Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of 1/(4+x^2)
Integral of √(x+4)
Integral of sin(2x)cos(2x)
Integral of dx/sqrt(1-2x)
Sum of series:
1/(4+x^2)
Limit of the function:
1/(4+x^2)
Identical expressions
one /(four +x^ two)
1 divide by (4 plus x squared )
one divide by (four plus x to the power of two)
1/(4+x2)
1/4+x2
1/(4+x²)
1/(4+x to the power of 2)
1/4+x^2
1 divide by (4+x^2)
1/(4+x^2)dx
Similar expressions
1/(4-x^2)

Solving integrals/ 1/(4+x^2)

Integral of 1/(4+x^2) dx

The solution

You have entered [src]

  1          
  /          
 |           
 |    1      
 |  ------ dx
 |       2   
 |  4 + x    
 |           
/            
0

\int\limits_{0}^{1} \frac{1}{x^{2} + 4}\, dx

Integral(1/(4 + x^2), (x, 0, 1))

Detail solution

We have the integral:

  /         
 |          
 |   1      
 | ------ dx
 |      2   
 | 4 + x    
 |          
/

Rewrite the integrand

  1            1       
------ = --------------
     2     /     2    \
4 + x      |/-x \     |
         4*||---|  + 1|
           \\ 2 /     /

  /           
 |            
 |   1        
 | ------ dx  
 |      2    =
 | 4 + x      
 |            
/

  /             
 |              
 |     1        
 | ---------- dx
 |      2       
 | /-x \        
 | |---|  + 1   
 | \ 2 /        
 |              
/               
----------------
       4

In the integral

  /             
 |              
 |     1        
 | ---------- dx
 |      2       
 | /-x \        
 | |---|  + 1   
 | \ 2 /        
 |              
/               
----------------
       4

do replacement

    -x 
v = ---
     2

then

the integral =

  /                   
 |                    
 |   1                
 | ------ dv          
 |      2             
 | 1 + v              
 |                    
/              atan(v)
------------ = -------
     4            4

do backward replacement

  /                       
 |                        
 |     1                  
 | ---------- dx          
 |      2                 
 | /-x \                  
 | |---|  + 1             
 | \ 2 /               /x\
 |                 atan|-|
/                      \2/
---------------- = -------
       4              2

Solution is:

        /x\
    atan|-|
        \2/
C + -------
       2

The answer (Indefinite) [src]

  /                    /x\
 |                 atan|-|
 |   1                 \2/
 | ------ dx = C + -------
 |      2             2   
 | 4 + x                  
 |                        
/

\int \frac{1}{x^{2} + 4}\, dx = C + \frac{\operatorname{atan}{\left(\frac{x}{2} \right)}}{2}

Simplify

The graph

Plot the graph f(x)

The answer [src]

atan(1/2)
---------
    2

\frac{\operatorname{atan}{\left(\frac{1}{2} \right)}}{2}

atan(1/2)
---------
    2

\frac{\operatorname{atan}{\left(\frac{1}{2} \right)}}{2}

atan(1/2)/2

Numerical answer [src]

0.231823804500403

0.231823804500403

The graph

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of 1/(4+x^2) dx

Limits of integration:

The graph:

Piecewise:

The solution