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  • Integral of d{x}:
  • Integral of cosx Integral of cosx
  • Integral of (1/x^2)dx Integral of (1/x^2)dx
  • Integral of x*cos(x/2) Integral of x*cos(x/2)
  • Integral of -x^3 Integral of -x^3

  • Identical expressions

  • (one /(e^x))*cosx/ two
  • (1 divide by (e to the power of x)) multiply by co sinus of e of x divide by 2
  • (one divide by (e to the power of x)) multiply by co sinus of e of x divide by two
  • (1/(ex))*cosx/2
  • 1/ex*cosx/2
  • (1/(e^x))cosx/2
  • (1/(ex))cosx/2
  • 1/excosx/2
  • 1/e^xcosx/2
  • (1 divide by (e^x))*cosx divide by 2
  • (1/(e^x))*cosx/2dx
Solving integrals/ (1/(e^x))*cosx/2

Integral of (1/(e^x))*cosx/2 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1            
  /            
 |             
 |  /cos(x)\   
 |  |------|   
 |  |   x  |   
 |  \  E   /   
 |  -------- dx
 |     2       
 |             
/              
0
$$\int\limits_{0}^{1} \frac{\frac{1}{e^{x}} \cos{\left(x \right)}}{2}\, dx$$ 
Integral((cos(x)/E^x)/2, (x, 0, 1))
Detail solution

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

    1. Don't know the steps in finding this integral.

      But the integral is

    So, the result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                         
 |                                          
 | /cos(x)\                                 
 | |------|                                 
 | |   x  |                  -x    -x       
 | \  E   /          cos(x)*e     e  *sin(x)
 | -------- dx = C - ---------- + ----------
 |    2                  4            4     
 |                                          
/
$$\int \frac{\frac{1}{e^{x}} \cos{\left(x \right)}}{2}\, dx = C + \frac{e^{- x} \sin{\left(x \right)}}{4} - \frac{e^{- x} \cos{\left(x \right)}}{4}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
            -1    -1       
1   cos(1)*e     e  *sin(1)
- - ---------- + ----------
4       4            4
$$- \frac{\cos{\left(1 \right)}}{4 e} + \frac{\sin{\left(1 \right)}}{4 e} + \frac{1}{4}$$ 
=
= 
            -1    -1       
1   cos(1)*e     e  *sin(1)
- - ---------- + ----------
4       4            4
$$- \frac{\cos{\left(1 \right)}}{4 e} + \frac{\sin{\left(1 \right)}}{4 e} + \frac{1}{4}$$ 
1/4 - cos(1)*exp(-1)/4 + exp(-1)*sin(1)/4
Numerical answer [src] 
0.277698441326675
0.277698441326675

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

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