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Identical expressions
arcctg^ two (x)/ one +x^ two
arcctg squared (x) divide by 1 plus x squared
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arcctg2(x)/1+x2
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arcctg²(x)/1+x²
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arcctg^2(x) divide by 1+x^2
arcctg^2(x)/1+x^2dx
Similar expressions
arcctg^2(x)/1-x^2

Integral of arcctg^2(x)/1+x^2 dx

The solution

You have entered [src]

  1                   
  /                   
 |                    
 |  /    2        \   
 |  |acot (x)    2|   
 |  |-------- + x | dx
 |  \   1         /   
 |                    
/                     
0

$$\int\limits_{0}^{1} \left(x^{2} + \frac{\operatorname{acot}^{2}{\left(x \right)}}{1}\right)\, dx$$

Integral(acot(x)^2/1 + x^2, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{2}\, dx = \frac{x^{3}}{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{\operatorname{acot}^{2}{\left(x \right)}}{1}\, dx = \int \operatorname{acot}^{2}{\left(x \right)}\, dx$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $\int \operatorname{acot}^{2}{\left(x \right)}\, dx$
  So, the result is: $\int \operatorname{acot}^{2}{\left(x \right)}\, dx$
The result is: $\frac{x^{3}}{3} + \int \operatorname{acot}^{2}{\left(x \right)}\, dx$
Add the constant of integration:

$\frac{x^{3}}{3} + \int \operatorname{acot}^{2}{\left(x \right)}\, dx+ \mathrm{constant}$

The answer is:

$\frac{x^{3}}{3} + \int \operatorname{acot}^{2}{\left(x \right)}\, dx+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                            
 |                                 /           
 | /    2        \           3    |            
 | |acot (x)    2|          x     |     2      
 | |-------- + x | dx = C + -- +  | acot (x) dx
 | \   1         /          3     |            
 |                               /             
/

$$\int \left(x^{2} + \frac{\operatorname{acot}^{2}{\left(x \right)}}{1}\right)\, dx = C + \frac{x^{3}}{3} + \int \operatorname{acot}^{2}{\left(x \right)}\, dx$$

Simplify

The answer [src]

  1                   
  /                   
 |                    
 |  / 2       2   \   
 |  \x  + acot (x)/ dx
 |                    
/                     
0

$$\int\limits_{0}^{1} \left(x^{2} + \operatorname{acot}^{2}{\left(x \right)}\right)\, dx$$

  1                   
  /                   
 |                    
 |  / 2       2   \   
 |  \x  + acot (x)/ dx
 |                    
/                     
0

$$\int\limits_{0}^{1} \left(x^{2} + \operatorname{acot}^{2}{\left(x \right)}\right)\, dx$$

Integral(x^2 + acot(x)^2, (x, 0, 1))

Numerical answer [src]

1.6674075819519

1.6674075819519

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

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Identical expressions

Similar expressions

Integral of arcctg^2(x)/1+x^2 dx

Limits of integration:

The graph:

Piecewise:

The solution