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cos(3*x)

Integral of cos(3*x) dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
  1            
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 |  cos(3*x) dx
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$$\int\limits_{0}^{1} \cos{\left(3 x \right)}\, dx$$
Integral(cos(3*x), (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. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                          
 |                   sin(3*x)
 | cos(3*x) dx = C + --------
 |                      3    
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$$\int \cos{\left(3 x \right)}\, dx = C + \frac{\sin{\left(3 x \right)}}{3}$$
The graph
The answer [src]
sin(3)
------
  3   
$$\frac{\sin{\left(3 \right)}}{3}$$
=
=
sin(3)
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  3   
$$\frac{\sin{\left(3 \right)}}{3}$$
sin(3)/3
Numerical answer [src]
0.0470400026866224
0.0470400026866224
The graph
Integral of cos(3*x) dx

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