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Solving integrals/ cos(5x+1)

Integral of cos(5x+1) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  2                
  /                
 |                 
 |  cos(5*x + 1) dx
 |                 
/                  
1
$$\int\limits_{1}^{2} \cos{\left(5 x + 1 \right)}\, dx$$ 
Integral(cos(5*x + 1), (x, 1, 2))
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 + 1)
 | cos(5*x + 1) dx = C + ------------
 |                            5      
/
$$\int \cos{\left(5 x + 1 \right)}\, dx = C + \frac{\sin{\left(5 x + 1 \right)}}{5}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  sin(6)   sin(11)
- ------ + -------
    5         5
$$\frac{\sin{\left(11 \right)}}{5} - \frac{\sin{\left(6 \right)}}{5}$$ 
=
= 
  sin(6)   sin(11)
- ------ + -------
    5         5
$$\frac{\sin{\left(11 \right)}}{5} - \frac{\sin{\left(6 \right)}}{5}$$ 
-sin(6)/5 + sin(11)/5
Numerical answer [src] 
-0.144114941670356
-0.144114941670356

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

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