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y/(sqrt(5+y^2))
Solving integrals/ y/(sqrt(5+y^2))

Integral of y/(sqrt(5+y^2)) dy

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |       y        
 |  ----------- dy
 |     ________   
 |    /      2    
 |  \/  5 + y     
 |                
/                 
0
∫01yy2+5 dy\int\limits_{0}^{1} \frac{y}{\sqrt{y^{2} + 5}}\, dy 
Integral(y/sqrt(5 + y^2), (y, 0, 1))
Detail solution

  1. Let u=y2+5u = \sqrt{y^{2} + 5}.

    Then let du=ydyy2+5du = \frac{y dy}{\sqrt{y^{2} + 5}} and substitute dudu:

    ∫1 du\int 1\, du

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

      ∫1 du=u\int 1\, du = u

    Now substitute uu back in:

    y2+5\sqrt{y^{2} + 5}

  2. Add the constant of integration:

    y2+5+constant\sqrt{y^{2} + 5}+ \mathrm{constant}

The answer is:

y2+5+constant\sqrt{y^{2} + 5}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                
 |                         ________
 |      y                 /      2 
 | ----------- dy = C + \/  5 + y  
 |    ________                     
 |   /      2                      
 | \/  5 + y                       
 |                                 
/
∫yy2+5 dy=C+y2+5\int \frac{y}{\sqrt{y^{2} + 5}}\, dy = C + \sqrt{y^{2} + 5}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.02.5
Plot the graph f(x)
The answer [src] 
  ___     ___
\/ 6  - \/ 5
−5+6- \sqrt{5} + \sqrt{6} 
=
= 
  ___     ___
\/ 6  - \/ 5
−5+6- \sqrt{5} + \sqrt{6} 
sqrt(6) - sqrt(5)
Numerical answer [src] 
0.213421765283388
0.213421765283388
The graph
Integral of y/(sqrt(5+y^2)) dy

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

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