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Solving integrals/ cos(5*x+1)

Integral of cos(5*x+1) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                
  /                
 |                 
 |  cos(5*x + 1) dx
 |                 
/                  
0
$$\int\limits_{0}^{1} \cos{\left(5 x + 1 \right)}\, dx$$ 
Integral(cos(5*x + 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] 
  /                                  
 |                       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(1)   sin(6)
- ------ + ------
    5        5
$$- \frac{\sin{\left(1 \right)}}{5} + \frac{\sin{\left(6 \right)}}{5}$$ 
=
= 
  sin(1)   sin(6)
- ------ + ------
    5        5
$$- \frac{\sin{\left(1 \right)}}{5} + \frac{\sin{\left(6 \right)}}{5}$$ 
-sin(1)/5 + sin(6)/5
Numerical answer [src] 
-0.224177296601364
-0.224177296601364

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

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