Mister Exam

Other calculators


(x-1)/(x+2)

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                               
 |                                
 | x - 1                          
 | ----- dx = C + x - 3*log(2 + x)
 | x + 2                          
 |                                
/                                 
$$\int \frac{x - 1}{x + 2}\, dx = C + x - 3 \log{\left(x + 2 \right)}$$
The graph
The answer [src]
1 - 3*log(3) + 3*log(2)
$$- 3 \log{\left(3 \right)} + 1 + 3 \log{\left(2 \right)}$$
=
=
1 - 3*log(3) + 3*log(2)
$$- 3 \log{\left(3 \right)} + 1 + 3 \log{\left(2 \right)}$$
1 - 3*log(3) + 3*log(2)
Numerical answer [src]
-0.216395324324493
-0.216395324324493
The graph
Integral of (x-1)/(x+2) dx

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