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Identical expressions
x+ two /x³+2x²+5xdx
x plus 2 divide by x³ plus 2x² plus 5xdx
x plus two divide by x³ plus 2x² plus 5xdx
x+2 divide by x³+2x²+5xdx
Similar expressions
x+2/x³+2x²-5xdx
x+2/x³-2x²+5xdx
x-2/x³+2x²+5xdx

Integral of x+2/x³+2x²+5xdx dx

The solution

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  1                         
  /                         
 |                          
 |  /    2       2      \   
 |  |x + -- + 2*x  + 5*x| dx
 |  |     3             |   
 |  \    x              /   
 |                          
/                           
0

$$\int\limits_{0}^{1} \left(5 x + \left(2 x^{2} + \left(x + \frac{2}{x^{3}}\right)\right)\right)\, dx$$

Integral(x + 2/x^3 + 2*x^2 + 5*x, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 5 x\, dx = 5 \int x\, dx$
  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: $\frac{5 x^{2}}{2}$
1. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 2 x^{2}\, dx = 2 \int x^{2}\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x^{2}\, dx = \frac{x^{3}}{3}$
    So, the result is: $\frac{2 x^{3}}{3}$
  1. 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:
      
      $\int \frac{2}{x^{3}}\, dx = 2 \int \frac{1}{x^{3}}\, dx$
      1. Don't know the steps in finding this integral.
        
        But the integral is
        
        $- \frac{1}{2 x^{2}}$
      So, the result is: $- \frac{1}{x^{2}}$
    The result is: $\frac{x^{2}}{2} - \frac{1}{x^{2}}$
  The result is: $\frac{2 x^{3}}{3} + \frac{x^{2}}{2} - \frac{1}{x^{2}}$
The result is: $\frac{2 x^{3}}{3} + 3 x^{2} - \frac{1}{x^{2}}$
Now simplify:

$\frac{x^{4} \left(2 x + 9\right) - 3}{3 x^{2}}$
Add the constant of integration:

$\frac{x^{4} \left(2 x + 9\right) - 3}{3 x^{2}}+ \mathrm{constant}$

The answer is:

$\frac{x^{4} \left(2 x + 9\right) - 3}{3 x^{2}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                               
 |                                               3
 | /    2       2      \          1       2   2*x 
 | |x + -- + 2*x  + 5*x| dx = C - -- + 3*x  + ----
 | |     3             |           2           3  
 | \    x              /          x               
 |                                                
/

$$\int \left(5 x + \left(2 x^{2} + \left(x + \frac{2}{x^{3}}\right)\right)\right)\, dx = C + \frac{2 x^{3}}{3} + 3 x^{2} - \frac{1}{x^{2}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

oo

$$\infty$$

oo

$$\infty$$

oo

Numerical answer [src]

1.83073007580698e+38

1.83073007580698e+38

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

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Identical expressions

Similar expressions

Integral of x+2/x³+2x²+5xdx dx

Limits of integration:

The graph:

Piecewise:

The solution