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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 plus 2)
x to the power of two divide by (x plus 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:
  
  $\int \left(-2\right)\, dx = - 2 x$
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]

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

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

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

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

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

Numerical answer [src]

0.121860432432658

0.121860432432658

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