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

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1          
  /          
 |           
 |     2     
 |    x      
 |  ------ dx
 |   2       
 |  x  + 4   
 |           
/            
0
$$\int\limits_{0}^{1} \frac{x^{2}}{x^{2} + 4}\, dx$$ 
Integral(x^2/(x^2 + 4), (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=4, context=1/(x**2 + 4), symbol=x), True), (ArccothRule(a=1, b=1, c=4, context=1/(x**2 + 4), symbol=x), False), (ArctanhRule(a=1, b=1, c=4, context=1/(x**2 + 4), symbol=x), False)], context=1/(x**2 + 4), symbol=x)

      So, the result is:

    The result is:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                             
 |                              
 |    2                         
 |   x                       /x\
 | ------ dx = C + x - 2*atan|-|
 |  2                        \2/
 | x  + 4                       
 |                              
/
$$\int \frac{x^{2}}{x^{2} + 4}\, dx = C + x - 2 \operatorname{atan}{\left(\frac{x}{2} \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
1 - 2*atan(1/2)
$$1 - 2 \operatorname{atan}{\left(\frac{1}{2} \right)}$$ 
=
= 
1 - 2*atan(1/2)
$$1 - 2 \operatorname{atan}{\left(\frac{1}{2} \right)}$$ 
1 - 2*atan(1/2)
Numerical answer [src] 
0.0727047819983878
0.0727047819983878
The graph
Integral of x^2/(x^2+4) dx

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

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