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Identical expressions
one /sqrt(x^ two - one)
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one divide by square root of (x to the power of two minus one)
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1/sqrt(x^2-1)dx
Similar expressions
1/sqrt(x^2+1)

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

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

The solution

You have entered [src]

  1               
  /               
 |                
 |       1        
 |  ----------- dx
 |     ________   
 |    /  2        
 |  \/  x  - 1    
 |                
/                 
0

$$\int\limits_{0}^{1} \frac{1}{\sqrt{x^{2} - 1}}\, dx$$

Integral(1/(sqrt(x^2 - 1)), (x, 0, 1))

Detail solution

TrigSubstitutionRule(theta=_theta, func=sec(_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=(x > -1) & (x < 1), context=1/(sqrt(x**2 - 1)), symbol=x)

Add the constant of integration:

$\begin{cases} \log{\left(x + \sqrt{x^{2} - 1} \right)} & \text{for}\: x > -1 \wedge x < 1 \end{cases}+ \mathrm{constant}$

The answer is:

$\begin{cases} \log{\left(x + \sqrt{x^{2} - 1} \right)} & \text{for}\: x > -1 \wedge x < 1 \end{cases}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                                     
 |                                                                      
 |      1               //   /       _________\                        \
 | ----------- dx = C + |<   |      /       2 |                        |
 |    ________          \\log\x + \/  -1 + x  /  for And(x > -1, x < 1)/
 |   /  2                                                               
 | \/  x  - 1                                                           
 |                                                                      
/

$$\int \frac{1}{\sqrt{x^{2} - 1}}\, dx = C + \begin{cases} \log{\left(x + \sqrt{x^{2} - 1} \right)} & \text{for}\: x > -1 \wedge x < 1 \end{cases}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-pi*I 
------
  2

$$- \frac{i \pi}{2}$$

-pi*I 
------
  2

$$- \frac{i \pi}{2}$$

-pi*i/2

Numerical answer [src]

(0.0 - 1.57079632641979j)

(0.0 - 1.57079632641979j)

The graph

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

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Identical expressions

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

Limits of integration:

The graph:

Piecewise:

The solution