Интеграл x/(1-sin(x)) (dx)

Вы ввели

  1              
  /              
 |               
 |      x        
 |  ---------- dx
 |  1 - sin(x)   
 |               
/                
0                

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

Ответ

  1                                                                                                                                                                                   
  /                                                                                                                                                                                   
 |                                       /       2     \                                                              /       2     \                                                 
 |      x                   1         log\1 + tan (1/2)/      tan(1/2)              2*(pi*I + log(1 - tan(1/2)))   log\1 + tan (1/2)/*tan(1/2)   2*(pi*I + log(1 - tan(1/2)))*tan(1/2)
 |  ---------- dx = - ------------- + ------------------ - ------------- - 2*pi*I - ---------------------------- - --------------------------- + -------------------------------------
 |  1 - sin(x)        -1 + tan(1/2)     -1 + tan(1/2)      -1 + tan(1/2)                   -1 + tan(1/2)                  -1 + tan(1/2)                      -1 + tan(1/2)            
 |                                                                                                                                                                                    
/                                                                                                                                                                                     
0                                                                                                                                                                                     

$${{\left(\sin ^21-2\,\sin 1+\cos ^21+1\right)\,\log \left(\sin ^21-2 \,\sin 1+\cos ^21+1\right)+2\,\cos 1}\over{\sin ^21-2\,\sin 1+\cos ^ 21+1}}-\log 2$$

Численный ответ

1.5664058010663

Ответ (Неопределённый)

  /                       /       2/x\\                      /        /x\\          /x\       /       2/x\\    /x\        /        /x\\    /x\
 |                     log|1 + tan |-||                 2*log|-1 + tan|-||     x*tan|-|    log|1 + tan |-||*tan|-|   2*log|-1 + tan|-||*tan|-|
 |     x                  \        \2//        x             \        \2//          \2/       \        \2//    \2/        \        \2//    \2/
 | ---------- dx = C + ---------------- - ----------- - ------------------ - ----------- - ----------------------- + -------------------------
 | 1 - sin(x)                    /x\              /x\              /x\               /x\                 /x\                        /x\       
 |                       -1 + tan|-|      -1 + tan|-|      -1 + tan|-|       -1 + tan|-|         -1 + tan|-|                -1 + tan|-|       
/                                \2/              \2/              \2/               \2/                 \2/                        \2/       

$${{\left(\sin ^2x-2\,\sin x+\cos ^2x+1\right)\,\log \left(\sin ^2x-2 \,\sin x+\cos ^2x+1\right)+2\,x\,\cos x}\over{\sin ^2x-2\,\sin x+ \cos ^2x+1}}$$