Integrand size = 260, antiderivative size = 30 \[ \int \frac {112+49 x+e^{2 x} \left (-2960-1061 x+211 x^2+28 x^3\right )+e^{4 x} \left (30800+5360 x-4464 x^2+112 x^3+64 x^4\right )+e^{6 x} \left (-158000+9600 x+28720 x^2-6784 x^3+224 x^4+32 x^5\right )+e^{8 x} \left (400000-120000 x-64000 x^2+35200 x^3-5760 x^4+320 x^5\right )+e^{10 x} \left (-400000+200000 x+40000 x^2-48000 x^3+12800 x^4-1472 x^5+64 x^6\right )}{32+e^{2 x} (-800+160 x)+e^{4 x} \left (8000-3200 x+320 x^2\right )+e^{6 x} \left (-40000+24000 x-4800 x^2+320 x^3\right )+e^{8 x} \left (100000-80000 x+24000 x^2-3200 x^3+160 x^4\right )+e^{10 x} \left (-100000+100000 x-40000 x^2+8000 x^3-800 x^4+32 x^5\right )} \, dx=-5+\left (-2-x+\frac {x}{8 \left (1-e^{2 x} (5-x)\right )^2}\right )^2 \]
Leaf count is larger than twice the leaf count of optimal. \(63\) vs. \(2(30)=60\).
Time = 19.45 (sec) , antiderivative size = 63, normalized size of antiderivative = 2.10 \[ \int \frac {112+49 x+e^{2 x} \left (-2960-1061 x+211 x^2+28 x^3\right )+e^{4 x} \left (30800+5360 x-4464 x^2+112 x^3+64 x^4\right )+e^{6 x} \left (-158000+9600 x+28720 x^2-6784 x^3+224 x^4+32 x^5\right )+e^{8 x} \left (400000-120000 x-64000 x^2+35200 x^3-5760 x^4+320 x^5\right )+e^{10 x} \left (-400000+200000 x+40000 x^2-48000 x^3+12800 x^4-1472 x^5+64 x^6\right )}{32+e^{2 x} (-800+160 x)+e^{4 x} \left (8000-3200 x+320 x^2\right )+e^{6 x} \left (-40000+24000 x-4800 x^2+320 x^3\right )+e^{8 x} \left (100000-80000 x+24000 x^2-3200 x^3+160 x^4\right )+e^{10 x} \left (-100000+100000 x-40000 x^2+8000 x^3-800 x^4+32 x^5\right )} \, dx=\frac {1}{32} \left (-1440+\left (128-\frac {16}{\left (1+e^{2 x} (-5+x)\right )^2}\right ) x+\left (32+\frac {1}{2 \left (1+e^{2 x} (-5+x)\right )^4}-\frac {8}{\left (1+e^{2 x} (-5+x)\right )^2}\right ) x^2\right ) \]
Integrate[(112 + 49*x + E^(2*x)*(-2960 - 1061*x + 211*x^2 + 28*x^3) + E^(4 *x)*(30800 + 5360*x - 4464*x^2 + 112*x^3 + 64*x^4) + E^(6*x)*(-158000 + 96 00*x + 28720*x^2 - 6784*x^3 + 224*x^4 + 32*x^5) + E^(8*x)*(400000 - 120000 *x - 64000*x^2 + 35200*x^3 - 5760*x^4 + 320*x^5) + E^(10*x)*(-400000 + 200 000*x + 40000*x^2 - 48000*x^3 + 12800*x^4 - 1472*x^5 + 64*x^6))/(32 + E^(2 *x)*(-800 + 160*x) + E^(4*x)*(8000 - 3200*x + 320*x^2) + E^(6*x)*(-40000 + 24000*x - 4800*x^2 + 320*x^3) + E^(8*x)*(100000 - 80000*x + 24000*x^2 - 3 200*x^3 + 160*x^4) + E^(10*x)*(-100000 + 100000*x - 40000*x^2 + 8000*x^3 - 800*x^4 + 32*x^5)),x]
(-1440 + (128 - 16/(1 + E^(2*x)*(-5 + x))^2)*x + (32 + 1/(2*(1 + E^(2*x)*( -5 + x))^4) - 8/(1 + E^(2*x)*(-5 + x))^2)*x^2)/32
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.
| \(\displaystyle \int \frac {e^{2 x} \left (28 x^3+211 x^2-1061 x-2960\right )+e^{4 x} \left (64 x^4+112 x^3-4464 x^2+5360 x+30800\right )+e^{6 x} \left (32 x^5+224 x^4-6784 x^3+28720 x^2+9600 x-158000\right )+e^{8 x} \left (320 x^5-5760 x^4+35200 x^3-64000 x^2-120000 x+400000\right )+e^{10 x} \left (64 x^6-1472 x^5+12800 x^4-48000 x^3+40000 x^2+200000 x-400000\right )+49 x+112}{e^{4 x} \left (320 x^2-3200 x+8000\right )+e^{6 x} \left (320 x^3-4800 x^2+24000 x-40000\right )+e^{8 x} \left (160 x^4-3200 x^3+24000 x^2-80000 x+100000\right )+e^{10 x} \left (32 x^5-800 x^4+8000 x^3-40000 x^2+100000 x-100000\right )+e^{2 x} (160 x-800)+32} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {16 e^{6 x} \left (2 x^3+34 x^2-134 x-395\right ) (x-5)^2+e^{2 x} \left (28 x^3+211 x^2-1061 x-2960\right )+16 e^{4 x} \left (4 x^4+7 x^3-279 x^2+335 x+1925\right )+64 e^{10 x} (x+2) (x-5)^5+320 e^{8 x} (x+2) (x-5)^4+7 (7 x+16)}{32 \left (e^{2 x} (x-5)+1\right )^5}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{32} \int \frac {-64 e^{10 x} (x+2) (5-x)^5+320 e^{8 x} (x+2) (5-x)^4-16 e^{6 x} \left (-2 x^3-34 x^2+134 x+395\right ) (5-x)^2+7 (7 x+16)-e^{2 x} \left (-28 x^3-211 x^2+1061 x+2960\right )+16 e^{4 x} \left (4 x^4+7 x^3-279 x^2+335 x+1925\right )}{\left (1-e^{2 x} (5-x)\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{32} \int \left (\frac {2 (2 x-9) x^2}{(x-5) \left (e^{2 x} x-5 e^{2 x}+1\right )^5}-\frac {16 \left (2 x^2-5 x-18\right ) x}{(x-5) \left (e^{2 x} x-5 e^{2 x}+1\right )^3}-\frac {\left (4 x^2-19 x+5\right ) x}{(x-5) \left (e^{2 x} x-5 e^{2 x}+1\right )^4}+64 (x+2)+\frac {16 \left (2 x^3-6 x^2-14 x+5\right )}{(x-5) \left (e^{2 x} x-5 e^{2 x}+1\right )^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {1}{32} \left (4 \int \frac {x^2}{\left (e^{2 x} x-5 e^{2 x}+1\right )^5}dx-4 \int \frac {x^2}{\left (e^{2 x} x-5 e^{2 x}+1\right )^4}dx-32 \int \frac {x^2}{\left (e^{2 x} x-5 e^{2 x}+1\right )^3}dx+32 \int \frac {x^2}{\left (e^{2 x} x-5 e^{2 x}+1\right )^2}dx+10 \int \frac {1}{\left (e^{2 x} x-5 e^{2 x}+1\right )^5}dx+50 \int \frac {1}{(x-5) \left (e^{2 x} x-5 e^{2 x}+1\right )^5}dx+2 \int \frac {x}{\left (e^{2 x} x-5 e^{2 x}+1\right )^5}dx-10 \int \frac {1}{\left (e^{2 x} x-5 e^{2 x}+1\right )^4}dx-50 \int \frac {1}{(x-5) \left (e^{2 x} x-5 e^{2 x}+1\right )^4}dx-\int \frac {x}{\left (e^{2 x} x-5 e^{2 x}+1\right )^4}dx-112 \int \frac {1}{\left (e^{2 x} x-5 e^{2 x}+1\right )^3}dx-560 \int \frac {1}{(x-5) \left (e^{2 x} x-5 e^{2 x}+1\right )^3}dx-80 \int \frac {x}{\left (e^{2 x} x-5 e^{2 x}+1\right )^3}dx+96 \int \frac {1}{\left (e^{2 x} x-5 e^{2 x}+1\right )^2}dx+560 \int \frac {1}{(x-5) \left (e^{2 x} x-5 e^{2 x}+1\right )^2}dx+64 \int \frac {x}{\left (e^{2 x} x-5 e^{2 x}+1\right )^2}dx+32 (x+2)^2\right )\) |
Int[(112 + 49*x + E^(2*x)*(-2960 - 1061*x + 211*x^2 + 28*x^3) + E^(4*x)*(3 0800 + 5360*x - 4464*x^2 + 112*x^3 + 64*x^4) + E^(6*x)*(-158000 + 9600*x + 28720*x^2 - 6784*x^3 + 224*x^4 + 32*x^5) + E^(8*x)*(400000 - 120000*x - 6 4000*x^2 + 35200*x^3 - 5760*x^4 + 320*x^5) + E^(10*x)*(-400000 + 200000*x + 40000*x^2 - 48000*x^3 + 12800*x^4 - 1472*x^5 + 64*x^6))/(32 + E^(2*x)*(- 800 + 160*x) + E^(4*x)*(8000 - 3200*x + 320*x^2) + E^(6*x)*(-40000 + 24000 *x - 4800*x^2 + 320*x^3) + E^(8*x)*(100000 - 80000*x + 24000*x^2 - 3200*x^ 3 + 160*x^4) + E^(10*x)*(-100000 + 100000*x - 40000*x^2 + 8000*x^3 - 800*x ^4 + 32*x^5)),x]
3.4.22.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(84\) vs. \(2(27)=54\).
Time = 0.41 (sec) , antiderivative size = 85, normalized size of antiderivative = 2.83
| method | result | size |
| risch | \(x^{2}+4 x -\frac {x \left (16 x^{3} {\mathrm e}^{4 x}-128 x^{2} {\mathrm e}^{4 x}+80 x \,{\mathrm e}^{4 x}+32 \,{\mathrm e}^{2 x} x^{2}+800 \,{\mathrm e}^{4 x}-96 x \,{\mathrm e}^{2 x}-320 \,{\mathrm e}^{2 x}+15 x +32\right )}{64 \left (x \,{\mathrm e}^{2 x}-5 \,{\mathrm e}^{2 x}+1\right )^{4}}\) | \(85\) |
| parallelrisch | \(\frac {22400+6720 x +720000 \,{\mathrm e}^{8 x} x^{2}+204800 \,{\mathrm e}^{6 x} x^{3}+11040 \,{\mathrm e}^{4 x} x^{4}-65280 x^{3} {\mathrm e}^{4 x}+2880000 x \,{\mathrm e}^{6 x}-4800 \,{\mathrm e}^{2 x} x^{2}-54400 x \,{\mathrm e}^{2 x}+1920 x^{6} {\mathrm e}^{8 x}-11200000 \,{\mathrm e}^{6 x}-40800 x^{2} {\mathrm e}^{4 x}-6400000 x \,{\mathrm e}^{8 x}-216000 x \,{\mathrm e}^{4 x}+14000000 \,{\mathrm e}^{8 x}+6720 \,{\mathrm e}^{2 x} x^{3}+3360000 \,{\mathrm e}^{4 x}+1470 x^{2}-448000 \,{\mathrm e}^{2 x}-30720 \,{\mathrm e}^{8 x} x^{5}+156800 \,{\mathrm e}^{8 x} x^{4}-256000 \,{\mathrm e}^{8 x} x^{3}+7680 \,{\mathrm e}^{6 x} x^{5}-84480 \,{\mathrm e}^{6 x} x^{4}}{1920 \,{\mathrm e}^{8 x} x^{4}-38400 \,{\mathrm e}^{8 x} x^{3}+288000 \,{\mathrm e}^{8 x} x^{2}+7680 \,{\mathrm e}^{6 x} x^{3}-960000 x \,{\mathrm e}^{8 x}-115200 \,{\mathrm e}^{6 x} x^{2}+1200000 \,{\mathrm e}^{8 x}+576000 x \,{\mathrm e}^{6 x}+11520 x^{2} {\mathrm e}^{4 x}-960000 \,{\mathrm e}^{6 x}-115200 x \,{\mathrm e}^{4 x}+288000 \,{\mathrm e}^{4 x}+7680 x \,{\mathrm e}^{2 x}-38400 \,{\mathrm e}^{2 x}+1920}\) | \(291\) |
int(((64*x^6-1472*x^5+12800*x^4-48000*x^3+40000*x^2+200000*x-400000)*exp(x )^10+(320*x^5-5760*x^4+35200*x^3-64000*x^2-120000*x+400000)*exp(x)^8+(32*x ^5+224*x^4-6784*x^3+28720*x^2+9600*x-158000)*exp(x)^6+(64*x^4+112*x^3-4464 *x^2+5360*x+30800)*exp(x)^4+(28*x^3+211*x^2-1061*x-2960)*exp(x)^2+49*x+112 )/((32*x^5-800*x^4+8000*x^3-40000*x^2+100000*x-100000)*exp(x)^10+(160*x^4- 3200*x^3+24000*x^2-80000*x+100000)*exp(x)^8+(320*x^3-4800*x^2+24000*x-4000 0)*exp(x)^6+(320*x^2-3200*x+8000)*exp(x)^4+(160*x-800)*exp(x)^2+32),x,meth od=_RETURNVERBOSE)
x^2+4*x-1/64*x*(16*x^3*exp(4*x)-128*x^2*exp(4*x)+80*x*exp(4*x)+32*exp(2*x) *x^2+800*exp(4*x)-96*x*exp(2*x)-320*exp(2*x)+15*x+32)/(x*exp(2*x)-5*exp(2* x)+1)^4
Leaf count of result is larger than twice the leaf count of optimal. 186 vs. \(2 (26) = 52\).
Time = 0.25 (sec) , antiderivative size = 186, normalized size of antiderivative = 6.20 \[ \int \frac {112+49 x+e^{2 x} \left (-2960-1061 x+211 x^2+28 x^3\right )+e^{4 x} \left (30800+5360 x-4464 x^2+112 x^3+64 x^4\right )+e^{6 x} \left (-158000+9600 x+28720 x^2-6784 x^3+224 x^4+32 x^5\right )+e^{8 x} \left (400000-120000 x-64000 x^2+35200 x^3-5760 x^4+320 x^5\right )+e^{10 x} \left (-400000+200000 x+40000 x^2-48000 x^3+12800 x^4-1472 x^5+64 x^6\right )}{32+e^{2 x} (-800+160 x)+e^{4 x} \left (8000-3200 x+320 x^2\right )+e^{6 x} \left (-40000+24000 x-4800 x^2+320 x^3\right )+e^{8 x} \left (100000-80000 x+24000 x^2-3200 x^3+160 x^4\right )+e^{10 x} \left (-100000+100000 x-40000 x^2+8000 x^3-800 x^4+32 x^5\right )} \, dx=\frac {49 \, x^{2} + 64 \, {\left (x^{6} - 16 \, x^{5} + 70 \, x^{4} + 100 \, x^{3} - 1375 \, x^{2} + 2500 \, x\right )} e^{\left (8 \, x\right )} + 256 \, {\left (x^{5} - 11 \, x^{4} + 15 \, x^{3} + 175 \, x^{2} - 500 \, x\right )} e^{\left (6 \, x\right )} + 16 \, {\left (23 \, x^{4} - 136 \, x^{3} - 365 \, x^{2} + 2350 \, x\right )} e^{\left (4 \, x\right )} + 32 \, {\left (7 \, x^{3} - 5 \, x^{2} - 150 \, x\right )} e^{\left (2 \, x\right )} + 224 \, x}{64 \, {\left ({\left (x^{4} - 20 \, x^{3} + 150 \, x^{2} - 500 \, x + 625\right )} e^{\left (8 \, x\right )} + 4 \, {\left (x^{3} - 15 \, x^{2} + 75 \, x - 125\right )} e^{\left (6 \, x\right )} + 6 \, {\left (x^{2} - 10 \, x + 25\right )} e^{\left (4 \, x\right )} + 4 \, {\left (x - 5\right )} e^{\left (2 \, x\right )} + 1\right )}} \]
integrate(((64*x^6-1472*x^5+12800*x^4-48000*x^3+40000*x^2+200000*x-400000) *exp(x)^10+(320*x^5-5760*x^4+35200*x^3-64000*x^2-120000*x+400000)*exp(x)^8 +(32*x^5+224*x^4-6784*x^3+28720*x^2+9600*x-158000)*exp(x)^6+(64*x^4+112*x^ 3-4464*x^2+5360*x+30800)*exp(x)^4+(28*x^3+211*x^2-1061*x-2960)*exp(x)^2+49 *x+112)/((32*x^5-800*x^4+8000*x^3-40000*x^2+100000*x-100000)*exp(x)^10+(16 0*x^4-3200*x^3+24000*x^2-80000*x+100000)*exp(x)^8+(320*x^3-4800*x^2+24000* x-40000)*exp(x)^6+(320*x^2-3200*x+8000)*exp(x)^4+(160*x-800)*exp(x)^2+32), x, algorithm=\
1/64*(49*x^2 + 64*(x^6 - 16*x^5 + 70*x^4 + 100*x^3 - 1375*x^2 + 2500*x)*e^ (8*x) + 256*(x^5 - 11*x^4 + 15*x^3 + 175*x^2 - 500*x)*e^(6*x) + 16*(23*x^4 - 136*x^3 - 365*x^2 + 2350*x)*e^(4*x) + 32*(7*x^3 - 5*x^2 - 150*x)*e^(2*x ) + 224*x)/((x^4 - 20*x^3 + 150*x^2 - 500*x + 625)*e^(8*x) + 4*(x^3 - 15*x ^2 + 75*x - 125)*e^(6*x) + 6*(x^2 - 10*x + 25)*e^(4*x) + 4*(x - 5)*e^(2*x) + 1)
Leaf count of result is larger than twice the leaf count of optimal. 129 vs. \(2 (20) = 40\).
Time = 0.37 (sec) , antiderivative size = 129, normalized size of antiderivative = 4.30 \[ \int \frac {112+49 x+e^{2 x} \left (-2960-1061 x+211 x^2+28 x^3\right )+e^{4 x} \left (30800+5360 x-4464 x^2+112 x^3+64 x^4\right )+e^{6 x} \left (-158000+9600 x+28720 x^2-6784 x^3+224 x^4+32 x^5\right )+e^{8 x} \left (400000-120000 x-64000 x^2+35200 x^3-5760 x^4+320 x^5\right )+e^{10 x} \left (-400000+200000 x+40000 x^2-48000 x^3+12800 x^4-1472 x^5+64 x^6\right )}{32+e^{2 x} (-800+160 x)+e^{4 x} \left (8000-3200 x+320 x^2\right )+e^{6 x} \left (-40000+24000 x-4800 x^2+320 x^3\right )+e^{8 x} \left (100000-80000 x+24000 x^2-3200 x^3+160 x^4\right )+e^{10 x} \left (-100000+100000 x-40000 x^2+8000 x^3-800 x^4+32 x^5\right )} \, dx=x^{2} + 4 x + \frac {- 15 x^{2} - 32 x + \left (- 32 x^{3} + 96 x^{2} + 320 x\right ) e^{2 x} + \left (- 16 x^{4} + 128 x^{3} - 80 x^{2} - 800 x\right ) e^{4 x}}{\left (256 x - 1280\right ) e^{2 x} + \left (384 x^{2} - 3840 x + 9600\right ) e^{4 x} + \left (256 x^{3} - 3840 x^{2} + 19200 x - 32000\right ) e^{6 x} + \left (64 x^{4} - 1280 x^{3} + 9600 x^{2} - 32000 x + 40000\right ) e^{8 x} + 64} \]
integrate(((64*x**6-1472*x**5+12800*x**4-48000*x**3+40000*x**2+200000*x-40 0000)*exp(x)**10+(320*x**5-5760*x**4+35200*x**3-64000*x**2-120000*x+400000 )*exp(x)**8+(32*x**5+224*x**4-6784*x**3+28720*x**2+9600*x-158000)*exp(x)** 6+(64*x**4+112*x**3-4464*x**2+5360*x+30800)*exp(x)**4+(28*x**3+211*x**2-10 61*x-2960)*exp(x)**2+49*x+112)/((32*x**5-800*x**4+8000*x**3-40000*x**2+100 000*x-100000)*exp(x)**10+(160*x**4-3200*x**3+24000*x**2-80000*x+100000)*ex p(x)**8+(320*x**3-4800*x**2+24000*x-40000)*exp(x)**6+(320*x**2-3200*x+8000 )*exp(x)**4+(160*x-800)*exp(x)**2+32),x)
x**2 + 4*x + (-15*x**2 - 32*x + (-32*x**3 + 96*x**2 + 320*x)*exp(2*x) + (- 16*x**4 + 128*x**3 - 80*x**2 - 800*x)*exp(4*x))/((256*x - 1280)*exp(2*x) + (384*x**2 - 3840*x + 9600)*exp(4*x) + (256*x**3 - 3840*x**2 + 19200*x - 3 2000)*exp(6*x) + (64*x**4 - 1280*x**3 + 9600*x**2 - 32000*x + 40000)*exp(8 *x) + 64)
Leaf count of result is larger than twice the leaf count of optimal. 186 vs. \(2 (26) = 52\).
Time = 0.37 (sec) , antiderivative size = 186, normalized size of antiderivative = 6.20 \[ \int \frac {112+49 x+e^{2 x} \left (-2960-1061 x+211 x^2+28 x^3\right )+e^{4 x} \left (30800+5360 x-4464 x^2+112 x^3+64 x^4\right )+e^{6 x} \left (-158000+9600 x+28720 x^2-6784 x^3+224 x^4+32 x^5\right )+e^{8 x} \left (400000-120000 x-64000 x^2+35200 x^3-5760 x^4+320 x^5\right )+e^{10 x} \left (-400000+200000 x+40000 x^2-48000 x^3+12800 x^4-1472 x^5+64 x^6\right )}{32+e^{2 x} (-800+160 x)+e^{4 x} \left (8000-3200 x+320 x^2\right )+e^{6 x} \left (-40000+24000 x-4800 x^2+320 x^3\right )+e^{8 x} \left (100000-80000 x+24000 x^2-3200 x^3+160 x^4\right )+e^{10 x} \left (-100000+100000 x-40000 x^2+8000 x^3-800 x^4+32 x^5\right )} \, dx=\frac {49 \, x^{2} + 64 \, {\left (x^{6} - 16 \, x^{5} + 70 \, x^{4} + 100 \, x^{3} - 1375 \, x^{2} + 2500 \, x\right )} e^{\left (8 \, x\right )} + 256 \, {\left (x^{5} - 11 \, x^{4} + 15 \, x^{3} + 175 \, x^{2} - 500 \, x\right )} e^{\left (6 \, x\right )} + 16 \, {\left (23 \, x^{4} - 136 \, x^{3} - 365 \, x^{2} + 2350 \, x\right )} e^{\left (4 \, x\right )} + 32 \, {\left (7 \, x^{3} - 5 \, x^{2} - 150 \, x\right )} e^{\left (2 \, x\right )} + 224 \, x}{64 \, {\left ({\left (x^{4} - 20 \, x^{3} + 150 \, x^{2} - 500 \, x + 625\right )} e^{\left (8 \, x\right )} + 4 \, {\left (x^{3} - 15 \, x^{2} + 75 \, x - 125\right )} e^{\left (6 \, x\right )} + 6 \, {\left (x^{2} - 10 \, x + 25\right )} e^{\left (4 \, x\right )} + 4 \, {\left (x - 5\right )} e^{\left (2 \, x\right )} + 1\right )}} \]
integrate(((64*x^6-1472*x^5+12800*x^4-48000*x^3+40000*x^2+200000*x-400000) *exp(x)^10+(320*x^5-5760*x^4+35200*x^3-64000*x^2-120000*x+400000)*exp(x)^8 +(32*x^5+224*x^4-6784*x^3+28720*x^2+9600*x-158000)*exp(x)^6+(64*x^4+112*x^ 3-4464*x^2+5360*x+30800)*exp(x)^4+(28*x^3+211*x^2-1061*x-2960)*exp(x)^2+49 *x+112)/((32*x^5-800*x^4+8000*x^3-40000*x^2+100000*x-100000)*exp(x)^10+(16 0*x^4-3200*x^3+24000*x^2-80000*x+100000)*exp(x)^8+(320*x^3-4800*x^2+24000* x-40000)*exp(x)^6+(320*x^2-3200*x+8000)*exp(x)^4+(160*x-800)*exp(x)^2+32), x, algorithm=\
1/64*(49*x^2 + 64*(x^6 - 16*x^5 + 70*x^4 + 100*x^3 - 1375*x^2 + 2500*x)*e^ (8*x) + 256*(x^5 - 11*x^4 + 15*x^3 + 175*x^2 - 500*x)*e^(6*x) + 16*(23*x^4 - 136*x^3 - 365*x^2 + 2350*x)*e^(4*x) + 32*(7*x^3 - 5*x^2 - 150*x)*e^(2*x ) + 224*x)/((x^4 - 20*x^3 + 150*x^2 - 500*x + 625)*e^(8*x) + 4*(x^3 - 15*x ^2 + 75*x - 125)*e^(6*x) + 6*(x^2 - 10*x + 25)*e^(4*x) + 4*(x - 5)*e^(2*x) + 1)
Leaf count of result is larger than twice the leaf count of optimal. 274 vs. \(2 (26) = 52\).
Time = 0.34 (sec) , antiderivative size = 274, normalized size of antiderivative = 9.13 \[ \int \frac {112+49 x+e^{2 x} \left (-2960-1061 x+211 x^2+28 x^3\right )+e^{4 x} \left (30800+5360 x-4464 x^2+112 x^3+64 x^4\right )+e^{6 x} \left (-158000+9600 x+28720 x^2-6784 x^3+224 x^4+32 x^5\right )+e^{8 x} \left (400000-120000 x-64000 x^2+35200 x^3-5760 x^4+320 x^5\right )+e^{10 x} \left (-400000+200000 x+40000 x^2-48000 x^3+12800 x^4-1472 x^5+64 x^6\right )}{32+e^{2 x} (-800+160 x)+e^{4 x} \left (8000-3200 x+320 x^2\right )+e^{6 x} \left (-40000+24000 x-4800 x^2+320 x^3\right )+e^{8 x} \left (100000-80000 x+24000 x^2-3200 x^3+160 x^4\right )+e^{10 x} \left (-100000+100000 x-40000 x^2+8000 x^3-800 x^4+32 x^5\right )} \, dx=\frac {64 \, x^{6} e^{\left (8 \, x\right )} - 1024 \, x^{5} e^{\left (8 \, x\right )} + 256 \, x^{5} e^{\left (6 \, x\right )} + 4480 \, x^{4} e^{\left (8 \, x\right )} - 2816 \, x^{4} e^{\left (6 \, x\right )} + 368 \, x^{4} e^{\left (4 \, x\right )} + 6400 \, x^{3} e^{\left (8 \, x\right )} + 3840 \, x^{3} e^{\left (6 \, x\right )} - 2176 \, x^{3} e^{\left (4 \, x\right )} + 224 \, x^{3} e^{\left (2 \, x\right )} - 88000 \, x^{2} e^{\left (8 \, x\right )} + 44800 \, x^{2} e^{\left (6 \, x\right )} - 5840 \, x^{2} e^{\left (4 \, x\right )} - 160 \, x^{2} e^{\left (2 \, x\right )} + 49 \, x^{2} + 160000 \, x e^{\left (8 \, x\right )} - 128000 \, x e^{\left (6 \, x\right )} + 37600 \, x e^{\left (4 \, x\right )} - 4800 \, x e^{\left (2 \, x\right )} + 224 \, x}{64 \, {\left (x^{4} e^{\left (8 \, x\right )} - 20 \, x^{3} e^{\left (8 \, x\right )} + 4 \, x^{3} e^{\left (6 \, x\right )} + 150 \, x^{2} e^{\left (8 \, x\right )} - 60 \, x^{2} e^{\left (6 \, x\right )} + 6 \, x^{2} e^{\left (4 \, x\right )} - 500 \, x e^{\left (8 \, x\right )} + 300 \, x e^{\left (6 \, x\right )} - 60 \, x e^{\left (4 \, x\right )} + 4 \, x e^{\left (2 \, x\right )} + 625 \, e^{\left (8 \, x\right )} - 500 \, e^{\left (6 \, x\right )} + 150 \, e^{\left (4 \, x\right )} - 20 \, e^{\left (2 \, x\right )} + 1\right )}} \]
integrate(((64*x^6-1472*x^5+12800*x^4-48000*x^3+40000*x^2+200000*x-400000) *exp(x)^10+(320*x^5-5760*x^4+35200*x^3-64000*x^2-120000*x+400000)*exp(x)^8 +(32*x^5+224*x^4-6784*x^3+28720*x^2+9600*x-158000)*exp(x)^6+(64*x^4+112*x^ 3-4464*x^2+5360*x+30800)*exp(x)^4+(28*x^3+211*x^2-1061*x-2960)*exp(x)^2+49 *x+112)/((32*x^5-800*x^4+8000*x^3-40000*x^2+100000*x-100000)*exp(x)^10+(16 0*x^4-3200*x^3+24000*x^2-80000*x+100000)*exp(x)^8+(320*x^3-4800*x^2+24000* x-40000)*exp(x)^6+(320*x^2-3200*x+8000)*exp(x)^4+(160*x-800)*exp(x)^2+32), x, algorithm=\
1/64*(64*x^6*e^(8*x) - 1024*x^5*e^(8*x) + 256*x^5*e^(6*x) + 4480*x^4*e^(8* x) - 2816*x^4*e^(6*x) + 368*x^4*e^(4*x) + 6400*x^3*e^(8*x) + 3840*x^3*e^(6 *x) - 2176*x^3*e^(4*x) + 224*x^3*e^(2*x) - 88000*x^2*e^(8*x) + 44800*x^2*e ^(6*x) - 5840*x^2*e^(4*x) - 160*x^2*e^(2*x) + 49*x^2 + 160000*x*e^(8*x) - 128000*x*e^(6*x) + 37600*x*e^(4*x) - 4800*x*e^(2*x) + 224*x)/(x^4*e^(8*x) - 20*x^3*e^(8*x) + 4*x^3*e^(6*x) + 150*x^2*e^(8*x) - 60*x^2*e^(6*x) + 6*x^ 2*e^(4*x) - 500*x*e^(8*x) + 300*x*e^(6*x) - 60*x*e^(4*x) + 4*x*e^(2*x) + 6 25*e^(8*x) - 500*e^(6*x) + 150*e^(4*x) - 20*e^(2*x) + 1)
Timed out. \[ \int \frac {112+49 x+e^{2 x} \left (-2960-1061 x+211 x^2+28 x^3\right )+e^{4 x} \left (30800+5360 x-4464 x^2+112 x^3+64 x^4\right )+e^{6 x} \left (-158000+9600 x+28720 x^2-6784 x^3+224 x^4+32 x^5\right )+e^{8 x} \left (400000-120000 x-64000 x^2+35200 x^3-5760 x^4+320 x^5\right )+e^{10 x} \left (-400000+200000 x+40000 x^2-48000 x^3+12800 x^4-1472 x^5+64 x^6\right )}{32+e^{2 x} (-800+160 x)+e^{4 x} \left (8000-3200 x+320 x^2\right )+e^{6 x} \left (-40000+24000 x-4800 x^2+320 x^3\right )+e^{8 x} \left (100000-80000 x+24000 x^2-3200 x^3+160 x^4\right )+e^{10 x} \left (-100000+100000 x-40000 x^2+8000 x^3-800 x^4+32 x^5\right )} \, dx=\int \frac {49\,x-{\mathrm {e}}^{2\,x}\,\left (-28\,x^3-211\,x^2+1061\,x+2960\right )+{\mathrm {e}}^{4\,x}\,\left (64\,x^4+112\,x^3-4464\,x^2+5360\,x+30800\right )+{\mathrm {e}}^{6\,x}\,\left (32\,x^5+224\,x^4-6784\,x^3+28720\,x^2+9600\,x-158000\right )-{\mathrm {e}}^{8\,x}\,\left (-320\,x^5+5760\,x^4-35200\,x^3+64000\,x^2+120000\,x-400000\right )+{\mathrm {e}}^{10\,x}\,\left (64\,x^6-1472\,x^5+12800\,x^4-48000\,x^3+40000\,x^2+200000\,x-400000\right )+112}{{\mathrm {e}}^{4\,x}\,\left (320\,x^2-3200\,x+8000\right )+{\mathrm {e}}^{6\,x}\,\left (320\,x^3-4800\,x^2+24000\,x-40000\right )+{\mathrm {e}}^{8\,x}\,\left (160\,x^4-3200\,x^3+24000\,x^2-80000\,x+100000\right )+{\mathrm {e}}^{10\,x}\,\left (32\,x^5-800\,x^4+8000\,x^3-40000\,x^2+100000\,x-100000\right )+{\mathrm {e}}^{2\,x}\,\left (160\,x-800\right )+32} \,d x \]
int((49*x - exp(2*x)*(1061*x - 211*x^2 - 28*x^3 + 2960) + exp(4*x)*(5360*x - 4464*x^2 + 112*x^3 + 64*x^4 + 30800) + exp(6*x)*(9600*x + 28720*x^2 - 6 784*x^3 + 224*x^4 + 32*x^5 - 158000) - exp(8*x)*(120000*x + 64000*x^2 - 35 200*x^3 + 5760*x^4 - 320*x^5 - 400000) + exp(10*x)*(200000*x + 40000*x^2 - 48000*x^3 + 12800*x^4 - 1472*x^5 + 64*x^6 - 400000) + 112)/(exp(4*x)*(320 *x^2 - 3200*x + 8000) + exp(6*x)*(24000*x - 4800*x^2 + 320*x^3 - 40000) + exp(8*x)*(24000*x^2 - 80000*x - 3200*x^3 + 160*x^4 + 100000) + exp(10*x)*( 100000*x - 40000*x^2 + 8000*x^3 - 800*x^4 + 32*x^5 - 100000) + exp(2*x)*(1 60*x - 800) + 32),x)
int((49*x - exp(2*x)*(1061*x - 211*x^2 - 28*x^3 + 2960) + exp(4*x)*(5360*x - 4464*x^2 + 112*x^3 + 64*x^4 + 30800) + exp(6*x)*(9600*x + 28720*x^2 - 6 784*x^3 + 224*x^4 + 32*x^5 - 158000) - exp(8*x)*(120000*x + 64000*x^2 - 35 200*x^3 + 5760*x^4 - 320*x^5 - 400000) + exp(10*x)*(200000*x + 40000*x^2 - 48000*x^3 + 12800*x^4 - 1472*x^5 + 64*x^6 - 400000) + 112)/(exp(4*x)*(320 *x^2 - 3200*x + 8000) + exp(6*x)*(24000*x - 4800*x^2 + 320*x^3 - 40000) + exp(8*x)*(24000*x^2 - 80000*x - 3200*x^3 + 160*x^4 + 100000) + exp(10*x)*( 100000*x - 40000*x^2 + 8000*x^3 - 800*x^4 + 32*x^5 - 100000) + exp(2*x)*(1 60*x - 800) + 32), x)