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

Integral of 1/sqrt(1+u^2) du

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

    TrigSubstitutionRule(theta=_theta, func=tan(_theta), rewritten=sec(_theta), substep=RewriteRule(rewritten=(tan(_theta)*sec(_theta) + sec(_theta)**2)/(tan(_theta) + sec(_theta)), substep=AlternativeRule(alternatives=[URule(u_var=_u, u_func=tan(_theta) + sec(_theta), constant=1, substep=ReciprocalRule(func=_u, context=1/_u, symbol=_u), context=(tan(_theta)*sec(_theta) + sec(_theta)**2)/(tan(_theta) + sec(_theta)), symbol=_theta)], context=(tan(_theta)*sec(_theta) + sec(_theta)**2)/(tan(_theta) + sec(_theta)), symbol=_theta), context=sec(_theta), symbol=_theta), restriction=True, context=1/(sqrt(u**2 + 1)), symbol=u)

  1. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                         
 |                         /       ________\
 |      1                  |      /      2 |
 | ----------- du = C + log\u + \/  1 + u  /
 |    ________                              
 |   /      2                               
 | \/  1 + u                                
 |                                          
/
$$\int \frac{1}{\sqrt{u^{2} + 1}}\, du = C + \log{\left(u + \sqrt{u^{2} + 1} \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
   /      ___\
log\1 + \/ 2 /
$$\log{\left(1 + \sqrt{2} \right)}$$ 
=
= 
   /      ___\
log\1 + \/ 2 /
$$\log{\left(1 + \sqrt{2} \right)}$$ 
log(1 + sqrt(2))
Numerical answer [src] 
0.881373587019543
0.881373587019543
The graph
Integral of 1/sqrt(1+u^2) du

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

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