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cos(3*x-pi/6)*dx
Solving integrals/ cos(3*x-pi/6)*dx

You entered:

cos(3*x-pi/6)*dx

What you mean?

cos((3*x - pi)/6)*dx
 
cos(3*(x - pi)/6)*dx
 
cos(3*x - pi/6)*dx
 
cos(3*x - pi/6)*dx

Integral of cos(3*x-pi/6)*dx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                   
  /                   
 |                    
 |     /      pi\     
 |  cos|3*x - --|*1 dx
 |     \      6 /     
 |                    
/                     
0
$$\int\limits_{0}^{1} \cos{\left(3 x - \frac{\pi}{6} \right)} 1\, dx$$ 
Integral(cos(3*x - pi/6)*1, (x, 0, 1))
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. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                            /      pi\
 |                          sin|3*x - --|
 |    /      pi\               \      6 /
 | cos|3*x - --|*1 dx = C + -------------
 |    \      6 /                  3      
 |                                       
/
$${{\sin \left(3\,x-{{\pi}\over{6}}\right)}\over{3}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
       /    pi\
    cos|3 + --|
1      \    3 /
- - -----------
6        3
$${{\sin \left({{\pi}\over{6}}\right)}\over{3}}-{{\sin \left({{\pi-18 }\over{6}}\right)}\over{3}}$$ 
=
= 
       /    pi\
    cos|3 + --|
1      \    3 /
- - -----------
6        3
$$\frac{1}{6} - \frac{\cos{\left(\frac{\pi}{3} + 3 \right)}}{3}$$
Simplify
Numerical answer [src] 
0.372403253420778
0.372403253420778
The graph
Integral of cos(3*x-pi/6)*dx dx

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

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