Mister exam

Integral ctg(2x) dx

from to

from to

The solution

You have entered [src]
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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 graph
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oo
21.6511079586689
21.6511079586689
The answer (Indefinite) [src]
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|                   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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