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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                
  /                
 |                 
 |        1        
 |  1*---------- dx
 |      /     2\   
 |    x*\1 + x /   
 |                 
/                  
0                  
$$\int\limits_{0}^{1} 1 \cdot \frac{1}{x \left(x^{2} + 1\right)}\, dx$$
Integral(1/(x*(1 + x^2)), (x, 0, 1))
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    1. Rewrite the integrand:

    2. Integrate term-by-term:

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

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

          1. Let .

            Then let and substitute :

            1. The integral of is .

            Now substitute back in:

          So, the result is:

        So, the result is:

      1. The integral of is .

      The result is:

    Method #2

    1. Rewrite the integrand:

    2. Rewrite the integrand:

    3. Integrate term-by-term:

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

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

          1. Let .

            Then let and substitute :

            1. The integral of is .

            Now substitute back in:

          So, the result is:

        So, the result is:

      1. The integral of is .

      The result is:

    Method #3

    1. Rewrite the integrand:

    2. Rewrite the integrand:

    3. Integrate term-by-term:

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

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

          1. Let .

            Then let and substitute :

            1. The integral of is .

            Now substitute back in:

          So, the result is:

        So, the result is:

      1. The integral of is .

      The result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                          
 |                          /     2\         
 |       1               log\1 + x /         
 | 1*---------- dx = C - ----------- + log(x)
 |     /     2\               2              
 |   x*\1 + x /                              
 |                                           
/                                            
$$\log x-{{\log \left(x^2+1\right)}\over{2}}$$
The answer [src]
oo
$${\it \%a}$$
=
=
oo
$$\infty$$
Numerical answer [src]
43.7438725437129
43.7438725437129

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