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ctg(2x)

Integral ctg(2x) dx

Limits of integration:

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The graph:

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Enter:

The solution

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 |  cot(2*x) dx
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$$\int\limits_{0}^{1} \cot{\left(2 x \right)}\, dx$$
Integral(cot(2*x), (x, 0, 1))
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 graph
The answer [src]
oo
$$\infty$$
=
=
oo
$$\infty$$
oo
Numerical answer [src]
21.6511079586689
21.6511079586689
The answer (Indefinite) [src]
  /                               
 |                   log(sin(2*x))
 | cot(2*x) dx = C + -------------
 |                         2      
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$$\int \cot{\left(2 x \right)}\, dx = C + \frac{\log{\left(\sin{\left(2 x \right)} \right)}}{2}$$

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

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