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(sqrt(3x))/(sqrt(3x^2-2))
Solving integrals/ (sqrt(3x))/(sqrt(3x^2-2))

Integral of (sqrt(3x))/(sqrt(3x^2-2)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |       _____      
 |     \/ 3*x       
 |  ------------- dx
 |     __________   
 |    /    2        
 |  \/  3*x  - 2    
 |                  
/                   
0
$$\int\limits_{0}^{1} \frac{\sqrt{3 x}}{\sqrt{3 x^{2} - 2}}\, dx$$ 
Integral(sqrt(3*x)/sqrt(3*x^2 - 2), (x, 0, 1))
The graph
Plot the graph f(x)
The answer [src] 
                      _                   
     ___             |_  /1/2, 3/4 |    \ 
-I*\/ 6 *Gamma(3/4)* |   |         | 3/2| 
                    2  1 \  7/4    |    / 
------------------------------------------
               4*Gamma(7/4)
$$- \frac{\sqrt{6} i \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{3}{2}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)}$$ 
=
= 
                      _                   
     ___             |_  /1/2, 3/4 |    \ 
-I*\/ 6 *Gamma(3/4)* |   |         | 3/2| 
                    2  1 \  7/4    |    / 
------------------------------------------
               4*Gamma(7/4)
$$- \frac{\sqrt{6} i \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{3}{2}} \right)}}{4 \Gamma\left(\frac{7}{4}\right)}$$ 
-i*sqrt(6)*gamma(3/4)*hyper((1/2, 3/4), (7/4,), 3/2)/(4*gamma(7/4))
Numerical answer [src] 
(0.559876078444639 - 1.0673152294649j)
(0.559876078444639 - 1.0673152294649j)
The graph
Integral of (sqrt(3x))/(sqrt(3x^2-2)) dx

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

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