Integral of -1/y dy

You have entered [src]

$$\int\limits_{0}^{1} \left(- \frac{1}{y}\right)\, dy$$

Integral(-1/y, (y, 0, 1))

Detail solution

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

$\int \left(- \frac{1}{y}\right)\, dy = - \int \frac{1}{y}\, dy$
1. The integral of $\frac{1}{y}$ is $\log{\left(y \right)}$ .
So, the result is: $- \log{\left(y \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                   
 |                    
 | -1                 
 | --- dy = C - log(y)
 |  y                 
 |                    
/

$$\int \left(- \frac{1}{y}\right)\, dy = C - \log{\left(y \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-oo

$$-\infty$$

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$$-\infty$$

-oo

Numerical answer [src]

-44.0904461339929

-44.0904461339929

The graph

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