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  • exp^(two *x)*cosx
  • exponent of to the power of (2 multiply by x) multiply by co sinus of e of x
  • exponent of to the power of (two multiply by x) multiply by co sinus of e of x
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  • exp^(2*x)*cosxdx
Solving integrals/ exp^(2*x)*cosx

Integral of exp^(2*x)*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))
The answer (Indefinite) [src] 
  /                                                
 |                       2*x                    2*x
 |  2*x                 e   *sin(x)   2*cos(x)*e   
 | E   *cos(x) dx = C + ----------- + -------------
 |                           5              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 graph
Plot the graph f(x)
The answer [src] 
       2                    2
  2   e *sin(1)   2*cos(1)*e 
- - + --------- + -----------
  5       5            5
$$- \frac{2}{5} + \frac{e^{2} \sin{\left(1 \right)}}{5} + \frac{2 e^{2} \cos{\left(1 \right)}}{5}$$ 
=
= 
       2                    2
  2   e *sin(1)   2*cos(1)*e 
- - + --------- + -----------
  5       5            5
$$- \frac{2}{5} + \frac{e^{2} \sin{\left(1 \right)}}{5} + \frac{2 e^{2} \cos{\left(1 \right)}}{5}$$ 
-2/5 + exp(2)*sin(1)/5 + 2*cos(1)*exp(2)/5
Numerical answer [src] 
2.4404648818501
2.4404648818501

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

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