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Resolución de integrales/ (sinx)/ 1+sinx/ (sinx)/((1+sinx)^2)

Integral de (sinx)/((1+sinx)^2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                 
  /                 
 |                  
 |      sin(x)      
 |  ------------- dx
 |              2   
 |  (1 + sin(x))    
 |                  
/                   
0
$$\int\limits_{0}^{1} \frac{\sin{\left(x \right)}}{\left(\sin{\left(x \right)} + 1\right)^{2}}\, dx$$ 
Integral(sin(x)/(1 + sin(x))^2, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                 /x\              
 |                                                                             6*tan|-|              
 |     sin(x)                              2                                        \2/              
 | ------------- dx = C - ------------------------------------ - ------------------------------------
 |             2                   3/x\        2/x\        /x\            3/x\        2/x\        /x\
 | (1 + sin(x))           3 + 3*tan |-| + 9*tan |-| + 9*tan|-|   3 + 3*tan |-| + 9*tan |-| + 9*tan|-|
 |                                  \2/         \2/        \2/             \2/         \2/        \2/
/
$$\int \frac{\sin{\left(x \right)}}{\left(\sin{\left(x \right)} + 1\right)^{2}}\, dx = C - \frac{6 \tan{\left(\frac{x}{2} \right)}}{3 \tan^{3}{\left(\frac{x}{2} \right)} + 9 \tan^{2}{\left(\frac{x}{2} \right)} + 9 \tan{\left(\frac{x}{2} \right)} + 3} - \frac{2}{3 \tan^{3}{\left(\frac{x}{2} \right)} + 9 \tan^{2}{\left(\frac{x}{2} \right)} + 9 \tan{\left(\frac{x}{2} \right)} + 3}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
2                       2                                        6*tan(1/2)                
- - ------------------------------------------ - ------------------------------------------
3            3             2                              3             2                  
    3 + 3*tan (1/2) + 9*tan (1/2) + 9*tan(1/2)   3 + 3*tan (1/2) + 9*tan (1/2) + 9*tan(1/2)
$$- \frac{6 \tan{\left(\frac{1}{2} \right)}}{3 \tan^{3}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)} + 3 + 9 \tan{\left(\frac{1}{2} \right)}} - \frac{2}{3 \tan^{3}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)} + 3 + 9 \tan{\left(\frac{1}{2} \right)}} + \frac{2}{3}$$ 
=
= 
2                       2                                        6*tan(1/2)                
- - ------------------------------------------ - ------------------------------------------
3            3             2                              3             2                  
    3 + 3*tan (1/2) + 9*tan (1/2) + 9*tan(1/2)   3 + 3*tan (1/2) + 9*tan (1/2) + 9*tan(1/2)
$$- \frac{6 \tan{\left(\frac{1}{2} \right)}}{3 \tan^{3}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)} + 3 + 9 \tan{\left(\frac{1}{2} \right)}} - \frac{2}{3 \tan^{3}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)} + 3 + 9 \tan{\left(\frac{1}{2} \right)}} + \frac{2}{3}$$ 
2/3 - 2/(3 + 3*tan(1/2)^3 + 9*tan(1/2)^2 + 9*tan(1/2)) - 6*tan(1/2)/(3 + 3*tan(1/2)^3 + 9*tan(1/2)^2 + 9*tan(1/2))
Respuesta numérica [src] 
0.190839166947762
0.190839166947762

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

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