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Identical expressions
(x- four)*(x- six)/x^ two
(x minus 4) multiply by (x minus 6) divide by x squared
(x minus four) multiply by (x minus six) divide by x to the power of two
(x-4)*(x-6)/x2
x-4*x-6/x2
(x-4)*(x-6)/x²
(x-4)*(x-6)/x to the power of 2
(x-4)(x-6)/x^2
(x-4)(x-6)/x2
x-4x-6/x2
x-4x-6/x^2
(x-4)*(x-6) divide by x^2
(x-4)*(x-6)/x^2dx
Similar expressions
(x+4)*(x-6)/x^2
(x-4)*(x+6)/x^2

Integral of (x-4)*(x-6)/x^2 dx

The solution

You have entered [src]

  1                   
  /                   
 |                    
 |  (x - 4)*(x - 6)   
 |  --------------- dx
 |          2         
 |         x          
 |                    
/                     
0

$$\int\limits_{0}^{1} \frac{\left(x - 6\right) \left(x - 4\right)}{x^{2}}\, dx$$

Integral(((x - 4)*(x - 6))/x^2, (x, 0, 1))

Detail solution

There are multiple ways to do this integral.
Method #1
1. Rewrite the integrand:
  
  $\frac{\left(x - 6\right) \left(x - 4\right)}{x^{2}} = 1 - \frac{10}{x} + \frac{24}{x^{2}}$
2. Integrate term-by-term:
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int 1\, dx = x$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- \frac{10}{x}\right)\, dx = - 10 \int \frac{1}{x}\, dx$
    1. The integral of $\frac{1}{x}$ is $\log{\left(x \right)}$ .
    So, the result is: $- 10 \log{\left(x \right)}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{24}{x^{2}}\, dx = 24 \int \frac{1}{x^{2}}\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int \frac{1}{x^{2}}\, dx = - \frac{1}{x}$
    So, the result is: $- \frac{24}{x}$
  The result is: $x - 10 \log{\left(x \right)} - \frac{24}{x}$
Method #2
1. Rewrite the integrand:
  
  $\frac{\left(x - 6\right) \left(x - 4\right)}{x^{2}} = \frac{x^{2} - 10 x + 24}{x^{2}}$
2. Rewrite the integrand:
  
  $\frac{x^{2} - 10 x + 24}{x^{2}} = 1 - \frac{10}{x} + \frac{24}{x^{2}}$
3. Integrate term-by-term:
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int 1\, dx = x$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- \frac{10}{x}\right)\, dx = - 10 \int \frac{1}{x}\, dx$
    1. The integral of $\frac{1}{x}$ is $\log{\left(x \right)}$ .
    So, the result is: $- 10 \log{\left(x \right)}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{24}{x^{2}}\, dx = 24 \int \frac{1}{x^{2}}\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int \frac{1}{x^{2}}\, dx = - \frac{1}{x}$
    So, the result is: $- \frac{24}{x}$
  The result is: $x - 10 \log{\left(x \right)} - \frac{24}{x}$
Add the constant of integration:

$x - 10 \log{\left(x \right)} - \frac{24}{x}+ \mathrm{constant}$

The answer is:

$x - 10 \log{\left(x \right)} - \frac{24}{x}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                           
 |                                            
 | (x - 4)*(x - 6)              24            
 | --------------- dx = C + x - -- - 10*log(x)
 |         2                    x             
 |        x                                   
 |                                            
/

$$\int \frac{\left(x - 6\right) \left(x - 4\right)}{x^{2}}\, dx = C + x - 10 \log{\left(x \right)} - \frac{24}{x}$$

Simplify

The answer [src]

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$$\infty$$

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$$\infty$$

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Numerical answer [src]

3.31037682707663e+20

3.31037682707663e+20

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

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Identical expressions

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Integral of (x-4)*(x-6)/x^2 dx

Limits of integration:

The graph:

Piecewise:

The solution

Method #1

Method #2