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Integral of (sin(5*x+3)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                
  /                
 |                 
 |  sin(5*x + 3) dx
 |                 
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0                  
$$\int\limits_{0}^{1} \sin{\left(5 x + 3 \right)}\, dx$$
Integral(sin(5*x + 3), (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 sine is negative cosine:

      So, the result is:

    Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                  
 |                       cos(5*x + 3)
 | sin(5*x + 3) dx = C - ------------
 |                            5      
/                                    
$$\int \sin{\left(5 x + 3 \right)}\, dx = C - \frac{\cos{\left(5 x + 3 \right)}}{5}$$
The graph
The answer [src]
  cos(8)   cos(3)
- ------ + ------
    5        5   
$$\frac{\cos{\left(3 \right)}}{5} - \frac{\cos{\left(8 \right)}}{5}$$
=
=
  cos(8)   cos(3)
- ------ + ------
    5        5   
$$\frac{\cos{\left(3 \right)}}{5} - \frac{\cos{\left(8 \right)}}{5}$$
-cos(8)/5 + cos(3)/5
Numerical answer [src]
-0.168898492558366
-0.168898492558366

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