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Integral de cos(2*x)/(sin(x)+cos(x)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
  1                   
  /                   
 |                    
 |      cos(2*x)      
 |  --------------- dx
 |  sin(x) + cos(x)   
 |                    
/                     
0                     
$$\int\limits_{0}^{1} \frac{\cos{\left(2 x \right)}}{\sin{\left(x \right)} + \cos{\left(x \right)}}\, dx$$
Integral(cos(2*x)/(sin(x) + cos(x)), (x, 0, 1))
Respuesta (Indefinida) [src]
  /                                           ___    /       ___      /x\\           /x\       ___    /       ___      /x\\       ___    /       ___      /x\\       ___    /       ___      /x\\       ___    2/x\    /       ___      /x\\       ___    2/x\    /       ___      /x\\
 |                                          \/ 2 *log|-1 - \/ 2  + tan|-||      8*tan|-|     \/ 2 *log|-1 + \/ 2  + tan|-||   2*\/ 2 *log|-1 - \/ 2  + tan|-||   2*\/ 2 *log|-1 + \/ 2  + tan|-||   2*\/ 2 *tan |-|*log|-1 - \/ 2  + tan|-||   2*\/ 2 *tan |-|*log|-1 + \/ 2  + tan|-||
 |     cos(2*x)                   8                  \                \2//           \2/              \                \2//              \                \2//              \                \2//               \2/    \                \2//               \2/    \                \2//
 | --------------- dx = C + ------------- + ------------------------------ + ------------- - ------------------------------ - -------------------------------- + -------------------------------- - ---------------------------------------- + ----------------------------------------
 | sin(x) + cos(x)                   2/x\                 2                           2/x\                 2                                    2/x\                               2/x\                                   2/x\                                       2/x\              
 |                          4 + 4*tan |-|                                    4 + 4*tan |-|                                             4 + 4*tan |-|                      4 + 4*tan |-|                          4 + 4*tan |-|                              4 + 4*tan |-|              
/                                     \2/                                              \2/                                                       \2/                                \2/                                    \2/                                        \2/              
$$\int \frac{\cos{\left(2 x \right)}}{\sin{\left(x \right)} + \cos{\left(x \right)}}\, dx = C - \frac{\sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 + \sqrt{2} \right)}}{2} + \frac{\sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} - 1 \right)}}{2} + \frac{2 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 + \sqrt{2} \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{4 \tan^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{2 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 + \sqrt{2} \right)}}{4 \tan^{2}{\left(\frac{x}{2} \right)} + 4} - \frac{2 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} - 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{4 \tan^{2}{\left(\frac{x}{2} \right)} + 4} - \frac{2 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} - 1 \right)}}{4 \tan^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{8 \tan{\left(\frac{x}{2} \right)}}{4 \tan^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{8}{4 \tan^{2}{\left(\frac{x}{2} \right)} + 4}$$
Gráfica
Respuesta numérica [src]
0.381773290676036
0.381773290676036

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.