Sr Examen

Otras calculadoras

Resolución de integrales/ cos(z)/ (xy^2)^cos(z)

Integral de (xy^2)^cos(z) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                
  /                
 |                 
 |        cos(z)   
 |  /   2\         
 |  \x*y /       dx
 |                 
/                  
0
∫01(xy2)cos⁡(z) dx\int\limits_{0}^{1} \left(x y^{2}\right)^{\cos{\left(z \right)}}\, dx 
Integral((x*y^2)^cos(z), (x, 0, 1))
Respuesta (Indefinida) [src] 
                         ///      1 + cos(z)                               \
                         |||/   2\                                         |
                         |||\x*y /                                         |
  /                      |||----------------  for cos(z) != -1             |
 |                       ||<   1 + cos(z)                                  |
 |       cos(z)          |||                                               |
 | /   2\                |||      /   2\                                   |
 | \x*y /       dx = C + |<|   log\x*y /         otherwise                 |
 |                       ||\                                         2     |
/                        ||-----------------------------------  for y  != 0|
                         ||                  2                             |
                         ||                 y                              |
                         ||                                                |
                         ||                cos(z)                          |
                         \\             x*0                      otherwise /
∫(xy2)cos⁡(z) dx=C+{{(xy2)cos⁡(z)+1cos⁡(z)+1for cos⁡(z)≠−1log⁡(xy2)otherwisey2for y2≠00cos⁡(z)xotherwise\int \left(x y^{2}\right)^{\cos{\left(z \right)}}\, dx = C + \begin{cases} \frac{\begin{cases} \frac{\left(x y^{2}\right)^{\cos{\left(z \right)} + 1}}{\cos{\left(z \right)} + 1} & \text{for}\: \cos{\left(z \right)} \neq -1 \\\log{\left(x y^{2} \right)} & \text{otherwise} \end{cases}}{y^{2}} & \text{for}\: y^{2} \neq 0 \\0^{\cos{\left(z \right)}} x & \text{otherwise} \end{cases}
Simplificar
Respuesta [src] 
/     1 + cos(z)                                                                       
| / 2\                1 + cos(z)                                                       
| \y /               0                                                                 
|--------------- - ---------------  for Or(And(z >= 0, z < pi), And(z <= 2*pi, z > pi))
| 2                 2                                                                  
|y *(1 + cos(z))   y *(1 + cos(z))                                                     
<                                                                                      
|                       / 2\                                                           
|             /1 \   log\y /                                                           
|      oo*sign|--| + -------                             otherwise                     
|             | 2|       2                                                             
|             \y /      y                                                              
\
{−0cos⁡(z)+1y2(cos⁡(z)+1)+(y2)cos⁡(z)+1y2(cos⁡(z)+1)for (z≥0∧z<π)∨(z≤2π∧z>π)∞sign⁡(1y2)+log⁡(y2)y2otherwise\begin{cases} - \frac{0^{\cos{\left(z \right)} + 1}}{y^{2} \left(\cos{\left(z \right)} + 1\right)} + \frac{\left(y^{2}\right)^{\cos{\left(z \right)} + 1}}{y^{2} \left(\cos{\left(z \right)} + 1\right)} & \text{for}\: \left(z \geq 0 \wedge z < \pi\right) \vee \left(z \leq 2 \pi \wedge z > \pi\right) \\\infty \operatorname{sign}{\left(\frac{1}{y^{2}} \right)} + \frac{\log{\left(y^{2} \right)}}{y^{2}} & \text{otherwise} \end{cases} 
=
= 
/     1 + cos(z)                                                                       
| / 2\                1 + cos(z)                                                       
| \y /               0                                                                 
|--------------- - ---------------  for Or(And(z >= 0, z < pi), And(z <= 2*pi, z > pi))
| 2                 2                                                                  
|y *(1 + cos(z))   y *(1 + cos(z))                                                     
<                                                                                      
|                       / 2\                                                           
|             /1 \   log\y /                                                           
|      oo*sign|--| + -------                             otherwise                     
|             | 2|       2                                                             
|             \y /      y                                                              
\
{−0cos⁡(z)+1y2(cos⁡(z)+1)+(y2)cos⁡(z)+1y2(cos⁡(z)+1)for (z≥0∧z<π)∨(z≤2π∧z>π)∞sign⁡(1y2)+log⁡(y2)y2otherwise\begin{cases} - \frac{0^{\cos{\left(z \right)} + 1}}{y^{2} \left(\cos{\left(z \right)} + 1\right)} + \frac{\left(y^{2}\right)^{\cos{\left(z \right)} + 1}}{y^{2} \left(\cos{\left(z \right)} + 1\right)} & \text{for}\: \left(z \geq 0 \wedge z < \pi\right) \vee \left(z \leq 2 \pi \wedge z > \pi\right) \\\infty \operatorname{sign}{\left(\frac{1}{y^{2}} \right)} + \frac{\log{\left(y^{2} \right)}}{y^{2}} & \text{otherwise} \end{cases} 
Piecewise(((y^2)^(1 + cos(z))/(y^2*(1 + cos(z))) - 0^(1 + cos(z))/(y^2*(1 + cos(z))), ((z >= 0)∧(z < pi))∨((z > pi)∧(z <= 2*pi))), (oo*sign(y^(-2)) + log(y^2)/y^2, True))

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

    © Sr Examen – Калькулятор