Integral of Cos(5x-6) dx

The solution

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  1                
  /                
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 |  cos(5*x - 6) dx
 |                 
/                  
0

$$\int\limits_{0}^{1} \cos{\left(5 x - 6 \right)}\, dx$$

Integral(cos(5*x - 1*6), (x, 0, 1))

Detail solution

Let $u = 5 x - 6$ .

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

$\int \frac{\cos{\left(u \right)}}{25}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{\cos{\left(u \right)}}{5}\, du = \frac{\int \cos{\left(u \right)}\, du}{5}$
  1. The integral of cosine is sine:
    
    $\int \cos{\left(u \right)}\, du = \sin{\left(u \right)}$
  So, the result is: $\frac{\sin{\left(u \right)}}{5}$
Now substitute $u$ back in:

$\frac{\sin{\left(5 x - 6 \right)}}{5}$
Now simplify:

$\frac{\sin{\left(5 x - 6 \right)}}{5}$
Add the constant of integration:

$\frac{\sin{\left(5 x - 6 \right)}}{5}+ \mathrm{constant}$

The answer is:

$\frac{\sin{\left(5 x - 6 \right)}}{5}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                  
 |                       sin(5*x - 6)
 | cos(5*x - 6) dx = C + ------------
 |                            5      
/

$${{\sin \left(5\,x-6\right)}\over{5}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

  sin(1)   sin(6)
- ------ + ------
    5        5

$${{\sin 6-\sin 1}\over{5}}$$

  sin(1)   sin(6)
- ------ + ------
    5        5

$$- \frac{\sin{\left(1 \right)}}{5} + \frac{\sin{\left(6 \right)}}{5}$$

Simplify

Numerical answer [src]

-0.224177296601364

-0.224177296601364

The graph

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

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Integral of Cos(5x-6) dx

Limits of integration:

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The solution