Mister Exam

Integral of ctg3x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  0            
  /            
 |             
 |  cot(3*x) dx
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$$\int\limits_{0}^{0} \cot{\left(3 x \right)}\, dx$$
Integral(cot(3*x), (x, 0, 0))
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(3*x))
 | cot(3*x) dx = C + -------------
 |                         3      
/                                 
$$\int \cot{\left(3 x \right)}\, dx = C + \frac{\log{\left(\sin{\left(3 x \right)} \right)}}{3}$$
The answer [src]
0
$$0$$
=
=
0
$$0$$
Numerical answer [src]
0.0
0.0

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