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dy/y
Solving integrals/ dy/y

Integral of dy/y dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1     
  /     
 |      
 |  1   
 |  - dy
 |  y   
 |      
/       
0
∫011y dy\int\limits_{0}^{1} \frac{1}{y}\, dy 
Integral(1/y, (y, 0, 1))
Detail solution

  1. The integral of 1y\frac{1}{y} is log⁡(y)\log{\left(y \right)}.

  2. Add the constant of integration:

    log⁡(y)+constant\log{\left(y \right)}+ \mathrm{constant}

The answer is:

log⁡(y)+constant\log{\left(y \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                 
 |                  
 | 1                
 | - dy = C + log(y)
 | y                
 |                  
/
∫1y dy=C+log⁡(y)\int \frac{1}{y}\, dy = C + \log{\left(y \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9020000-10000
Plot the graph f(x)
The answer [src] 
oo
∞\infty 
=
= 
oo
∞\infty 
oo
Numerical answer [src] 
44.0904461339929
44.0904461339929
The graph
Integral of dy/y dx

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

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