Mister exam

# Integral ctg(2x) dx

from to

from to

### The solution

You have entered [src]
  1
/
|
|  cot(2*x) dx
|
/
0              
$$\int\limits_{0}^{1} \cot{\left(2 x \right)}\, dx$$
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
oo
$$\infty$$
=
=
oo
$$\infty$$
oo
21.6511079586689
21.6511079586689
  /
/                                 
$$\int \cot{\left(2 x \right)}\, dx = C + \frac{\log{\left(\sin{\left(2 x \right)} \right)}}{2}$$