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Resolución de integrales/ e^(x/2)/ e^(2*x)/ (e^x+e^(x/2))/(e^(2*x)+1)

Integral de (e^x+e^(x/2))/(e^(2*x)+1) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1            
  /            
 |             
 |        x    
 |        -    
 |   x    2    
 |  E  + E     
 |  -------- dx
 |   2*x       
 |  E    + 1   
 |             
/              
0
∫01ex+ex2e2x+1 dx\int\limits_{0}^{1} \frac{e^{x} + e^{\frac{x}{2}}}{e^{2 x} + 1}\, dx 
Integral((E^x + E^(x/2))/(E^(2*x) + 1), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                     
 |                                                                      
 |       x                                                              
 |       -                  /                     /       x\\           
 |  x    2                  |                     |       -||           
 | E  + E                   |    4                |       2||       / x\
 | -------- dx = C + RootSum\16*z  + 1, i -> i*log\2*i + e // + atan\e /
 |  2*x                                                                 
 | E    + 1                                                             
 |                                                                      
/
∫ex+ex2e2x+1 dx=C+atan⁡(ex)+RootSum⁡(16z4+1,(i↦ilog⁡(2i+ex2)))\int \frac{e^{x} + e^{\frac{x}{2}}}{e^{2 x} + 1}\, dx = C + \operatorname{atan}{\left(e^{x} \right)} + \operatorname{RootSum} {\left(16 z^{4} + 1, \left( i \mapsto i \log{\left(2 i + e^{\frac{x}{2}} \right)} \right)\right)}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.902.5-2.5
Trazar el gráfico f(x)
Respuesta [src] 
         /                                 /              3      2\\          /                                 /              3      2       \\
         |   4      2                      |8         16*i    4*i ||          |   4      2                      |5         16*i    4*i     1/2||
- RootSum|8*z  + 4*z  - 4*z + 1, i -> i*log|- - 2*i - ----- - ----|| + RootSum|8*z  + 4*z  - 4*z + 1, i -> i*log|- - 2*i - ----- - ---- + e   ||
         \                                 \3           3      3  //          \                                 \3           3      3         //
−RootSum⁡(8z4+4z2−4z+1,(i↦ilog⁡(−16i33−4i23−2i+83)))+RootSum⁡(8z4+4z2−4z+1,(i↦ilog⁡(−16i33−4i23−2i+e12+53)))- \operatorname{RootSum} {\left(8 z^{4} + 4 z^{2} - 4 z + 1, \left( i \mapsto i \log{\left(- \frac{16 i^{3}}{3} - \frac{4 i^{2}}{3} - 2 i + \frac{8}{3} \right)} \right)\right)} + \operatorname{RootSum} {\left(8 z^{4} + 4 z^{2} - 4 z + 1, \left( i \mapsto i \log{\left(- \frac{16 i^{3}}{3} - \frac{4 i^{2}}{3} - 2 i + e^{\frac{1}{2}} + \frac{5}{3} \right)} \right)\right)} 
=
= 
         /                                 /              3      2\\          /                                 /              3      2       \\
         |   4      2                      |8         16*i    4*i ||          |   4      2                      |5         16*i    4*i     1/2||
- RootSum|8*z  + 4*z  - 4*z + 1, i -> i*log|- - 2*i - ----- - ----|| + RootSum|8*z  + 4*z  - 4*z + 1, i -> i*log|- - 2*i - ----- - ---- + e   ||
         \                                 \3           3      3  //          \                                 \3           3      3         //
−RootSum⁡(8z4+4z2−4z+1,(i↦ilog⁡(−16i33−4i23−2i+83)))+RootSum⁡(8z4+4z2−4z+1,(i↦ilog⁡(−16i33−4i23−2i+e12+53)))- \operatorname{RootSum} {\left(8 z^{4} + 4 z^{2} - 4 z + 1, \left( i \mapsto i \log{\left(- \frac{16 i^{3}}{3} - \frac{4 i^{2}}{3} - 2 i + \frac{8}{3} \right)} \right)\right)} + \operatorname{RootSum} {\left(8 z^{4} + 4 z^{2} - 4 z + 1, \left( i \mapsto i \log{\left(- \frac{16 i^{3}}{3} - \frac{4 i^{2}}{3} - 2 i + e^{\frac{1}{2}} + \frac{5}{3} \right)} \right)\right)} 
-RootSum(8*_z^4 + 4*_z^2 - 4*_z + 1, Lambda(_i, _i*log(8/3 - 2*_i - 16*_i^3/3 - 4*_i^2/3))) + RootSum(8*_z^4 + 4*_z^2 - 4*_z + 1, Lambda(_i, _i*log(5/3 - 2*_i - 16*_i^3/3 - 4*_i^2/3 + exp(1/2))))
Respuesta numérica [src] 
0.779578225861259
0.779578225861259

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

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