^{7}}{128}+\frac {3 x^{7} {\mathrm e}^{6}}{128}-\frac {15 x^{7} {\mathrm e}^{3}}{64}+\frac {5 x^{8}}{32}-\frac {{\mathrm e}^{3} x^{8}}{32}+\frac {x^{9}}{64}\right ) {\mathrm e}^{x}-\frac {125 x^{6} {\mathrm e}^{9}}{2048}+\frac {375 x^{7} {\mathrm e}^{6}}{1024}-\frac {x^{6} {\mathrm e}^{15}}{4096}+\frac {25 x^{6} {\mathrm e}^{12}}{4096}-\frac {5 x^{8} {\mathrm e}^{9}}{512}+\frac {75 x^{8} {\mathrm e}^{6}}{512}+\frac {5 x^{7} {\mathrm e}^{12}}{2048}-\frac {25 x^{7} {\mathrm e}^{9}}{512}-\frac {5 \,{\mathrm e}^{3} x^{10}}{256}+\frac {5 x^{9} {\mathrm e}^{6}}{256}-\frac {25 \,{\mathrm e}^{3} x^{9}}{128}\)	\(547\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((20*x+4)*exp(x)^2+(6*x^2*exp(3)-12*x^3-28*x^2)*exp(x))*exp(5*x)/(16*exp(x)^2+(8*x*exp(3)-16*x^2-40*x)*exp
(x)+x^2*exp(3)^2+(-4*x^3-10*x^2)*exp(3)+4*x^4+20*x^3+25*x^2),x,method=_RETURNVERBOSE)

[Out]

1/128*x^11+3125/2048*x^7+625/512*x^8+25/256*x^10+125/256*x^9+3125/4096*x^6-625/512*x^7*exp(3)+625/2048*x^6*exp
(6)+1/4*x*exp(5*x)-3125/4096*x^6*exp(3)-375/512*exp(3)*x^8+(5/16*x^2-1/16*x^2*exp(3)+1/8*x^3)*exp(4*x)+(25/64*
x^3+1/64*x^3*exp(6)-5/32*x^3*exp(3)+5/16*x^4-1/16*x^4*exp(3)+1/16*x^5)*exp(3*x)+(125/256*x^4-1/256*x^4*exp(9)+
15/256*exp(6)*x^4-75/256*x^4*exp(3)+75/128*x^5+3/128*exp(6)*x^5-15/64*x^5*exp(3)+15/64*x^6-3/64*x^6*exp(3)+1/3
2*x^7)*exp(2*x)+(625/1024*x^5+1/1024*exp(12)*x^5-5/256*exp(9)*x^5+75/512*exp(6)*x^5-125/256*x^5*exp(3)+125/128
*x^6-1/128*x^6*exp(9)+15/128*x^6*exp(6)-75/128*x^6*exp(3)+75/128*x^7+3/128*x^7*exp(6)-15/64*x^7*exp(3)+5/32*x^
8-1/32*exp(3)*x^8+1/64*x^9)*exp(x)-125/2048*x^6*exp(9)+375/1024*x^7*exp(6)-1/4096*x^6*exp(15)+25/4096*x^6*exp(
12)-5/512*x^8*exp(9)+75/512*x^8*exp(6)+5/2048*x^7*exp(12)-25/512*x^7*exp(9)-5/256*exp(3)*x^10+5/256*x^9*exp(6)
-25/128*exp(3)*x^9+1/4096*(15625+37500*x-12*x*exp(15)+9000*x^2*exp(6)+2400*x^3*exp(6)-2500*exp(9)+9375*exp(6)-
18750*exp(3)+64*x^6+960*x^5+6000*x^4+20000*x^3+37500*x^2-3000*x*exp(9)+15000*x*exp(6)-2400*x^4*exp(3)-37500*x*
exp(3)-12000*x^3*exp(3)-192*x^5*exp(3)-30000*x^2*exp(3)-1200*x^2*exp(9)+exp(18)+375*exp(12)-30*exp(15)-160*x^3
*exp(9)+300*x*exp(12)+60*x^2*exp(12)+240*exp(6)*x^4)*x^7/(x*exp(3)-2*x^2+4*exp(x)-5*x)

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maxima [A]  time = 0.43, size = 26, normalized size = 0.84 \begin {gather*} -\frac {x e^{\left (6 \, x\right )}}{2 \, x^{2} - x {\left (e^{3} - 5\right )} - 4 \, e^{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((20*x+4)*exp(x)^2+(6*x^2*exp(3)-12*x^3-28*x^2)*exp(x))*exp(5*x)/(16*exp(x)^2+(8*x*exp(3)-16*x^2-40*
x)*exp(x)+x^2*exp(3)^2+(-4*x^3-10*x^2)*exp(3)+4*x^4+20*x^3+25*x^2),x, algorithm="maxima")

[Out]

-x*e^(6*x)/(2*x^2 - x*(e^3 - 5) - 4*e^x)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} -\int \frac {{\mathrm {e}}^{5\,x}\,\left ({\mathrm {e}}^x\,\left (28\,x^2-6\,x^2\,{\mathrm {e}}^3+12\,x^3\right )-{\mathrm {e}}^{2\,x}\,\left (20\,x+4\right )\right )}{16\,{\mathrm {e}}^{2\,x}-{\mathrm {e}}^3\,\left (4\,x^3+10\,x^2\right )+x^2\,{\mathrm {e}}^6+25\,x^2+20\,x^3+4\,x^4-{\mathrm {e}}^x\,\left (40\,x-8\,x\,{\mathrm {e}}^3+16\,x^2\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(5*x)*(exp(x)*(28*x^2 - 6*x^2*exp(3) + 12*x^3) - exp(2*x)*(20*x + 4)))/(16*exp(2*x) - exp(3)*(10*x^2
+ 4*x^3) + x^2*exp(6) + 25*x^2 + 20*x^3 + 4*x^4 - exp(x)*(40*x - 8*x*exp(3) + 16*x^2)),x)

[Out]

-int((exp(5*x)*(exp(x)*(28*x^2 - 6*x^2*exp(3) + 12*x^3) - exp(2*x)*(20*x + 4)))/(16*exp(2*x) - exp(3)*(10*x^2
+ 4*x^3) + x^2*exp(6) + 25*x^2 + 20*x^3 + 4*x^4 - exp(x)*(40*x - 8*x*exp(3) + 16*x^2)), x)

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sympy [B]  time = 0.81, size = 646, normalized size = 20.84 \begin {gather*} \frac {x^{11}}{128} + x^{10} \left (\frac {25}{256} - \frac {5 e^{3}}{256}\right ) + x^{9} \left (- \frac {25 e^{3}}{128} + \frac {125}{256} + \frac {5 e^{6}}{256}\right ) + x^{8} \left (- \frac {5 e^{9}}{512} - \frac {375 e^{3}}{512} + \frac {625}{512} + \frac {75 e^{6}}{512}\right ) + x^{7} \left (- \frac {25 e^{9}}{512} - \frac {625 e^{3}}{512} + \frac {3125}{2048} + \frac {375 e^{6}}{1024} + \frac {5 e^{12}}{2048}\right ) + x^{6} \left (- \frac {e^{15}}{4096} - \frac {125 e^{9}}{2048} - \frac {3125 e^{3}}{4096} + \frac {3125}{4096} + \frac {625 e^{6}}{2048} + \frac {25 e^{12}}{4096}\right ) + \frac {x e^{5 x}}{4} + \frac {\left (134217728 x^{3} - 67108864 x^{2} e^{3} + 335544320 x^{2}\right ) e^{4 x}}{1073741824} + \frac {\left (67108864 x^{5} - 67108864 x^{4} e^{3} + 335544320 x^{4} - 167772160 x^{3} e^{3} + 419430400 x^{3} + 16777216 x^{3} e^{6}\right ) e^{3 x}}{1073741824} + \frac {\left (33554432 x^{7} - 50331648 x^{6} e^{3} + 251658240 x^{6} - 251658240 x^{5} e^{3} + 629145600 x^{5} + 25165824 x^{5} e^{6} - 4194304 x^{4} e^{9} - 314572800 x^{4} e^{3} + 524288000 x^{4} + 62914560 x^{4} e^{6}\right ) e^{2 x}}{1073741824} + \frac {\left (16777216 x^{9} - 33554432 x^{8} e^{3} + 167772160 x^{8} - 251658240 x^{7} e^{3} + 629145600 x^{7} + 25165824 x^{7} e^{6} - 8388608 x^{6} e^{9} - 629145600 x^{6} e^{3} + 1048576000 x^{6} + 125829120 x^{6} e^{6} - 20971520 x^{5} e^{9} - 524288000 x^{5} e^{3} + 655360000 x^{5} + 157286400 x^{5} e^{6} + 1048576 x^{5} e^{12}\right ) e^{x}}{1073741824} + \frac {64 x^{13} - 192 x^{12} e^{3} + 960 x^{12} - 2400 x^{11} e^{3} + 6000 x^{11} + 240 x^{11} e^{6} - 160 x^{10} e^{9} - 12000 x^{10} e^{3} + 20000 x^{10} + 2400 x^{10} e^{6} - 1200 x^{9} e^{9} - 30000 x^{9} e^{3} + 37500 x^{9} + 9000 x^{9} e^{6} + 60 x^{9} e^{12} - 12 x^{8} e^{15} - 3000 x^{8} e^{9} - 37500 x^{8} e^{3} + 37500 x^{8} + 15000 x^{8} e^{6} + 300 x^{8} e^{12} - 30 x^{7} e^{15} - 2500 x^{7} e^{9} - 18750 x^{7} e^{3} + 15625 x^{7} + 9375 x^{7} e^{6} + 375 x^{7} e^{12} + x^{7} e^{18}}{- 8192 x^{2} - 20480 x + 4096 x e^{3} + 16384 e^{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((20*x+4)*exp(x)**2+(6*x**2*exp(3)-12*x**3-28*x**2)*exp(x))*exp(5*x)/(16*exp(x)**2+(8*x*exp(3)-16*x*
*2-40*x)*exp(x)+x**2*exp(3)**2+(-4*x**3-10*x**2)*exp(3)+4*x**4+20*x**3+25*x**2),x)

[Out]

x**11/128 + x**10*(25/256 - 5*exp(3)/256) + x**9*(-25*exp(3)/128 + 125/256 + 5*exp(6)/256) + x**8*(-5*exp(9)/5
12 - 375*exp(3)/512 + 625/512 + 75*exp(6)/512) + x**7*(-25*exp(9)/512 - 625*exp(3)/512 + 3125/2048 + 375*exp(6
)/1024 + 5*exp(12)/2048) + x**6*(-exp(15)/4096 - 125*exp(9)/2048 - 3125*exp(3)/4096 + 3125/4096 + 625*exp(6)/2
048 + 25*exp(12)/4096) + x*exp(5*x)/4 + (134217728*x**3 - 67108864*x**2*exp(3) + 335544320*x**2)*exp(4*x)/1073
741824 + (67108864*x**5 - 67108864*x**4*exp(3) + 335544320*x**4 - 167772160*x**3*exp(3) + 419430400*x**3 + 167
77216*x**3*exp(6))*exp(3*x)/1073741824 + (33554432*x**7 - 50331648*x**6*exp(3) + 251658240*x**6 - 251658240*x*
*5*exp(3) + 629145600*x**5 + 25165824*x**5*exp(6) - 4194304*x**4*exp(9) - 314572800*x**4*exp(3) + 524288000*x*
*4 + 62914560*x**4*exp(6))*exp(2*x)/1073741824 + (16777216*x**9 - 33554432*x**8*exp(3) + 167772160*x**8 - 2516
58240*x**7*exp(3) + 629145600*x**7 + 25165824*x**7*exp(6) - 8388608*x**6*exp(9) - 629145600*x**6*exp(3) + 1048
576000*x**6 + 125829120*x**6*exp(6) - 20971520*x**5*exp(9) - 524288000*x**5*exp(3) + 655360000*x**5 + 15728640
0*x**5*exp(6) + 1048576*x**5*exp(12))*exp(x)/1073741824 + (64*x**13 - 192*x**12*exp(3) + 960*x**12 - 2400*x**1
1*exp(3) + 6000*x**11 + 240*x**11*exp(6) - 160*x**10*exp(9) - 12000*x**10*exp(3) + 20000*x**10 + 2400*x**10*ex
p(6) - 1200*x**9*exp(9) - 30000*x**9*exp(3) + 37500*x**9 + 9000*x**9*exp(6) + 60*x**9*exp(12) - 12*x**8*exp(15
) - 3000*x**8*exp(9) - 37500*x**8*exp(3) + 37500*x**8 + 15000*x**8*exp(6) + 300*x**8*exp(12) - 30*x**7*exp(15)
- 2500*x**7*exp(9) - 18750*x**7*exp(3) + 15625*x**7 + 9375*x**7*exp(6) + 375*x**7*exp(12) + x**7*exp(18))/(-8
192*x**2 - 20480*x + 4096*x*exp(3) + 16384*exp(x))

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