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

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1          
  /          
 |           
 |     2     
 |    x      
 |  ------ dx
 |       2   
 |  1 + x    
 |           
/            
0
$$\int\limits_{0}^{1} \frac{x^{2}}{x^{2} + 1}\, dx$$ 
Integral(x^2/(1 + x^2), (x, 0, 1))
Detail solution

  1. Rewrite the integrand:

  2. Integrate term-by-term:

    1. The integral of a constant is the constant times the variable of integration:

    1. The integral of a constant times a function is the constant times the integral of the function:

        PiecewiseRule(subfunctions=[(ArctanRule(a=1, b=1, c=1, context=1/(x**2 + 1), symbol=x), True), (ArccothRule(a=1, b=1, c=1, context=1/(x**2 + 1), symbol=x), False), (ArctanhRule(a=1, b=1, c=1, context=1/(x**2 + 1), symbol=x), False)], context=1/(x**2 + 1), symbol=x)

      So, the result is:

    The result is:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                           
 |                            
 |    2                       
 |   x                        
 | ------ dx = C + x - atan(x)
 |      2                     
 | 1 + x                      
 |                            
/
$$\int \frac{x^{2}}{x^{2} + 1}\, dx = C + x - \operatorname{atan}{\left(x \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
    pi
1 - --
    4
$$1 - \frac{\pi}{4}$$ 
=
= 
    pi
1 - --
    4
$$1 - \frac{\pi}{4}$$ 
1 - pi/4
Numerical answer [src] 
0.214601836602552
0.214601836602552
The graph
Integral of (x^2)/(1+x^2) dx

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

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