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Identical expressions
cos(two *x+pi/ four)
co sinus of e of (2 multiply by x plus Pi divide by 4)
co sinus of e of (two multiply by x plus Pi divide by four)
cos(2x+pi/4)
cos2x+pi/4
cos(2*x+pi divide by 4)
cos(2*x+pi/4)dx
Similar expressions
x*cos(2x+(pi/4))
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)

You entered:

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

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

Let $u = 2 x + \frac{\pi}{4}$ .

Then let $du = 2 dx$ and substitute $\frac{du}{2}$ :

$\int \frac{\cos{\left(u \right)}}{4}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{\cos{\left(u \right)}}{2}\, du = \frac{\int \cos{\left(u \right)}\, du}{2}$
  1. The integral of cosine is sine:
    
    $\int \cos{\left(u \right)}\, du = \sin{\left(u \right)}$
  So, the result is: $\frac{\sin{\left(u \right)}}{2}$
Now substitute $u$ back in:

$\frac{\sin{\left(2 x + \frac{\pi}{4} \right)}}{2}$
Add the constant of integration:

$\frac{\sin{\left(2 x + \frac{\pi}{4} \right)}}{2}+ \mathrm{constant}$

The answer is:

$\frac{\sin{\left(2 x + \frac{\pi}{4} \right)}}{2}+ \mathrm{constant}$

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

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

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Identical expressions

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You entered:

What you mean?

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

Limits of integration:

The graph:

Piecewise:

The solution