Mister Exam

Other calculators

Solving integrals/ (e)^(-2x)*cosxdx

Integral of (e)^(-2x)*cosxdx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 oo                
  /                
 |                 
 |   -2*x          
 |  E    *cos(x) dx
 |                 
/                  
2
∫2∞e−2xcos⁡(x) dx\int\limits_{2}^{\infty} e^{- 2 x} \cos{\left(x \right)}\, dx 
Integral(E^(-2*x)*cos(x), (x, 2, oo))
The answer (Indefinite) [src] 
  /                                                   
 |                                 -2*x    -2*x       
 |  -2*x                 2*cos(x)*e       e    *sin(x)
 | E    *cos(x) dx = C - -------------- + ------------
 |                             5               5      
/
∫e−2xcos⁡(x) dx=C+e−2xsin⁡(x)5−2e−2xcos⁡(x)5\int e^{- 2 x} \cos{\left(x \right)}\, dx = C + \frac{e^{- 2 x} \sin{\left(x \right)}}{5} - \frac{2 e^{- 2 x} \cos{\left(x \right)}}{5}
Simplify
The answer [src] 
   -4                    -4
  e  *sin(2)   2*cos(2)*e  
- ---------- + ------------
      5             5
−sin⁡(2)5e4+2cos⁡(2)5e4- \frac{\sin{\left(2 \right)}}{5 e^{4}} + \frac{2 \cos{\left(2 \right)}}{5 e^{4}} 
=
= 
   -4                    -4
  e  *sin(2)   2*cos(2)*e  
- ---------- + ------------
      5             5
−sin⁡(2)5e4+2cos⁡(2)5e4- \frac{\sin{\left(2 \right)}}{5 e^{4}} + \frac{2 \cos{\left(2 \right)}}{5 e^{4}} 
-exp(-4)*sin(2)/5 + 2*cos(2)*exp(-4)/5

    Use the examples entering the upper and lower limits of integration.

    © Mister Exam – Calculator