\(\int \frac {-2500-3000 x+18800 x^2+11840 x^3+47360 x^5-300800 x^6-192000 x^7+640000 x^8}{81 x^5+432 e^5 x^5+864 e^{10} x^5+768 e^{15} x^5+256 e^{20} x^5} \, dx\) [416]

Optimal result

Integrand size = 76, antiderivative size = 22 \[ \int \frac {-2500-3000 x+18800 x^2+11840 x^3+47360 x^5-300800 x^6-192000 x^7+640000 x^8}{81 x^5+432 e^5 x^5+864 e^{10} x^5+768 e^{15} x^5+256 e^{20} x^5} \, dx=\frac {\left (2+\frac {5}{x}-20 x\right )^4}{\left (3+4 e^5\right )^4} \]

[Out]

(5/x+2-20*x)^4/(4*exp(5)+3)^4

Rubi [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(111\) vs. \(2(22)=44\).

Time = 0.06 (sec) , antiderivative size = 111, normalized size of antiderivative = 5.05, number of steps used = 7, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.039, Rules used = {6, 12, 14} \[ \int \frac {-2500-3000 x+18800 x^2+11840 x^3+47360 x^5-300800 x^6-192000 x^7+640000 x^8}{81 x^5+432 e^5 x^5+864 e^{10} x^5+768 e^{15} x^5+256 e^{20} x^5} \, dx=\frac {160000 x^4}{\left (3+4 e^5\right )^4}+\frac {625}{\left (3+4 e^5\right )^4 x^4}-\frac {64000 x^3}{\left (3+4 e^5\right )^4}+\frac {1000}{\left (3+4 e^5\right )^4 x^3}-\frac {150400 x^2}{\left (3+4 e^5\right )^4}-\frac {9400}{\left (3+4 e^5\right )^4 x^2}+\frac {47360 x}{\left (3+4 e^5\right )^4}-\frac {11840}{\left (3+4 e^5\right )^4 x} \]

[In]

Int[(-2500 - 3000*x + 18800*x^2 + 11840*x^3 + 47360*x^5 - 300800*x^6 - 192000*x^7 + 640000*x^8)/(81*x^5 + 432*
E^5*x^5 + 864*E^10*x^5 + 768*E^15*x^5 + 256*E^20*x^5),x]

[Out]

625/((3 + 4*E^5)^4*x^4) + 1000/((3 + 4*E^5)^4*x^3) - 9400/((3 + 4*E^5)^4*x^2) - 11840/((3 + 4*E^5)^4*x) + (473
60*x)/(3 + 4*E^5)^4 - (150400*x^2)/(3 + 4*E^5)^4 - (64000*x^3)/(3 + 4*E^5)^4 + (160000*x^4)/(3 + 4*E^5)^4

Rule 6

Int[(u_.)*((w_.) + (a_.)*(v_) + (b_.)*(v_))^(p_.), x_Symbol] :> Int[u*((a + b)*v + w)^p, x] /; FreeQ[{a, b}, x
] &&  !FreeQ[v, x]

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 14

Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x], x] /; FreeQ[{c, m}, x] && SumQ[u]
&&  !LinearQ[u, x] &&  !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]

Rubi steps \begin{align*} \text {integral}& = \int \frac {-2500-3000 x+18800 x^2+11840 x^3+47360 x^5-300800 x^6-192000 x^7+640000 x^8}{864 e^{10} x^5+768 e^{15} x^5+256 e^{20} x^5+\left (81+432 e^5\right ) x^5} \, dx \\ & = \int \frac {-2500-3000 x+18800 x^2+11840 x^3+47360 x^5-300800 x^6-192000 x^7+640000 x^8}{256 e^{20} x^5+\left (81+432 e^5\right ) x^5+\left (864 e^{10}+768 e^{15}\right ) x^5} \, dx \\ & = \int \frac {-2500-3000 x+18800 x^2+11840 x^3+47360 x^5-300800 x^6-192000 x^7+640000 x^8}{\left (864 e^{10}+768 e^{15}\right ) x^5+\left (81+432 e^5+256 e^{20}\right ) x^5} \, dx \\ & = \int \frac {-2500-3000 x+18800 x^2+11840 x^3+47360 x^5-300800 x^6-192000 x^7+640000 x^8}{\left (81+432 e^5+864 e^{10}+768 e^{15}+256 e^{20}\right ) x^5} \, dx \\ & = \frac {\int \frac {-2500-3000 x+18800 x^2+11840 x^3+47360 x^5-300800 x^6-192000 x^7+640000 x^8}{x^5} \, dx}{\left (3+4 e^5\right )^4} \\ & = \frac {\int \left (47360-\frac {2500}{x^5}-\frac {3000}{x^4}+\frac {18800}{x^3}+\frac {11840}{x^2}-300800 x-192000 x^2+640000 x^3\right ) \, dx}{\left (3+4 e^5\right )^4} \\ & = \frac {625}{\left (3+4 e^5\right )^4 x^4}+\frac {1000}{\left (3+4 e^5\right )^4 x^3}-\frac {9400}{\left (3+4 e^5\right )^4 x^2}-\frac {11840}{\left (3+4 e^5\right )^4 x}+\frac {47360 x}{\left (3+4 e^5\right )^4}-\frac {150400 x^2}{\left (3+4 e^5\right )^4}-\frac {64000 x^3}{\left (3+4 e^5\right )^4}+\frac {160000 x^4}{\left (3+4 e^5\right )^4} \\ \end{align*}

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(52\) vs. \(2(22)=44\).

Time = 0.01 (sec) , antiderivative size = 52, normalized size of antiderivative = 2.36 \[ \int \frac {-2500-3000 x+18800 x^2+11840 x^3+47360 x^5-300800 x^6-192000 x^7+640000 x^8}{81 x^5+432 e^5 x^5+864 e^{10} x^5+768 e^{15} x^5+256 e^{20} x^5} \, dx=\frac {20 \left (\frac {125}{4 x^4}+\frac {50}{x^3}-\frac {470}{x^2}-\frac {592}{x}+2368 x-7520 x^2-3200 x^3+8000 x^4\right )}{\left (3+4 e^5\right )^4} \]

[In]

Integrate[(-2500 - 3000*x + 18800*x^2 + 11840*x^3 + 47360*x^5 - 300800*x^6 - 192000*x^7 + 640000*x^8)/(81*x^5
+ 432*E^5*x^5 + 864*E^10*x^5 + 768*E^15*x^5 + 256*E^20*x^5),x]

[Out]

(20*(125/(4*x^4) + 50/x^3 - 470/x^2 - 592/x + 2368*x - 7520*x^2 - 3200*x^3 + 8000*x^4))/(3 + 4*E^5)^4

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(65\) vs. \(2(21)=42\).

Time = 0.10 (sec) , antiderivative size = 66, normalized size of antiderivative = 3.00

method	result	size
parallelrisch	\(\frac {160000 x^{8}-64000 x^{7}-150400 x^{6}+47360 x^{5}-11840 x^{3}-9400 x^{2}+1000 x +625}{\left (256 \,{\mathrm e}^{20}+768 \,{\mathrm e}^{15}+864 \,{\mathrm e}^{10}+432 \,{\mathrm e}^{5}+81\right ) x^{4}}\)	\(66\)
gosper	\(\frac {160000 x^{8}-64000 x^{7}-150400 x^{6}+47360 x^{5}-11840 x^{3}-9400 x^{2}+1000 x +625}{\left (256 \,{\mathrm e}^{20}+768 \,{\mathrm e}^{15}+864 \,{\mathrm e}^{10}+432 \,{\mathrm e}^{5}+81\right ) x^{4}}\)	\(67\)
default	\(\frac {160000 x^{4}-64000 x^{3}-150400 x^{2}+47360 x +\frac {625}{x^{4}}-\frac {11840}{x}-\frac {9400}{x^{2}}+\frac {1000}{x^{3}}}{256 \,{\mathrm e}^{20}+768 \,{\mathrm e}^{15}+864 \,{\mathrm e}^{10}+432 \,{\mathrm e}^{5}+81}\)	\(68\)
norman	\(\frac {\frac {625}{4 \,{\mathrm e}^{5}+3}+\frac {1000 x}{4 \,{\mathrm e}^{5}+3}-\frac {9400 x^{2}}{4 \,{\mathrm e}^{5}+3}-\frac {11840 x^{3}}{4 \,{\mathrm e}^{5}+3}+\frac {47360 x^{5}}{4 \,{\mathrm e}^{5}+3}-\frac {150400 x^{6}}{4 \,{\mathrm e}^{5}+3}-\frac {64000 x^{7}}{4 \,{\mathrm e}^{5}+3}+\frac {160000 x^{8}}{4 \,{\mathrm e}^{5}+3}}{x^{4} \left (4 \,{\mathrm e}^{5}+3\right )^{3}}\)	\(113\)
risch	\(\frac {160000 x^{4}}{256 \,{\mathrm e}^{20}+768 \,{\mathrm e}^{15}+864 \,{\mathrm e}^{10}+432 \,{\mathrm e}^{5}+81}-\frac {64000 x^{3}}{256 \,{\mathrm e}^{20}+768 \,{\mathrm e}^{15}+864 \,{\mathrm e}^{10}+432 \,{\mathrm e}^{5}+81}-\frac {150400 x^{2}}{256 \,{\mathrm e}^{20}+768 \,{\mathrm e}^{15}+864 \,{\mathrm e}^{10}+432 \,{\mathrm e}^{5}+81}+\frac {47360 x}{256 \,{\mathrm e}^{20}+768 \,{\mathrm e}^{15}+864 \,{\mathrm e}^{10}+432 \,{\mathrm e}^{5}+81}+\frac {256 \left (-11840 \,{\mathrm e}^{20}-35520 \,{\mathrm e}^{15}-39960 \,{\mathrm e}^{10}-19980 \,{\mathrm e}^{5}-\frac {14985}{4}\right ) x^{3}+256 \left (-9400 \,{\mathrm e}^{20}-28200 \,{\mathrm e}^{15}-31725 \,{\mathrm e}^{10}-\frac {31725 \,{\mathrm e}^{5}}{2}-\frac {95175}{32}\right ) x^{2}+256 \left (1000 \,{\mathrm e}^{20}+3000 \,{\mathrm e}^{15}+3375 \,{\mathrm e}^{10}+\frac {3375 \,{\mathrm e}^{5}}{2}+\frac {10125}{32}\right ) x +160000 \,{\mathrm e}^{20}+480000 \,{\mathrm e}^{15}+540000 \,{\mathrm e}^{10}+270000 \,{\mathrm e}^{5}+50625}{\left (256 \,{\mathrm e}^{20}+768 \,{\mathrm e}^{15}+864 \,{\mathrm e}^{10}+432 \,{\mathrm e}^{5}+81\right )^{2} x^{4}}\)	\(207\)

[In]

int((640000*x^8-192000*x^7-300800*x^6+47360*x^5+11840*x^3+18800*x^2-3000*x-2500)/(256*x^5*exp(5)^4+768*x^5*exp
(5)^3+864*x^5*exp(5)^2+432*x^5*exp(5)+81*x^5),x,method=_RETURNVERBOSE)

[Out]

(160000*x^8-64000*x^7-150400*x^6+47360*x^5-11840*x^3-9400*x^2+1000*x+625)/(256*exp(5)^4+768*exp(5)^3+864*exp(5
)^2+432*exp(5)+81)/x^4

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 73 vs. \(2 (21) = 42\).

Time = 0.23 (sec) , antiderivative size = 73, normalized size of antiderivative = 3.32 \[ \int \frac {-2500-3000 x+18800 x^2+11840 x^3+47360 x^5-300800 x^6-192000 x^7+640000 x^8}{81 x^5+432 e^5 x^5+864 e^{10} x^5+768 e^{15} x^5+256 e^{20} x^5} \, dx=\frac {5 \, {\left (32000 \, x^{8} - 12800 \, x^{7} - 30080 \, x^{6} + 9472 \, x^{5} - 2368 \, x^{3} - 1880 \, x^{2} + 200 \, x + 125\right )}}{256 \, x^{4} e^{20} + 768 \, x^{4} e^{15} + 864 \, x^{4} e^{10} + 432 \, x^{4} e^{5} + 81 \, x^{4}} \]

[In]

integrate((640000*x^8-192000*x^7-300800*x^6+47360*x^5+11840*x^3+18800*x^2-3000*x-2500)/(256*x^5*exp(5)^4+768*x
^5*exp(5)^3+864*x^5*exp(5)^2+432*x^5*exp(5)+81*x^5),x, algorithm="fricas")

[Out]

5*(32000*x^8 - 12800*x^7 - 30080*x^6 + 9472*x^5 - 2368*x^3 - 1880*x^2 + 200*x + 125)/(256*x^4*e^20 + 768*x^4*e
^15 + 864*x^4*e^10 + 432*x^4*e^5 + 81*x^4)

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 58 vs. \(2 (17) = 34\).

Time = 0.05 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.64 \[ \int \frac {-2500-3000 x+18800 x^2+11840 x^3+47360 x^5-300800 x^6-192000 x^7+640000 x^8}{81 x^5+432 e^5 x^5+864 e^{10} x^5+768 e^{15} x^5+256 e^{20} x^5} \, dx=\frac {160000 x^{4} - 64000 x^{3} - 150400 x^{2} + 47360 x + \frac {- 11840 x^{3} - 9400 x^{2} + 1000 x + 625}{x^{4}}}{81 + 432 e^{5} + 864 e^{10} + 768 e^{15} + 256 e^{20}} \]

[In]

integrate((640000*x**8-192000*x**7-300800*x**6+47360*x**5+11840*x**3+18800*x**2-3000*x-2500)/(256*x**5*exp(5)*
*4+768*x**5*exp(5)**3+864*x**5*exp(5)**2+432*x**5*exp(5)+81*x**5),x)

[Out]

(160000*x**4 - 64000*x**3 - 150400*x**2 + 47360*x + (-11840*x**3 - 9400*x**2 + 1000*x + 625)/x**4)/(81 + 432*e
xp(5) + 864*exp(10) + 768*exp(15) + 256*exp(20))

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 82 vs. \(2 (21) = 42\).

Time = 0.19 (sec) , antiderivative size = 82, normalized size of antiderivative = 3.73 \[ \int \frac {-2500-3000 x+18800 x^2+11840 x^3+47360 x^5-300800 x^6-192000 x^7+640000 x^8}{81 x^5+432 e^5 x^5+864 e^{10} x^5+768 e^{15} x^5+256 e^{20} x^5} \, dx=\frac {640 \, {\left (250 \, x^{4} - 100 \, x^{3} - 235 \, x^{2} + 74 \, x\right )}}{256 \, e^{20} + 768 \, e^{15} + 864 \, e^{10} + 432 \, e^{5} + 81} - \frac {5 \, {\left (2368 \, x^{3} + 1880 \, x^{2} - 200 \, x - 125\right )}}{x^{4} {\left (256 \, e^{20} + 768 \, e^{15} + 864 \, e^{10} + 432 \, e^{5} + 81\right )}} \]

[In]

integrate((640000*x^8-192000*x^7-300800*x^6+47360*x^5+11840*x^3+18800*x^2-3000*x-2500)/(256*x^5*exp(5)^4+768*x
^5*exp(5)^3+864*x^5*exp(5)^2+432*x^5*exp(5)+81*x^5),x, algorithm="maxima")

[Out]

640*(250*x^4 - 100*x^3 - 235*x^2 + 74*x)/(256*e^20 + 768*e^15 + 864*e^10 + 432*e^5 + 81) - 5*(2368*x^3 + 1880*
x^2 - 200*x - 125)/(x^4*(256*e^20 + 768*e^15 + 864*e^10 + 432*e^5 + 81))

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 442 vs. \(2 (21) = 42\).

Time = 0.30 (sec) , antiderivative size = 442, normalized size of antiderivative = 20.09 \[ \int \frac {-2500-3000 x+18800 x^2+11840 x^3+47360 x^5-300800 x^6-192000 x^7+640000 x^8}{81 x^5+432 e^5 x^5+864 e^{10} x^5+768 e^{15} x^5+256 e^{20} x^5} \, dx=\frac {640 \, {\left (4194304000 \, x^{4} e^{60} + 37748736000 \, x^{4} e^{55} + 155713536000 \, x^{4} e^{50} + 389283840000 \, x^{4} e^{45} + 656916480000 \, x^{4} e^{40} + 788299776000 \, x^{4} e^{35} + 689762304000 \, x^{4} e^{30} + 443418624000 \, x^{4} e^{25} + 207852480000 \, x^{4} e^{20} + 69284160000 \, x^{4} e^{15} + 15588936000 \, x^{4} e^{10} + 2125764000 \, x^{4} e^{5} + 132860250 \, x^{4} - 1677721600 \, x^{3} e^{60} - 15099494400 \, x^{3} e^{55} - 62285414400 \, x^{3} e^{50} - 155713536000 \, x^{3} e^{45} - 262766592000 \, x^{3} e^{40} - 315319910400 \, x^{3} e^{35} - 275904921600 \, x^{3} e^{30} - 177367449600 \, x^{3} e^{25} - 83140992000 \, x^{3} e^{20} - 27713664000 \, x^{3} e^{15} - 6235574400 \, x^{3} e^{10} - 850305600 \, x^{3} e^{5} - 53144100 \, x^{3} - 3942645760 \, x^{2} e^{60} - 35483811840 \, x^{2} e^{55} - 146370723840 \, x^{2} e^{50} - 365926809600 \, x^{2} e^{45} - 617501491200 \, x^{2} e^{40} - 741001789440 \, x^{2} e^{35} - 648376565760 \, x^{2} e^{30} - 416813506560 \, x^{2} e^{25} - 195381331200 \, x^{2} e^{20} - 65127110400 \, x^{2} e^{15} - 14653599840 \, x^{2} e^{10} - 1998218160 \, x^{2} e^{5} - 124888635 \, x^{2} + 1241513984 \, x e^{60} + 11173625856 \, x e^{55} + 46091206656 \, x e^{50} + 115228016640 \, x e^{45} + 194447278080 \, x e^{40} + 233336733696 \, x e^{35} + 204169641984 \, x e^{30} + 131251912704 \, x e^{25} + 61524334080 \, x e^{20} + 20508111360 \, x e^{15} + 4614325056 \, x e^{10} + 629226144 \, x e^{5} + 39326634 \, x\right )}}{4294967296 \, e^{80} + 51539607552 \, e^{75} + 289910292480 \, e^{70} + 1014686023680 \, e^{65} + 2473297182720 \, e^{60} + 4451934928896 \, e^{55} + 6121410527232 \, e^{50} + 6558654136320 \, e^{45} + 5533864427520 \, e^{40} + 3689242951680 \, e^{35} + 1936852549632 \, e^{30} + 792348770304 \, e^{25} + 247608990720 \, e^{20} + 57140536320 \, e^{15} + 9183300480 \, e^{10} + 918330048 \, e^{5} + 43046721} - \frac {5 \, {\left (2368 \, x^{3} + 1880 \, x^{2} - 200 \, x - 125\right )}}{x^{4} {\left (256 \, e^{20} + 768 \, e^{15} + 864 \, e^{10} + 432 \, e^{5} + 81\right )}} \]

[In]

integrate((640000*x^8-192000*x^7-300800*x^6+47360*x^5+11840*x^3+18800*x^2-3000*x-2500)/(256*x^5*exp(5)^4+768*x
^5*exp(5)^3+864*x^5*exp(5)^2+432*x^5*exp(5)+81*x^5),x, algorithm="giac")

[Out]

640*(4194304000*x^4*e^60 + 37748736000*x^4*e^55 + 155713536000*x^4*e^50 + 389283840000*x^4*e^45 + 656916480000
*x^4*e^40 + 788299776000*x^4*e^35 + 689762304000*x^4*e^30 + 443418624000*x^4*e^25 + 207852480000*x^4*e^20 + 69
284160000*x^4*e^15 + 15588936000*x^4*e^10 + 2125764000*x^4*e^5 + 132860250*x^4 - 1677721600*x^3*e^60 - 1509949
4400*x^3*e^55 - 62285414400*x^3*e^50 - 155713536000*x^3*e^45 - 262766592000*x^3*e^40 - 315319910400*x^3*e^35 -
275904921600*x^3*e^30 - 177367449600*x^3*e^25 - 83140992000*x^3*e^20 - 27713664000*x^3*e^15 - 6235574400*x^3*
e^10 - 850305600*x^3*e^5 - 53144100*x^3 - 3942645760*x^2*e^60 - 35483811840*x^2*e^55 - 146370723840*x^2*e^50 -
365926809600*x^2*e^45 - 617501491200*x^2*e^40 - 741001789440*x^2*e^35 - 648376565760*x^2*e^30 - 416813506560*
x^2*e^25 - 195381331200*x^2*e^20 - 65127110400*x^2*e^15 - 14653599840*x^2*e^10 - 1998218160*x^2*e^5 - 12488863
5*x^2 + 1241513984*x*e^60 + 11173625856*x*e^55 + 46091206656*x*e^50 + 115228016640*x*e^45 + 194447278080*x*e^4
0 + 233336733696*x*e^35 + 204169641984*x*e^30 + 131251912704*x*e^25 + 61524334080*x*e^20 + 20508111360*x*e^15
+ 4614325056*x*e^10 + 629226144*x*e^5 + 39326634*x)/(4294967296*e^80 + 51539607552*e^75 + 289910292480*e^70 +
1014686023680*e^65 + 2473297182720*e^60 + 4451934928896*e^55 + 6121410527232*e^50 + 6558654136320*e^45 + 55338
64427520*e^40 + 3689242951680*e^35 + 1936852549632*e^30 + 792348770304*e^25 + 247608990720*e^20 + 57140536320*
e^15 + 9183300480*e^10 + 918330048*e^5 + 43046721) - 5*(2368*x^3 + 1880*x^2 - 200*x - 125)/(x^4*(256*e^20 + 76
8*e^15 + 864*e^10 + 432*e^5 + 81))

Mupad [B] (verification not implemented)

Time = 0.11 (sec) , antiderivative size = 90, normalized size of antiderivative = 4.09 \[ \int \frac {-2500-3000 x+18800 x^2+11840 x^3+47360 x^5-300800 x^6-192000 x^7+640000 x^8}{81 x^5+432 e^5 x^5+864 e^{10} x^5+768 e^{15} x^5+256 e^{20} x^5} \, dx=\frac {47360\,x}{{\left (4\,{\mathrm {e}}^5+3\right )}^4}-\frac {150400\,x^2}{{\left (4\,{\mathrm {e}}^5+3\right )}^4}-\frac {64000\,x^3}{{\left (4\,{\mathrm {e}}^5+3\right )}^4}+\frac {160000\,x^4}{{\left (4\,{\mathrm {e}}^5+3\right )}^4}+\frac {-11840\,x^3-9400\,x^2+1000\,x+625}{x^4\,\left (432\,{\mathrm {e}}^5+864\,{\mathrm {e}}^{10}+768\,{\mathrm {e}}^{15}+256\,{\mathrm {e}}^{20}+81\right )} \]

[In]

int(-(3000*x - 18800*x^2 - 11840*x^3 - 47360*x^5 + 300800*x^6 + 192000*x^7 - 640000*x^8 + 2500)/(432*x^5*exp(5
) + 864*x^5*exp(10) + 768*x^5*exp(15) + 256*x^5*exp(20) + 81*x^5),x)

[Out]

(47360*x)/(4*exp(5) + 3)^4 - (150400*x^2)/(4*exp(5) + 3)^4 - (64000*x^3)/(4*exp(5) + 3)^4 + (160000*x^4)/(4*ex
p(5) + 3)^4 + (1000*x - 9400*x^2 - 11840*x^3 + 625)/(x^4*(432*exp(5) + 864*exp(10) + 768*exp(15) + 256*exp(20)
+ 81))