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

Integral of y/sqrt(1+y^2) dy

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

  1. Let .

    Then let and substitute :

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

    Now substitute back in:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                
 |                         ________
 |      y                 /      2 
 | ----------- dy = C + \/  1 + y  
 |    ________                     
 |   /      2                      
 | \/  1 + y                       
 |                                 
/
$$\int \frac{y}{\sqrt{y^{2} + 1}}\, dy = C + \sqrt{y^{2} + 1}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
       ___
-1 + \/ 2
$$-1 + \sqrt{2}$$ 
=
= 
       ___
-1 + \/ 2
$$-1 + \sqrt{2}$$ 
-1 + sqrt(2)
Numerical answer [src] 
0.414213562373095
0.414213562373095
The graph
Integral of y/sqrt(1+y^2) dy

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

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