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Integral of d{x}:
Integral of xinxdx
Integral of secx^2
Integral of (dx)/((2x^2)+(8x)+(20))
Integral of cos(2x−5)
Identical expressions
cos(2x− five)
co sinus of e of (2x−5)
co sinus of e of (2x− five)
cos2x−5
cos(2x−5)dx

Integral of cos(2x−5) dx

The solution

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 52                
 --                
 19                
  /                
 |                 
 |  cos(2*x - 5) dx
 |                 
/                  
103                
---                
 38

$$\int\limits_{\frac{103}{38}}^{\frac{52}{19}} \cos{\left(2 x - 5 \right)}\, dx$$

Integral(cos(2*x - 5), (x, 103/38, 52/19))

Detail solution

Let $u = 2 x - 5$ .

Then let $du = 2 dx$ and substitute $\frac{du}{2}$ :

$\int \frac{\cos{\left(u \right)}}{2}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \cos{\left(u \right)}\, du = \frac{\int \cos{\left(u \right)}\, du}{2}$
  1. The integral of cosine is sine:
    
    $\int \cos{\left(u \right)}\, du = \sin{\left(u \right)}$
  So, the result is: $\frac{\sin{\left(u \right)}}{2}$
Now substitute $u$ back in:

$\frac{\sin{\left(2 x - 5 \right)}}{2}$
Now simplify:

$\frac{\sin{\left(2 x - 5 \right)}}{2}$
Add the constant of integration:

$\frac{\sin{\left(2 x - 5 \right)}}{2}+ \mathrm{constant}$

The answer is:

$\frac{\sin{\left(2 x - 5 \right)}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                  
 |                       sin(2*x - 5)
 | cos(2*x - 5) dx = C + ------------
 |                            2      
/

$$\int \cos{\left(2 x - 5 \right)}\, dx = C + \frac{\sin{\left(2 x - 5 \right)}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

sin(9/19)   sin(8/19)
--------- - ---------
    2           2

$$- \frac{\sin{\left(\frac{8}{19} \right)}}{2} + \frac{\sin{\left(\frac{9}{19} \right)}}{2}$$

sin(9/19)   sin(8/19)
--------- - ---------
    2           2

$$- \frac{\sin{\left(\frac{8}{19} \right)}}{2} + \frac{\sin{\left(\frac{9}{19} \right)}}{2}$$

sin(9/19)/2 - sin(8/19)/2

Numerical answer [src]

0.0237232781950296

0.0237232781950296

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

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Identical expressions

Integral of cos(2x−5) dx

Limits of integration:

The graph:

Piecewise:

The solution