Mister Exam

Other calculators

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

You entered:

t^2/(t^2+1)

What you mean?

t^2/(t^2 + 1)
 
t^2/(t^2) + 1
 
t^2*2/t + 1
 
t^2/(t^2) + 1
 
t*2/(t^2 + 1)
 
t*2/t^2 + 1
 
t^2/(t^2) + 1

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1          
  /          
 |           
 |     2     
 |    t      
 |  ------ dt
 |   2       
 |  t  + 1   
 |           
/            
0
$$\int\limits_{0}^{1} \frac{t^{2}}{t^{2} + 1}\, dt$$
Simplify
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:

      1. The integral of is .

      So, the result is:

    The result is:

  3. Add the constant of integration:

The answer is:

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

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

    © Mister Exam – Calculator