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(x^2)/(1+x)

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1         
  /         
 |          
 |     2    
 |    x     
 |  ----- dx
 |  1 + x   
 |          
/           
0           
$$\int\limits_{0}^{1} \frac{x^{2}}{x + 1}\, dx$$
Integral(x^2/(1 + x), (x, 0, 1))
Detail solution
  1. Rewrite the integrand:

  2. Integrate term-by-term:

    1. The integral of is when :

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

    1. Let .

      Then let and substitute :

      1. The integral of is .

      Now substitute back in:

    The result is:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                  
 |                                   
 |    2            2                 
 |   x            x                  
 | ----- dx = C + -- - x + log(1 + x)
 | 1 + x          2                  
 |                                   
/                                    
$$\int \frac{x^{2}}{x + 1}\, dx = C + \frac{x^{2}}{2} - x + \log{\left(x + 1 \right)}$$
The graph
The answer [src]
-1/2 + log(2)
$$- \frac{1}{2} + \log{\left(2 \right)}$$
=
=
-1/2 + log(2)
$$- \frac{1}{2} + \log{\left(2 \right)}$$
-1/2 + log(2)
Numerical answer [src]
0.193147180559945
0.193147180559945
The graph
Integral of (x^2)/(1+x) dx

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