Integral of ctgx/2 dx

The solution

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  1          
  /          
 |           
 |  cot(x)   
 |  ------ dx
 |    2      
 |           
/            
0

$$\int\limits_{0}^{1} \frac{\cot{\left(x \right)}}{2}\, dx$$

Integral(cot(x)/2, (x, 0, 1))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int \frac{\cot{\left(x \right)}}{2}\, dx = \frac{\int \cot{\left(x \right)}\, dx}{2}$
1. Rewrite the integrand:
  
  $\cot{\left(x \right)} = \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$
2. Let $u = \sin{\left(x \right)}$ .
  
  Then let $du = \cos{\left(x \right)} dx$ and substitute $du$ :
  
  $\int \frac{1}{u}\, du$
  1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
  Now substitute $u$ back in:
  
  $\log{\left(\sin{\left(x \right)} \right)}$
So, the result is: $\frac{\log{\left(\sin{\left(x \right)} \right)}}{2}$
Add the constant of integration:

$\frac{\log{\left(\sin{\left(x \right)} \right)}}{2}+ \mathrm{constant}$

The answer is:

$\frac{\log{\left(\sin{\left(x \right)} \right)}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                           
 |                            
 | cot(x)          log(sin(x))
 | ------ dx = C + -----------
 |   2                  2     
 |                            
/

$${{\log \sin x}\over{2}}$$

Simplify

The answer [src]

oo

$${\it \%a}$$

oo

$$\infty$$

Simplify

Numerical answer [src]

21.9589211938619

21.9589211938619

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

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Integral of ctgx/2 dx

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