Integral of cosy/siny dx

The solution

You have entered [src]

  1          
  /          
 |           
 |  cos(y)   
 |  ------ dy
 |  sin(y)   
 |           
/            
0

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

Simplify

Detail solution

Let $u = \sin{\left(y \right)}$ .

Then let $du = \cos{\left(y \right)} dy$ and substitute $du$ :

$\int \frac{1}{u}\, du$
1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
Now substitute $u$ back in:

$\log{\left(\sin{\left(y \right)} \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                           
 |                            
 | cos(y)                     
 | ------ dy = C + log(sin(y))
 | sin(y)                     
 |                            
/

$$\log \sin y$$

Simplify

The answer [src]

oo

$${\it \%a}$$

oo

$$\infty$$

Simplify

Numerical answer [src]

43.9178423877238

43.9178423877238

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

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Integral of cosy/siny dx

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The solution