Интеграл 1/(sin(x)^(2)*(1-cos(x))) (dx)

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  1                        
  /                        
 |                         
 |           1             
 |  -------------------- dx
 |     2                   
 |  sin (x)*(1 - cos(x))   
 |                         
/                          
0                          

$$\int_{0}^{1} \frac{1}{\left(- \cos{\left (x \right )} + 1\right) \sin^{2}{\left (x \right )}}\, dx$$

Ответ

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  1                                                         
  /                                                         
 |                                                          
 |           1                         1             1      
 |  -------------------- dx = oo - ---------- - ------------
 |     2                           2*tan(1/2)         3     
 |  sin (x)*(1 - cos(x))                        12*tan (1/2)
 |                                                          
/                                                           
0                                                           

$${\it \%a}$$

Ответ (Неопределённый)

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  /                                                         /x\
 |                                                       tan|-|
 |          1                       1           1           \2/
 | -------------------- dx = C - -------- - ---------- + ------
 |    2                               /x\         3/x\     4   
 | sin (x)*(1 - cos(x))          2*tan|-|   12*tan |-|         
 |                                    \2/          \2/         
/                                                              

$$2\,\left({{\sin x}\over{8\,\left(\cos x+1\right)}}-{{\left(\cos x+1 \right)^3\,\left({{6\,\sin ^2x}\over{\left(\cos x+1\right)^2}}+1 \right)}\over{24\,\sin ^3x}}\right)$$

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