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Solving integrals/ (1/x-y)dy

Integral of (1/x-y)dy dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1           
  /           
 |            
 |  /1    \   
 |  |- - y| dy
 |  \x    /   
 |            
/             
0
$$\int\limits_{0}^{1} \left(- y + \frac{1}{x}\right)\, dy$$ 
Integral(1/x - y, (y, 0, 1))
Detail solution

  1. Integrate term-by-term:

    1. The integral of a constant times a function is the constant times the integral of the function:

      1. The integral of is when :

      So, the result is:

    1. The integral of a constant is the constant times the variable of integration:

    The result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                       
 |                   2    
 | /1    \          y    y
 | |- - y| dy = C - -- + -
 | \x    /          2    x
 |                        
/
$$\int \left(- y + \frac{1}{x}\right)\, dy = C - \frac{y^{2}}{2} + \frac{y}{x}$$
Simplify
The answer [src] 
  1   1
- - + -
  2   x
$$- \frac{1}{2} + \frac{1}{x}$$ 
=
= 
  1   1
- - + -
  2   x
$$- \frac{1}{2} + \frac{1}{x}$$ 
-1/2 + 1/x

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

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