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Derivative of:
x^2/(x-2)
Graphing y =:
x^2/(x-2)
Identical expressions
x^ two /(x- two)
x squared divide by (x minus 2)
x to the power of two divide by (x minus two)
x2/(x-2)
x2/x-2
x²/(x-2)
x to the power of 2/(x-2)
x^2/x-2
x^2 divide by (x-2)
x^2/(x-2)dx
Similar expressions
x^2/(x+2)

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

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

The solution

You have entered [src]

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

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

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

Detail solution

Rewrite the integrand:

$\frac{x^{2}}{x - 2} = x + 2 + \frac{4}{x - 2}$
Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x\, dx = \frac{x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 2\, dx = 2 x$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{4}{x - 2}\, dx = 4 \int \frac{1}{x - 2}\, dx$
  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: $4 \log{\left(x - 2 \right)}$
The result is: $\frac{x^{2}}{2} + 2 x + 4 \log{\left(x - 2 \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

5/2 - 4*log(2)

$$\frac{5}{2} - 4 \log{\left(2 \right)}$$

5/2 - 4*log(2)

$$\frac{5}{2} - 4 \log{\left(2 \right)}$$

5/2 - 4*log(2)

Numerical answer [src]

-0.272588722239781

-0.272588722239781

The graph

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

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Identical expressions

Similar expressions

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

Limits of integration:

The graph:

Piecewise:

The solution