Интеграл 1/(5+2*cos(x)) (dx)

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  1                
  /                
 |                 
 |       1         
 |  ------------ dx
 |  5 + 2*cos(x)   
 |                 
/                  
0                  

$$\int_{0}^{1} \frac{1}{2 \cos{\left (x \right )} + 5}\, dx$$

Ответ

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  1                                 /    ____\               /      ____           \               /     ____ \               /    ____           \
  /                         ____    |I*\/ 21 |       ____    |  I*\/ 21            |       ____    |-I*\/ 21  |       ____    |I*\/ 21            |
 |                      I*\/ 21 *log|--------|   I*\/ 21 *log|- -------- + tan(1/2)|   I*\/ 21 *log|----------|   I*\/ 21 *log|-------- + tan(1/2)|
 |       1                          \   3    /               \     3               /               \    3     /               \   3               /
 |  ------------ dx = - ---------------------- - ----------------------------------- + ------------------------ + ---------------------------------
 |  5 + 2*cos(x)                  21                              21                              21                              21               
 |                                                                                                                                                 
/                                                                                                                                                  
0                                                                                                                                                  

$${{2\,\arctan \left({{\sqrt{21}\,\sin 1}\over{7\,\cos 1+7}}\right) }\over{\sqrt{21}}}$$

Численный ответ

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0.149899903641621

Ответ (Неопределённый)

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                                     /      ____         \               /    ____         \
  /                          ____    |  I*\/ 21       /x\|       ____    |I*\/ 21       /x\|
 |                       I*\/ 21 *log|- -------- + tan|-||   I*\/ 21 *log|-------- + tan|-||
 |      1                            \     3          \2//               \   3          \2//
 | ------------ dx = C - --------------------------------- + -------------------------------
 | 5 + 2*cos(x)                          21                                 21              
 |                                                                                          
/                                                                                           

$${{2\,\arctan \left({{3\,\sin x}\over{\sqrt{21}\,\left(\cos x+1 \right)}}\right)}\over{\sqrt{21}}}$$

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