Интеграл 1/(1+(cos(x))^2) (dx)

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  1                               /  ___       ___\              /    ___       ___\              /  ___       ___           \              /    ___       ___           \              /  ___       ___\              /    ___       ___\              /  ___       ___           \              /    ___       ___           \
  /                        ___    |\/ 2    I*\/ 2 |       ___    |  \/ 2    I*\/ 2 |       ___    |\/ 2    I*\/ 2            |       ___    |  \/ 2    I*\/ 2            |       ___    |\/ 2    I*\/ 2 |       ___    |  \/ 2    I*\/ 2 |       ___    |\/ 2    I*\/ 2            |       ___    |  \/ 2    I*\/ 2            |
 |                     I*\/ 2 *log|----- + -------|   I*\/ 2 *log|- ----- + -------|   I*\/ 2 *log|----- - ------- + tan(1/2)|   I*\/ 2 *log|- ----- - ------- + tan(1/2)|   I*\/ 2 *log|----- - -------|   I*\/ 2 *log|- ----- - -------|   I*\/ 2 *log|----- + ------- + tan(1/2)|   I*\/ 2 *log|- ----- + ------- + tan(1/2)|
 |       1                        \  2        2   /              \    2        2   /              \  2        2              /              \    2        2              /              \  2        2   /              \    2        2   /              \  2        2              /              \    2        2              /
 |  ----------- dx = - ---------------------------- - ------------------------------ - --------------------------------------- - ----------------------------------------- + ---------------------------- + ------------------------------ + --------------------------------------- + -----------------------------------------
 |         2                        4                               4                                     4                                          4                                    4                               4                                     4                                          4                    
 |  1 + cos (x)                                                                                                                                                                                                                                                                                                                 
 |                                                                                                                                                                                                                                                                                                                              
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0                                                                                                                                                                                                                                                                                                                               

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

Численный ответ

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0.589407539463719

Ответ (Неопределённый)

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                                   /  ___       ___         \              /    ___       ___         \              /  ___       ___         \              /    ___       ___         \
  /                         ___    |\/ 2    I*\/ 2       /x\|       ___    |  \/ 2    I*\/ 2       /x\|       ___    |\/ 2    I*\/ 2       /x\|       ___    |  \/ 2    I*\/ 2       /x\|
 |                      I*\/ 2 *log|----- - ------- + tan|-||   I*\/ 2 *log|- ----- - ------- + tan|-||   I*\/ 2 *log|----- + ------- + tan|-||   I*\/ 2 *log|- ----- + ------- + tan|-||
 |      1                          \  2        2         \2//              \    2        2         \2//              \  2        2         \2//              \    2        2         \2//
 | ----------- dx = C - ------------------------------------- - --------------------------------------- + ------------------------------------- + ---------------------------------------
 |        2                               4                                        4                                        4                                        4                   
 | 1 + cos (x)                                                                                                                                                                           
 |                                                                                                                                                                                       
/                                                                                                                                                                                        

$${{\arctan \left({{\tan x}\over{\sqrt{2}}}\right)}\over{\sqrt{2}}}$$

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