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Solving integrals/ cos(5x+19)

Integral of cos(5x+19) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |  cos(5*x + 19) dx
 |                  
/                   
0
$$\int\limits_{0}^{1} \cos{\left(5 x + 19 \right)}\, dx$$ 
Integral(cos(5*x + 19), (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] 
  /                                    
 |                        sin(5*x + 19)
 | cos(5*x + 19) dx = C + -------------
 |                              5      
/
$$\int \cos{\left(5 x + 19 \right)}\, dx = C + \frac{\sin{\left(5 x + 19 \right)}}{5}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  sin(19)   sin(24)
- ------- + -------
     5         5
$$\frac{\sin{\left(24 \right)}}{5} - \frac{\sin{\left(19 \right)}}{5}$$ 
=
= 
  sin(19)   sin(24)
- ------- + -------
     5         5
$$\frac{\sin{\left(24 \right)}}{5} - \frac{\sin{\left(19 \right)}}{5}$$ 
-sin(19)/5 + sin(24)/5
Numerical answer [src] 
-0.211091114333915
-0.211091114333915

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

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