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Identical expressions
sin(8x- three)
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Similar expressions
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Solving integrals/ sin(8x-3)

Integral of sin(8x-3) dx

The solution

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  1                
  /                
 |                 
 |  sin(8*x - 3) dx
 |                 
/                  
0

$$\int\limits_{0}^{1} \sin{\left(8 x - 3 \right)}\, dx$$

Integral(sin(8*x - 1*3), (x, 0, 1))

Detail solution

Let $u = 8 x - 3$ .

Then let $du = 8 dx$ and substitute $\frac{du}{8}$ :

$\int \frac{\sin{\left(u \right)}}{64}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{\sin{\left(u \right)}}{8}\, du = \frac{\int \sin{\left(u \right)}\, du}{8}$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(u \right)}\, du = - \cos{\left(u \right)}$
  So, the result is: $- \frac{\cos{\left(u \right)}}{8}$
Now substitute $u$ back in:

$- \frac{\cos{\left(8 x - 3 \right)}}{8}$
Now simplify:

$- \frac{\cos{\left(8 x - 3 \right)}}{8}$
Add the constant of integration:

$- \frac{\cos{\left(8 x - 3 \right)}}{8}+ \mathrm{constant}$

The answer is:

$- \frac{\cos{\left(8 x - 3 \right)}}{8}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                  
 |                       cos(8*x - 3)
 | sin(8*x - 3) dx = C - ------------
 |                            8      
/

$$-{{\cos \left(8\,x-3\right)}\over{8}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

  cos(5)   cos(3)
- ------ + ------
    8        8

$${{\cos 3}\over{8}}-{{\cos 5}\over{8}}$$

  cos(5)   cos(3)
- ------ + ------
    8        8

$$\frac{\cos{\left(3 \right)}}{8} - \frac{\cos{\left(5 \right)}}{8}$$

Упростить

Numerical answer [src]

-0.159206835257959

-0.159206835257959

The graph

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

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Integral of sin(8x-3) dx

Limits of integration:

The graph:

Piecewise:

The solution