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Derivative of:
cos(1-2x)
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Solving integrals/ cos(1-2x)

Integral of cos(1-2x) dx

The solution

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  1                
  /                
 |                 
 |  cos(1 - 2*x) dx
 |                 
/                  
0

$$\int\limits_{0}^{1} \cos{\left(1 - 2 x \right)}\, dx$$

Integral(cos(1 - 2*x), (x, 0, 1))

Detail solution

Let $u = 1 - 2 x$ .

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

$\int \left(- \frac{\cos{\left(u \right)}}{2}\right)\, du$
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:

$\frac{\sin{\left(2 x - 1 \right)}}{2}$
Add the constant of integration:

$\frac{\sin{\left(2 x - 1 \right)}}{2}+ \mathrm{constant}$

The answer is:

$\frac{\sin{\left(2 x - 1 \right)}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                   
 |                       sin(-1 + 2*x)
 | cos(1 - 2*x) dx = C + -------------
 |                             2      
/

$$\int \cos{\left(1 - 2 x \right)}\, dx = C + \frac{\sin{\left(2 x - 1 \right)}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

sin(1)

$$\sin{\left(1 \right)}$$

sin(1)

$$\sin{\left(1 \right)}$$

sin(1)

Numerical answer [src]

0.841470984807897

0.841470984807897

The graph

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

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Identical expressions

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Integral of cos(1-2x) dx

Limits of integration:

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The solution