Mister Exam

Integral of ctg(2x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1            
  /            
 |             
 |  cot(2*x) dx
 |             
/              
0              
$$\int\limits_{0}^{1} \cot{\left(2 x \right)}\, dx$$
Detail solution
  1. Rewrite the integrand:

  2. There are multiple ways to do this integral.

    Method #1

    1. Let .

      Then let and substitute :

      1. The integral of a constant times a function is the constant times the integral of the function:

        1. The integral of is .

        So, the result is:

      Now substitute back in:

    Method #2

    1. Let .

      Then let and substitute :

      1. The integral of a constant times a function is the constant times the integral of the function:

        1. Let .

          Then let and substitute :

          1. The integral of is .

          Now substitute back in:

        So, the result is:

      Now substitute back in:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                               
 |                   log(sin(2*x))
 | cot(2*x) dx = C + -------------
 |                         2      
/                                 
$${{\log \sin \left(2\,x\right)}\over{2}}$$
The answer [src]
oo
$${\it \%a}$$
=
=
oo
$$\infty$$
Numerical answer [src]
21.6511079586689
21.6511079586689

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