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

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1              
  /              
 |               
 |      2        
 |   sin (x)     
 |  ---------- dx
 |  1 + sin(x)   
 |               
/                
0
∫01sin⁡2(x)sin⁡(x)+1 dx\int\limits_{0}^{1} \frac{\sin^{2}{\left(x \right)}}{\sin{\left(x \right)} + 1}\, dx 
Integral(sin(x)^2/(1 + sin(x)), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                                                                                                        
 |                                                                                                      2/x\                              /x\                             2/x\                             3/x\                              /x\           
 |     2                                                                                           2*tan |-|                         2*tan|-|                        x*tan |-|                        x*tan |-|                         x*tan|-|           
 |  sin (x)                          4                                x                                  \2/                              \2/                              \2/                              \2/                              \2/           
 | ---------- dx = C - ------------------------------ - ------------------------------ - ------------------------------ - ------------------------------ - ------------------------------ - ------------------------------ - ------------------------------
 | 1 + sin(x)                 2/x\      3/x\      /x\          2/x\      3/x\      /x\          2/x\      3/x\      /x\          2/x\      3/x\      /x\          2/x\      3/x\      /x\          2/x\      3/x\      /x\          2/x\      3/x\      /x\
 |                     1 + tan |-| + tan |-| + tan|-|   1 + tan |-| + tan |-| + tan|-|   1 + tan |-| + tan |-| + tan|-|   1 + tan |-| + tan |-| + tan|-|   1 + tan |-| + tan |-| + tan|-|   1 + tan |-| + tan |-| + tan|-|   1 + tan |-| + tan |-| + tan|-|
/                              \2/       \2/      \2/           \2/       \2/      \2/           \2/       \2/      \2/           \2/       \2/      \2/           \2/       \2/      \2/           \2/       \2/      \2/           \2/       \2/      \2/
∫sin⁡2(x)sin⁡(x)+1 dx=C−xtan⁡3(x2)tan⁡3(x2)+tan⁡2(x2)+tan⁡(x2)+1−xtan⁡2(x2)tan⁡3(x2)+tan⁡2(x2)+tan⁡(x2)+1−xtan⁡(x2)tan⁡3(x2)+tan⁡2(x2)+tan⁡(x2)+1−xtan⁡3(x2)+tan⁡2(x2)+tan⁡(x2)+1−2tan⁡2(x2)tan⁡3(x2)+tan⁡2(x2)+tan⁡(x2)+1−2tan⁡(x2)tan⁡3(x2)+tan⁡2(x2)+tan⁡(x2)+1−4tan⁡3(x2)+tan⁡2(x2)+tan⁡(x2)+1\int \frac{\sin^{2}{\left(x \right)}}{\sin{\left(x \right)} + 1}\, dx = C - \frac{x \tan^{3}{\left(\frac{x}{2} \right)}}{\tan^{3}{\left(\frac{x}{2} \right)} + \tan^{2}{\left(\frac{x}{2} \right)} + \tan{\left(\frac{x}{2} \right)} + 1} - \frac{x \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{3}{\left(\frac{x}{2} \right)} + \tan^{2}{\left(\frac{x}{2} \right)} + \tan{\left(\frac{x}{2} \right)} + 1} - \frac{x \tan{\left(\frac{x}{2} \right)}}{\tan^{3}{\left(\frac{x}{2} \right)} + \tan^{2}{\left(\frac{x}{2} \right)} + \tan{\left(\frac{x}{2} \right)} + 1} - \frac{x}{\tan^{3}{\left(\frac{x}{2} \right)} + \tan^{2}{\left(\frac{x}{2} \right)} + \tan{\left(\frac{x}{2} \right)} + 1} - \frac{2 \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{3}{\left(\frac{x}{2} \right)} + \tan^{2}{\left(\frac{x}{2} \right)} + \tan{\left(\frac{x}{2} \right)} + 1} - \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{3}{\left(\frac{x}{2} \right)} + \tan^{2}{\left(\frac{x}{2} \right)} + \tan{\left(\frac{x}{2} \right)} + 1} - \frac{4}{\tan^{3}{\left(\frac{x}{2} \right)} + \tan^{2}{\left(\frac{x}{2} \right)} + \tan{\left(\frac{x}{2} \right)} + 1}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.905-5
Trazar el gráfico f(x)
Respuesta [src] 
                                                           3                                       2                                                         
                     5                                  tan (1/2)                             3*tan (1/2)                             3*tan(1/2)             
4 - ------------------------------------ - ------------------------------------ - ------------------------------------ - ------------------------------------
           2           3                          2           3                          2           3                          2           3                
    1 + tan (1/2) + tan (1/2) + tan(1/2)   1 + tan (1/2) + tan (1/2) + tan(1/2)   1 + tan (1/2) + tan (1/2) + tan(1/2)   1 + tan (1/2) + tan (1/2) + tan(1/2)
−5tan⁡3(12)+tan⁡2(12)+tan⁡(12)+1−3tan⁡(12)tan⁡3(12)+tan⁡2(12)+tan⁡(12)+1−3tan⁡2(12)tan⁡3(12)+tan⁡2(12)+tan⁡(12)+1−tan⁡3(12)tan⁡3(12)+tan⁡2(12)+tan⁡(12)+1+4- \frac{5}{\tan^{3}{\left(\frac{1}{2} \right)} + \tan^{2}{\left(\frac{1}{2} \right)} + \tan{\left(\frac{1}{2} \right)} + 1} - \frac{3 \tan{\left(\frac{1}{2} \right)}}{\tan^{3}{\left(\frac{1}{2} \right)} + \tan^{2}{\left(\frac{1}{2} \right)} + \tan{\left(\frac{1}{2} \right)} + 1} - \frac{3 \tan^{2}{\left(\frac{1}{2} \right)}}{\tan^{3}{\left(\frac{1}{2} \right)} + \tan^{2}{\left(\frac{1}{2} \right)} + \tan{\left(\frac{1}{2} \right)} + 1} - \frac{\tan^{3}{\left(\frac{1}{2} \right)}}{\tan^{3}{\left(\frac{1}{2} \right)} + \tan^{2}{\left(\frac{1}{2} \right)} + \tan{\left(\frac{1}{2} \right)} + 1} + 4 
=
= 
                                                           3                                       2                                                         
                     5                                  tan (1/2)                             3*tan (1/2)                             3*tan(1/2)             
4 - ------------------------------------ - ------------------------------------ - ------------------------------------ - ------------------------------------
           2           3                          2           3                          2           3                          2           3                
    1 + tan (1/2) + tan (1/2) + tan(1/2)   1 + tan (1/2) + tan (1/2) + tan(1/2)   1 + tan (1/2) + tan (1/2) + tan(1/2)   1 + tan (1/2) + tan (1/2) + tan(1/2)
−5tan⁡3(12)+tan⁡2(12)+tan⁡(12)+1−3tan⁡(12)tan⁡3(12)+tan⁡2(12)+tan⁡(12)+1−3tan⁡2(12)tan⁡3(12)+tan⁡2(12)+tan⁡(12)+1−tan⁡3(12)tan⁡3(12)+tan⁡2(12)+tan⁡(12)+1+4- \frac{5}{\tan^{3}{\left(\frac{1}{2} \right)} + \tan^{2}{\left(\frac{1}{2} \right)} + \tan{\left(\frac{1}{2} \right)} + 1} - \frac{3 \tan{\left(\frac{1}{2} \right)}}{\tan^{3}{\left(\frac{1}{2} \right)} + \tan^{2}{\left(\frac{1}{2} \right)} + \tan{\left(\frac{1}{2} \right)} + 1} - \frac{3 \tan^{2}{\left(\frac{1}{2} \right)}}{\tan^{3}{\left(\frac{1}{2} \right)} + \tan^{2}{\left(\frac{1}{2} \right)} + \tan{\left(\frac{1}{2} \right)} + 1} - \frac{\tan^{3}{\left(\frac{1}{2} \right)}}{\tan^{3}{\left(\frac{1}{2} \right)} + \tan^{2}{\left(\frac{1}{2} \right)} + \tan{\left(\frac{1}{2} \right)} + 1} + 4 
4 - 5/(1 + tan(1/2)^2 + tan(1/2)^3 + tan(1/2)) - tan(1/2)^3/(1 + tan(1/2)^2 + tan(1/2)^3 + tan(1/2)) - 3*tan(1/2)^2/(1 + tan(1/2)^2 + tan(1/2)^3 + tan(1/2)) - 3*tan(1/2)/(1 + tan(1/2)^2 + tan(1/2)^3 + tan(1/2))
Respuesta numérica [src] 
0.166289701105837
0.166289701105837

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

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