Integral of cos(4x-5)dx dx

The solution

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 |  cos(4*x - 5)*1 dx
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$$\int\limits_{0}^{1} \cos{\left(4 x - 5 \right)} 1\, dx$$

Integral(cos(4*x - 1*5)*1, (x, 0, 1))

Detail solution

Let $u = 4 x - 5$ .

Then let $du = 4 dx$ and substitute $\frac{du}{4}$ :

$\int \frac{\cos{\left(u \right)}}{16}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{\cos{\left(u \right)}}{4}\, du = \frac{\int \cos{\left(u \right)}\, du}{4}$
  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:

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

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                                    
 |                         sin(4*x - 5)
 | cos(4*x - 5)*1 dx = C + ------------
 |                              4      
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$${{\sin \left(4\,x-5\right)}\over{4}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

  sin(1)   sin(5)
- ------ + ------
    4        4

$${{\sin 5-\sin 1}\over{4}}$$

  sin(1)   sin(5)
- ------ + ------
    4        4

$$\frac{\sin{\left(5 \right)}}{4} - \frac{\sin{\left(1 \right)}}{4}$$

Упростить

Numerical answer [src]

-0.450098814867759

-0.450098814867759

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

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Integral of cos(4x-5)dx dx

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The solution