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

You entered:

x^2/(1+x^4)

What you mean?

x^2/(1 + x^4)
 
x^2*4/(1 + x)
 
x^2/((1 + x)^4)
 
x^2/1 + x^4
 
x*2/(1 + x^4)
 
x*2*4/(1 + x)
 
x^2/1 + x^4

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1          
  /          
 |           
 |     2     
 |    x      
 |  ------ dx
 |       4   
 |  1 + x    
 |           
/            
0
$$\int\limits_{0}^{1} \frac{x^{2}}{x^{4} + 1}\, dx$$ 
Integral(x^2/(1 + x^4), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                                                                              
 |                                                                                                                               
 |    2              ___    /     2       ___\     ___     /        ___\     ___     /         ___\     ___    /     2       ___\
 |   x             \/ 2 *log\1 + x  + x*\/ 2 /   \/ 2 *atan\1 + x*\/ 2 /   \/ 2 *atan\-1 + x*\/ 2 /   \/ 2 *log\1 + x  - x*\/ 2 /
 | ------ dx = C - --------------------------- + ----------------------- + ------------------------ + ---------------------------
 |      4                       8                           4                         4                            8             
 | 1 + x                                                                                                                         
 |                                                                                                                               
/
$$-{{\log \left(x^2+\sqrt{2}\,x+1\right)}\over{2^{{{5}\over{2}}}}}+{{ \log \left(x^2-\sqrt{2}\,x+1\right)}\over{2^{{{5}\over{2}}}}}+{{ \arctan \left({{2\,x+\sqrt{2}}\over{\sqrt{2}}}\right)}\over{2^{{{3 }\over{2}}}}}+{{\arctan \left({{2\,x-\sqrt{2}}\over{\sqrt{2}}} \right)}\over{2^{{{3}\over{2}}}}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
    ___    /      ___\        ___     ___    /      ___\
  \/ 2 *log\2 + \/ 2 /   pi*\/ 2    \/ 2 *log\2 - \/ 2 /
- -------------------- + -------- + --------------------
           8                8                8
$$-{{\log \left(\sqrt{2}+2\right)}\over{2^{{{5}\over{2}}}}}+{{\log \left(2-\sqrt{2}\right)}\over{2^{{{5}\over{2}}}}}+{{\pi}\over{2^{{{5 }\over{2}}}}}$$ 
=
= 
    ___    /      ___\        ___     ___    /      ___\
  \/ 2 *log\2 + \/ 2 /   pi*\/ 2    \/ 2 *log\2 - \/ 2 /
- -------------------- + -------- + --------------------
           8                8                8
$$- \frac{\sqrt{2} \log{\left(\sqrt{2} + 2 \right)}}{8} + \frac{\sqrt{2} \log{\left(- \sqrt{2} + 2 \right)}}{8} + \frac{\sqrt{2} \pi}{8}$$
Simplify
Numerical answer [src] 
0.243747747199681
0.243747747199681
The graph
Integral of x^2/(1+x^4) dx

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

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