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Resolución de integrales/ exp(x)*cosh^2(sqrt(exp(x)+1))

Integral de exp(x)*cosh^2(sqrt(exp(x)+1)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                         
  /                         
 |                          
 |          /   ________\   
 |   x     2|  /  x     |   
 |  e *cosh \\/  e  + 1 / dx
 |                          
/                           
0
$$\int\limits_{0}^{1} e^{x} \cosh^{2}{\left(\sqrt{e^{x} + 1} \right)}\, dx$$ 
Integral(exp(x)*cosh(sqrt(exp(x) + 1))^2, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                 /                        
 |                                 |                         
 |         /   ________\           |      /   ________\      
 |  x     2|  /  x     |           |     2|  /  x     |  x   
 | e *cosh \\/  e  + 1 / dx = C +  | cosh \\/  e  + 1 /*e  dx
 |                                 |                         
/                                 /
$$\int e^{x} \cosh^{2}{\left(\sqrt{e^{x} + 1} \right)}\, dx = C + \int e^{x} \cosh^{2}{\left(\sqrt{e^{x} + 1} \right)}\, dx$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
    2/  ___\       2/  _______\         2/  _______\         2/  _______\                                                                            
sinh \\/ 2 /   cosh \\/ 1 + E /   E*cosh \\/ 1 + E /   E*sinh \\/ 1 + E /     _______     /  _______\     /  _______\     ___     /  ___\     /  ___\
------------ - ---------------- + ------------------ - ------------------ + \/ 1 + E *cosh\\/ 1 + E /*sinh\\/ 1 + E / - \/ 2 *cosh\\/ 2 /*sinh\\/ 2 /
     2                2                   2                    2
$$- \frac{e \sinh^{2}{\left(\sqrt{1 + e} \right)}}{2} - \frac{\cosh^{2}{\left(\sqrt{1 + e} \right)}}{2} - \sqrt{2} \sinh{\left(\sqrt{2} \right)} \cosh{\left(\sqrt{2} \right)} + \frac{\sinh^{2}{\left(\sqrt{2} \right)}}{2} + \frac{e \cosh^{2}{\left(\sqrt{1 + e} \right)}}{2} + \sqrt{1 + e} \sinh{\left(\sqrt{1 + e} \right)} \cosh{\left(\sqrt{1 + e} \right)}$$ 
=
= 
    2/  ___\       2/  _______\         2/  _______\         2/  _______\                                                                            
sinh \\/ 2 /   cosh \\/ 1 + E /   E*cosh \\/ 1 + E /   E*sinh \\/ 1 + E /     _______     /  _______\     /  _______\     ___     /  ___\     /  ___\
------------ - ---------------- + ------------------ - ------------------ + \/ 1 + E *cosh\\/ 1 + E /*sinh\\/ 1 + E / - \/ 2 *cosh\\/ 2 /*sinh\\/ 2 /
     2                2                   2                    2
$$- \frac{e \sinh^{2}{\left(\sqrt{1 + e} \right)}}{2} - \frac{\cosh^{2}{\left(\sqrt{1 + e} \right)}}{2} - \sqrt{2} \sinh{\left(\sqrt{2} \right)} \cosh{\left(\sqrt{2} \right)} + \frac{\sinh^{2}{\left(\sqrt{2} \right)}}{2} + \frac{e \cosh^{2}{\left(\sqrt{1 + e} \right)}}{2} + \sqrt{1 + e} \sinh{\left(\sqrt{1 + e} \right)} \cosh{\left(\sqrt{1 + e} \right)}$$ 
sinh(sqrt(2))^2/2 - cosh(sqrt(1 + E))^2/2 + E*cosh(sqrt(1 + E))^2/2 - E*sinh(sqrt(1 + E))^2/2 + sqrt(1 + E)*cosh(sqrt(1 + E))*sinh(sqrt(1 + E)) - sqrt(2)*cosh(sqrt(2))*sinh(sqrt(2))
Respuesta numérica [src] 
13.8982009735269
13.8982009735269

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

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