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cos(2*x+pi/4)
Solving integrals/ cos(2*x+pi/4)

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cos(2*x+pi/4)

What you mean?

cos((2*x + pi)/4)
 
cos(2*(x + pi)/4)
 
cos(2*x + pi/4)
 
cos(2*x + pi/4)

Integral of cos(2*x+pi/4) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi                 
  /                 
 |                  
 |     /      pi\   
 |  cos|2*x + --| dx
 |     \      4 /   
 |                  
/                   
2
$$\int\limits_{2}^{\pi} \cos{\left(2 x + \frac{\pi}{4} \right)}\, dx$$ 
Integral(cos(2*x + pi/4), (x, 2, pi))
Detail solution

  1. Let .

    Then let and substitute :

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

      1. The integral of cosine is sine:

      So, the result is:

    Now substitute back in:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                          /      pi\
 |                        sin|2*x + --|
 |    /      pi\             \      4 /
 | cos|2*x + --| dx = C + -------------
 |    \      4 /                2      
 |                                     
/
$$\int \cos{\left(2 x + \frac{\pi}{4} \right)}\, dx = C + \frac{\sin{\left(2 x + \frac{\pi}{4} \right)}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
     /    pi\        
  sin|4 + --|     ___
     \    4 /   \/ 2 
- ----------- + -----
       2          4
$$\frac{\sqrt{2}}{4} - \frac{\sin{\left(\frac{\pi}{4} + 4 \right)}}{2}$$ 
=
= 
     /    pi\        
  sin|4 + --|     ___
     \    4 /   \/ 2 
- ----------- + -----
       2          4
$$\frac{\sqrt{2}}{4} - \frac{\sin{\left(\frac{\pi}{4} + 4 \right)}}{2}$$
Упростить
Numerical answer [src] 
0.852221397214836
0.852221397214836
The graph
Integral of cos(2*x+pi/4) dx

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

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