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  • Integral of d{x}:
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  • Integral of -lnx Integral of -lnx
  • Integral of du Integral of du
  • Integral of ln|x|
  • Identical expressions

  • (arctg^ four (x)/(x^ two + one))
  • (arctg to the power of 4(x) divide by (x squared plus 1))
  • (arctg to the power of four (x) divide by (x to the power of two plus one))
  • (arctg4(x)/(x2+1))
  • arctg4x/x2+1
  • (arctg⁴(x)/(x²+1))
  • (arctg to the power of 4(x)/(x to the power of 2+1))
  • arctg^4x/x^2+1
  • (arctg^4(x) divide by (x^2+1))
  • (arctg^4(x)/(x^2+1))dx
  • Similar expressions

  • (arctg^4(x)/(x^2-1))

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 oo            
  /            
 |             
 |      4      
 |  atan (x)   
 |  -------- dx
 |    2        
 |   x  + 1    
 |             
/              
-oo            
$$\int\limits_{-\infty}^{\infty} \frac{\operatorname{atan}^{4}{\left(x \right)}}{x^{2} + 1}\, dx$$
Integral(atan(x)^4/(x^2 + 1), (x, -oo, oo))
Detail solution
  1. Let .

    Then let and substitute :

    1. The integral of is when :

    Now substitute back in:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                          
 |                           
 |     4                 5   
 | atan (x)          atan (x)
 | -------- dx = C + --------
 |   2                  5    
 |  x  + 1                   
 |                           
/                            
$$\int \frac{\operatorname{atan}^{4}{\left(x \right)}}{x^{2} + 1}\, dx = C + \frac{\operatorname{atan}^{5}{\left(x \right)}}{5}$$
The graph
The answer [src]
  5
pi 
---
 80
$$\frac{\pi^{5}}{80}$$
=
=
  5
pi 
---
 80
$$\frac{\pi^{5}}{80}$$
pi^5/80
Numerical answer [src]
3.82524605981602
3.82524605981602

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