Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of e^x^3
Integral of 1/(1+e^-x)
Integral of (4-x^2)^1/2
Integral of x^2*sinx
Graphing y =:
2/(x^2-4)
Derivative of:
2/(x^2-4)
Identical expressions
two /(x^ two - four)
2 divide by (x squared minus 4)
two divide by (x to the power of two minus four)
2/(x2-4)
2/x2-4
2/(x²-4)
2/(x to the power of 2-4)
2/x^2-4
2 divide by (x^2-4)
2/(x^2-4)dx
Similar expressions
2/(x^2+4)

Solving integrals/ 2/(x^2-4)

Integral of 2/(x^2-4) dx

The solution

You have entered [src]

  1          
  /          
 |           
 |    2      
 |  ------ dx
 |   2       
 |  x  - 4   
 |           
/            
0

$$\int\limits_{0}^{1} \frac{2}{x^{2} - 4}\, dx$$

Integral(2/(x^2 - 4), (x, 0, 1))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int \frac{2}{x^{2} - 4}\, dx = 2 \int \frac{1}{x^{2} - 4}\, dx$
So, the result is: $2 \left(\begin{cases} - \frac{\operatorname{acoth}{\left(\frac{x}{2} \right)}}{2} & \text{for}\: x^{2} > 4 \\- \frac{\operatorname{atanh}{\left(\frac{x}{2} \right)}}{2} & \text{for}\: x^{2} < 4 \end{cases}\right)$
Now simplify:

$\begin{cases} - \operatorname{acoth}{\left(\frac{x}{2} \right)} & \text{for}\: x^{2} > 4 \\- \operatorname{atanh}{\left(\frac{x}{2} \right)} & \text{for}\: x^{2} < 4 \end{cases}$
Add the constant of integration:

$\begin{cases} - \operatorname{acoth}{\left(\frac{x}{2} \right)} & \text{for}\: x^{2} > 4 \\- \operatorname{atanh}{\left(\frac{x}{2} \right)} & \text{for}\: x^{2} < 4 \end{cases}+ \mathrm{constant}$

The answer is:

$\begin{cases} - \operatorname{acoth}{\left(\frac{x}{2} \right)} & \text{for}\: x^{2} > 4 \\- \operatorname{atanh}{\left(\frac{x}{2} \right)} & \text{for}\: x^{2} < 4 \end{cases}+ \mathrm{constant}$

The answer (Indefinite) [src]

                     //      /x\             \
                     ||-acoth|-|             |
  /                  ||      \2/        2    |
 |                   ||----------  for x  > 4|
 |   2               ||    2                 |
 | ------ dx = C + 2*|<                      |
 |  2                ||      /x\             |
 | x  - 4            ||-atanh|-|             |
 |                   ||      \2/        2    |
/                    ||----------  for x  < 4|
                     \\    2                 /

$$\int \frac{2}{x^{2} - 4}\, dx = C + 2 \left(\begin{cases} - \frac{\operatorname{acoth}{\left(\frac{x}{2} \right)}}{2} & \text{for}\: x^{2} > 4 \\- \frac{\operatorname{atanh}{\left(\frac{x}{2} \right)}}{2} & \text{for}\: x^{2} < 4 \end{cases}\right)$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-log(3) 
--------
   2

$$- \frac{\log{\left(3 \right)}}{2}$$

-log(3) 
--------
   2

$$- \frac{\log{\left(3 \right)}}{2}$$

-log(3)/2

Numerical answer [src]

-0.549306144334055

-0.549306144334055

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 2/(x^2-4) dx

Limits of integration:

The graph:

Piecewise:

The solution