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Solving integrals/ 2*e^(2x)cos(2y)

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

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src] 
  1                   
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 |     2*x            
 |  2*e   *cos(2*y) dx
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0
∫012e2xcos⁡(2y) dx\int\limits_{0}^{1} 2 e^{2 x} \cos{\left(2 y \right)}\, dx
Simplify
Detail solution

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

    ∫2e2xcos⁡(2y) dx=2cos⁡(2y)∫e2x dx\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

      e2x2\frac{e^{2 x}}{2}

    So, the result is: e2xcos⁡(2y)e^{2 x} \cos{\left(2 y \right)}

  2. Add the constant of integration:

    e2xcos⁡(2y)+constante^{2 x} \cos{\left(2 y \right)}+ \mathrm{constant}

The answer is:

e2xcos⁡(2y)+constante^{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   
 |                                       
/
e2 x cos⁡(2 y)e^{2\,x}\,\cos \left(2\,y\right)
Simplify
The answer [src] 
                      2
-cos(2*y) + cos(2*y)*e
2 (e22−12) cos⁡(2 y)2\,\left({{e^2}\over{2}}-{{1}\over{2}}\right)\,\cos \left(2\,y \right) 
=
= 
                      2
-cos(2*y) + cos(2*y)*e
−cos⁡(2y)+e2cos⁡(2y)- \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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