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(x^2+1)/(x+2)

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1          
  /          
 |           
 |   2       
 |  x  + 1   
 |  ------ dx
 |  x + 2    
 |           
/            
0            
$$\int\limits_{0}^{1} \frac{x^{2} + 1}{x + 2}\, dx$$
Integral((x^2 + 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 is when :

      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:

    Method #2

    1. Rewrite the integrand:

    2. Integrate term-by-term:

      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. 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:

      1. Let .

        Then let and substitute :

        1. The integral of is .

        Now substitute back in:

      The result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                       
 |                                        
 |  2               2                     
 | x  + 1          x                      
 | ------ dx = C + -- - 2*x + 5*log(2 + x)
 | x + 2           2                      
 |                                        
/                                         
$$\int \frac{x^{2} + 1}{x + 2}\, dx = C + \frac{x^{2}}{2} - 2 x + 5 \log{\left(x + 2 \right)}$$
The graph
The answer [src]
-3/2 - 5*log(2) + 5*log(3)
$$- 5 \log{\left(2 \right)} - \frac{3}{2} + 5 \log{\left(3 \right)}$$
=
=
-3/2 - 5*log(2) + 5*log(3)
$$- 5 \log{\left(2 \right)} - \frac{3}{2} + 5 \log{\left(3 \right)}$$
-3/2 - 5*log(2) + 5*log(3)
Numerical answer [src]
0.527325540540822
0.527325540540822
The graph
Integral of (x^2+1)/(x+2) dx

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