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e^(2x)cosx

Integral of e^(2x)cosx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1               
  /               
 |                
 |   2*x          
 |  e   *cos(x) dx
 |                
/                 
0                 
$$\int\limits_{0}^{1} e^{2 x} \cos{\left(x \right)}\, dx$$
Integral(E^(2*x)*cos(x), (x, 0, 1))
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]
  /                                                
 |                       2*x                    2*x
 |  2*x                 e   *sin(x)   2*cos(x)*e   
 | e   *cos(x) dx = C + ----------- + -------------
 |                           5              5      
/                                                  
$${{e^{2\,x}\,\left(\sin x+2\,\cos x\right)}\over{5}}$$
The graph
The answer [src]
       2                    2
  2   e *sin(1)   2*cos(1)*e 
- - + --------- + -----------
  5       5            5     
$${{e^2\,\sin 1+2\,e^2\,\cos 1}\over{5}}-{{2}\over{5}}$$
=
=
       2                    2
  2   e *sin(1)   2*cos(1)*e 
- - + --------- + -----------
  5       5            5     
$$- \frac{2}{5} + \frac{e^{2} \sin{\left(1 \right)}}{5} + \frac{2 e^{2} \cos{\left(1 \right)}}{5}$$
Numerical answer [src]
2.4404648818501
2.4404648818501
The graph
Integral of e^(2x)cosx dx

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