### Other calculators # Integral ctg(2x) dx

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### The solution

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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 graph
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21.6511079586689
21.6511079586689
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$$\int \cot{\left(2 x \right)}\, dx = C + \frac{\log{\left(\sin{\left(2 x \right)} \right)}}{2}$$