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Identical expressions
eight *cos(4x- twelve)
8 multiply by co sinus of e of (4x minus 12)
eight multiply by co sinus of e of (4x minus twelve)
8cos(4x-12)
8cos4x-12
8*cos(4x-12)dx
Similar expressions
8*cos(4x+12)

Integral of 8*cos(4x-12) dx

The solution

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 |  8*cos(4*x - 12) dx
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$$\int\limits_{0}^{1} 8 \cos{\left(4 x - 12 \right)}\, dx$$

Integral(8*cos(4*x - 12), (x, 0, 1))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int 8 \cos{\left(4 x - 12 \right)}\, dx = 8 \int \cos{\left(4 x - 12 \right)}\, dx$
1. Let $u = 4 x - 12$ .
  
  Then let $du = 4 dx$ and substitute $\frac{du}{4}$ :
  
  $\int \frac{\cos{\left(u \right)}}{4}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \cos{\left(u \right)}\, du = \frac{\int \cos{\left(u \right)}\, du}{4}$
    1. The integral of cosine is sine:
      
      $\int \cos{\left(u \right)}\, du = \sin{\left(u \right)}$
    So, the result is: $\frac{\sin{\left(u \right)}}{4}$
  Now substitute $u$ back in:
  
  $\frac{\sin{\left(4 x - 12 \right)}}{4}$
So, the result is: $2 \sin{\left(4 x - 12 \right)}$
Now simplify:

$2 \sin{\left(4 x - 12 \right)}$
Add the constant of integration:

$2 \sin{\left(4 x - 12 \right)}+ \mathrm{constant}$

The answer is:

$2 \sin{\left(4 x - 12 \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

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 | 8*cos(4*x - 12) dx = C + 2*sin(4*x - 12)
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$$\int 8 \cos{\left(4 x - 12 \right)}\, dx = C + 2 \sin{\left(4 x - 12 \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-2*sin(8) + 2*sin(12)

$$- 2 \sin{\left(8 \right)} + 2 \sin{\left(12 \right)}$$

-2*sin(8) + 2*sin(12)

$$- 2 \sin{\left(8 \right)} + 2 \sin{\left(12 \right)}$$

-2*sin(8) + 2*sin(12)

Numerical answer [src]

-3.05186232924763

-3.05186232924763

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

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Integral of 8*cos(4x-12) dx

Limits of integration:

The graph:

Piecewise:

The solution