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Solving integrals/ 6*x-3*y-1/y

Integral of 6*x-3*y-1/y dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src] 
 11/5                  
   /                   
  |                    
  |  /            1\   
  |  |6*x - 3*y - -| dx
  |  \            y/   
  |                    
 /                     
 11                    
 --                    
 10
$$\int\limits_{\frac{11}{10}}^{\frac{11}{5}} \left(\left(6 x - 3 y\right) - \frac{1}{y}\right)\, dx$$ 
Integral(6*x - 3*y - 1/y, (x, 11/10, 11/5))
Detail solution

  1. Integrate term-by-term:

    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:

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

    The result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                         
 |                                          
 | /            1\             2   x        
 | |6*x - 3*y - -| dx = C + 3*x  - - - 3*x*y
 | \            y/                 y        
 |                                          
/
$$\int \left(\left(6 x - 3 y\right) - \frac{1}{y}\right)\, dx = C + 3 x^{2} - 3 x y - \frac{x}{y}$$
Simplify
The answer [src] 
          /        2\
1089   11*\-1 - 3*y /
---- + --------------
100         10*y
$$\frac{1089}{100} + \frac{11 \left(- 3 y^{2} - 1\right)}{10 y}$$ 
=
= 
          /        2\
1089   11*\-1 - 3*y /
---- + --------------
100         10*y
$$\frac{1089}{100} + \frac{11 \left(- 3 y^{2} - 1\right)}{10 y}$$ 
1089/100 + 11*(-1 - 3*y^2)/(10*y)

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

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