Mister Exam

Other calculators

x/(x^4+2x^2+5)
Solving integrals/ x/(x^4+2x^2+5)

Integral of x/(x^4+2x^2+5) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |        x         
 |  ------------- dx
 |   4      2       
 |  x  + 2*x  + 5   
 |                  
/                   
0
$$\int\limits_{0}^{1} \frac{x}{\left(x^{4} + 2 x^{2}\right) + 5}\, dx$$ 
Integral(x/(x^4 + 2*x^2 + 5), (x, 0, 1))
The answer (Indefinite) [src] 
                              /     2\
  /                           |1   x |
 |                        atan|- + --|
 |       x                    \2   2 /
 | ------------- dx = C + ------------
 |  4      2                   4      
 | x  + 2*x  + 5                      
 |                                    
/
$$\int \frac{x}{\left(x^{4} + 2 x^{2}\right) + 5}\, dx = C + \frac{\operatorname{atan}{\left(\frac{x^{2}}{2} + \frac{1}{2} \right)}}{4}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  atan(1/2)   pi
- --------- + --
      4       16
$$- \frac{\operatorname{atan}{\left(\frac{1}{2} \right)}}{4} + \frac{\pi}{16}$$ 
=
= 
  atan(1/2)   pi
- --------- + --
      4       16
$$- \frac{\operatorname{atan}{\left(\frac{1}{2} \right)}}{4} + \frac{\pi}{16}$$ 
-atan(1/2)/4 + pi/16
Numerical answer [src] 
0.0804376385991605
0.0804376385991605
The graph
Integral of x/(x^4+2x^2+5) dx

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

    © Mister Exam – Calculator