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Resolución de integrales/ (e^-absolute(x))*cosxy*cosx

Integral de (e^-absolute(x))*cosxy*cosx dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 100000                         
    /                           
   |                            
   |     -|x|                   
   |    E    *cos(x)*y*cos(x) dx
   |                            
  /                             
-100000
$$\int\limits_{-100000}^{100000} y e^{- \left|{x}\right|} \cos{\left(x \right)} \cos{\left(x \right)}\, dx$$ 
Integral(((E^(-|x|)*cos(x))*y)*cos(x), (x, -100000, 100000))
Respuesta (Indefinida) [src] 
  /                                   /                
 |                                   |                 
 |  -|x|                             |    2     -|x|   
 | E    *cos(x)*y*cos(x) dx = C + y* | cos (x)*e     dx
 |                                   |                 
/                                   /
$$\int y e^{- \left|{x}\right|} \cos{\left(x \right)} \cos{\left(x \right)}\, dx = C + y \int e^{- \left|{x}\right|} \cos^{2}{\left(x \right)}\, dx$$
Simplificar
Respuesta [src] 
        /       2          -100000        2          -100000                  -100000            \     /     2          -100000        2          -100000                  -100000            \
6*y     |  3*cos (100000)*e          2*sin (100000)*e          2*cos(100000)*e       *sin(100000)|     |2*sin (100000)*e          3*cos (100000)*e          2*cos(100000)*e       *sin(100000)|
--- + y*|- ----------------------- - ----------------------- + ----------------------------------| - y*|----------------------- + ----------------------- - ----------------------------------|
 5      \             5                         5                              5                 /     \           5                         5                              5                 /
$$y \left(- \frac{3 \cos^{2}{\left(100000 \right)}}{5 e^{100000}} - \frac{2 \sin^{2}{\left(100000 \right)}}{5 e^{100000}} + \frac{2 \sin{\left(100000 \right)} \cos{\left(100000 \right)}}{5 e^{100000}}\right) - y \left(\frac{2 \sin^{2}{\left(100000 \right)}}{5 e^{100000}} + \frac{3 \cos^{2}{\left(100000 \right)}}{5 e^{100000}} - \frac{2 \sin{\left(100000 \right)} \cos{\left(100000 \right)}}{5 e^{100000}}\right) + \frac{6 y}{5}$$ 
=
= 
        /       2          -100000        2          -100000                  -100000            \     /     2          -100000        2          -100000                  -100000            \
6*y     |  3*cos (100000)*e          2*sin (100000)*e          2*cos(100000)*e       *sin(100000)|     |2*sin (100000)*e          3*cos (100000)*e          2*cos(100000)*e       *sin(100000)|
--- + y*|- ----------------------- - ----------------------- + ----------------------------------| - y*|----------------------- + ----------------------- - ----------------------------------|
 5      \             5                         5                              5                 /     \           5                         5                              5                 /
$$y \left(- \frac{3 \cos^{2}{\left(100000 \right)}}{5 e^{100000}} - \frac{2 \sin^{2}{\left(100000 \right)}}{5 e^{100000}} + \frac{2 \sin{\left(100000 \right)} \cos{\left(100000 \right)}}{5 e^{100000}}\right) - y \left(\frac{2 \sin^{2}{\left(100000 \right)}}{5 e^{100000}} + \frac{3 \cos^{2}{\left(100000 \right)}}{5 e^{100000}} - \frac{2 \sin{\left(100000 \right)} \cos{\left(100000 \right)}}{5 e^{100000}}\right) + \frac{6 y}{5}$$ 
6*y/5 + y*(-3*cos(100000)^2*exp(-100000)/5 - 2*sin(100000)^2*exp(-100000)/5 + 2*cos(100000)*exp(-100000)*sin(100000)/5) - y*(2*sin(100000)^2*exp(-100000)/5 + 3*cos(100000)^2*exp(-100000)/5 - 2*cos(100000)*exp(-100000)*sin(100000)/5)

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

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