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Similar expressions
x+2/(x-3)^3
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Integral of x+2/(x+3)^3 dx

The solution

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  0                  
  /                  
 |                   
 |  /       2    \   
 |  |x + --------| dx
 |  |           3|   
 |  \    (x + 3) /   
 |                   
/                    
0

$$\int\limits_{0}^{0} \left(x + \frac{2}{\left(x + 3\right)^{3}}\right)\, dx$$

Integral(x + 2/(x + 3)^3, (x, 0, 0))

Detail solution

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:
  
  $\int \frac{2}{\left(x + 3\right)^{3}}\, dx = 2 \int \frac{1}{\left(x + 3\right)^{3}}\, dx$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $- \frac{1}{2 x^{2} + 12 x + 18}$
  So, the result is: $- \frac{2}{2 x^{2} + 12 x + 18}$
The result is: $\frac{x^{2}}{2} - \frac{2}{2 x^{2} + 12 x + 18}$
Now simplify:

$\frac{x^{2} \left(x^{2} + 6 x + 9\right) - 2}{2 \left(x^{2} + 6 x + 9\right)}$
Add the constant of integration:

$\frac{x^{2} \left(x^{2} + 6 x + 9\right) - 2}{2 \left(x^{2} + 6 x + 9\right)}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(x^{2} + 6 x + 9\right) - 2}{2 \left(x^{2} + 6 x + 9\right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                             
 |                          2                   
 | /       2    \          x           2        
 | |x + --------| dx = C + -- - ----------------
 | |           3|          2            2       
 | \    (x + 3) /               18 + 2*x  + 12*x
 |                                              
/

$$\int \left(x + \frac{2}{\left(x + 3\right)^{3}}\right)\, dx = C + \frac{x^{2}}{2} - \frac{2}{2 x^{2} + 12 x + 18}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$0$$

Numerical answer [src]

0.0

0.0

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

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

Limits of integration:

The graph:

Piecewise:

The solution