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Integral of d{x}:
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Integral of 1/sqrt(x^2+4)
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Derivative of:
1/sqrt(x^2+4)
Identical expressions
one /sqrt(x^ two + four)
1 divide by square root of (x squared plus 4)
one divide by square root of (x to the power of two plus four)
1/√(x^2+4)
1/sqrt(x2+4)
1/sqrtx2+4
1/sqrt(x²+4)
1/sqrt(x to the power of 2+4)
1/sqrtx^2+4
1 divide by sqrt(x^2+4)
1/sqrt(x^2+4)dx
Similar expressions
1/sqrt(x^2-4)

Solving integrals/ 1/sqrt(x^2+4)

Integral of 1/sqrt(x^2+4) dx

The solution

You have entered [src]

  1                 
  /                 
 |                  
 |         1        
 |  1*----------- dx
 |       ________   
 |      /  2        
 |    \/  x  + 4    
 |                  
/                   
0

$$\int\limits_{0}^{1} 1 \cdot \frac{1}{\sqrt{x^{2} + 4}}\, dx$$

Integral(1/sqrt(x^2 + 4), (x, 0, 1))

Detail solution

TrigSubstitutionRule(theta=_theta, func=2*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 + 4), symbol=x)

Now simplify:

$\log{\left(\frac{x}{2} + \frac{\sqrt{x^{2} + 4}}{2} \right)}$
Add the constant of integration:

$\log{\left(\frac{x}{2} + \frac{\sqrt{x^{2} + 4}}{2} \right)}+ \mathrm{constant}$

The answer is:

$\log{\left(\frac{x}{2} + \frac{\sqrt{x^{2} + 4}}{2} \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                          /     ________    \
 |                           |    /      2     |
 |        1                  |   /      x     x|
 | 1*----------- dx = C + log|  /   1 + --  + -|
 |      ________             \\/        4     2/
 |     /  2                                     
 |   \/  x  + 4                                 
 |                                              
/

$${\rm asinh}\; \left({{x}\over{2}}\right)$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

asinh(1/2)

$${\rm asinh}\; \left({{1}\over{2}}\right)$$

asinh(1/2)

$$\operatorname{asinh}{\left(\frac{1}{2} \right)}$$

Упростить

Numerical answer [src]

0.481211825059603

0.481211825059603

The graph

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of 1/sqrt(x^2+4) dx

Limits of integration:

The graph:

Piecewise:

The solution