Integral of arctgx/y dy

The solution

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  2           
  /           
 |            
 |  acot(x)   
 |  ------- dy
 |     y      
 |            
/             
1

$$\int\limits_{1}^{2} \frac{\operatorname{acot}{\left(x \right)}}{y}\, dy$$

Integral(acot(x)/y, (y, 1, 2))

Detail solution

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

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

$\log{\left(y \right)} \operatorname{acot}{\left(x \right)}+ \mathrm{constant}$

The answer is:

$\log{\left(y \right)} \operatorname{acot}{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               
 |                                
 | acot(x)                        
 | ------- dy = C + acot(x)*log(y)
 |    y                           
 |                                
/

$$\int \frac{\operatorname{acot}{\left(x \right)}}{y}\, dy = C + \log{\left(y \right)} \operatorname{acot}{\left(x \right)}$$

Simplify

The answer [src]

acot(x)*log(2)

$$\log{\left(2 \right)} \operatorname{acot}{\left(x \right)}$$

acot(x)*log(2)

$$\log{\left(2 \right)} \operatorname{acot}{\left(x \right)}$$

acot(x)*log(2)

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

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Identical expressions

Integral of arctgx/y dy

Limits of integration:

The graph:

Piecewise:

The solution