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Integral of d{x}:
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Integral of (-2)/x^3
Integral of (x/(x+1))^x²
Graphing y =:
(x-1)^2/x
Identical expressions
(x- one)^ two /x
(x minus 1) squared divide by x
(x minus one) to the power of two divide by x
(x-1)2/x
x-12/x
(x-1)²/x
(x-1) to the power of 2/x
x-1^2/x
(x-1)^2 divide by x
(x-1)^2/xdx
Similar expressions
(x+1)^2/x
What you mean?
(x - 1)^2/x
(x - 1)^(2/x)
(x - 1)^(2/x)

You entered:

(x-1)^2/x

What you mean?

(x - 1)^2/x

(x - 1)^(2/x)

(x - 1)^(2/x)

Integral of (x-1)^2/x dx

The solution

You have entered [src]

  1            
  /            
 |             
 |         2   
 |  (x - 1)    
 |  -------- dx
 |     x       
 |             
/              
0

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

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

Detail solution

There are multiple ways to do this integral.
Method #1
1. Rewrite the integrand:
  
  $\frac{\left(x - 1\right)^{2}}{x} = x - 2 + \frac{1}{x}$
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 $\frac{1}{x}$ is $\log{\left(x \right)}$ .
  The result is: $\frac{x^{2}}{2} - 2 x + \log{\left(x \right)}$
Method #2
1. Rewrite the integrand:
  
  $\frac{\left(x - 1\right)^{2}}{x} = \frac{x^{2} - 2 x + 1}{x}$
2. Rewrite the integrand:
  
  $\frac{x^{2} - 2 x + 1}{x} = x - 2 + \frac{1}{x}$
3. 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 $\frac{1}{x}$ is $\log{\left(x \right)}$ .
  The result is: $\frac{x^{2}}{2} - 2 x + \log{\left(x \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                                   
 |                                    
 |        2           2               
 | (x - 1)           x                
 | -------- dx = C + -- - 2*x + log(x)
 |    x              2                
 |                                    
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

oo

$$\infty$$

oo

$$\infty$$

oo

Numerical answer [src]

42.5904461339929

42.5904461339929

The graph

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

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Identical expressions

Similar expressions

What you mean?

You entered:

What you mean?

Integral of (x-1)^2/x dx

Limits of integration:

The graph:

Piecewise:

The solution

Method #1

Method #2