Sr Examen

Otras calculadoras

Resolución de integrales/ cos(t)/ sin(t)/ sin(t)/(1-kcos(t))

Integral de sin(t)/(1-kcos(t)) dt

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 pi                
  /                
 |                 
 |     sin(t)      
 |  ------------ dt
 |  1 - k*cos(t)   
 |                 
/                  
0
∫0πsin⁡(t)−kcos⁡(t)+1 dt\int\limits_{0}^{\pi} \frac{\sin{\left(t \right)}}{- k \cos{\left(t \right)} + 1}\, dt 
Integral(sin(t)/(1 - k*cos(t)), (t, 0, pi))
Respuesta (Indefinida) [src] 
  /                                                      
 |                       //log(1 - k*cos(t))            \
 |    sin(t)             ||-----------------  for k != 0|
 | ------------ dt = C + |<        k                    |
 | 1 - k*cos(t)          ||                             |
 |                       \\     -cos(t)       otherwise /
/
∫sin⁡(t)−kcos⁡(t)+1 dt=C+{log⁡(−kcos⁡(t)+1)kfor k≠0−cos⁡(t)otherwise\int \frac{\sin{\left(t \right)}}{- k \cos{\left(t \right)} + 1}\, dt = C + \begin{cases} \frac{\log{\left(- k \cos{\left(t \right)} + 1 \right)}}{k} & \text{for}\: k \neq 0 \\- \cos{\left(t \right)} & \text{otherwise} \end{cases}
Simplificar
Respuesta [src] 
/   /     1\      /    1\                                  
|log|-1 - -|   log|1 - -|                                  
|   \     k/      \    k/                                  
<----------- - ----------  for And(k > -oo, k < oo, k != 0)
|     k            k                                       
|                                                          
\           2                         otherwise
{log⁡(−1−1k)k−log⁡(1−1k)kfor k>−∞∧k<∞∧k≠02otherwise\begin{cases} \frac{\log{\left(-1 - \frac{1}{k} \right)}}{k} - \frac{\log{\left(1 - \frac{1}{k} \right)}}{k} & \text{for}\: k > -\infty \wedge k < \infty \wedge k \neq 0 \\2 & \text{otherwise} \end{cases} 
=
= 
/   /     1\      /    1\                                  
|log|-1 - -|   log|1 - -|                                  
|   \     k/      \    k/                                  
<----------- - ----------  for And(k > -oo, k < oo, k != 0)
|     k            k                                       
|                                                          
\           2                         otherwise
{log⁡(−1−1k)k−log⁡(1−1k)kfor k>−∞∧k<∞∧k≠02otherwise\begin{cases} \frac{\log{\left(-1 - \frac{1}{k} \right)}}{k} - \frac{\log{\left(1 - \frac{1}{k} \right)}}{k} & \text{for}\: k > -\infty \wedge k < \infty \wedge k \neq 0 \\2 & \text{otherwise} \end{cases} 
Piecewise((log(-1 - 1/k)/k - log(1 - 1/k)/k, (k > -oo)∧(k < oo)∧(Ne(k, 0))), (2, True))

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

    © Sr Examen – Калькулятор