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cos(3x+5)dx
Solving integrals/ cos(3x+5)dx

Integral of cos(3x+5)dx dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                
  /                
 |                 
 |  cos(3*x + 5) dx
 |                 
/                  
0
$$\int\limits_{0}^{1} \cos{\left(3 x + 5 \right)}\, dx$$ 
Integral(cos(3*x + 5), (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(3*x + 5)
 | cos(3*x + 5) dx = C + ------------
 |                            3      
/
$$\int \cos{\left(3 x + 5 \right)}\, dx = C + \frac{\sin{\left(3 x + 5 \right)}}{3}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  sin(5)   sin(8)
- ------ + ------
    3        3
$$- \frac{\sin{\left(5 \right)}}{3} + \frac{\sin{\left(8 \right)}}{3}$$ 
=
= 
  sin(5)   sin(8)
- ------ + ------
    3        3
$$- \frac{\sin{\left(5 \right)}}{3} + \frac{\sin{\left(8 \right)}}{3}$$ 
-sin(5)/3 + sin(8)/3
Numerical answer [src] 
0.649427507095507
0.649427507095507
The graph
Integral of cos(3x+5)dx dx

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

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