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Resolución de integrales/ e^(3x)/ e^(5*x)/ (e^(3x))/(5e^(5*x)+1)

Integral de (e^(3x))/(5e^(5*x)+1) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1              
  /              
 |               
 |      3*x      
 |     E         
 |  ---------- dx
 |     5*x       
 |  5*E    + 1   
 |               
/                
0
∫01e3x5e5x+1 dx\int\limits_{0}^{1} \frac{e^{3 x}}{5 e^{5 x} + 1}\, dx 
Integral(E^(3*x)/(5*E^(5*x) + 1), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                   
 |                                                                    
 |     3*x                                                            
 |    E                       /        5                /     2    x\\
 | ---------- dx = C + RootSum\390625*z  - 1, i -> i*log\125*i  + e //
 |    5*x                                                             
 | 5*E    + 1                                                         
 |                                                                    
/
∫e3x5e5x+1 dx=C+RootSum⁡(390625z5−1,(i↦ilog⁡(125i2+ex)))\int \frac{e^{3 x}}{5 e^{5 x} + 1}\, dx = C + \operatorname{RootSum} {\left(390625 z^{5} - 1, \left( i \mapsto i \log{\left(125 i^{2} + e^{x} \right)} \right)\right)}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.25-0.25
Trazar el gráfico f(x)
Respuesta [src] 
         /        5                /         2\\          /        5                /         2\\
- RootSum\390625*z  - 1, i -> i*log\1 + 125*i // + RootSum\390625*z  - 1, i -> i*log\E + 125*i //
−RootSum⁡(390625z5−1,(i↦ilog⁡(125i2+1)))+RootSum⁡(390625z5−1,(i↦ilog⁡(125i2+e)))- \operatorname{RootSum} {\left(390625 z^{5} - 1, \left( i \mapsto i \log{\left(125 i^{2} + 1 \right)} \right)\right)} + \operatorname{RootSum} {\left(390625 z^{5} - 1, \left( i \mapsto i \log{\left(125 i^{2} + e \right)} \right)\right)} 
=
= 
         /        5                /         2\\          /        5                /         2\\
- RootSum\390625*z  - 1, i -> i*log\1 + 125*i // + RootSum\390625*z  - 1, i -> i*log\E + 125*i //
−RootSum⁡(390625z5−1,(i↦ilog⁡(125i2+1)))+RootSum⁡(390625z5−1,(i↦ilog⁡(125i2+e)))- \operatorname{RootSum} {\left(390625 z^{5} - 1, \left( i \mapsto i \log{\left(125 i^{2} + 1 \right)} \right)\right)} + \operatorname{RootSum} {\left(390625 z^{5} - 1, \left( i \mapsto i \log{\left(125 i^{2} + e \right)} \right)\right)} 
-RootSum(390625*_z^5 - 1, Lambda(_i, _i*log(1 + 125*_i^2))) + RootSum(390625*_z^5 - 1, Lambda(_i, _i*log(E + 125*_i^2)))
Respuesta numérica [src] 
0.0813424578833767
0.0813424578833767

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

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