Expert Answers
lfryerda eNotes educator| Certified Educator

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`

lfryerda eNotes educator| Certified Educator

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` .

Access hundreds of thousands of answers with a free trial.

Start Free Trial
Ask a Question