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

You entered:

x^2/sqrt(1+x^2)

What you mean?

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

Integral of x^2/sqrt(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
$$\int\limits_{0}^{1} \frac{x^{2}}{\sqrt{x^{2} + 1}}\, dx$$ 
Integral(x^2/(sqrt(1 + x^2)), (x, 0, 1))
Detail solution

    SqrtQuadraticDenomRule(a=1, b=0, c=1, coeffs=[1, 0, 0], context=x**2/(sqrt(x**2 + 1)), symbol=x)

  1. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                             
 |                                      ________
 |       2                             /      2 
 |      x               asinh(x)   x*\/  1 + x  
 | ----------- dx = C - -------- + -------------
 |    ________             2             2      
 |   /      2                                   
 | \/  1 + x                                    
 |                                              
/
$${{x\,\sqrt{x^2+1}}\over{2}}-{{{\rm asinh}\; x}\over{2}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  ___      /      ___\
\/ 2    log\1 + \/ 2 /
----- - --------------
  2           2
$$-{{{\rm asinh}\; 1-\sqrt{2}}\over{2}}$$ 
=
= 
  ___      /      ___\
\/ 2    log\1 + \/ 2 /
----- - --------------
  2           2
$$- \frac{\log{\left(1 + \sqrt{2} \right)}}{2} + \frac{\sqrt{2}}{2}$$
Упростить
Numerical answer [src] 
0.266419987676776
0.266419987676776
The graph
Integral of x^2/sqrt(1+x^2) dx

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

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