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Resolución de integrales/ ch(x)/ 1/(ch^3(x)+3ch(x))

Integral de 1/(ch^3(x)+3ch(x)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                        
  /                        
 |                         
 |           1             
 |  -------------------- dx
 |      3                  
 |  cosh (x) + 3*cosh(x)   
 |                         
/                          
0
$$\int\limits_{0}^{1} \frac{1}{\cosh^{3}{\left(x \right)} + 3 \cosh{\left(x \right)}}\, dx$$ 
Integral(1/(cosh(x)^3 + 3*cosh(x)), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                  /  ___         /x\\       /    ___         /x\\         /    /x\\
 |                               atan|\/ 3  + 2*tanh|-||   atan|- \/ 3  + 2*tanh|-||   2*atan|tanh|-||
 |          1                        \              \2//       \                \2//         \    \2//
 | -------------------- dx = C - ----------------------- - ------------------------- + ---------------
 |     3                                    6                          6                      3       
 | cosh (x) + 3*cosh(x)                                                                               
 |                                                                                                    
/
$$\int \frac{1}{\cosh^{3}{\left(x \right)} + 3 \cosh{\left(x \right)}}\, dx = C - \frac{\operatorname{atan}{\left(2 \tanh{\left(\frac{x}{2} \right)} - \sqrt{3} \right)}}{6} - \frac{\operatorname{atan}{\left(2 \tanh{\left(\frac{x}{2} \right)} + \sqrt{3} \right)}}{6} + \frac{2 \operatorname{atan}{\left(\tanh{\left(\frac{x}{2} \right)} \right)}}{3}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
      /  ___              \       /  ___              \                    
  atan\\/ 3  + 2*tanh(1/2)/   atan\\/ 3  - 2*tanh(1/2)/   2*atan(tanh(1/2))
- ------------------------- + ------------------------- + -----------------
              6                           6                       3
$$- \frac{\operatorname{atan}{\left(2 \tanh{\left(\frac{1}{2} \right)} + \sqrt{3} \right)}}{6} + \frac{\operatorname{atan}{\left(- 2 \tanh{\left(\frac{1}{2} \right)} + \sqrt{3} \right)}}{6} + \frac{2 \operatorname{atan}{\left(\tanh{\left(\frac{1}{2} \right)} \right)}}{3}$$ 
=
= 
      /  ___              \       /  ___              \                    
  atan\\/ 3  + 2*tanh(1/2)/   atan\\/ 3  - 2*tanh(1/2)/   2*atan(tanh(1/2))
- ------------------------- + ------------------------- + -----------------
              6                           6                       3
$$- \frac{\operatorname{atan}{\left(2 \tanh{\left(\frac{1}{2} \right)} + \sqrt{3} \right)}}{6} + \frac{\operatorname{atan}{\left(- 2 \tanh{\left(\frac{1}{2} \right)} + \sqrt{3} \right)}}{6} + \frac{2 \operatorname{atan}{\left(\tanh{\left(\frac{1}{2} \right)} \right)}}{3}$$ 
-atan(sqrt(3) + 2*tanh(1/2))/6 + atan(sqrt(3) - 2*tanh(1/2))/6 + 2*atan(tanh(1/2))/3
Respuesta numérica [src] 
0.200047761008488
0.200047761008488

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

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