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Derivative of:
(1-2*x)/x^2
Identical expressions
(one - two *x)/x^ two
(1 minus 2 multiply by x) divide by x squared
(one minus two multiply by x) divide by x to the power of two
(1-2*x)/x2
1-2*x/x2
(1-2*x)/x²
(1-2*x)/x to the power of 2
(1-2x)/x^2
(1-2x)/x2
1-2x/x2
1-2x/x^2
(1-2*x) divide by x^2
(1-2*x)/x^2dx
Similar expressions
(1+2*x)/x^2

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

The solution

You have entered [src]

  1           
  /           
 |            
 |  1 - 2*x   
 |  ------- dx
 |      2     
 |     x      
 |            
/             
0

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

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

Detail solution

There are multiple ways to do this integral.
Method #1
1. Rewrite the integrand:
  
  $\frac{1 - 2 x}{x^{2}} = - \frac{2}{x} + \frac{1}{x^{2}}$
2. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- \frac{2}{x}\right)\, dx = - 2 \int \frac{1}{x}\, dx$
    1. The integral of $\frac{1}{x}$ is $\log{\left(x \right)}$ .
    So, the result is: $- 2 \log{\left(x \right)}$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int \frac{1}{x^{2}}\, dx = - \frac{1}{x}$
  The result is: $- 2 \log{\left(x \right)} - \frac{1}{x}$
Method #2
1. Rewrite the integrand:
  
  $\frac{1 - 2 x}{x^{2}} = - \frac{2 x - 1}{x^{2}}$
2. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \frac{2 x - 1}{x^{2}}\right)\, dx = - \int \frac{2 x - 1}{x^{2}}\, dx$
  1. Rewrite the integrand:
    
    $\frac{2 x - 1}{x^{2}} = \frac{2}{x} - \frac{1}{x^{2}}$
  2. Integrate term-by-term:
    1. The integral of a constant times a function is the constant times the integral of the function:
      
      $\int \frac{2}{x}\, dx = 2 \int \frac{1}{x}\, dx$
      
      The integral of $\frac{1}{x}$ is $\log{\left(x \right)}$ .
      
      So, the result is: $2 \log{\left(x \right)}$
    1. The integral of a constant times a function is the constant times the integral of the function:
      
      $\int \left(- \frac{1}{x^{2}}\right)\, dx = - \int \frac{1}{x^{2}}\, dx$
      
      The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int \frac{1}{x^{2}}\, dx = - \frac{1}{x}$
      
      So, the result is: $\frac{1}{x}$
    The result is: $2 \log{\left(x \right)} + \frac{1}{x}$
  So, the result is: $- 2 \log{\left(x \right)} - \frac{1}{x}$
Add the constant of integration:

$- 2 \log{\left(x \right)} - \frac{1}{x}+ \mathrm{constant}$

The answer is:

$- 2 \log{\left(x \right)} - \frac{1}{x}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The answer [src]

oo

$$\infty$$

oo

$$\infty$$

oo

Numerical answer [src]

1.3793236779486e+19

1.3793236779486e+19

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

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Identical expressions

Similar expressions

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

Limits of integration:

The graph:

Piecewise:

The solution

Method #1

Method #2