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2*e^(2x)cos(2y)dx

Integral of 2*e^(2x)cos(2y) dx

The solution

You have entered [src]

  1                   
  /                   
 |                    
 |     2*x            
 |  2*e   *cos(2*y) dx
 |                    
/                     
0

$$\int\limits_{0}^{1} 2 e^{2 x} \cos{\left(2 y \right)}\, dx$$

Simplify

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int 2 e^{2 x} \cos{\left(2 y \right)}\, dx = 2 \cos{\left(2 y \right)} \int e^{2 x}\, dx$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\frac{e^{2 x}}{2}$
So, the result is: $e^{2 x} \cos{\left(2 y \right)}$
Add the constant of integration:

$e^{2 x} \cos{\left(2 y \right)}+ \mathrm{constant}$

The answer is:

$e^{2 x} \cos{\left(2 y \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                      
 |                                       
 |    2*x                             2*x
 | 2*e   *cos(2*y) dx = C + cos(2*y)*e   
 |                                       
/

$$e^{2\,x}\,\cos \left(2\,y\right)$$

Simplify

The answer [src]

                      2
-cos(2*y) + cos(2*y)*e

$$2\,\left({{e^2}\over{2}}-{{1}\over{2}}\right)\,\cos \left(2\,y \right)$$

                      2
-cos(2*y) + cos(2*y)*e

$$- \cos{\left(2 y \right)} + e^{2} \cos{\left(2 y \right)}$$

Simplify

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

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Identical expressions

Integral of 2*e^(2x)cos(2y) dx

Limits of integration:

The graph:

Piecewise:

The solution