Mister Exam

Other calculators

Solving integrals/ d/dx(arctg(1/x))dx

Integral of d/dx(arctg(1/x))dx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1           
  /           
 |            
 |     d      
 |  ------- dx
 |      /1\   
 |  atan|-|   
 |      \x/   
 |            
/             
-1
$$\int\limits_{-1}^{1} \frac{d}{\operatorname{atan}{\left(\frac{1}{x} \right)}}\, dx$$ 
Integral(d/atan(1/x), (x, -1, 1))
Detail solution

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

    1. Don't know the steps in finding this integral.

      But the integral is

    So, the result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                     /          
 |                     |           
 |    d                |    1      
 | ------- dx = C + d* | ------- dx
 |     /1\             |     /1\   
 | atan|-|             | atan|-|   
 |     \x/             |     \x/   
 |                     |           
/                     /
$$\int \frac{d}{\operatorname{atan}{\left(\frac{1}{x} \right)}}\, dx = C + d \int \frac{1}{\operatorname{atan}{\left(\frac{1}{x} \right)}}\, dx$$
Simplify
The answer [src] 
    1           
    /           
   |            
   |     1      
d* |  ------- dx
   |      /1\   
   |  atan|-|   
   |      \x/   
   |            
  /             
  -1
$$d \int\limits_{-1}^{1} \frac{1}{\operatorname{atan}{\left(\frac{1}{x} \right)}}\, dx$$ 
=
= 
    1           
    /           
   |            
   |     1      
d* |  ------- dx
   |      /1\   
   |  atan|-|   
   |      \x/   
   |            
  /             
  -1
$$d \int\limits_{-1}^{1} \frac{1}{\operatorname{atan}{\left(\frac{1}{x} \right)}}\, dx$$ 
d*Integral(1/atan(1/x), (x, -1, 1))

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

    © Mister Exam – Calculator