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(x^2-2)/x

Integral of (x^2-2)/x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

    Method #1

    1. Let .

      Then let and substitute :

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

        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. The integral of is .

            So, the result is:

          The result is:

        So, the result is:

      Now substitute back in:

    Method #2

    1. Rewrite the integrand:

    2. Integrate term-by-term:

      1. The integral of is when :

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

        1. The integral of is .

        So, the result is:

      The result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                            
 |                             
 |  2               2          
 | x  - 2          x       / 2\
 | ------ dx = C + -- - log\x /
 |   x             2           
 |                             
/                              
$$\int \frac{x^{2} - 2}{x}\, dx = C + \frac{x^{2}}{2} - \log{\left(x^{2} \right)}$$
The graph
The answer [src]
-oo
$$-\infty$$
=
=
-oo
$$-\infty$$
-oo
Numerical answer [src]
-87.6808922679858
-87.6808922679858
The graph
Integral of (x^2-2)/x dx

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