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Resolución de integrales/ tg(2x)/ 1/((ctg(2x))^(2)+1)

Integral de 1/((ctg(2x))^(2)+1) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                 
  /                 
 |                  
 |        1         
 |  ------------- dx
 |     2            
 |  cot (2*x) + 1   
 |                  
/                   
0
$$\int\limits_{0}^{1} \frac{1}{\cot^{2}{\left(2 x \right)} + 1}\, dx$$ 
Integral(1/(cot(2*x)^2 + 1), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                          
 |                                                                    2      
 |       1                    cot(2*x)            2*x          2*x*cot (2*x) 
 | ------------- dx = C - --------------- + --------------- + ---------------
 |    2                            2                 2                 2     
 | cot (2*x) + 1          4 + 4*cot (2*x)   4 + 4*cot (2*x)   4 + 4*cot (2*x)
 |                                                                           
/
$$\int \frac{1}{\cot^{2}{\left(2 x \right)} + 1}\, dx = C + \frac{2 x \cot^{2}{\left(2 x \right)}}{4 \cot^{2}{\left(2 x \right)} + 4} + \frac{2 x}{4 \cot^{2}{\left(2 x \right)} + 4} - \frac{\cot{\left(2 x \right)}}{4 \cot^{2}{\left(2 x \right)} + 4}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
                                       2     
      2             cot(2)        2*cot (2)  
------------- - ------------- + -------------
         2               2               2   
4 + 4*cot (2)   4 + 4*cot (2)   4 + 4*cot (2)
$$\frac{2 \cot^{2}{\left(2 \right)}}{4 \cot^{2}{\left(2 \right)} + 4} - \frac{\cot{\left(2 \right)}}{4 \cot^{2}{\left(2 \right)} + 4} + \frac{2}{4 \cot^{2}{\left(2 \right)} + 4}$$ 
=
= 
                                       2     
      2             cot(2)        2*cot (2)  
------------- - ------------- + -------------
         2               2               2   
4 + 4*cot (2)   4 + 4*cot (2)   4 + 4*cot (2)
$$\frac{2 \cot^{2}{\left(2 \right)}}{4 \cot^{2}{\left(2 \right)} + 4} - \frac{\cot{\left(2 \right)}}{4 \cot^{2}{\left(2 \right)} + 4} + \frac{2}{4 \cot^{2}{\left(2 \right)} + 4}$$ 
2/(4 + 4*cot(2)^2) - cot(2)/(4 + 4*cot(2)^2) + 2*cot(2)^2/(4 + 4*cot(2)^2)
Respuesta numérica [src] 
0.594600311913491
0.594600311913491

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

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