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  • Identical expressions

  • one /(x^ two + one)*sqrt(arctg(x)+ one)
  • 1 divide by (x squared plus 1) multiply by square root of (arctg(x) plus 1)
  • one divide by (x to the power of two plus one) multiply by square root of (arctg(x) plus one)
  • 1/(x^2+1)*√(arctg(x)+1)
  • 1/(x2+1)*sqrt(arctg(x)+1)
  • 1/x2+1*sqrtarctgx+1
  • 1/(x²+1)*sqrt(arctg(x)+1)
  • 1/(x to the power of 2+1)*sqrt(arctg(x)+1)
  • 1/(x^2+1)sqrt(arctg(x)+1)
  • 1/(x2+1)sqrt(arctg(x)+1)
  • 1/x2+1sqrtarctgx+1
  • 1/x^2+1sqrtarctgx+1
  • 1 divide by (x^2+1)*sqrt(arctg(x)+1)
  • 1/(x^2+1)*sqrt(arctg(x)+1)dx

  • Similar expressions

  • 1/(x^2+1)*sqrt(arctg(x)-1)
  • 1/(x^2-1)*sqrt(arctg(x)+1)
Solving integrals/ 1/(x^2+1)*sqrt(arctg(x)+1)

Integral of 1/(x^2+1)*sqrt(arctg(x)+1) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                   
  /                   
 |                    
 |    _____________   
 |  \/ atan(x) + 1    
 |  --------------- dx
 |        2           
 |       x  + 1       
 |                    
/                     
0
$$\int\limits_{0}^{1} \frac{\sqrt{\operatorname{atan}{\left(x \right)} + 1}}{x^{2} + 1}\, dx$$ 
Integral(sqrt(atan(x) + 1)/(x^2 + 1), (x, 0, 1))
Detail solution

  1. Let .

    Then let and substitute :

    1. The integral of is when :

    Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                           
 |                                            
 |   _____________                         3/2
 | \/ atan(x) + 1           2*(atan(x) + 1)   
 | --------------- dx = C + ------------------
 |       2                          3         
 |      x  + 1                                
 |                                            
/
$$\int \frac{\sqrt{\operatorname{atan}{\left(x \right)} + 1}}{x^{2} + 1}\, dx = C + \frac{2 \left(\operatorname{atan}{\left(x \right)} + 1\right)^{\frac{3}{2}}}{3}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
                3/2
        /    pi\   
      2*|1 + --|   
  2     \    4 /   
- - + -------------
  3         3
$$- \frac{2}{3} + \frac{2 \left(\frac{\pi}{4} + 1\right)^{\frac{3}{2}}}{3}$$ 
=
= 
                3/2
        /    pi\   
      2*|1 + --|   
  2     \    4 /   
- - + -------------
  3         3
$$- \frac{2}{3} + \frac{2 \left(\frac{\pi}{4} + 1\right)^{\frac{3}{2}}}{3}$$ 
-2/3 + 2*(1 + pi/4)^(3/2)/3
Numerical answer [src] 
0.923751641483919
0.923751641483919

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

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