Решение интегралов/ Определённый интеграл

Интеграл x/cos(x)^(2) (dx)

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Примеры

↑ Введите нижнюю границу интеграла и верхнюю границу интеграла b, подинтегральную функцию f(x) - смотрите пример

Кусочно-заданная:

{ кусочно-заданную функцию ввести здесь.

    Виды выражений

    уравнение x/cos(x)^(2) = 0
    неявная функция x/cos(x)^(2)
    производная неявной x/cos(x)^(2)
    канонический вид x/cos(x)^(2)
    система уравнений x/cos(x)^(2)
    интеграл x/cos(x)^(2)
    построить график x/cos(x)^(2)
    предел x/cos(x)^(2)
    производная x/cos(x)^(2)
    упростить x/cos(x)^(2)
    обычный калькулятор x/cos(x)^(2)

    Решение

    Вы ввели [src]
      1           
  /           
 |            
 |     x      
 |  ------- dx
 |     2      
 |  cos (x)   
 |            
/             
0
    ∫01xcos⁡2(x) dx\int\limits_{0}^{1} \frac{x}{\cos^{2}{\left(x \right)}}\, dx
    График
    0.001.000.100.200.300.400.500.600.700.800.9005
    Построить график f(x)
    Ответ [src]
       /       2     \                                                                             2                                      2                             2         /       2     \
log\1 + tan (1/2)/          pi*I + log(1 - tan(1/2))   log(1 + tan(1/2))     2*tan(1/2)     tan (1/2)*(pi*I + log(1 - tan(1/2)))   tan (1/2)*log(1 + tan(1/2))   tan (1/2)*log\1 + tan (1/2)/
------------------ - pi*I - ------------------------ - ----------------- - -------------- + ------------------------------------ + --------------------------- - ----------------------------
          2                              2                       2                 2                           2                                  2                             2            
  -1 + tan (1/2)                 -1 + tan (1/2)          -1 + tan (1/2)    -1 + tan (1/2)              -1 + tan (1/2)                     -1 + tan (1/2)                -1 + tan (1/2)
    log⁡(tan⁡2(12)+1)−1+tan⁡2(12)+log⁡(tan⁡(12)+1)tan⁡2(12)−1+tan⁡2(12)−log⁡(tan⁡2(12)+1)tan⁡2(12)−1+tan⁡2(12)−log⁡(tan⁡(12)+1)−1+tan⁡2(12)−2tan⁡(12)−1+tan⁡2(12)−iπ+(log⁡(1−tan⁡(12))+iπ)tan⁡2(12)−1+tan⁡2(12)−log⁡(1−tan⁡(12))+iπ−1+tan⁡2(12)\frac{\log{\left(\tan^{2}{\left(\frac{1}{2} \right)} + 1 \right)}}{-1 + \tan^{2}{\left(\frac{1}{2} \right)}} + \frac{\log{\left(\tan{\left(\frac{1}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{1}{2} \right)}}{-1 + \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{\log{\left(\tan^{2}{\left(\frac{1}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{1}{2} \right)}}{-1 + \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{\log{\left(\tan{\left(\frac{1}{2} \right)} + 1 \right)}}{-1 + \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{2 \tan{\left(\frac{1}{2} \right)}}{-1 + \tan^{2}{\left(\frac{1}{2} \right)}} - i \pi + \frac{\left(\log{\left(1 - \tan{\left(\frac{1}{2} \right)} \right)} + i \pi\right) \tan^{2}{\left(\frac{1}{2} \right)}}{-1 + \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{\log{\left(1 - \tan{\left(\frac{1}{2} \right)} \right)} + i \pi}{-1 + \tan^{2}{\left(\frac{1}{2} \right)}}
    =
    =
       /       2     \                                                                             2                                      2                             2         /       2     \
log\1 + tan (1/2)/          pi*I + log(1 - tan(1/2))   log(1 + tan(1/2))     2*tan(1/2)     tan (1/2)*(pi*I + log(1 - tan(1/2)))   tan (1/2)*log(1 + tan(1/2))   tan (1/2)*log\1 + tan (1/2)/
------------------ - pi*I - ------------------------ - ----------------- - -------------- + ------------------------------------ + --------------------------- - ----------------------------
          2                              2                       2                 2                           2                                  2                             2            
  -1 + tan (1/2)                 -1 + tan (1/2)          -1 + tan (1/2)    -1 + tan (1/2)              -1 + tan (1/2)                     -1 + tan (1/2)                -1 + tan (1/2)
    log⁡(tan⁡2(12)+1)−1+tan⁡2(12)+log⁡(tan⁡(12)+1)tan⁡2(12)−1+tan⁡2(12)−log⁡(tan⁡2(12)+1)tan⁡2(12)−1+tan⁡2(12)−log⁡(tan⁡(12)+1)−1+tan⁡2(12)−2tan⁡(12)−1+tan⁡2(12)−iπ+(log⁡(1−tan⁡(12))+iπ)tan⁡2(12)−1+tan⁡2(12)−log⁡(1−tan⁡(12))+iπ−1+tan⁡2(12)\frac{\log{\left(\tan^{2}{\left(\frac{1}{2} \right)} + 1 \right)}}{-1 + \tan^{2}{\left(\frac{1}{2} \right)}} + \frac{\log{\left(\tan{\left(\frac{1}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{1}{2} \right)}}{-1 + \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{\log{\left(\tan^{2}{\left(\frac{1}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{1}{2} \right)}}{-1 + \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{\log{\left(\tan{\left(\frac{1}{2} \right)} + 1 \right)}}{-1 + \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{2 \tan{\left(\frac{1}{2} \right)}}{-1 + \tan^{2}{\left(\frac{1}{2} \right)}} - i \pi + \frac{\left(\log{\left(1 - \tan{\left(\frac{1}{2} \right)} \right)} + i \pi\right) \tan^{2}{\left(\frac{1}{2} \right)}}{-1 + \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{\log{\left(1 - \tan{\left(\frac{1}{2} \right)} \right)} + i \pi}{-1 + \tan^{2}{\left(\frac{1}{2} \right)}}
    Упростить
    Численный ответ [src]
    0.941781254268888
    Ответ (Неопределённый) [src]
      /                    /       2/x\\      /       /x\\      /        /x\\      2/x\    /       /x\\      2/x\    /        /x\\      2/x\    /       2/x\\           /x\ 
 |                  log|1 + tan |-||   log|1 + tan|-||   log|-1 + tan|-||   tan |-|*log|1 + tan|-||   tan |-|*log|-1 + tan|-||   tan |-|*log|1 + tan |-||    2*x*tan|-| 
 |    x                \        \2//      \       \2//      \        \2//       \2/    \       \2//       \2/    \        \2//       \2/    \        \2//           \2/ 
 | ------- dx = C + ---------------- - --------------- - ---------------- + ----------------------- + ------------------------ - ------------------------ - ------------
 |    2                       2/x\               2/x\              2/x\                   2/x\                      2/x\                       2/x\                 2/x\
 | cos (x)            -1 + tan |-|       -1 + tan |-|      -1 + tan |-|           -1 + tan |-|              -1 + tan |-|               -1 + tan |-|         -1 + tan |-|
 |                             \2/                \2/               \2/                    \2/                       \2/                        \2/                  \2/
/
    ∫xcos⁡2(x) dx=C−2xtan⁡(x2)tan⁡2(x2)−1+log⁡(tan⁡(x2)−1)tan⁡2(x2)tan⁡2(x2)−1−log⁡(tan⁡(x2)−1)tan⁡2(x2)−1+log⁡(tan⁡(x2)+1)tan⁡2(x2)tan⁡2(x2)−1−log⁡(tan⁡(x2)+1)tan⁡2(x2)−1−log⁡(tan⁡2(x2)+1)tan⁡2(x2)tan⁡2(x2)−1+log⁡(tan⁡2(x2)+1)tan⁡2(x2)−1\int \frac{x}{\cos^{2}{\left(x \right)}}\, dx = C - \frac{2 x \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} + \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} - \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} + \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} - \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} - \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} + \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1}
    Упростить
    График
    Интеграл x/cos(x)^(2) (dx) /media/krcore-image-pods/hash/indefinite/8/4d/9be4f97c956a9b8da4189a7c1713c.png