Integral of (x-y)/x dx

The solution

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  1         
  /         
 |          
 |  x - y   
 |  ----- dx
 |    x     
 |          
/           
0

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

Integral((x - y)/x, (x, 0, 1))

Detail solution

Rewrite the integrand:

$\frac{x - y}{x} = 1 - \frac{y}{x}$
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:
  
  $\int \left(- \frac{y}{x}\right)\, dx = - y \int \frac{1}{x}\, dx$
  1. The integral of $\frac{1}{x}$ is $\log{\left(x \right)}$ .
  So, the result is: $- y \log{\left(x \right)}$
The result is: $x - y \log{\left(x \right)}$
Add the constant of integration:

$x - y \log{\left(x \right)}+ \mathrm{constant}$

The answer is:

$x - y \log{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The answer [src]

1 - oo*sign(y)

$$- \infty \operatorname{sign}{\left(y \right)} + 1$$

1 - oo*sign(y)

$$- \infty \operatorname{sign}{\left(y \right)} + 1$$

1 - oo*sign(y)

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

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Integral of (x-y)/x dx

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