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Integral of d{x}:
Integral of 1/(2+x^2)
Integral of x*sin2x
Integral of y^(-2/3)
Integral of x/(x^3-3x+2)
Derivative of:
x^3/(x^2-4)
Graphing y =:
x^3/(x^2-4)
How do you in partial fractions?:
x^3/(x^2-4)
Identical expressions
x^ three /(x^ two - four)
x cubed divide by (x squared minus 4)
x to the power of three divide by (x to the power of two minus four)
x3/(x2-4)
x3/x2-4
x³/(x²-4)
x to the power of 3/(x to the power of 2-4)
x^3/x^2-4
x^3 divide by (x^2-4)
x^3/(x^2-4)dx
Similar expressions
x^3/(x^2+4)

Solving integrals/ x^3/(x^2-4)

Integral of x^3/(x^2-4) dx

The solution

You have entered [src]

  1          
  /          
 |           
 |     3     
 |    x      
 |  ------ dx
 |   2       
 |  x  - 4   
 |           
/            
0

$$\int\limits_{0}^{1} \frac{x^{3}}{x^{2} - 4}\, dx$$

Integral(x^3/(x^2 - 4), (x, 0, 1))

Detail solution

There are multiple ways to do this integral.
Method #1
1. Let $u = x^{2}$ .
  
  Then let $du = 2 x dx$ and substitute $du$ :
  
  $\int \frac{u}{2 u - 8}\, du$
  1. Rewrite the integrand:
    
    $\frac{u}{2 u - 8} = \frac{1}{2} + \frac{2}{u - 4}$
  2. Integrate term-by-term:
    1. The integral of a constant is the constant times the variable of integration:
      
      $\int \frac{1}{2}\, du = \frac{u}{2}$
    1. The integral of a constant times a function is the constant times the integral of the function:
      
      $\int \frac{2}{u - 4}\, du = 2 \int \frac{1}{u - 4}\, du$
      
      Let $u = u - 4$ .
      
      Then let $du = du$ and substitute $du$ :
      
      $\int \frac{1}{u}\, du$
      
      The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
      
      Now substitute $u$ back in:
      
      $\log{\left(u - 4 \right)}$
      
      So, the result is: $2 \log{\left(u - 4 \right)}$
    The result is: $\frac{u}{2} + 2 \log{\left(u - 4 \right)}$
  Now substitute $u$ back in:
  
  $\frac{x^{2}}{2} + 2 \log{\left(x^{2} - 4 \right)}$
Method #2
1. Rewrite the integrand:
  
  $\frac{x^{3}}{x^{2} - 4} = x + \frac{2}{x + 2} + \frac{2}{x - 2}$
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 times a function is the constant times the integral of the function:
    
    $\int \frac{2}{x + 2}\, dx = 2 \int \frac{1}{x + 2}\, dx$
    1. Let $u = x + 2$ .
      
      Then let $du = dx$ and substitute $du$ :
      
      $\int \frac{1}{u}\, du$
      
      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: $2 \log{\left(x + 2 \right)}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{2}{x - 2}\, dx = 2 \int \frac{1}{x - 2}\, dx$
    1. Let $u = x - 2$ .
      
      Then let $du = dx$ and substitute $du$ :
      
      $\int \frac{1}{u}\, du$
      
      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: $2 \log{\left(x - 2 \right)}$
  The result is: $\frac{x^{2}}{2} + 2 \log{\left(x - 2 \right)} + 2 \log{\left(x + 2 \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                                   
 |                                    
 |    3             2                 
 |   x             x         /      2\
 | ------ dx = C + -- + 2*log\-4 + x /
 |  2              2                  
 | x  - 4                             
 |                                    
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

1/2 - 2*log(4) + 2*log(3)

$$- 2 \log{\left(4 \right)} + \frac{1}{2} + 2 \log{\left(3 \right)}$$

1/2 - 2*log(4) + 2*log(3)

$$- 2 \log{\left(4 \right)} + \frac{1}{2} + 2 \log{\left(3 \right)}$$

1/2 - 2*log(4) + 2*log(3)

Numerical answer [src]

-0.0753641449035619

-0.0753641449035619

The graph

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

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Identical expressions

Similar expressions

Integral of x^3/(x^2-4) dx

Limits of integration:

The graph:

Piecewise:

The solution

Method #1

Method #2