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  • Identical expressions

  • one /x*sqrt(x^ two + one)
  • 1 divide by x multiply by square root of (x squared plus 1)
  • one divide by x multiply by square root of (x to the power of two plus one)
  • 1/x*√(x^2+1)
  • 1/x*sqrt(x2+1)
  • 1/x*sqrtx2+1
  • 1/x*sqrt(x²+1)
  • 1/x*sqrt(x to the power of 2+1)
  • 1/xsqrt(x^2+1)
  • 1/xsqrt(x2+1)
  • 1/xsqrtx2+1
  • 1/xsqrtx^2+1
  • 1 divide by x*sqrt(x^2+1)
  • 1/x*sqrt(x^2+1)dx

  • Similar expressions

  • 1/x*sqrt(x^2-1)
Solving integrals/ 1/x*sqrt(x^2+1)

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |     ________   
 |    /  2        
 |  \/  x  + 1    
 |  ----------- dx
 |       x        
 |                
/                 
 2                
a
∫a21x2+1x dx\int\limits_{a^{2}}^{1} \frac{\sqrt{x^{2} + 1}}{x}\, dx 
Integral(sqrt(x^2 + 1)/x, (x, a^2, 1))
The answer (Indefinite) [src] 
  /                                                               
 |                                                                
 |    ________                                                    
 |   /  2                                                         
 | \/  x  + 1                /1\         x                1       
 | ----------- dx = C - asinh|-| + ------------- + ---------------
 |      x                    \x/        ________          ________
 |                                     /     1           /     1  
/                                     /  1 + --    x*   /  1 + -- 
                                     /        2        /        2 
                                   \/        x       \/        x
∫x2+1x dx=C+x1+1x2−asinh⁡(1x)+1x1+1x2\int \frac{\sqrt{x^{2} + 1}}{x}\, dx = C + \frac{x}{\sqrt{1 + \frac{1}{x^{2}}}} - \operatorname{asinh}{\left(\frac{1}{x} \right)} + \frac{1}{x \sqrt{1 + \frac{1}{x^{2}}}}
Simplify
The answer [src] 
                                                   2                 
  ___      /      ___\          1                 a              /1 \
\/ 2  - log\1 + \/ 2 / - ---------------- - ------------- + asinh|--|
                                 ________        ________        | 2|
                          2     /     1         /     1          \a /
                         a *   /  1 + --       /  1 + --             
                              /        4      /        4             
                            \/        a     \/        a
−a21+1a4+asinh⁡(1a2)−log⁡(1+2)+2−1a21+1a4- \frac{a^{2}}{\sqrt{1 + \frac{1}{a^{4}}}} + \operatorname{asinh}{\left(\frac{1}{a^{2}} \right)} - \log{\left(1 + \sqrt{2} \right)} + \sqrt{2} - \frac{1}{a^{2} \sqrt{1 + \frac{1}{a^{4}}}} 
=
= 
                                                   2                 
  ___      /      ___\          1                 a              /1 \
\/ 2  - log\1 + \/ 2 / - ---------------- - ------------- + asinh|--|
                                 ________        ________        | 2|
                          2     /     1         /     1          \a /
                         a *   /  1 + --       /  1 + --             
                              /        4      /        4             
                            \/        a     \/        a
−a21+1a4+asinh⁡(1a2)−log⁡(1+2)+2−1a21+1a4- \frac{a^{2}}{\sqrt{1 + \frac{1}{a^{4}}}} + \operatorname{asinh}{\left(\frac{1}{a^{2}} \right)} - \log{\left(1 + \sqrt{2} \right)} + \sqrt{2} - \frac{1}{a^{2} \sqrt{1 + \frac{1}{a^{4}}}} 
sqrt(2) - log(1 + sqrt(2)) - 1/(a^2*sqrt(1 + a^(-4))) - a^2/sqrt(1 + a^(-4)) + asinh(a^(-2))

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

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