3.4.22 \(\int \frac {112+49 x+e^{2 x} (-2960-1061 x+211 x^2+28 x^3)+e^{4 x} (30800+5360 x-4464 x^2+112 x^3+64 x^4)+e^{6 x} (-158000+9600 x+28720 x^2-6784 x^3+224 x^4+32 x^5)+e^{8 x} (400000-120000 x-64000 x^2+35200 x^3-5760 x^4+320 x^5)+e^{10 x} (-400000+200000 x+40000 x^2-48000 x^3+12800 x^4-1472 x^5+64 x^6)}{32+e^{2 x} (-800+160 x)+e^{4 x} (8000-3200 x+320 x^2)+e^{6 x} (-40000+24000 x-4800 x^2+320 x^3)+e^{8 x} (100000-80000 x+24000 x^2-3200 x^3+160 x^4)+e^{10 x} (-100000+100000 x-40000 x^2+8000 x^3-800 x^4+32 x^5)} \, dx\)

Optimal. Leaf size=30 \[ -5+\left (-2-x+\frac {x}{8 \left (1-e^{2 x} (5-x)\right )^2}\right )^2 \]

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Rubi [F]  time = 5.06, 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 {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 \end {gather*}

Verification is not applicable to the result.

[In]

Int[(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 + 9600*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 + 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 + 2
4000*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]

[Out]

(2 + x)^2 + (5*Defer[Int][(1 + E^(2*x)*(-5 + x))^(-5), x])/16 - (5*Defer[Int][(1 + E^(2*x)*(-5 + x))^(-4), x])
/16 - (7*Defer[Int][(1 + E^(2*x)*(-5 + x))^(-3), x])/2 + 3*Defer[Int][(1 + E^(2*x)*(-5 + x))^(-2), x] - (25*De
fer[Int][1/((1 + E^(2*x)*(-5 + x))^4*(-5 + x)), x])/16 + (35*Defer[Int][1/((1 + E^(2*x)*(-5 + x))^2*(-5 + x)),
x])/2 + Defer[Int][x/(1 + E^(2*x)*(-5 + x))^5, x]/16 - Defer[Int][x/(1 + E^(2*x)*(-5 + x))^4, x]/32 - (5*Defe
r[Int][x/(1 + E^(2*x)*(-5 + x))^3, x])/2 + 2*Defer[Int][x/(1 + E^(2*x)*(-5 + x))^2, x] + Defer[Int][x^2/(1 + E
^(2*x)*(-5 + x))^5, x]/8 - Defer[Int][x^2/(1 + E^(2*x)*(-5 + x))^4, x]/8 - Defer[Int][x^2/(1 + E^(2*x)*(-5 + x
))^3, x] + Defer[Int][x^2/(1 + E^(2*x)*(-5 + x))^2, x] + (25*Defer[Int][1/((-5 + x)*(1 - 5*E^(2*x) + E^(2*x)*x
)^5), x])/16 - (35*Defer[Int][1/((-5 + x)*(1 - 5*E^(2*x) + E^(2*x)*x)^3), x])/2

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {320 e^{8 x} (-5+x)^4 (2+x)+64 e^{10 x} (-5+x)^5 (2+x)+7 (16+7 x)+16 e^{6 x} (-5+x)^2 \left (-395-134 x+34 x^2+2 x^3\right )+e^{2 x} \left (-2960-1061 x+211 x^2+28 x^3\right )+16 e^{4 x} \left (1925+335 x-279 x^2+7 x^3+4 x^4\right )}{32 \left (1+e^{2 x} (-5+x)\right )^5} \, dx\\ &=\frac {1}{32} \int \frac {320 e^{8 x} (-5+x)^4 (2+x)+64 e^{10 x} (-5+x)^5 (2+x)+7 (16+7 x)+16 e^{6 x} (-5+x)^2 \left (-395-134 x+34 x^2+2 x^3\right )+e^{2 x} \left (-2960-1061 x+211 x^2+28 x^3\right )+16 e^{4 x} \left (1925+335 x-279 x^2+7 x^3+4 x^4\right )}{\left (1+e^{2 x} (-5+x)\right )^5} \, dx\\ &=\frac {1}{32} \int \left (64 (2+x)+\frac {2 x^2 (-9+2 x)}{(-5+x) \left (1-5 e^{2 x}+e^{2 x} x\right )^5}-\frac {16 x \left (-18-5 x+2 x^2\right )}{(-5+x) \left (1-5 e^{2 x}+e^{2 x} x\right )^3}-\frac {x \left (5-19 x+4 x^2\right )}{(-5+x) \left (1-5 e^{2 x}+e^{2 x} x\right )^4}+\frac {16 \left (5-14 x-6 x^2+2 x^3\right )}{(-5+x) \left (1-5 e^{2 x}+e^{2 x} x\right )^2}\right ) \, dx\\ &=(2+x)^2-\frac {1}{32} \int \frac {x \left (5-19 x+4 x^2\right )}{(-5+x) \left (1-5 e^{2 x}+e^{2 x} x\right )^4} \, dx+\frac {1}{16} \int \frac {x^2 (-9+2 x)}{(-5+x) \left (1-5 e^{2 x}+e^{2 x} x\right )^5} \, dx-\frac {1}{2} \int \frac {x \left (-18-5 x+2 x^2\right )}{(-5+x) \left (1-5 e^{2 x}+e^{2 x} x\right )^3} \, dx+\frac {1}{2} \int \frac {5-14 x-6 x^2+2 x^3}{(-5+x) \left (1-5 e^{2 x}+e^{2 x} x\right )^2} \, dx\\ &=(2+x)^2-\frac {1}{32} \int \left (\frac {10}{\left (1-5 e^{2 x}+e^{2 x} x\right )^4}+\frac {50}{(-5+x) \left (1-5 e^{2 x}+e^{2 x} x\right )^4}+\frac {x}{\left (1-5 e^{2 x}+e^{2 x} x\right )^4}+\frac {4 x^2}{\left (1-5 e^{2 x}+e^{2 x} x\right )^4}\right ) \, dx+\frac {1}{16} \int \left (\frac {5}{\left (1-5 e^{2 x}+e^{2 x} x\right )^5}+\frac {25}{(-5+x) \left (1-5 e^{2 x}+e^{2 x} x\right )^5}+\frac {x}{\left (1-5 e^{2 x}+e^{2 x} x\right )^5}+\frac {2 x^2}{\left (1-5 e^{2 x}+e^{2 x} x\right )^5}\right ) \, dx-\frac {1}{2} \int \left (\frac {7}{\left (1-5 e^{2 x}+e^{2 x} x\right )^3}+\frac {35}{(-5+x) \left (1-5 e^{2 x}+e^{2 x} x\right )^3}+\frac {5 x}{\left (1-5 e^{2 x}+e^{2 x} x\right )^3}+\frac {2 x^2}{\left (1-5 e^{2 x}+e^{2 x} x\right )^3}\right ) \, dx+\frac {1}{2} \int \left (\frac {6}{\left (1-5 e^{2 x}+e^{2 x} x\right )^2}+\frac {35}{(-5+x) \left (1-5 e^{2 x}+e^{2 x} x\right )^2}+\frac {4 x}{\left (1-5 e^{2 x}+e^{2 x} x\right )^2}+\frac {2 x^2}{\left (1-5 e^{2 x}+e^{2 x} x\right )^2}\right ) \, dx\\ &=(2+x)^2-\frac {1}{32} \int \frac {x}{\left (1-5 e^{2 x}+e^{2 x} x\right )^4} \, dx+\frac {1}{16} \int \frac {x}{\left (1-5 e^{2 x}+e^{2 x} x\right )^5} \, dx+\frac {1}{8} \int \frac {x^2}{\left (1-5 e^{2 x}+e^{2 x} x\right )^5} \, dx-\frac {1}{8} \int \frac {x^2}{\left (1-5 e^{2 x}+e^{2 x} x\right )^4} \, dx+\frac {5}{16} \int \frac {1}{\left (1-5 e^{2 x}+e^{2 x} x\right )^5} \, dx-\frac {5}{16} \int \frac {1}{\left (1-5 e^{2 x}+e^{2 x} x\right )^4} \, dx+\frac {25}{16} \int \frac {1}{(-5+x) \left (1-5 e^{2 x}+e^{2 x} x\right )^5} \, dx-\frac {25}{16} \int \frac {1}{(-5+x) \left (1-5 e^{2 x}+e^{2 x} x\right )^4} \, dx+2 \int \frac {x}{\left (1-5 e^{2 x}+e^{2 x} x\right )^2} \, dx-\frac {5}{2} \int \frac {x}{\left (1-5 e^{2 x}+e^{2 x} x\right )^3} \, dx+3 \int \frac {1}{\left (1-5 e^{2 x}+e^{2 x} x\right )^2} \, dx-\frac {7}{2} \int \frac {1}{\left (1-5 e^{2 x}+e^{2 x} x\right )^3} \, dx-\frac {35}{2} \int \frac {1}{(-5+x) \left (1-5 e^{2 x}+e^{2 x} x\right )^3} \, dx+\frac {35}{2} \int \frac {1}{(-5+x) \left (1-5 e^{2 x}+e^{2 x} x\right )^2} \, dx-\int \frac {x^2}{\left (1-5 e^{2 x}+e^{2 x} x\right )^3} \, dx+\int \frac {x^2}{\left (1-5 e^{2 x}+e^{2 x} x\right )^2} \, dx\\ &=(2+x)^2-\frac {1}{32} \int \frac {x}{\left (1+e^{2 x} (-5+x)\right )^4} \, dx+\frac {1}{16} \int \frac {x}{\left (1+e^{2 x} (-5+x)\right )^5} \, dx+\frac {1}{8} \int \frac {x^2}{\left (1+e^{2 x} (-5+x)\right )^5} \, dx-\frac {1}{8} \int \frac {x^2}{\left (1+e^{2 x} (-5+x)\right )^4} \, dx+\frac {5}{16} \int \frac {1}{\left (1+e^{2 x} (-5+x)\right )^5} \, dx-\frac {5}{16} \int \frac {1}{\left (1+e^{2 x} (-5+x)\right )^4} \, dx-\frac {25}{16} \int \frac {1}{\left (1+e^{2 x} (-5+x)\right )^4 (-5+x)} \, dx+\frac {25}{16} \int \frac {1}{(-5+x) \left (1-5 e^{2 x}+e^{2 x} x\right )^5} \, dx+2 \int \frac {x}{\left (1+e^{2 x} (-5+x)\right )^2} \, dx-\frac {5}{2} \int \frac {x}{\left (1+e^{2 x} (-5+x)\right )^3} \, dx+3 \int \frac {1}{\left (1+e^{2 x} (-5+x)\right )^2} \, dx-\frac {7}{2} \int \frac {1}{\left (1+e^{2 x} (-5+x)\right )^3} \, dx+\frac {35}{2} \int \frac {1}{\left (1+e^{2 x} (-5+x)\right )^2 (-5+x)} \, dx-\frac {35}{2} \int \frac {1}{(-5+x) \left (1-5 e^{2 x}+e^{2 x} x\right )^3} \, dx-\int \frac {x^2}{\left (1+e^{2 x} (-5+x)\right )^3} \, dx+\int \frac {x^2}{\left (1+e^{2 x} (-5+x)\right )^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.17, size = 63, normalized size = 2.10 \begin {gather*} \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 ) \end {gather*}

Antiderivative was successfully verified.

[In]

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 + 9600*x + 28720*x^2 - 6784*x^3 + 224*x^4 + 32*x^5) + E^(8*x)*(400000 - 1200
00*x - 64000*x^2 + 35200*x^3 - 5760*x^4 + 320*x^5) + E^(10*x)*(-400000 + 200000*x + 40000*x^2 - 48000*x^3 + 12
800*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)*(-400
00 + 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]

[Out]

(-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

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fricas [B]  time = 0.80, size = 186, normalized size = 6.20 \begin {gather*} \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 )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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+(160*x^4-3200*x^3+24000*x^2-80000*x+100000)*exp(x)^8+(320*x^3-4800*x^2+24
000*x-40000)*exp(x)^6+(320*x^2-3200*x+8000)*exp(x)^4+(160*x-800)*exp(x)^2+32),x, algorithm="fricas")

[Out]

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)

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giac [B]  time = 0.88, size = 274, normalized size = 9.13 \begin {gather*} \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 )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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+(160*x^4-3200*x^3+24000*x^2-80000*x+100000)*exp(x)^8+(320*x^3-4800*x^2+24
000*x-40000)*exp(x)^6+(320*x^2-3200*x+8000)*exp(x)^4+(160*x-800)*exp(x)^2+32),x, algorithm="giac")

[Out]

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) + 625*e^(8*x) - 500*e^(6*x) + 150*e
^(4*x) - 20*e^(2*x) + 1)

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maple [B]  time = 0.09, size = 85, normalized size = 2.83

method	result	size
risch	\(x^{2}+4 x -\frac {x \left (16 x^{3} {\mathrm e}^{4 x}-128 x^{2} {\mathrm e}^{4 x}+80 x \,{\mathrm e}^{4 x}+32 \,{\mathrm e}^{2 x} x^{2}+800 \,{\mathrm e}^{4 x}-96 x \,{\mathrm e}^{2 x}-320 \,{\mathrm e}^{2 x}+15 x +32\right )}{64 \left (x \,{\mathrm e}^{2 x}-5 \,{\mathrm e}^{2 x}+1\right )^{4}}\)	\(85\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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^3-640
00*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^3-44
64*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-
40000)*exp(x)^6+(320*x^2-3200*x+8000)*exp(x)^4+(160*x-800)*exp(x)^2+32),x,method=_RETURNVERBOSE)

[Out]

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

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maxima [B]  time = 0.85, size = 186, normalized size = 6.20 \begin {gather*} \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 )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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+(160*x^4-3200*x^3+24000*x^2-80000*x+100000)*exp(x)^8+(320*x^3-4800*x^2+24
000*x-40000)*exp(x)^6+(320*x^2-3200*x+8000)*exp(x)^4+(160*x-800)*exp(x)^2+32),x, algorithm="maxima")

[Out]

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)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \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 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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 + 308
00) + exp(6*x)*(9600*x + 28720*x^2 - 6784*x^3 + 224*x^4 + 32*x^5 - 158000) - exp(8*x)*(120000*x + 64000*x^2 -
35200*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)*(160*x - 800) + 32),x)

[Out]

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 + 308
00) + exp(6*x)*(9600*x + 28720*x^2 - 6784*x^3 + 224*x^4 + 32*x^5 - 158000) - exp(8*x)*(120000*x + 64000*x^2 -
35200*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)*(160*x - 800) + 32), x)

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sympy [B]  time = 0.72, size = 129, normalized size = 4.30 \begin {gather*} 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} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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)/((3
2*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-40000)*exp(x)**6+(320*x**2-3200*x+8000)*exp(x)**4+(160*x-800)*exp(x)**
2+32),x)

[Out]

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 -
32000)*exp(6*x) + (64*x**4 - 1280*x**3 + 9600*x**2 - 32000*x + 40000)*exp(8*x) + 64)

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