Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of cos^3xsinx
Integral of xyz
Integral of cosx/sqrt(sinx)
Integral of ctg(x)^4
Identical expressions
cos(one -2x)dx
co sinus of e of (1 minus 2x)dx
co sinus of e of (one minus 2x)dx
cos1-2xdx
Similar expressions
cos(1+2x)dx

Integral of cos(1-2x)dx dx

The solution

You have entered [src]

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

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

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

Detail solution

Let $u = 1 - 2 x$ .

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

$\int \frac{\cos{\left(u \right)}}{4}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \frac{\cos{\left(u \right)}}{2}\right)\, du = - \frac{\int \cos{\left(u \right)}\, du}{2}$
  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)*1 dx = C + -------------
 |                               2      
/

$${{\sin \left(2\,x-1\right)}\over{2}}$$

Simplify

The answer [src]

sin(1)

$$\sin 1$$

sin(1)

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

Упростить

Numerical answer [src]

0.841470984807897

0.841470984807897

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of cos(1-2x)dx dx

Limits of integration:

The graph:

Piecewise:

The solution