Integrand size = 131, antiderivative size = 23 \[ \int \frac {-5124800+1310720 e^{15} x^3-131072 e^{20} x^4+e^5 (19200+8199680 x)+e^{10} \left (-7680 x-4917504 x^2\right )}{23011209+15350400 x+2560000 x^2+e^5 \left (-36840960 x-24568320 x^2-4096000 x^3\right )+e^{10} \left (22113792 x^2+14744064 x^3+2457600 x^4\right )+e^{15} \left (-5898240 x^3-3932160 x^4-655360 x^5\right )+e^{20} \left (589824 x^4+393216 x^5+65536 x^6\right )} \, dx=\frac {5+x}{3+x-\frac {3}{64 \left (-5+2 e^5 x\right )^2}} \] Output:
(5+x)/(3+x-3/16/(2*x*exp(5)-5)/(8*x*exp(5)-20))
Leaf count is larger than twice the leaf count of optimal. \(55\) vs. \(2(23)=46\).
Time = 0.03 (sec) , antiderivative size = 55, normalized size of antiderivative = 2.39 \[ \int \frac {-5124800+1310720 e^{15} x^3-131072 e^{20} x^4+e^5 (19200+8199680 x)+e^{10} \left (-7680 x-4917504 x^2\right )}{23011209+15350400 x+2560000 x^2+e^5 \left (-36840960 x-24568320 x^2-4096000 x^3\right )+e^{10} \left (22113792 x^2+14744064 x^3+2457600 x^4\right )+e^{15} \left (-5898240 x^3-3932160 x^4-655360 x^5\right )+e^{20} \left (589824 x^4+393216 x^5+65536 x^6\right )} \, dx=-\frac {-3203+2560 e^5 x-512 e^{10} x^2}{4797+1600 x-3840 e^5 x-1280 e^5 x^2+768 e^{10} x^2+256 e^{10} x^3} \] Input:
Integrate[(-5124800 + 1310720*E^15*x^3 - 131072*E^20*x^4 + E^5*(19200 + 81 99680*x) + E^10*(-7680*x - 4917504*x^2))/(23011209 + 15350400*x + 2560000* x^2 + E^5*(-36840960*x - 24568320*x^2 - 4096000*x^3) + E^10*(22113792*x^2 + 14744064*x^3 + 2457600*x^4) + E^15*(-5898240*x^3 - 3932160*x^4 - 655360* x^5) + E^20*(589824*x^4 + 393216*x^5 + 65536*x^6)),x]
Output:
-((-3203 + 2560*E^5*x - 512*E^10*x^2)/(4797 + 1600*x - 3840*E^5*x - 1280*E ^5*x^2 + 768*E^10*x^2 + 256*E^10*x^3))
Leaf count is larger than twice the leaf count of optimal. \(140\) vs. \(2(23)=46\).
Time = 10.97 (sec) , antiderivative size = 140, normalized size of antiderivative = 6.09, number of steps used = 9, number of rules used = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.069, Rules used = {2462, 7239, 27, 25, 2527, 27, 2527, 27, 2021}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {-131072 e^{20} x^4+1310720 e^{15} x^3+e^{10} \left (-4917504 x^2-7680 x\right )+e^5 (8199680 x+19200)-5124800}{2560000 x^2+e^5 \left (-4096000 x^3-24568320 x^2-36840960 x\right )+e^{20} \left (65536 x^6+393216 x^5+589824 x^4\right )+e^{15} \left (-655360 x^5-3932160 x^4-5898240 x^3\right )+e^{10} \left (2457600 x^4+14744064 x^3+22113792 x^2\right )+15350400 x+23011209} \, dx\) |
| \(\Big \downarrow \) 2462 |
| \(\displaystyle \int \left (\frac {512 e^5 \left (-e^5 x+3 e^5+5\right )}{256 e^{10} x^3-256 e^5 \left (5-3 e^5\right ) x^2+320 \left (5-12 e^5\right ) x+4797}+\frac {64 \left (-4 e^{10} \left (3209+7680 e^5+4608 e^{10}\right ) x^2+8 e^5 \left (8015+19182 e^5+11520 e^{10}\right ) x-115128 e^{10}-191580 e^5-80075\right )}{\left (256 e^{10} x^3-256 e^5 \left (5-3 e^5\right ) x^2+320 \left (5-12 e^5\right ) x+4797\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {64 \left (-2048 e^{20} x^4+20480 e^{15} x^3-76836 e^{10} x^2+40 e^5 \left (3203-3 e^5\right ) x-25 \left (3203-12 e^5\right )\right )}{\left (256 e^{10} x^3-256 e^5 \left (5-3 e^5\right ) x^2+320 \left (5-12 e^5\right ) x+4797\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 64 \int -\frac {2048 e^{20} x^4-20480 e^{15} x^3+76836 e^{10} x^2-40 e^5 \left (3203-3 e^5\right ) x+25 \left (3203-12 e^5\right )}{\left (256 e^{10} x^3-256 e^5 \left (5-3 e^5\right ) x^2+320 \left (5-12 e^5\right ) x+4797\right )^2}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -64 \int \frac {2048 e^{20} x^4-20480 e^{15} x^3+76836 e^{10} x^2-40 e^5 \left (3203-3 e^5\right ) x+25 \left (3203-12 e^5\right )}{\left (256 e^{10} x^3-256 e^5 \left (5-3 e^5\right ) x^2+320 \left (5-12 e^5\right ) x+4797\right )^2}dx\) |
| \(\Big \downarrow \) 2527 |
| \(\displaystyle -64 \left (-\frac {\int -\frac {256 \left (-20480 e^{25} x^3+4 e^{20} \left (22409-7680 e^5\right ) x^2-25624 e^{15} \left (5-3 e^5\right ) x+25 e^{10} \left (3203-12 e^5\right )\right )}{\left (256 e^{10} x^3-256 e^5 \left (5-3 e^5\right ) x^2+320 \left (5-12 e^5\right ) x+4797\right )^2}dx}{256 e^{10}}-\frac {8 e^{10} x^2}{256 e^{10} x^3-256 e^5 \left (5-3 e^5\right ) x^2+320 \left (5-12 e^5\right ) x+4797}\right )\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle -64 \left (\frac {\int \frac {-20480 e^{25} x^3+4 e^{20} \left (22409-7680 e^5\right ) x^2-25624 e^{15} \left (5-3 e^5\right ) x+25 e^{10} \left (3203-12 e^5\right )}{\left (256 e^{10} x^3-256 e^5 \left (5-3 e^5\right ) x^2+320 \left (5-12 e^5\right ) x+4797\right )^2}dx}{e^{10}}-\frac {8 e^{10} x^2}{256 e^{10} x^3-256 e^5 \left (5-3 e^5\right ) x^2+320 \left (5-12 e^5\right ) x+4797}\right )\) |
| \(\Big \downarrow \) 2527 |
| \(\displaystyle -64 \left (\frac {\frac {40 e^{15} x}{256 e^{10} x^3-256 e^5 \left (5-3 e^5\right ) x^2+320 \left (5-12 e^5\right ) x+4797}-\frac {\int -\frac {1639936 \left (12 e^{30} x^2-8 e^{25} \left (5-3 e^5\right ) x+5 e^{20} \left (5-12 e^5\right )\right )}{\left (256 e^{10} x^3-256 e^5 \left (5-3 e^5\right ) x^2+320 \left (5-12 e^5\right ) x+4797\right )^2}dx}{512 e^{10}}}{e^{10}}-\frac {8 e^{10} x^2}{256 e^{10} x^3-256 e^5 \left (5-3 e^5\right ) x^2+320 \left (5-12 e^5\right ) x+4797}\right )\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle -64 \left (\frac {\frac {3203 \int \frac {12 e^{30} x^2-8 e^{25} \left (5-3 e^5\right ) x+5 e^{20} \left (5-12 e^5\right )}{\left (256 e^{10} x^3-256 e^5 \left (5-3 e^5\right ) x^2+320 \left (5-12 e^5\right ) x+4797\right )^2}dx}{e^{10}}+\frac {40 e^{15} x}{256 e^{10} x^3-256 e^5 \left (5-3 e^5\right ) x^2+320 \left (5-12 e^5\right ) x+4797}}{e^{10}}-\frac {8 e^{10} x^2}{256 e^{10} x^3-256 e^5 \left (5-3 e^5\right ) x^2+320 \left (5-12 e^5\right ) x+4797}\right )\) |
| \(\Big \downarrow \) 2021 |
| \(\displaystyle -64 \left (\frac {\frac {40 e^{15} x}{256 e^{10} x^3-256 e^5 \left (5-3 e^5\right ) x^2+320 \left (5-12 e^5\right ) x+4797}-\frac {3203 e^{10}}{64 \left (256 e^{10} x^3-256 e^5 \left (5-3 e^5\right ) x^2+320 \left (5-12 e^5\right ) x+4797\right )}}{e^{10}}-\frac {8 e^{10} x^2}{256 e^{10} x^3-256 e^5 \left (5-3 e^5\right ) x^2+320 \left (5-12 e^5\right ) x+4797}\right )\) |
Input:
Int[(-5124800 + 1310720*E^15*x^3 - 131072*E^20*x^4 + E^5*(19200 + 8199680* x) + E^10*(-7680*x - 4917504*x^2))/(23011209 + 15350400*x + 2560000*x^2 + E^5*(-36840960*x - 24568320*x^2 - 4096000*x^3) + E^10*(22113792*x^2 + 1474 4064*x^3 + 2457600*x^4) + E^15*(-5898240*x^3 - 3932160*x^4 - 655360*x^5) + E^20*(589824*x^4 + 393216*x^5 + 65536*x^6)),x]
Output:
-64*((-8*E^10*x^2)/(4797 + 320*(5 - 12*E^5)*x - 256*E^5*(5 - 3*E^5)*x^2 + 256*E^10*x^3) + ((-3203*E^10)/(64*(4797 + 320*(5 - 12*E^5)*x - 256*E^5*(5 - 3*E^5)*x^2 + 256*E^10*x^3)) + (40*E^15*x)/(4797 + 320*(5 - 12*E^5)*x - 2 56*E^5*(5 - 3*E^5)*x^2 + 256*E^10*x^3))/E^10)
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[(Pp_)*(Qq_)^(m_.), x_Symbol] :> With[{p = Expon[Pp, x], q = Expon[Qq, x ]}, Simp[Coeff[Pp, x, p]*x^(p - q + 1)*(Qq^(m + 1)/((p + m*q + 1)*Coeff[Qq, x, q])), x] /; NeQ[p + m*q + 1, 0] && EqQ[(p + m*q + 1)*Coeff[Qq, x, q]*Pp , Coeff[Pp, x, p]*x^(p - q)*((p - q + 1)*Qq + (m + 1)*x*D[Qq, x])]] /; Free Q[m, x] && PolyQ[Pp, x] && PolyQ[Qq, x] && NeQ[m, -1]
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{Qx = Factor[Px]}, Int[ExpandIntegr and[u*Qx^p, x], x] /; !SumQ[NonfreeFactors[Qx, x]]] /; PolyQ[Px, x] && GtQ [Expon[Px, x], 2] && !BinomialQ[Px, x] && !TrinomialQ[Px, x] && ILtQ[p, 0 ] && RationalFunctionQ[u, x]
Int[(Pm_)*(Qn_)^(p_.), x_Symbol] :> With[{m = Expon[Pm, x], n = Expon[Qn, x ]}, Simp[Coeff[Pm, x, m]*x^(m - n + 1)*(Qn^(p + 1)/((m + n*p + 1)*Coeff[Qn, x, n])), x] + Simp[1/((m + n*p + 1)*Coeff[Qn, x, n]) Int[ExpandToSum[(m + n*p + 1)*Coeff[Qn, x, n]*Pm - Coeff[Pm, x, m]*x^(m - n)*((m - n + 1)*Qn + (p + 1)*x*D[Qn, x]), x]*Qn^p, x], x] /; LtQ[1, n, m + 1] && m + n*p + 1 < 0] /; FreeQ[p, x] && PolyQ[Pm, x] && PolyQ[Qn, x] && LtQ[p, -1]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Time = 0.70 (sec) , antiderivative size = 54, normalized size of antiderivative = 2.35
| method | result | size |
| risch | \(\frac {2 x^{2} {\mathrm e}^{10}-10 x \,{\mathrm e}^{5}+\frac {3203}{256}}{x^{3} {\mathrm e}^{10}+3 x^{2} {\mathrm e}^{10}-5 x^{2} {\mathrm e}^{5}-15 x \,{\mathrm e}^{5}+\frac {25 x}{4}+\frac {4797}{256}}\) | \(54\) |
| gosper | \(\frac {512 x^{2} {\mathrm e}^{10}-2560 x \,{\mathrm e}^{5}+3203}{256 x^{3} {\mathrm e}^{10}+768 x^{2} {\mathrm e}^{10}-1280 x^{2} {\mathrm e}^{5}-3840 x \,{\mathrm e}^{5}+1600 x +4797}\) | \(55\) |
| norman | \(\frac {-\frac {819968 x^{3} {\mathrm e}^{10}}{4797}+\left (-\frac {5124800}{4797}+\frac {6400 \,{\mathrm e}^{5}}{1599}\right ) x +\left (-\frac {1280 \,{\mathrm e}^{10}}{1599}+\frac {4099840 \,{\mathrm e}^{5}}{4797}\right ) x^{2}}{256 x^{3} {\mathrm e}^{10}+768 x^{2} {\mathrm e}^{10}-1280 x^{2} {\mathrm e}^{5}-3840 x \,{\mathrm e}^{5}+1600 x +4797}\) | \(72\) |
| parallelrisch | \(\frac {-819968 x^{3} {\mathrm e}^{10}-3840 x^{2} {\mathrm e}^{10}+4099840 x^{2} {\mathrm e}^{5}+19200 x \,{\mathrm e}^{5}-5124800 x}{1228032 x^{3} {\mathrm e}^{10}+3684096 x^{2} {\mathrm e}^{10}-6140160 x^{2} {\mathrm e}^{5}-18420480 x \,{\mathrm e}^{5}+7675200 x +23011209}\) | \(74\) |
| default | \(-\frac {\left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (23011209+65536 \,{\mathrm e}^{20} \textit {\_Z}^{6}-\left (655360 \,{\mathrm e}^{15}-393216 \,{\mathrm e}^{20}\right ) \textit {\_Z}^{5}-\left (3932160 \,{\mathrm e}^{15}-2457600 \,{\mathrm e}^{10}-589824 \,{\mathrm e}^{20}\right ) \textit {\_Z}^{4}-\left (5898240 \,{\mathrm e}^{15}-14744064 \,{\mathrm e}^{10}+4096000 \,{\mathrm e}^{5}\right ) \textit {\_Z}^{3}-\left (-22113792 \,{\mathrm e}^{10}+24568320 \,{\mathrm e}^{5}-2560000\right ) \textit {\_Z}^{2}-\left (36840960 \,{\mathrm e}^{5}-15350400\right ) \textit {\_Z} \right )}{\sum }\frac {\left (-80075-2048 \,{\mathrm e}^{20} \textit {\_R}^{4}+20480 \textit {\_R}^{3} {\mathrm e}^{15}-76836 \textit {\_R}^{2} {\mathrm e}^{10}+40 \left (-3 \,{\mathrm e}^{10}+3203 \,{\mathrm e}^{5}\right ) \textit {\_R} +300 \,{\mathrm e}^{5}\right ) \ln \left (x -\textit {\_R} \right )}{-119925-3072 \,{\mathrm e}^{20} \textit {\_R}^{5}-15360 \,{\mathrm e}^{20} \textit {\_R}^{4}-18432 \,{\mathrm e}^{20} \textit {\_R}^{3}+25600 \,{\mathrm e}^{15} \textit {\_R}^{4}+122880 \textit {\_R}^{3} {\mathrm e}^{15}+138240 \textit {\_R}^{2} {\mathrm e}^{15}-76800 \textit {\_R}^{3} {\mathrm e}^{10}-345564 \textit {\_R}^{2} {\mathrm e}^{10}-345528 \textit {\_R} \,{\mathrm e}^{10}+96000 \textit {\_R}^{2} {\mathrm e}^{5}+383880 \textit {\_R} \,{\mathrm e}^{5}+287820 \,{\mathrm e}^{5}-40000 \textit {\_R}}\right )}{2}\) | \(220\) |
Input:
int((-131072*x^4*exp(5)^4+1310720*x^3*exp(5)^3+(-4917504*x^2-7680*x)*exp(5 )^2+(8199680*x+19200)*exp(5)-5124800)/((65536*x^6+393216*x^5+589824*x^4)*e xp(5)^4+(-655360*x^5-3932160*x^4-5898240*x^3)*exp(5)^3+(2457600*x^4+147440 64*x^3+22113792*x^2)*exp(5)^2+(-4096000*x^3-24568320*x^2-36840960*x)*exp(5 )+2560000*x^2+15350400*x+23011209),x,method=_RETURNVERBOSE)
Output:
(2*x^2*exp(5)^2-10*x*exp(5)+3203/256)/(x^3*exp(5)^2+3*x^2*exp(5)^2-5*x^2*e xp(5)-15*x*exp(5)+25/4*x+4797/256)
Time = 0.08 (sec) , antiderivative size = 46, normalized size of antiderivative = 2.00 \[ \int \frac {-5124800+1310720 e^{15} x^3-131072 e^{20} x^4+e^5 (19200+8199680 x)+e^{10} \left (-7680 x-4917504 x^2\right )}{23011209+15350400 x+2560000 x^2+e^5 \left (-36840960 x-24568320 x^2-4096000 x^3\right )+e^{10} \left (22113792 x^2+14744064 x^3+2457600 x^4\right )+e^{15} \left (-5898240 x^3-3932160 x^4-655360 x^5\right )+e^{20} \left (589824 x^4+393216 x^5+65536 x^6\right )} \, dx=\frac {512 \, x^{2} e^{10} - 2560 \, x e^{5} + 3203}{256 \, {\left (x^{3} + 3 \, x^{2}\right )} e^{10} - 1280 \, {\left (x^{2} + 3 \, x\right )} e^{5} + 1600 \, x + 4797} \] Input:
integrate((-131072*x^4*exp(5)^4+1310720*x^3*exp(5)^3+(-4917504*x^2-7680*x) *exp(5)^2+(8199680*x+19200)*exp(5)-5124800)/((65536*x^6+393216*x^5+589824* x^4)*exp(5)^4+(-655360*x^5-3932160*x^4-5898240*x^3)*exp(5)^3+(2457600*x^4+ 14744064*x^3+22113792*x^2)*exp(5)^2+(-4096000*x^3-24568320*x^2-36840960*x) *exp(5)+2560000*x^2+15350400*x+23011209),x, algorithm="fricas")
Output:
(512*x^2*e^10 - 2560*x*e^5 + 3203)/(256*(x^3 + 3*x^2)*e^10 - 1280*(x^2 + 3 *x)*e^5 + 1600*x + 4797)
Time = 1.61 (sec) , antiderivative size = 49, normalized size of antiderivative = 2.13 \[ \int \frac {-5124800+1310720 e^{15} x^3-131072 e^{20} x^4+e^5 (19200+8199680 x)+e^{10} \left (-7680 x-4917504 x^2\right )}{23011209+15350400 x+2560000 x^2+e^5 \left (-36840960 x-24568320 x^2-4096000 x^3\right )+e^{10} \left (22113792 x^2+14744064 x^3+2457600 x^4\right )+e^{15} \left (-5898240 x^3-3932160 x^4-655360 x^5\right )+e^{20} \left (589824 x^4+393216 x^5+65536 x^6\right )} \, dx=- \frac {- 512 x^{2} e^{10} + 2560 x e^{5} - 3203}{256 x^{3} e^{10} + x^{2} \left (- 1280 e^{5} + 768 e^{10}\right ) + x \left (1600 - 3840 e^{5}\right ) + 4797} \] Input:
integrate((-131072*x**4*exp(5)**4+1310720*x**3*exp(5)**3+(-4917504*x**2-76 80*x)*exp(5)**2+(8199680*x+19200)*exp(5)-5124800)/((65536*x**6+393216*x**5 +589824*x**4)*exp(5)**4+(-655360*x**5-3932160*x**4-5898240*x**3)*exp(5)**3 +(2457600*x**4+14744064*x**3+22113792*x**2)*exp(5)**2+(-4096000*x**3-24568 320*x**2-36840960*x)*exp(5)+2560000*x**2+15350400*x+23011209),x)
Output:
-(-512*x**2*exp(10) + 2560*x*exp(5) - 3203)/(256*x**3*exp(10) + x**2*(-128 0*exp(5) + 768*exp(10)) + x*(1600 - 3840*exp(5)) + 4797)
Leaf count of result is larger than twice the leaf count of optimal. 49 vs. \(2 (23) = 46\).
Time = 0.04 (sec) , antiderivative size = 49, normalized size of antiderivative = 2.13 \[ \int \frac {-5124800+1310720 e^{15} x^3-131072 e^{20} x^4+e^5 (19200+8199680 x)+e^{10} \left (-7680 x-4917504 x^2\right )}{23011209+15350400 x+2560000 x^2+e^5 \left (-36840960 x-24568320 x^2-4096000 x^3\right )+e^{10} \left (22113792 x^2+14744064 x^3+2457600 x^4\right )+e^{15} \left (-5898240 x^3-3932160 x^4-655360 x^5\right )+e^{20} \left (589824 x^4+393216 x^5+65536 x^6\right )} \, dx=\frac {512 \, x^{2} e^{10} - 2560 \, x e^{5} + 3203}{256 \, x^{3} e^{10} + 256 \, x^{2} {\left (3 \, e^{10} - 5 \, e^{5}\right )} - 320 \, x {\left (12 \, e^{5} - 5\right )} + 4797} \] Input:
integrate((-131072*x^4*exp(5)^4+1310720*x^3*exp(5)^3+(-4917504*x^2-7680*x) *exp(5)^2+(8199680*x+19200)*exp(5)-5124800)/((65536*x^6+393216*x^5+589824* x^4)*exp(5)^4+(-655360*x^5-3932160*x^4-5898240*x^3)*exp(5)^3+(2457600*x^4+ 14744064*x^3+22113792*x^2)*exp(5)^2+(-4096000*x^3-24568320*x^2-36840960*x) *exp(5)+2560000*x^2+15350400*x+23011209),x, algorithm="maxima")
Output:
(512*x^2*e^10 - 2560*x*e^5 + 3203)/(256*x^3*e^10 + 256*x^2*(3*e^10 - 5*e^5 ) - 320*x*(12*e^5 - 5) + 4797)
Leaf count of result is larger than twice the leaf count of optimal. 48 vs. \(2 (23) = 46\).
Time = 0.12 (sec) , antiderivative size = 48, normalized size of antiderivative = 2.09 \[ \int \frac {-5124800+1310720 e^{15} x^3-131072 e^{20} x^4+e^5 (19200+8199680 x)+e^{10} \left (-7680 x-4917504 x^2\right )}{23011209+15350400 x+2560000 x^2+e^5 \left (-36840960 x-24568320 x^2-4096000 x^3\right )+e^{10} \left (22113792 x^2+14744064 x^3+2457600 x^4\right )+e^{15} \left (-5898240 x^3-3932160 x^4-655360 x^5\right )+e^{20} \left (589824 x^4+393216 x^5+65536 x^6\right )} \, dx=\frac {512 \, x^{2} e^{10} - 2560 \, x e^{5} + 3203}{256 \, x^{3} e^{10} + 768 \, x^{2} e^{10} - 1280 \, x^{2} e^{5} - 3840 \, x e^{5} + 1600 \, x + 4797} \] Input:
integrate((-131072*x^4*exp(5)^4+1310720*x^3*exp(5)^3+(-4917504*x^2-7680*x) *exp(5)^2+(8199680*x+19200)*exp(5)-5124800)/((65536*x^6+393216*x^5+589824* x^4)*exp(5)^4+(-655360*x^5-3932160*x^4-5898240*x^3)*exp(5)^3+(2457600*x^4+ 14744064*x^3+22113792*x^2)*exp(5)^2+(-4096000*x^3-24568320*x^2-36840960*x) *exp(5)+2560000*x^2+15350400*x+23011209),x, algorithm="giac")
Output:
(512*x^2*e^10 - 2560*x*e^5 + 3203)/(256*x^3*e^10 + 768*x^2*e^10 - 1280*x^2 *e^5 - 3840*x*e^5 + 1600*x + 4797)
Time = 0.19 (sec) , antiderivative size = 48, normalized size of antiderivative = 2.09 \[ \int \frac {-5124800+1310720 e^{15} x^3-131072 e^{20} x^4+e^5 (19200+8199680 x)+e^{10} \left (-7680 x-4917504 x^2\right )}{23011209+15350400 x+2560000 x^2+e^5 \left (-36840960 x-24568320 x^2-4096000 x^3\right )+e^{10} \left (22113792 x^2+14744064 x^3+2457600 x^4\right )+e^{15} \left (-5898240 x^3-3932160 x^4-655360 x^5\right )+e^{20} \left (589824 x^4+393216 x^5+65536 x^6\right )} \, dx=-\frac {512\,{\mathrm {e}}^{10}\,x^2-2560\,{\mathrm {e}}^5\,x+3203}{-256\,{\mathrm {e}}^{10}\,x^3+\left (1280\,{\mathrm {e}}^5-768\,{\mathrm {e}}^{10}\right )\,x^2+\left (3840\,{\mathrm {e}}^5-1600\right )\,x-4797} \] Input:
int(-(exp(10)*(7680*x + 4917504*x^2) - 1310720*x^3*exp(15) + 131072*x^4*ex p(20) - exp(5)*(8199680*x + 19200) + 5124800)/(15350400*x - exp(5)*(368409 60*x + 24568320*x^2 + 4096000*x^3) + exp(20)*(589824*x^4 + 393216*x^5 + 65 536*x^6) - exp(15)*(5898240*x^3 + 3932160*x^4 + 655360*x^5) + exp(10)*(221 13792*x^2 + 14744064*x^3 + 2457600*x^4) + 2560000*x^2 + 23011209),x)
Output:
-(512*x^2*exp(10) - 2560*x*exp(5) + 3203)/(x^2*(1280*exp(5) - 768*exp(10)) - 256*x^3*exp(10) + x*(3840*exp(5) - 1600) - 4797)
Time = 0.16 (sec) , antiderivative size = 86, normalized size of antiderivative = 3.74 \[ \int \frac {-5124800+1310720 e^{15} x^3-131072 e^{20} x^4+e^5 (19200+8199680 x)+e^{10} \left (-7680 x-4917504 x^2\right )}{23011209+15350400 x+2560000 x^2+e^5 \left (-36840960 x-24568320 x^2-4096000 x^3\right )+e^{10} \left (22113792 x^2+14744064 x^3+2457600 x^4\right )+e^{15} \left (-5898240 x^3-3932160 x^4-655360 x^5\right )+e^{20} \left (589824 x^4+393216 x^5+65536 x^6\right )} \, dx=\frac {-512 e^{15} x^{3}+9600 e^{5} x +15 e^{5}-16015}{768 e^{15} x^{3}+2304 e^{15} x^{2}-1280 e^{10} x^{3}-7680 e^{10} x^{2}-11520 e^{10} x +6400 e^{5} x^{2}+24000 e^{5} x +14391 e^{5}-8000 x -23985} \] Input:
int((-131072*x^4*exp(5)^4+1310720*x^3*exp(5)^3+(-4917504*x^2-7680*x)*exp(5 )^2+(8199680*x+19200)*exp(5)-5124800)/((65536*x^6+393216*x^5+589824*x^4)*e xp(5)^4+(-655360*x^5-3932160*x^4-5898240*x^3)*exp(5)^3+(2457600*x^4+147440 64*x^3+22113792*x^2)*exp(5)^2+(-4096000*x^3-24568320*x^2-36840960*x)*exp(5 )+2560000*x^2+15350400*x+23011209),x)
Output:
( - 512*e**15*x**3 + 9600*e**5*x + 15*e**5 - 16015)/(768*e**15*x**3 + 2304 *e**15*x**2 - 1280*e**10*x**3 - 7680*e**10*x**2 - 11520*e**10*x + 6400*e** 5*x**2 + 24000*e**5*x + 14391*e**5 - 8000*x - 23985)