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x/(x+1)
Solving integrals/ x/(x+1)

Integral of x/(x+1) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

  1. Rewrite the integrand:

  2. Integrate term-by-term:

    1. The integral of a constant is the constant times the variable of integration:

    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:

    The result is:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                             
 |                              
 |   x                          
 | ----- dx = C + x - log(1 + x)
 | x + 1                        
 |                              
/
$$\int \frac{x}{x + 1}\, dx = C + x - \log{\left(x + 1 \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
1 - log(2)
$$1 - \log{\left(2 \right)}$$ 
=
= 
1 - log(2)
$$1 - \log{\left(2 \right)}$$ 
1 - log(2)
Numerical answer [src] 
0.306852819440055
0.306852819440055
The graph
Integral of x/(x+1) dx

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

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