Mister Exam

Integral of cosec(x) dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
  1          
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 |  csc(x) dx
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0            
$$\int\limits_{0}^{1} \csc{\left(x \right)}\, dx$$
Integral(csc(x), (x, 0, 1))
Detail solution
  1. Rewrite the integrand:

  2. 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:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                    
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 | csc(x) dx = C - log(cot(x) + csc(x))
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$$\int \csc{\left(x \right)}\, dx = C - \log{\left(\cot{\left(x \right)} + \csc{\left(x \right)} \right)}$$
The graph
The answer [src]
     pi*I
oo + ----
      2  
$$\infty + \frac{i \pi}{2}$$
=
=
     pi*I
oo + ----
      2  
$$\infty + \frac{i \pi}{2}$$
oo + pi*i/2
Numerical answer [src]
44.1790108686112
44.1790108686112
The graph
Integral of cosec(x) dx

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