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Identical expressions
(3arctan^ two x)/(one +x)^2
(3arc tangent of squared x) divide by (1 plus x) squared
(3arc tangent of to the power of two x) divide by (one plus x) squared
(3arctan2x)/(1+x)2
3arctan2x/1+x2
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(3arctan to the power of 2x)/(1+x) to the power of 2
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(3arctan^2x)/(1+x)^2dx
Similar expressions
(3arctan^2x)/(1-x)^2

Integral of (3arctan^2x)/(1+x)^2 dx

The solution

You have entered [src]

  1              
  /              
 |               
 |        2      
 |  3*atan (x)   
 |  ---------- dx
 |          2    
 |   (1 + x)     
 |               
/                
0

$$\int\limits_{0}^{1} \frac{3 \operatorname{atan}^{2}{\left(x \right)}}{\left(x + 1\right)^{2}}\, dx$$

Integral((3*atan(x)^2)/(1 + x)^2, (x, 0, 1))

Detail solution

Rewrite the integrand:

$\frac{3 \operatorname{atan}^{2}{\left(x \right)}}{\left(x + 1\right)^{2}} = \frac{3 \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 2 x + 1}$
The integral of a constant times a function is the constant times the integral of the function:

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The answer [src]

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

$$3 \int\limits_{0}^{1} \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 2 x + 1}\, dx$$

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

$$3 \int\limits_{0}^{1} \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 2 x + 1}\, dx$$

3*Integral(atan(x)^2/(1 + x^2 + 2*x), (x, 0, 1))

Numerical answer [src]

0.259241176461873

0.259241176461873

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

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Identical expressions

Similar expressions

Integral of (3arctan^2x)/(1+x)^2 dx

Limits of integration:

The graph:

Piecewise:

The solution