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e^(-x)*cos(x)*dx

Integral of e^(-x)*cos(x)*dx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                
  /                
 |                 
 |   -x            
 |  e  *cos(x)*1 dx
 |                 
/                  
0                  
$$\int\limits_{0}^{1} e^{- x} \cos{\left(x \right)} 1\, dx$$
Detail solution
  1. Use integration by parts, noting that the integrand eventually repeats itself.

    1. For the integrand :

      Let and let .

      Then .

    2. For the integrand :

      Let and let .

      Then .

    3. Notice that the integrand has repeated itself, so move it to one side:

      Therefore,

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                             
 |                        -x                  -x
 |  -x                   e  *sin(x)   cos(x)*e  
 | e  *cos(x)*1 dx = C + ---------- - ----------
 |                           2            2     
/                                               
$${{e^ {- x }\,\left(\sin x-\cos x\right)}\over{2}}$$
The graph
The answer [src]
     -1                  -1
1   e  *sin(1)   cos(1)*e  
- + ---------- - ----------
2       2            2     
$${{e^ {- 1 }\,\left(\sin 1-\cos 1\right)}\over{2}}+{{1}\over{2}}$$
=
=
     -1                  -1
1   e  *sin(1)   cos(1)*e  
- + ---------- - ----------
2       2            2     
$$- \frac{\cos{\left(1 \right)}}{2 e} + \frac{\sin{\left(1 \right)}}{2 e} + \frac{1}{2}$$
Numerical answer [src]
0.55539688265335
0.55539688265335
The graph
Integral of e^(-x)*cos(x)*dx dx

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