Integral of sin(5x+4) dx

The solution

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  1                
  /                
 |                 
 |  sin(5*x + 4) dx
 |                 
/                  
0

$$\int\limits_{0}^{1} \sin{\left(5 x + 4 \right)}\, dx$$

Integral(sin(5*x + 4), (x, 0, 1))

Detail solution

Let $u = 5 x + 4$ .

Then let $du = 5 dx$ and substitute $\frac{du}{5}$ :

$\int \frac{\sin{\left(u \right)}}{5}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \sin{\left(u \right)}\, du = \frac{\int \sin{\left(u \right)}\, du}{5}$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(u \right)}\, du = - \cos{\left(u \right)}$
  So, the result is: $- \frac{\cos{\left(u \right)}}{5}$
Now substitute $u$ back in:

$- \frac{\cos{\left(5 x + 4 \right)}}{5}$
Now simplify:

$- \frac{\cos{\left(5 x + 4 \right)}}{5}$
Add the constant of integration:

$- \frac{\cos{\left(5 x + 4 \right)}}{5}+ \mathrm{constant}$

The answer is:

$- \frac{\cos{\left(5 x + 4 \right)}}{5}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                  
 |                       cos(5*x + 4)
 | sin(5*x + 4) dx = C - ------------
 |                            5      
/

$$\int \sin{\left(5 x + 4 \right)}\, dx = C - \frac{\cos{\left(5 x + 4 \right)}}{5}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

  cos(9)   cos(4)
- ------ + ------
    5        5

$$\frac{\cos{\left(4 \right)}}{5} - \frac{\cos{\left(9 \right)}}{5}$$

  cos(9)   cos(4)
- ------ + ------
    5        5

$$\frac{\cos{\left(4 \right)}}{5} - \frac{\cos{\left(9 \right)}}{5}$$

-cos(9)/5 + cos(4)/5

Numerical answer [src]

0.051497328204213

0.051497328204213

The graph

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

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Identical expressions

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Integral of sin(5x+4) dx

Limits of integration:

The graph:

Piecewise:

The solution