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Integral of d{x}:
Integral of (1-x^2)/(1+x^2)
Integral of x^3*exp(x^2)
Integral of sin^2*x
Integral of x^2/(x^2-4)
Derivative of:
x^2/(x^2-4)
Graphing y =:
x^2/(x^2-4)
How do you in partial fractions?:
x^2/(x^2-4)
Identical expressions
x^ two /(x^ two - four)
x squared divide by (x squared minus 4)
x to the power of two divide by (x to the power of two minus four)
x2/(x2-4)
x2/x2-4
x²/(x²-4)
x to the power of 2/(x to the power of 2-4)
x^2/x^2-4
x^2 divide by (x^2-4)
x^2/(x^2-4)dx
Similar expressions
x^2/(x^2+4)
What you mean?
x^2/(x^2 - 1*4)
x^2/(x^2) - 1*4
x^2*2/x - 1*4
x^2/(x^2) - 1*4
x*2/(x^2 - 1*4)
x*2/x^2 - 1*4
x^2/(x^2) - 1*4

You entered:

x^2/(x^2-4)

What you mean?

x^2/(x^2 - 1*4)

x^2/(x^2) - 1*4

x^2*2/x - 1*4

x^2/(x^2) - 1*4

x*2/(x^2 - 1*4)

x*2/x^2 - 1*4

x^2/(x^2) - 1*4

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

The solution

You have entered [src]

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

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

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

Detail solution

Rewrite the integrand:

$\frac{x^{2}}{x^{2} - 4} = 1 - \frac{1}{x + 2} + \frac{1}{x - 2}$
Integrate term-by-term:
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 1\, dx = x$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \frac{1}{x + 2}\right)\, dx = - \int \frac{1}{x + 2}\, dx$
  1. Let $u = x + 2$ .
    
    Then let $du = dx$ and substitute $du$ :
    
    $\int \frac{1}{u}\, du$
    1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
    Now substitute $u$ back in:
    
    $\log{\left(x + 2 \right)}$
  So, the result is: $- \log{\left(x + 2 \right)}$
1. Let $u = x - 2$ .
  
  Then let $du = dx$ and substitute $du$ :
  
  $\int \frac{1}{u}\, du$
  1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
  Now substitute $u$ back in:
  
  $\log{\left(x - 2 \right)}$
The result is: $x + \log{\left(x - 2 \right)} - \log{\left(x + 2 \right)}$
Add the constant of integration:

$x + \log{\left(x - 2 \right)} - \log{\left(x + 2 \right)}+ \mathrm{constant}$

The answer is:

$x + \log{\left(x - 2 \right)} - \log{\left(x + 2 \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                            
 |                                             
 |    2                                        
 |   x                                         
 | ------ dx = C + x - log(2 + x) + log(-2 + x)
 |  2                                          
 | x  - 4                                      
 |                                             
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

1 - log(3)

$$1 - \log{\left(3 \right)}$$

1 - log(3)

$$1 - \log{\left(3 \right)}$$

Упростить

Numerical answer [src]

-0.0986122886681097

-0.0986122886681097

The graph

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

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You entered:

What you mean?

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

Limits of integration:

The graph:

Piecewise:

The solution