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Solving integrals/ x^2/y^2

Integral of x^2/y^2 dy

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 4*x     
  /      
 |       
 |   2   
 |  x    
 |  -- dy
 |   2   
 |  y    
 |       
/        
1        
-        
x
$$\int\limits_{\frac{1}{x}}^{4 x} \frac{x^{2}}{y^{2}}\, dy$$ 
Integral(x^2/y^2, (y, 1/x, 4*x))
Detail solution

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

      PiecewiseRule(subfunctions=[(ArctanRule(a=1, b=1, c=0, context=1/(y**2), symbol=y), False), (ArccothRule(a=1, b=1, c=0, context=1/(y**2), symbol=y), False), (ArctanhRule(a=1, b=1, c=0, context=1/(y**2), symbol=y), False)], context=1/(y**2), symbol=y)

    So, the result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /           
 |            
 |  2         
 | x          
 | -- dy = nan
 |  2         
 | y          
 |            
/
$$\int \frac{x^{2}}{y^{2}}\, dy = \text{NaN}$$
Simplify
The answer [src] 
 3   x
x  - -
     4
$$x^{3} - \frac{x}{4}$$ 
=
= 
 3   x
x  - -
     4
$$x^{3} - \frac{x}{4}$$ 
x^3 - x/4

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

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