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Integral of d{x}:
Integral of 1/(2x-1)
Integral of (4-x^2)^(1/2)
Integral of 1/tanx
Integral of x^2/(x-1)
Graphing y =:
tg(x/4)
Identical expressions
tg(x/ four)
tg(x divide by 4)
tg(x divide by four)
tgx/4
tg(x/4)dx
Similar expressions
((x^4-1)arctgx)/4

Integral of tg(x/4) dx

The solution

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 2*pi         
   /          
  |           
  |     /x\   
  |  tan|-| dx
  |     \4/   
  |           
 /            
 0

$$\int\limits_{0}^{2 \pi} \tan{\left(\frac{x}{4} \right)}\, dx$$

Integral(tan(x/4), (x, 0, 2*pi))

Detail solution

Rewrite the integrand:

$\tan{\left(\frac{x}{4} \right)} = \frac{\sin{\left(\frac{x}{4} \right)}}{\cos{\left(\frac{x}{4} \right)}}$
There are multiple ways to do this integral.
Method #1
1. Let $u = \cos{\left(\frac{x}{4} \right)}$ .
  
  Then let $du = - \frac{\sin{\left(\frac{x}{4} \right)} dx}{4}$ and substitute $- 4 du$ :
  
  $\int \left(- \frac{4}{u}\right)\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{1}{u}\, du = - 4 \int \frac{1}{u}\, du$
    1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
    So, the result is: $- 4 \log{\left(u \right)}$
  Now substitute $u$ back in:
  
  $- 4 \log{\left(\cos{\left(\frac{x}{4} \right)} \right)}$
Method #2
1. Let $u = \frac{x}{4}$ .
  
  Then let $du = \frac{dx}{4}$ and substitute $4 du$ :
  
  $\int \frac{4 \sin{\left(u \right)}}{\cos{\left(u \right)}}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{\sin{\left(u \right)}}{\cos{\left(u \right)}}\, du = 4 \int \frac{\sin{\left(u \right)}}{\cos{\left(u \right)}}\, du$
    1. Let $u = \cos{\left(u \right)}$ .
      
      Then let $du = - \sin{\left(u \right)} du$ and substitute $- du$ :
      
      $\int \left(- \frac{1}{u}\right)\, du$
      
      The integral of a constant times a function is the constant times the integral of the function:
      
      $\int \frac{1}{u}\, du = - \int \frac{1}{u}\, du$
      
      The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
      
      So, the result is: $- \log{\left(u \right)}$
      
      Now substitute $u$ back in:
      
      $- \log{\left(\cos{\left(u \right)} \right)}$
    So, the result is: $- 4 \log{\left(\cos{\left(u \right)} \right)}$
  Now substitute $u$ back in:
  
  $- 4 \log{\left(\cos{\left(\frac{x}{4} \right)} \right)}$
Now simplify:

$- 4 \log{\left(\cos{\left(\frac{x}{4} \right)} \right)}$
Add the constant of integration:

$- 4 \log{\left(\cos{\left(\frac{x}{4} \right)} \right)}+ \mathrm{constant}$

The answer is:

$- 4 \log{\left(\cos{\left(\frac{x}{4} \right)} \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                             
 |                              
 |    /x\               /   /x\\
 | tan|-| dx = C - 4*log|cos|-||
 |    \4/               \   \4//
 |                              
/

$$\int \tan{\left(\frac{x}{4} \right)}\, dx = C - 4 \log{\left(\cos{\left(\frac{x}{4} \right)} \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

oo

$$\infty$$

oo

$$\infty$$

oo

Numerical answer [src]

149.320280806695

149.320280806695

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

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Identical expressions

Similar expressions

Integral of tg(x/4) dx

Limits of integration:

The graph:

Piecewise:

The solution

Method #1

Method #2