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Resolución de integrales/ e^(2x)/ e^(-2x)/ e^(-2x)dx/((e^(2x)+5))^7

Integral de e^(-2x)dx/((e^(2x)+5))^7 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1               
  /               
 |                
 |      -2*x      
 |     E          
 |  ----------- dx
 |            7   
 |  / 2*x    \    
 |  \E    + 5/    
 |                
/                 
0
∫01e−2x(e2x+5)7 dx\int\limits_{0}^{1} \frac{e^{- 2 x}}{\left(e^{2 x} + 5\right)^{7}}\, dx 
Integral(E^(-2*x)/(E^(2*x) + 5)^7, (x, 0, 1))
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.000005-0.000005
Trazar el gráfico f(x)
Respuesta [src] 
                                           /1    -2\                                                                                                                            
                               -2     7*log|- + e  |                                         -2           -4            -6            -8            -10                         
   2709743      7*log(6/5)    e            \5      /                            669 + 18270*e   + 202125*e   + 1137500*e   + 3281250*e   + 3937500*e                            
------------- - ---------- - ------ + -------------- + -------------------------------------------------------------------------------------------------------------------------
1093500000000     781250     156250       781250                              -2                -4                 -6                 -8                 -12                 -10
                                                       46875000 + 1406250000*e   + 17578125000*e   + 117187500000*e   + 439453125000*e   + 732421875000*e    + 878906250000*e
7log⁡(e−2+15)781250−7log⁡(65)781250−1156250e2+27097431093500000000+3937500e10+669+3281250e8+18270e2+1137500e6+202125e4732421875000e12+878906250000e10+46875000+439453125000e8+1406250000e2+117187500000e6+17578125000e4\frac{7 \log{\left(e^{-2} + \frac{1}{5} \right)}}{781250} - \frac{7 \log{\left(\frac{6}{5} \right)}}{781250} - \frac{1}{156250 e^{2}} + \frac{2709743}{1093500000000} + \frac{\frac{3937500}{e^{10}} + 669 + \frac{3281250}{e^{8}} + \frac{18270}{e^{2}} + \frac{1137500}{e^{6}} + \frac{202125}{e^{4}}}{\frac{732421875000}{e^{12}} + \frac{878906250000}{e^{10}} + 46875000 + \frac{439453125000}{e^{8}} + \frac{1406250000}{e^{2}} + \frac{117187500000}{e^{6}} + \frac{17578125000}{e^{4}}} 
=
= 
                                           /1    -2\                                                                                                                            
                               -2     7*log|- + e  |                                         -2           -4            -6            -8            -10                         
   2709743      7*log(6/5)    e            \5      /                            669 + 18270*e   + 202125*e   + 1137500*e   + 3281250*e   + 3937500*e                            
------------- - ---------- - ------ + -------------- + -------------------------------------------------------------------------------------------------------------------------
1093500000000     781250     156250       781250                              -2                -4                 -6                 -8                 -12                 -10
                                                       46875000 + 1406250000*e   + 17578125000*e   + 117187500000*e   + 439453125000*e   + 732421875000*e    + 878906250000*e
7log⁡(e−2+15)781250−7log⁡(65)781250−1156250e2+27097431093500000000+3937500e10+669+3281250e8+18270e2+1137500e6+202125e4732421875000e12+878906250000e10+46875000+439453125000e8+1406250000e2+117187500000e6+17578125000e4\frac{7 \log{\left(e^{-2} + \frac{1}{5} \right)}}{781250} - \frac{7 \log{\left(\frac{6}{5} \right)}}{781250} - \frac{1}{156250 e^{2}} + \frac{2709743}{1093500000000} + \frac{\frac{3937500}{e^{10}} + 669 + \frac{3281250}{e^{8}} + \frac{18270}{e^{2}} + \frac{1137500}{e^{6}} + \frac{202125}{e^{4}}}{\frac{732421875000}{e^{12}} + \frac{878906250000}{e^{10}} + 46875000 + \frac{439453125000}{e^{8}} + \frac{1406250000}{e^{2}} + \frac{117187500000}{e^{6}} + \frac{17578125000}{e^{4}}} 
2709743/1093500000000 - 7*log(6/5)/781250 - exp(-2)/156250 + 7*log(1/5 + exp(-2))/781250 + (669 + 18270*exp(-2) + 202125*exp(-4) + 1137500*exp(-6) + 3281250*exp(-8) + 3937500*exp(-10))/(46875000 + 1406250000*exp(-2) + 17578125000*exp(-4) + 117187500000*exp(-6) + 439453125000*exp(-8) + 732421875000*exp(-12) + 878906250000*exp(-10))
Respuesta numérica [src] 
6.95604112891754e-7
6.95604112891754e-7

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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