`int (x-3/x+2 )dx`

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lfryerda | High School Teacher | (Level 2) Educator

Posted on

Sometimes formatting errors in posting the question can result in different questions being posed.

Phrasing the question instead as:

`int{x-3}/{x+2}dx`   split apart into two integrals

`=int {(x+2) - 2-3}/{x+2}dx`  

`=int {x+2}/{x+2}dx -5int 1/{x+2}dx`   simplify

`=int dx - 5 int 1/{x+2}dx`

`=x-5 ln|x+2| + C`  where C is a constant of integration

The integral is `x-5ln|x+2|+C`

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lfryerda | High School Teacher | (Level 2) Educator

Posted on

To solve this question, we need to use the power rule for each of the first term and last term, then the logarithm rule for the middle term.

`int(x-3/x+2)dx`

`=int xdx-3int 1/x dx+2int dx`

`=1/2x^2-3ln|x|+2x + C`  where C is the constant of integration

The integral is `1/2x^2-3ln|x|+2x+C` .

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