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Derivative of:
sqrt(x^2-1)/x
Identical expressions
sqrt(x^ two - one)/x
square root of (x squared minus 1) divide by x
square root of (x to the power of two minus one) divide by x
√(x^2-1)/x
sqrt(x2-1)/x
sqrtx2-1/x
sqrt(x²-1)/x
sqrt(x to the power of 2-1)/x
sqrtx^2-1/x
sqrt(x^2-1) divide by x
sqrt(x^2-1)/xdx
Similar expressions
sqrt(x^2+1)/x

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

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

The solution

You have entered [src]

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

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

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

Detail solution

TrigSubstitutionRule(theta=_theta, func=sec(_theta), rewritten=tan(_theta)**2, substep=RewriteRule(rewritten=sec(_theta)**2 - 1, substep=AddRule(substeps=[TrigRule(func='sec**2', arg=_theta, context=sec(_theta)**2, symbol=_theta), ConstantRule(constant=-1, context=-1, symbol=_theta)], context=sec(_theta)**2 - 1, symbol=_theta), context=tan(_theta)**2, symbol=_theta), restriction=(x > -1) & (x < 1), context=sqrt(x**2 - 1)/x, symbol=x)

Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

Numerical answer [src]

(0.0 + 43.7835933145528j)

(0.0 + 43.7835933145528j)

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 sqrt(x^2-1)/x dx

Limits of integration:

The graph:

Piecewise:

The solution