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How do you in partial fractions?:
x^3/(x-2)
Derivative of:
x^3/(x-2)
Identical expressions
x^ three /(x- two)
x cubed divide by (x minus 2)
x to the power of three divide by (x minus two)
x3/(x-2)
x3/x-2
x³/(x-2)
x to the power of 3/(x-2)
x^3/x-2
x^3 divide by (x-2)
x^3/(x-2)dx
Similar expressions
x^3/(x+2)

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

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

The solution

You have entered [src]

  1         
  /         
 |          
 |     3    
 |    x     
 |  ----- dx
 |  x - 2   
 |          
/           
0

$$\int\limits_{0}^{1} \frac{x^{3}}{x - 2}\, dx$$

Integral(x^3/(x - 2), (x, 0, 1))

Detail solution

Rewrite the integrand:

$\frac{x^{3}}{x - 2} = x^{2} + 2 x + 4 + \frac{8}{x - 2}$
Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{2}\, dx = \frac{x^{3}}{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 2 x\, dx = 2 \int x\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  So, the result is: $x^{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 4\, dx = 4 x$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{8}{x - 2}\, dx = 8 \int \frac{1}{x - 2}\, dx$
  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: $8 \log{\left(x - 2 \right)}$
The result is: $\frac{x^{3}}{3} + x^{2} + 4 x + 8 \log{\left(x - 2 \right)}$
Add the constant of integration:

$\frac{x^{3}}{3} + x^{2} + 4 x + 8 \log{\left(x - 2 \right)}+ \mathrm{constant}$

The answer is:

$\frac{x^{3}}{3} + x^{2} + 4 x + 8 \log{\left(x - 2 \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                            
 |                                             
 |    3                                       3
 |   x             2                         x 
 | ----- dx = C + x  + 4*x + 8*log(-2 + x) + --
 | x - 2                                     3 
 |                                             
/

$$\int \frac{x^{3}}{x - 2}\, dx = C + \frac{x^{3}}{3} + x^{2} + 4 x + 8 \log{\left(x - 2 \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

16/3 - 8*log(2)

$$\frac{16}{3} - 8 \log{\left(2 \right)}$$

16/3 - 8*log(2)

$$\frac{16}{3} - 8 \log{\left(2 \right)}$$

16/3 - 8*log(2)

Numerical answer [src]

-0.211844111146229

-0.211844111146229

The graph

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

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Identical expressions

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

Limits of integration:

The graph:

Piecewise:

The solution