Integrand size = 156, antiderivative size = 24 \[ \int \frac {76800-156160 x+36000 x^2+50200 x^3-31650 x^4+6750 x^5-500 x^6+e^{3 e} \left (512-896 x-384 x^2+256 x^3\right )+e^{2 e} \left (8192-15104 x-2784 x^2+5280 x^3-960 x^4\right )+e^e \left (43520-84352 x+2880 x^2+30200 x^3-11400 x^4+1200 x^5\right )}{8000+64 e^{3 e}+e^{2 e} (960-240 x)-6000 x+1500 x^2-125 x^3+e^e \left (4800-2400 x+300 x^2\right )} \, dx=\left (4+x+\frac {x}{5+e^e-\frac {5 x}{4}}-x^2\right )^2 \]
Leaf count is larger than twice the leaf count of optimal. \(157\) vs. \(2(24)=48\).
Time = 0.13 (sec) , antiderivative size = 157, normalized size of antiderivative = 6.54 \[ \int \frac {76800-156160 x+36000 x^2+50200 x^3-31650 x^4+6750 x^5-500 x^6+e^{3 e} \left (512-896 x-384 x^2+256 x^3\right )+e^{2 e} \left (8192-15104 x-2784 x^2+5280 x^3-960 x^4\right )+e^e \left (43520-84352 x+2880 x^2+30200 x^3-11400 x^4+1200 x^5\right )}{8000+64 e^{3 e}+e^{2 e} (960-240 x)-6000 x+1500 x^2-125 x^3+e^e \left (4800-2400 x+300 x^2\right )} \, dx=\frac {-4096 e^{6 e}+10240 e^{5 e} (-11+x)-1280 e^{4 e} \left (989-180 x+5 x^2\right )-3200 e^{3 e} \left (2324-629 x+35 x^2\right )+400 e^{2 e} \left (-60016+21520 x-1920 x^2-50 x^3+25 x^4\right )-1000 e^e \left (40064-18256 x+2720 x^2+45 x^3-150 x^4+25 x^5\right )+625 \left (-42496+25088 x-7040 x^2+600 x^3+665 x^4-250 x^5+25 x^6\right )}{625 \left (20+4 e^e-5 x\right )^2} \]
Integrate[(76800 - 156160*x + 36000*x^2 + 50200*x^3 - 31650*x^4 + 6750*x^5 - 500*x^6 + E^(3*E)*(512 - 896*x - 384*x^2 + 256*x^3) + E^(2*E)*(8192 - 1 5104*x - 2784*x^2 + 5280*x^3 - 960*x^4) + E^E*(43520 - 84352*x + 2880*x^2 + 30200*x^3 - 11400*x^4 + 1200*x^5))/(8000 + 64*E^(3*E) + E^(2*E)*(960 - 2 40*x) - 6000*x + 1500*x^2 - 125*x^3 + E^E*(4800 - 2400*x + 300*x^2)),x]
(-4096*E^(6*E) + 10240*E^(5*E)*(-11 + x) - 1280*E^(4*E)*(989 - 180*x + 5*x ^2) - 3200*E^(3*E)*(2324 - 629*x + 35*x^2) + 400*E^(2*E)*(-60016 + 21520*x - 1920*x^2 - 50*x^3 + 25*x^4) - 1000*E^E*(40064 - 18256*x + 2720*x^2 + 45 *x^3 - 150*x^4 + 25*x^5) + 625*(-42496 + 25088*x - 7040*x^2 + 600*x^3 + 66 5*x^4 - 250*x^5 + 25*x^6))/(625*(20 + 4*E^E - 5*x)^2)
Leaf count is larger than twice the leaf count of optimal. \(86\) vs. \(2(24)=48\).
Time = 0.52 (sec) , antiderivative size = 86, normalized size of antiderivative = 3.58, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {2007, 2389, 2009}
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.
| \(\displaystyle \int \frac {-500 x^6+6750 x^5-31650 x^4+50200 x^3+36000 x^2+e^{3 e} \left (256 x^3-384 x^2-896 x+512\right )+e^{2 e} \left (-960 x^4+5280 x^3-2784 x^2-15104 x+8192\right )+e^e \left (1200 x^5-11400 x^4+30200 x^3+2880 x^2-84352 x+43520\right )-156160 x+76800}{-125 x^3+1500 x^2+e^e \left (300 x^2-2400 x+4800\right )-6000 x+e^{2 e} (960-240 x)+64 e^{3 e}+8000} \, dx\) |
| \(\Big \downarrow \) 2007 |
| \(\displaystyle \int \frac {-500 x^6+6750 x^5-31650 x^4+50200 x^3+36000 x^2+e^{3 e} \left (256 x^3-384 x^2-896 x+512\right )+e^{2 e} \left (-960 x^4+5280 x^3-2784 x^2-15104 x+8192\right )+e^e \left (1200 x^5-11400 x^4+30200 x^3+2880 x^2-84352 x+43520\right )-156160 x+76800}{\left (4 \left (5+e^e\right )-5 x\right )^3}dx\) |
| \(\Big \downarrow \) 2389 |
| \(\displaystyle \int \left (4 x^3-6 x^2-\frac {54 x}{5}+\frac {128 \left (5+e^e\right ) \left (-55-35 e^e-4 e^{2 e}\right )}{25 \left (-5 x+4 e^e+20\right )^2}+\frac {512 \left (5+e^e\right )^2}{5 \left (-5 x+4 e^e+20\right )^3}+\frac {32}{25} \left (10+e^e\right )\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle x^4-2 x^3-\frac {27 x^2}{5}+\frac {32}{25} \left (10+e^e\right ) x-\frac {128 \left (5+e^e\right ) \left (55+35 e^e+4 e^{2 e}\right )}{125 \left (4 \left (5+e^e\right )-5 x\right )}+\frac {256 \left (5+e^e\right )^2}{25 \left (4 \left (5+e^e\right )-5 x\right )^2}\) |
Int[(76800 - 156160*x + 36000*x^2 + 50200*x^3 - 31650*x^4 + 6750*x^5 - 500 *x^6 + E^(3*E)*(512 - 896*x - 384*x^2 + 256*x^3) + E^(2*E)*(8192 - 15104*x - 2784*x^2 + 5280*x^3 - 960*x^4) + E^E*(43520 - 84352*x + 2880*x^2 + 3020 0*x^3 - 11400*x^4 + 1200*x^5))/(8000 + 64*E^(3*E) + E^(2*E)*(960 - 240*x) - 6000*x + 1500*x^2 - 125*x^3 + E^E*(4800 - 2400*x + 300*x^2)),x]
(256*(5 + E^E)^2)/(25*(4*(5 + E^E) - 5*x)^2) - (128*(5 + E^E)*(55 + 35*E^E + 4*E^(2*E)))/(125*(4*(5 + E^E) - 5*x)) + (32*(10 + E^E)*x)/25 - (27*x^2) /5 - 2*x^3 + x^4
3.6.45.3.1 Defintions of rubi rules used
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{a = Rt[Coeff[Px, x, 0], Expon[Px, x]], b = Rt[Coeff[Px, x, Expon[Px, x]], Expon[Px, x]]}, Int[u*(a + b*x)^(Ex pon[Px, x]*p), x] /; EqQ[Px, (a + b*x)^Expon[Px, x]]] /; IntegerQ[p] && Pol yQ[Px, x] && GtQ[Expon[Px, x], 1] && NeQ[Coeff[Px, x, 0], 0]
Int[(Pq_)*((a_) + (b_.)*(x_)^(n_.))^(p_.), x_Symbol] :> Int[ExpandIntegrand [Pq*(a + b*x^n)^p, x], x] /; FreeQ[{a, b, n}, x] && PolyQ[Pq, x] && (IGtQ[p , 0] || EqQ[n, 1])
Leaf count of result is larger than twice the leaf count of optimal. \(104\) vs. \(2(22)=44\).
Time = 0.11 (sec) , antiderivative size = 105, normalized size of antiderivative = 4.38
| method | result | size |
| risch | \(x^{4}-2 x^{3}+\frac {32 x \,{\mathrm e}^{{\mathrm e}}}{25}-\frac {27 x^{2}}{5}+\frac {64 x}{5}+\frac {\frac {\left (32 \,{\mathrm e}^{3 \,{\mathrm e}}+440 \,{\mathrm e}^{2 \,{\mathrm e}}+1840 \,{\mathrm e}^{{\mathrm e}}+2200\right ) x}{25}-\frac {128 \,{\mathrm e}^{4 \,{\mathrm e}}}{125}-\frac {96 \,{\mathrm e}^{3 \,{\mathrm e}}}{5}-\frac {3216 \,{\mathrm e}^{2 \,{\mathrm e}}}{25}-\frac {1792 \,{\mathrm e}^{{\mathrm e}}}{5}-336}{{\mathrm e}^{2 \,{\mathrm e}}-\frac {5 x \,{\mathrm e}^{{\mathrm e}}}{2}+\frac {25 x^{2}}{16}+10 \,{\mathrm e}^{{\mathrm e}}-\frac {25 x}{2}+25}\) | \(105\) |
| norman | \(\frac {\left (-40 \,{\mathrm e}^{{\mathrm e}}-250\right ) x^{5}+\left (-32 \,{\mathrm e}^{2 \,{\mathrm e}}-72 \,{\mathrm e}^{{\mathrm e}}+600\right ) x^{3}+\left (16 \,{\mathrm e}^{2 \,{\mathrm e}}+240 \,{\mathrm e}^{{\mathrm e}}+665\right ) x^{4}+\left (-\frac {896 \,{\mathrm e}^{3 \,{\mathrm e}}}{5}-\frac {15104 \,{\mathrm e}^{2 \,{\mathrm e}}}{5}-31232-\frac {84352 \,{\mathrm e}^{{\mathrm e}}}{5}\right ) x +25 x^{6}+\frac {1792 \,{\mathrm e}^{4 \,{\mathrm e}}}{25}+\frac {40448 \,{\mathrm e}^{3 \,{\mathrm e}}}{25}+\frac {340224 \,{\mathrm e}^{2 \,{\mathrm e}}}{25}+\frac {252928 \,{\mathrm e}^{{\mathrm e}}}{5}+70144}{\left (4 \,{\mathrm e}^{{\mathrm e}}-5 x +20\right )^{2}}\) | \(117\) |
| gosper | \(\frac {400 x^{4} {\mathrm e}^{2 \,{\mathrm e}}-1000 x^{5} {\mathrm e}^{{\mathrm e}}+625 x^{6}-800 \,{\mathrm e}^{2 \,{\mathrm e}} x^{3}+6000 x^{4} {\mathrm e}^{{\mathrm e}}-6250 x^{5}+1792 \,{\mathrm e}^{4 \,{\mathrm e}}-4480 \,{\mathrm e}^{3 \,{\mathrm e}} x -1800 x^{3} {\mathrm e}^{{\mathrm e}}+16625 x^{4}+40448 \,{\mathrm e}^{3 \,{\mathrm e}}-75520 \,{\mathrm e}^{2 \,{\mathrm e}} x +15000 x^{3}+340224 \,{\mathrm e}^{2 \,{\mathrm e}}-421760 x \,{\mathrm e}^{{\mathrm e}}+1264640 \,{\mathrm e}^{{\mathrm e}}-780800 x +1753600}{400 \,{\mathrm e}^{2 \,{\mathrm e}}-1000 x \,{\mathrm e}^{{\mathrm e}}+625 x^{2}+4000 \,{\mathrm e}^{{\mathrm e}}-5000 x +10000}\) | \(150\) |
| parallelrisch | \(\frac {400 x^{4} {\mathrm e}^{2 \,{\mathrm e}}-1000 x^{5} {\mathrm e}^{{\mathrm e}}+625 x^{6}-800 \,{\mathrm e}^{2 \,{\mathrm e}} x^{3}+6000 x^{4} {\mathrm e}^{{\mathrm e}}-6250 x^{5}+1792 \,{\mathrm e}^{4 \,{\mathrm e}}-4480 \,{\mathrm e}^{3 \,{\mathrm e}} x -1800 x^{3} {\mathrm e}^{{\mathrm e}}+16625 x^{4}+40448 \,{\mathrm e}^{3 \,{\mathrm e}}-75520 \,{\mathrm e}^{2 \,{\mathrm e}} x +15000 x^{3}+340224 \,{\mathrm e}^{2 \,{\mathrm e}}-421760 x \,{\mathrm e}^{{\mathrm e}}+1264640 \,{\mathrm e}^{{\mathrm e}}-780800 x +1753600}{400 \,{\mathrm e}^{2 \,{\mathrm e}}-1000 x \,{\mathrm e}^{{\mathrm e}}+625 x^{2}+4000 \,{\mathrm e}^{{\mathrm e}}-5000 x +10000}\) | \(150\) |
| default | \(x^{4}-2 x^{3}-\frac {27 x^{2}}{5}+\frac {32 x \,{\mathrm e}^{{\mathrm e}}}{25}+\frac {64 x}{5}-\frac {128 \left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (125 \textit {\_Z}^{3}+\left (-300 \,{\mathrm e}^{{\mathrm e}}-1500\right ) \textit {\_Z}^{2}+\left (2400 \,{\mathrm e}^{{\mathrm e}}+240 \,{\mathrm e}^{2 \,{\mathrm e}}+6000\right ) \textit {\_Z} -4800 \,{\mathrm e}^{{\mathrm e}}-960 \,{\mathrm e}^{2 \,{\mathrm e}}-64 \,{\mathrm e}^{3 \,{\mathrm e}}-8000\right )}{\sum }\frac {\left (-5000+1150 \textit {\_R} \,{\mathrm e}^{{\mathrm e}}+275 \,{\mathrm e}^{2 \,{\mathrm e}} \textit {\_R} +20 \,{\mathrm e}^{3 \,{\mathrm e}} \textit {\_R} -5500 \,{\mathrm e}^{{\mathrm e}}-16 \,{\mathrm e}^{4 \,{\mathrm e}}-2000 \,{\mathrm e}^{2 \,{\mathrm e}}-300 \,{\mathrm e}^{3 \,{\mathrm e}}+1375 \textit {\_R} \right ) \ln \left (x -\textit {\_R} \right )}{400+16 \,{\mathrm e}^{2 \,{\mathrm e}}-40 \textit {\_R} \,{\mathrm e}^{{\mathrm e}}+25 \textit {\_R}^{2}+160 \,{\mathrm e}^{{\mathrm e}}-200 \textit {\_R}}\right )}{375}\) | \(173\) |
int(((256*x^3-384*x^2-896*x+512)*exp(exp(1))^3+(-960*x^4+5280*x^3-2784*x^2 -15104*x+8192)*exp(exp(1))^2+(1200*x^5-11400*x^4+30200*x^3+2880*x^2-84352* x+43520)*exp(exp(1))-500*x^6+6750*x^5-31650*x^4+50200*x^3+36000*x^2-156160 *x+76800)/(64*exp(exp(1))^3+(-240*x+960)*exp(exp(1))^2+(300*x^2-2400*x+480 0)*exp(exp(1))-125*x^3+1500*x^2-6000*x+8000),x,method=_RETURNVERBOSE)
x^4-2*x^3+32/25*x*exp(exp(1))-27/5*x^2+64/5*x+(1/25*(32*exp(3*exp(1))+440* exp(2*exp(1))+1840*exp(exp(1))+2200)*x-128/125*exp(4*exp(1))-96/5*exp(3*ex p(1))-3216/25*exp(2*exp(1))-1792/5*exp(exp(1))-336)/(exp(2*exp(1))-5/2*x*e xp(exp(1))+25/16*x^2+10*exp(exp(1))-25/2*x+25)
Leaf count of result is larger than twice the leaf count of optimal. 135 vs. \(2 (25) = 50\).
Time = 0.25 (sec) , antiderivative size = 135, normalized size of antiderivative = 5.62 \[ \int \frac {76800-156160 x+36000 x^2+50200 x^3-31650 x^4+6750 x^5-500 x^6+e^{3 e} \left (512-896 x-384 x^2+256 x^3\right )+e^{2 e} \left (8192-15104 x-2784 x^2+5280 x^3-960 x^4\right )+e^e \left (43520-84352 x+2880 x^2+30200 x^3-11400 x^4+1200 x^5\right )}{8000+64 e^{3 e}+e^{2 e} (960-240 x)-6000 x+1500 x^2-125 x^3+e^e \left (4800-2400 x+300 x^2\right )} \, dx=\frac {3125 \, x^{6} - 31250 \, x^{5} + 83125 \, x^{4} + 75000 \, x^{3} - 590000 \, x^{2} + 2560 \, {\left (2 \, x - 15\right )} e^{\left (3 \, e\right )} + 80 \, {\left (25 \, x^{4} - 50 \, x^{3} - 215 \, x^{2} + 1080 \, x - 3216\right )} e^{\left (2 \, e\right )} - 200 \, {\left (25 \, x^{5} - 150 \, x^{4} + 45 \, x^{3} + 1020 \, x^{2} - 2336 \, x + 3584\right )} e^{e} + 816000 \, x - 2048 \, e^{\left (4 \, e\right )} - 672000}{125 \, {\left (25 \, x^{2} - 40 \, {\left (x - 4\right )} e^{e} - 200 \, x + 16 \, e^{\left (2 \, e\right )} + 400\right )}} \]
integrate(((256*x^3-384*x^2-896*x+512)*exp(exp(1))^3+(-960*x^4+5280*x^3-27 84*x^2-15104*x+8192)*exp(exp(1))^2+(1200*x^5-11400*x^4+30200*x^3+2880*x^2- 84352*x+43520)*exp(exp(1))-500*x^6+6750*x^5-31650*x^4+50200*x^3+36000*x^2- 156160*x+76800)/(64*exp(exp(1))^3+(-240*x+960)*exp(exp(1))^2+(300*x^2-2400 *x+4800)*exp(exp(1))-125*x^3+1500*x^2-6000*x+8000),x, algorithm=\
1/125*(3125*x^6 - 31250*x^5 + 83125*x^4 + 75000*x^3 - 590000*x^2 + 2560*(2 *x - 15)*e^(3*e) + 80*(25*x^4 - 50*x^3 - 215*x^2 + 1080*x - 3216)*e^(2*e) - 200*(25*x^5 - 150*x^4 + 45*x^3 + 1020*x^2 - 2336*x + 3584)*e^e + 816000* x - 2048*e^(4*e) - 672000)/(25*x^2 - 40*(x - 4)*e^e - 200*x + 16*e^(2*e) + 400)
Leaf count of result is larger than twice the leaf count of optimal. 122 vs. \(2 (20) = 40\).
Time = 0.58 (sec) , antiderivative size = 122, normalized size of antiderivative = 5.08 \[ \int \frac {76800-156160 x+36000 x^2+50200 x^3-31650 x^4+6750 x^5-500 x^6+e^{3 e} \left (512-896 x-384 x^2+256 x^3\right )+e^{2 e} \left (8192-15104 x-2784 x^2+5280 x^3-960 x^4\right )+e^e \left (43520-84352 x+2880 x^2+30200 x^3-11400 x^4+1200 x^5\right )}{8000+64 e^{3 e}+e^{2 e} (960-240 x)-6000 x+1500 x^2-125 x^3+e^e \left (4800-2400 x+300 x^2\right )} \, dx=x^{4} - 2 x^{3} - \frac {27 x^{2}}{5} + x \left (\frac {64}{5} + \frac {32 e^{e}}{25}\right ) + \frac {x \left (176000 + 147200 e^{e} + 35200 e^{2 e} + 2560 e^{3 e}\right ) - 38400 e^{3 e} - 2048 e^{4 e} - 257280 e^{2 e} - 716800 e^{e} - 672000}{3125 x^{2} + x \left (- 5000 e^{e} - 25000\right ) + 50000 + 20000 e^{e} + 2000 e^{2 e}} \]
integrate(((256*x**3-384*x**2-896*x+512)*exp(exp(1))**3+(-960*x**4+5280*x* *3-2784*x**2-15104*x+8192)*exp(exp(1))**2+(1200*x**5-11400*x**4+30200*x**3 +2880*x**2-84352*x+43520)*exp(exp(1))-500*x**6+6750*x**5-31650*x**4+50200* x**3+36000*x**2-156160*x+76800)/(64*exp(exp(1))**3+(-240*x+960)*exp(exp(1) )**2+(300*x**2-2400*x+4800)*exp(exp(1))-125*x**3+1500*x**2-6000*x+8000),x)
x**4 - 2*x**3 - 27*x**2/5 + x*(64/5 + 32*exp(E)/25) + (x*(176000 + 147200* exp(E) + 35200*exp(2*E) + 2560*exp(3*E)) - 38400*exp(3*E) - 2048*exp(4*E) - 257280*exp(2*E) - 716800*exp(E) - 672000)/(3125*x**2 + x*(-5000*exp(E) - 25000) + 50000 + 20000*exp(E) + 2000*exp(2*E))
Leaf count of result is larger than twice the leaf count of optimal. 105 vs. \(2 (25) = 50\).
Time = 0.19 (sec) , antiderivative size = 105, normalized size of antiderivative = 4.38 \[ \int \frac {76800-156160 x+36000 x^2+50200 x^3-31650 x^4+6750 x^5-500 x^6+e^{3 e} \left (512-896 x-384 x^2+256 x^3\right )+e^{2 e} \left (8192-15104 x-2784 x^2+5280 x^3-960 x^4\right )+e^e \left (43520-84352 x+2880 x^2+30200 x^3-11400 x^4+1200 x^5\right )}{8000+64 e^{3 e}+e^{2 e} (960-240 x)-6000 x+1500 x^2-125 x^3+e^e \left (4800-2400 x+300 x^2\right )} \, dx=x^{4} - 2 \, x^{3} - \frac {27}{5} \, x^{2} + \frac {32}{25} \, x {\left (e^{e} + 10\right )} + \frac {128 \, {\left (5 \, x {\left (4 \, e^{\left (3 \, e\right )} + 55 \, e^{\left (2 \, e\right )} + 230 \, e^{e} + 275\right )} - 16 \, e^{\left (4 \, e\right )} - 300 \, e^{\left (3 \, e\right )} - 2010 \, e^{\left (2 \, e\right )} - 5600 \, e^{e} - 5250\right )}}{125 \, {\left (25 \, x^{2} - 40 \, x {\left (e^{e} + 5\right )} + 16 \, e^{\left (2 \, e\right )} + 160 \, e^{e} + 400\right )}} \]
integrate(((256*x^3-384*x^2-896*x+512)*exp(exp(1))^3+(-960*x^4+5280*x^3-27 84*x^2-15104*x+8192)*exp(exp(1))^2+(1200*x^5-11400*x^4+30200*x^3+2880*x^2- 84352*x+43520)*exp(exp(1))-500*x^6+6750*x^5-31650*x^4+50200*x^3+36000*x^2- 156160*x+76800)/(64*exp(exp(1))^3+(-240*x+960)*exp(exp(1))^2+(300*x^2-2400 *x+4800)*exp(exp(1))-125*x^3+1500*x^2-6000*x+8000),x, algorithm=\
x^4 - 2*x^3 - 27/5*x^2 + 32/25*x*(e^e + 10) + 128/125*(5*x*(4*e^(3*e) + 55 *e^(2*e) + 230*e^e + 275) - 16*e^(4*e) - 300*e^(3*e) - 2010*e^(2*e) - 5600 *e^e - 5250)/(25*x^2 - 40*x*(e^e + 5) + 16*e^(2*e) + 160*e^e + 400)
\[ \int \frac {76800-156160 x+36000 x^2+50200 x^3-31650 x^4+6750 x^5-500 x^6+e^{3 e} \left (512-896 x-384 x^2+256 x^3\right )+e^{2 e} \left (8192-15104 x-2784 x^2+5280 x^3-960 x^4\right )+e^e \left (43520-84352 x+2880 x^2+30200 x^3-11400 x^4+1200 x^5\right )}{8000+64 e^{3 e}+e^{2 e} (960-240 x)-6000 x+1500 x^2-125 x^3+e^e \left (4800-2400 x+300 x^2\right )} \, dx=\int { \frac {2 \, {\left (250 \, x^{6} - 3375 \, x^{5} + 15825 \, x^{4} - 25100 \, x^{3} - 18000 \, x^{2} - 64 \, {\left (2 \, x^{3} - 3 \, x^{2} - 7 \, x + 4\right )} e^{\left (3 \, e\right )} + 16 \, {\left (30 \, x^{4} - 165 \, x^{3} + 87 \, x^{2} + 472 \, x - 256\right )} e^{\left (2 \, e\right )} - 4 \, {\left (150 \, x^{5} - 1425 \, x^{4} + 3775 \, x^{3} + 360 \, x^{2} - 10544 \, x + 5440\right )} e^{e} + 78080 \, x - 38400\right )}}{125 \, x^{3} - 1500 \, x^{2} + 240 \, {\left (x - 4\right )} e^{\left (2 \, e\right )} - 300 \, {\left (x^{2} - 8 \, x + 16\right )} e^{e} + 6000 \, x - 64 \, e^{\left (3 \, e\right )} - 8000} \,d x } \]
integrate(((256*x^3-384*x^2-896*x+512)*exp(exp(1))^3+(-960*x^4+5280*x^3-27 84*x^2-15104*x+8192)*exp(exp(1))^2+(1200*x^5-11400*x^4+30200*x^3+2880*x^2- 84352*x+43520)*exp(exp(1))-500*x^6+6750*x^5-31650*x^4+50200*x^3+36000*x^2- 156160*x+76800)/(64*exp(exp(1))^3+(-240*x+960)*exp(exp(1))^2+(300*x^2-2400 *x+4800)*exp(exp(1))-125*x^3+1500*x^2-6000*x+8000),x, algorithm=\
integrate(2*(250*x^6 - 3375*x^5 + 15825*x^4 - 25100*x^3 - 18000*x^2 - 64*( 2*x^3 - 3*x^2 - 7*x + 4)*e^(3*e) + 16*(30*x^4 - 165*x^3 + 87*x^2 + 472*x - 256)*e^(2*e) - 4*(150*x^5 - 1425*x^4 + 3775*x^3 + 360*x^2 - 10544*x + 544 0)*e^e + 78080*x - 38400)/(125*x^3 - 1500*x^2 + 240*(x - 4)*e^(2*e) - 300* (x^2 - 8*x + 16)*e^e + 6000*x - 64*e^(3*e) - 8000), x)
Time = 8.21 (sec) , antiderivative size = 195, normalized size of antiderivative = 8.12 \[ \int \frac {76800-156160 x+36000 x^2+50200 x^3-31650 x^4+6750 x^5-500 x^6+e^{3 e} \left (512-896 x-384 x^2+256 x^3\right )+e^{2 e} \left (8192-15104 x-2784 x^2+5280 x^3-960 x^4\right )+e^e \left (43520-84352 x+2880 x^2+30200 x^3-11400 x^4+1200 x^5\right )}{8000+64 e^{3 e}+e^{2 e} (960-240 x)-6000 x+1500 x^2-125 x^3+e^e \left (4800-2400 x+300 x^2\right )} \, dx=x^2\,\left (\frac {96\,{\mathrm {e}}^{2\,\mathrm {e}}}{25}+\frac {192\,{\mathrm {e}}^{\mathrm {e}}}{5}-\frac {96\,{\left ({\mathrm {e}}^{\mathrm {e}}+5\right )}^2}{25}+\frac {453}{5}\right )-x\,\left (\frac {1056\,{\mathrm {e}}^{2\,\mathrm {e}}}{25}+\frac {256\,{\mathrm {e}}^{3\,\mathrm {e}}}{125}+\frac {1208\,{\mathrm {e}}^{\mathrm {e}}}{5}-\frac {288\,{\left ({\mathrm {e}}^{\mathrm {e}}+5\right )}^2}{25}-\frac {256\,{\left ({\mathrm {e}}^{\mathrm {e}}+5\right )}^3}{125}-\left (\frac {12\,{\mathrm {e}}^{\mathrm {e}}}{5}+12\right )\,\left (\frac {192\,{\mathrm {e}}^{2\,\mathrm {e}}}{25}+\frac {384\,{\mathrm {e}}^{\mathrm {e}}}{5}-\frac {192\,{\left ({\mathrm {e}}^{\mathrm {e}}+5\right )}^2}{25}+\frac {906}{5}\right )+\frac {2008}{5}\right )-\frac {51456\,{\mathrm {e}}^{2\,\mathrm {e}}+7680\,{\mathrm {e}}^{3\,\mathrm {e}}+\frac {2048\,{\mathrm {e}}^{4\,\mathrm {e}}}{5}+143360\,{\mathrm {e}}^{\mathrm {e}}-x\,\left (7040\,{\mathrm {e}}^{2\,\mathrm {e}}+512\,{\mathrm {e}}^{3\,\mathrm {e}}+29440\,{\mathrm {e}}^{\mathrm {e}}+35200\right )+134400}{625\,x^2+\left (-1000\,{\mathrm {e}}^{\mathrm {e}}-5000\right )\,x+400\,{\mathrm {e}}^{2\,\mathrm {e}}+4000\,{\mathrm {e}}^{\mathrm {e}}+10000}-2\,x^3+x^4 \]
int(-(156160*x + exp(3*exp(1))*(896*x + 384*x^2 - 256*x^3 - 512) - exp(exp (1))*(2880*x^2 - 84352*x + 30200*x^3 - 11400*x^4 + 1200*x^5 + 43520) + exp (2*exp(1))*(15104*x + 2784*x^2 - 5280*x^3 + 960*x^4 - 8192) - 36000*x^2 - 50200*x^3 + 31650*x^4 - 6750*x^5 + 500*x^6 - 76800)/(64*exp(3*exp(1)) - 60 00*x + exp(exp(1))*(300*x^2 - 2400*x + 4800) - exp(2*exp(1))*(240*x - 960) + 1500*x^2 - 125*x^3 + 8000),x)
x^2*((96*exp(2*exp(1)))/25 + (192*exp(exp(1)))/5 - (96*(exp(exp(1)) + 5)^2 )/25 + 453/5) - x*((1056*exp(2*exp(1)))/25 + (256*exp(3*exp(1)))/125 + (12 08*exp(exp(1)))/5 - (288*(exp(exp(1)) + 5)^2)/25 - (256*(exp(exp(1)) + 5)^ 3)/125 - ((12*exp(exp(1)))/5 + 12)*((192*exp(2*exp(1)))/25 + (384*exp(exp( 1)))/5 - (192*(exp(exp(1)) + 5)^2)/25 + 906/5) + 2008/5) - (51456*exp(2*ex p(1)) + 7680*exp(3*exp(1)) + (2048*exp(4*exp(1)))/5 + 143360*exp(exp(1)) - x*(7040*exp(2*exp(1)) + 512*exp(3*exp(1)) + 29440*exp(exp(1)) + 35200) + 134400)/(400*exp(2*exp(1)) + 4000*exp(exp(1)) - x*(1000*exp(exp(1)) + 5000 ) + 625*x^2 + 10000) - 2*x^3 + x^4