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Similar expressions
1/sqrt(4-3x^2)

Integral of 1/sqrt(4+3x^2) dx

The solution

You have entered [src]

  0                 
  /                 
 |                  
 |        1         
 |  ------------- dx
 |     __________   
 |    /        2    
 |  \/  4 + 3*x     
 |                  
/                   
0

$$\int\limits_{0}^{0} \frac{1}{\sqrt{3 x^{2} + 4}}\, dx$$

Integral(1/(sqrt(4 + 3*x^2)), (x, 0, 0))

Detail solution

TrigSubstitutionRule(theta=_theta, func=2*sqrt(3)*tan(_theta)/3, rewritten=sqrt(3)*sec(_theta)/3, substep=ConstantTimesRule(constant=sqrt(3)/3, other=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), context=sqrt(3)*sec(_theta)/3, symbol=_theta), restriction=True, context=1/(sqrt(3*x**2 + 4)), symbol=x)

Now simplify:

$\frac{\sqrt{3} \log{\left(\frac{\sqrt{3} x}{2} + \frac{\sqrt{3 x^{2} + 4}}{2} \right)}}{3}$
Add the constant of integration:

$\frac{\sqrt{3} \log{\left(\frac{\sqrt{3} x}{2} + \frac{\sqrt{3 x^{2} + 4}}{2} \right)}}{3}+ \mathrm{constant}$

The answer is:

$\frac{\sqrt{3} \log{\left(\frac{\sqrt{3} x}{2} + \frac{\sqrt{3 x^{2} + 4}}{2} \right)}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

                                   /     __________          \
                                   |    /        2        ___|
  /                         ___    |   /      3*x     x*\/ 3 |
 |                        \/ 3 *log|  /   1 + ----  + -------|
 |       1                         \\/         4         2   /
 | ------------- dx = C + ------------------------------------
 |    __________                           3                  
 |   /        2                                               
 | \/  4 + 3*x                                                
 |                                                            
/

$$\int \frac{1}{\sqrt{3 x^{2} + 4}}\, dx = C + \frac{\sqrt{3} \log{\left(\frac{\sqrt{3} x}{2} + \sqrt{\frac{3 x^{2}}{4} + 1} \right)}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$0$$

Numerical answer [src]

0.0

0.0

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

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Identical expressions

Similar expressions

Integral of 1/sqrt(4+3x^2) dx

Limits of integration:

The graph:

Piecewise:

The solution