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Integral of d{x}:
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Integral of cosx^2
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Integral of xcos(nx)
Derivative of:
cos(4x)/8
Identical expressions
cos(4x)/ eight
co sinus of e of (4x) divide by 8
co sinus of e of (4x) divide by eight
cos4x/8
cos(4x) divide by 8
cos(4x)/8dx
Similar expressions
cos^4(x/8)

Integral of cos(4x)/8 dx

The solution

You have entered [src]

 pi            
  /            
 |             
 |  cos(4*x)   
 |  -------- dx
 |     8       
 |             
/              
0

$$\int\limits_{0}^{\pi} \frac{\cos{\left(4 x \right)}}{8}\, dx$$

Integral(cos(4*x)/8, (x, 0, pi))

Detail solution

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

$\int \frac{\cos{\left(4 x \right)}}{8}\, dx = \frac{\int \cos{\left(4 x \right)}\, dx}{8}$
1. Let $u = 4 x$ .
  
  Then let $du = 4 dx$ and substitute $\frac{du}{4}$ :
  
  $\int \frac{\cos{\left(u \right)}}{4}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \cos{\left(u \right)}\, du = \frac{\int \cos{\left(u \right)}\, du}{4}$
    1. The integral of cosine is sine:
      
      $\int \cos{\left(u \right)}\, du = \sin{\left(u \right)}$
    So, the result is: $\frac{\sin{\left(u \right)}}{4}$
  Now substitute $u$ back in:
  
  $\frac{\sin{\left(4 x \right)}}{4}$
So, the result is: $\frac{\sin{\left(4 x \right)}}{32}$
Add the constant of integration:

$\frac{\sin{\left(4 x \right)}}{32}+ \mathrm{constant}$

The answer is:

$\frac{\sin{\left(4 x \right)}}{32}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                          
 |                           
 | cos(4*x)          sin(4*x)
 | -------- dx = C + --------
 |    8                 32   
 |                           
/

$$\int \frac{\cos{\left(4 x \right)}}{8}\, dx = C + \frac{\sin{\left(4 x \right)}}{32}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$0$$

Numerical answer [src]

-1.53372390894752e-17

-1.53372390894752e-17

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

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Identical expressions

Similar expressions

Integral of cos(4x)/8 dx

Limits of integration:

The graph:

Piecewise:

The solution