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  • Identical expressions

  • one /(sqrt(five)- three *x^ two)
  • 1 divide by ( square root of (5) minus 3 multiply by x squared )
  • one divide by ( square root of (five) minus three multiply by x to the power of two)
  • 1/(√(5)-3*x^2)
  • 1/(sqrt(5)-3*x2)
  • 1/sqrt5-3*x2
  • 1/(sqrt(5)-3*x²)
  • 1/(sqrt(5)-3*x to the power of 2)
  • 1/(sqrt(5)-3x^2)
  • 1/(sqrt(5)-3x2)
  • 1/sqrt5-3x2
  • 1/sqrt5-3x^2
  • 1 divide by (sqrt(5)-3*x^2)
  • 1/(sqrt(5)-3*x^2)dx

  • Similar expressions

  • 1/(sqrt(5)+3*x^2)
Solving integrals/ 1/(sqrt(5)-3*x^2)

Integral of 1/(sqrt(5)-3*x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                
  /                
 |                 
 |       1         
 |  ------------ dx
 |    ___      2   
 |  \/ 5  - 3*x    
 |                 
/                  
0
$$\int\limits_{0}^{1} \frac{1}{- 3 x^{2} + \sqrt{5}}\, dx$$ 
Integral(1/(sqrt(5) - 3*x^2), (x, 0, 1))
Detail solution

    PiecewiseRule(subfunctions=[(ArctanRule(a=1, b=-3, c=sqrt(5), context=1/(-3*x**2 + sqrt(5)), symbol=x), False), (ArccothRule(a=1, b=-3, c=sqrt(5), context=1/(-3*x**2 + sqrt(5)), symbol=x), x**2 > sqrt(5)/3), (ArctanhRule(a=1, b=-3, c=sqrt(5), context=1/(-3*x**2 + sqrt(5)), symbol=x), x**2 < sqrt(5)/3)], context=1/(-3*x**2 + sqrt(5)), symbol=x)

  1. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
                         //                /    ___  3/4\                \
                         ||  ___  3/4      |x*\/ 3 *5   |                |
                         ||\/ 3 *5   *acoth|------------|             ___|
  /                      ||                \     5      /       2   \/ 5 |
 |                       ||------------------------------  for x  > -----|
 |      1                ||              15                           3  |
 | ------------ dx = C + |<                                              |
 |   ___      2          ||                /    ___  3/4\                |
 | \/ 5  - 3*x           ||  ___  3/4      |x*\/ 3 *5   |                |
 |                       ||\/ 3 *5   *atanh|------------|             ___|
/                        ||                \     5      /       2   \/ 5 |
                         ||------------------------------  for x  < -----|
                         \\              15                           3  /
$$\int \frac{1}{- 3 x^{2} + \sqrt{5}}\, dx = C + \begin{cases} \frac{\sqrt{3} \cdot 5^{\frac{3}{4}} \operatorname{acoth}{\left(\frac{\sqrt{3} \cdot 5^{\frac{3}{4}} x}{5} \right)}}{15} & \text{for}\: x^{2} > \frac{\sqrt{5}}{3} \\\frac{\sqrt{3} \cdot 5^{\frac{3}{4}} \operatorname{atanh}{\left(\frac{\sqrt{3} \cdot 5^{\frac{3}{4}} x}{5} \right)}}{15} & \text{for}\: x^{2} < \frac{\sqrt{5}}{3} \end{cases}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
nan
$$\text{NaN}$$ 
=
= 
nan
$$\text{NaN}$$ 
nan
Numerical answer [src] 
0.132130626206719
0.132130626206719

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

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