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Resolución de integrales/ x/2+1/ cos(x/2+1)^2

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  0               
  /               
 |                
 |     2/x    \   
 |  cos |- + 1| dx
 |      \2    /   
 |                
/                 
-1
$$\int\limits_{-1}^{0} \cos^{2}{\left(\frac{x}{2} + 1 \right)}\, dx$$ 
Integral(cos(x/2 + 1)^2, (x, -1, 0))
Respuesta (Indefinida) [src] 
  /                                                                        3/1   x\                             /1   x\                            4/1   x\                             2/1   x\         
 |                                                                    4*tan |- + -|                        4*tan|- + -|                       x*tan |- + -|                      2*x*tan |- + -|         
 |    2/x    \                          x                                   \2   4/                             \2   4/                             \2   4/                              \2   4/         
 | cos |- + 1| dx = C + --------------------------------- - --------------------------------- + --------------------------------- + --------------------------------- + ---------------------------------
 |     \2    /                   4/1   x\        2/1   x\            4/1   x\        2/1   x\            4/1   x\        2/1   x\            4/1   x\        2/1   x\            4/1   x\        2/1   x\
 |                      2 + 2*tan |- + -| + 4*tan |- + -|   2 + 2*tan |- + -| + 4*tan |- + -|   2 + 2*tan |- + -| + 4*tan |- + -|   2 + 2*tan |- + -| + 4*tan |- + -|   2 + 2*tan |- + -| + 4*tan |- + -|
/                                 \2   4/         \2   4/             \2   4/         \2   4/             \2   4/         \2   4/             \2   4/         \2   4/             \2   4/         \2   4/
$$\int \cos^{2}{\left(\frac{x}{2} + 1 \right)}\, dx = C + \frac{x \tan^{4}{\left(\frac{x}{4} + \frac{1}{2} \right)}}{2 \tan^{4}{\left(\frac{x}{4} + \frac{1}{2} \right)} + 4 \tan^{2}{\left(\frac{x}{4} + \frac{1}{2} \right)} + 2} + \frac{2 x \tan^{2}{\left(\frac{x}{4} + \frac{1}{2} \right)}}{2 \tan^{4}{\left(\frac{x}{4} + \frac{1}{2} \right)} + 4 \tan^{2}{\left(\frac{x}{4} + \frac{1}{2} \right)} + 2} + \frac{x}{2 \tan^{4}{\left(\frac{x}{4} + \frac{1}{2} \right)} + 4 \tan^{2}{\left(\frac{x}{4} + \frac{1}{2} \right)} + 2} - \frac{4 \tan^{3}{\left(\frac{x}{4} + \frac{1}{2} \right)}}{2 \tan^{4}{\left(\frac{x}{4} + \frac{1}{2} \right)} + 4 \tan^{2}{\left(\frac{x}{4} + \frac{1}{2} \right)} + 2} + \frac{4 \tan{\left(\frac{x}{4} + \frac{1}{2} \right)}}{2 \tan^{4}{\left(\frac{x}{4} + \frac{1}{2} \right)} + 4 \tan^{2}{\left(\frac{x}{4} + \frac{1}{2} \right)} + 2}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
   2           2                                         
cos (1/2)   sin (1/2)                                    
--------- + --------- + cos(1)*sin(1) - cos(1/2)*sin(1/2)
    2           2
$$- \sin{\left(\frac{1}{2} \right)} \cos{\left(\frac{1}{2} \right)} + \frac{\sin^{2}{\left(\frac{1}{2} \right)}}{2} + \frac{\cos^{2}{\left(\frac{1}{2} \right)}}{2} + \sin{\left(1 \right)} \cos{\left(1 \right)}$$ 
=
= 
   2           2                                         
cos (1/2)   sin (1/2)                                    
--------- + --------- + cos(1)*sin(1) - cos(1/2)*sin(1/2)
    2           2
$$- \sin{\left(\frac{1}{2} \right)} \cos{\left(\frac{1}{2} \right)} + \frac{\sin^{2}{\left(\frac{1}{2} \right)}}{2} + \frac{\cos^{2}{\left(\frac{1}{2} \right)}}{2} + \sin{\left(1 \right)} \cos{\left(1 \right)}$$ 
cos(1/2)^2/2 + sin(1/2)^2/2 + cos(1)*sin(1) - cos(1/2)*sin(1/2)
Respuesta numérica [src] 
0.533913221008893
0.533913221008893

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

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