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

Integral of 1/(sqrt(1+x^2)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |         1        
 |  1*----------- dx
 |       ________   
 |      /      2    
 |    \/  1 + x     
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0
∫011⋅1x2+1 dx\int\limits_{0}^{1} 1 \cdot \frac{1}{\sqrt{x^{2} + 1}}\, dx 
Integral(1/sqrt(1 + x^2), (x, 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(x**2 + 1), symbol=x)

  1. Add the constant of integration:

    log⁡(x+x2+1)+constant\log{\left(x + \sqrt{x^{2} + 1} \right)}+ \mathrm{constant}

The answer is:

log⁡(x+x2+1)+constant\log{\left(x + \sqrt{x^{2} + 1} \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                           
 |                           /       ________\
 |        1                  |      /      2 |
 | 1*----------- dx = C + log\x + \/  1 + x  /
 |      ________                              
 |     /      2                               
 |   \/  1 + x                                
 |                                            
/
∫1⋅1x2+1 dx=C+log⁡(x+x2+1)\int 1 \cdot \frac{1}{\sqrt{x^{2} + 1}}\, dx = C + \log{\left(x + \sqrt{x^{2} + 1} \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9002
Plot the graph f(x)
The answer [src] 
   /      ___\
log\1 + \/ 2 /
log⁡(1+2)\log{\left(1 + \sqrt{2} \right)} 
=
= 
   /      ___\
log\1 + \/ 2 /
log⁡(1+2)\log{\left(1 + \sqrt{2} \right)}
Упростить
Numerical answer [src] 
0.881373587019543
0.881373587019543
The graph
Integral of 1/(sqrt(1+x^2)) dx

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

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