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Resolución de integrales/ 2*x+3/ (2*x+3)*cos(x*K)

Integral de (2*x+3)*cos(x*K) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 pi                      
  /                      
 |                       
 |  (2*x + 3)*cos(x*k) dx
 |                       
/                        
-pi
∫−ππ(2x+3)cos⁡(kx) dx\int\limits_{- \pi}^{\pi} \left(2 x + 3\right) \cos{\left(k x \right)}\, dx 
Integral((2*x + 3)*cos(x*k), (x, -pi, pi))
Respuesta (Indefinida) [src] 
                                 //           2                      \                                                        
                                 ||          x                       |                                                        
                                 ||          --             for k = 0|                                                        
                                 ||          2                       |                                                        
  /                              ||                                  |     //   x      for k = 0\       //   x      for k = 0\
 |                               ||/-cos(k*x)                        |     ||                   |       ||                   |
 | (2*x + 3)*cos(x*k) dx = C - 2*|<|----------  for k != 0           | + 3*|
∫(2x+3)cos⁡(kx) dx=C+2x({xfor k=0sin⁡(kx)kotherwise)+3({xfor k=0sin⁡(kx)kotherwise)−2({x22for k=0{−cos⁡(kx)kfor k≠00otherwisekotherwise)\int \left(2 x + 3\right) \cos{\left(k x \right)}\, dx = C + 2 x \left(\begin{cases} x & \text{for}\: k = 0 \\\frac{\sin{\left(k x \right)}}{k} & \text{otherwise} \end{cases}\right) + 3 \left(\begin{cases} x & \text{for}\: k = 0 \\\frac{\sin{\left(k x \right)}}{k} & \text{otherwise} \end{cases}\right) - 2 \left(\begin{cases} \frac{x^{2}}{2} & \text{for}\: k = 0 \\\frac{\begin{cases} - \frac{\cos{\left(k x \right)}}{k} & \text{for}\: k \neq 0 \\0 & \text{otherwise} \end{cases}}{k} & \text{otherwise} \end{cases}\right)
Simplificar
Respuesta [src] 
/6*sin(pi*k)                                  
|-----------  for And(k > -oo, k < oo, k != 0)
<     k                                       
|                                             
\   6*pi                 otherwise
{6sin⁡(πk)kfor k>−∞∧k<∞∧k≠06πotherwise\begin{cases} \frac{6 \sin{\left(\pi k \right)}}{k} & \text{for}\: k > -\infty \wedge k < \infty \wedge k \neq 0 \\6 \pi & \text{otherwise} \end{cases} 
=
= 
/6*sin(pi*k)                                  
|-----------  for And(k > -oo, k < oo, k != 0)
<     k                                       
|                                             
\   6*pi                 otherwise
{6sin⁡(πk)kfor k>−∞∧k<∞∧k≠06πotherwise\begin{cases} \frac{6 \sin{\left(\pi k \right)}}{k} & \text{for}\: k > -\infty \wedge k < \infty \wedge k \neq 0 \\6 \pi & \text{otherwise} \end{cases} 
Piecewise((6*sin(pi*k)/k, (k > -oo)∧(k < oo)∧(Ne(k, 0))), (6*pi, True))

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

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