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Solving integrals/ y/x+y^2/x^2

Integral of y/x+y^2/x^2 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1            
  /            
 |             
 |  /     2\   
 |  |y   y |   
 |  |- + --| dx
 |  |x    2|   
 |  \    x /   
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/              
0
$$\int\limits_{0}^{1} \left(\frac{y^{2}}{x^{2}} + \frac{y}{x}\right)\, dx$$ 
Integral(y/x + y^2/x^2, (x, 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:

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

      So, the result is:

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

      1. The integral of is .

      So, the result is:

    The result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                 
 |                  
 | /     2\         
 | |y   y |         
 | |- + --| dx = nan
 | |x    2|         
 | \    x /         
 |                  
/
$$\int \left(\frac{y^{2}}{x^{2}} + \frac{y}{x}\right)\, dx = \text{NaN}$$
Simplify
The answer [src] 
       / 2\    2
oo*sign\y / - y
$$- y^{2} + \infty \operatorname{sign}{\left(y^{2} \right)}$$ 
=
= 
       / 2\    2
oo*sign\y / - y
$$- y^{2} + \infty \operatorname{sign}{\left(y^{2} \right)}$$ 
oo*sign(y^2) - y^2

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

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