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Identical expressions
((Artan(x))^ two)/ one +x^ two
((Ar tangent of (x)) squared ) divide by 1 plus x squared
((Ar tangent of (x)) to the power of two) divide by one plus x to the power of two
((Artan(x))2)/1+x2
Artanx2/1+x2
((Artan(x))²)/1+x²
((Artan(x)) to the power of 2)/1+x to the power of 2
Artanx^2/1+x^2
((Artan(x))^2) divide by 1+x^2
((Artan(x))^2)/1+x^2dx
Similar expressions
((Artan(x))^2)/1-x^2

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

The solution

You have entered [src]

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

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

Integral(atan(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:
  
  $\int \frac{\operatorname{atan}^{2}{\left(x \right)}}{1}\, dx = \int \operatorname{atan}^{2}{\left(x \right)}\, dx$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $\int \operatorname{atan}^{2}{\left(x \right)}\, dx$
  So, the result is: $\int \operatorname{atan}^{2}{\left(x \right)}\, dx$
The result is: $\frac{x^{3}}{3} + \int \operatorname{atan}^{2}{\left(x \right)}\, dx$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The answer [src]

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

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

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

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

Упростить

Numerical answer [src]

0.5786145368001

0.5786145368001

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

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Identical expressions

Similar expressions

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

Limits of integration:

The graph:

Piecewise:

The solution