Greetings all

I am trying to integrade

1/(x/2 + 1) dx

I get the answer 2 ln (x/2 + 1)

my friend did it this way

1/(x/2 + 1) * (2/2) dx

2/(x+2) dx

2 ln (x+2)

What is going on??

What's going on is that both your answers are wrong - for two reasons. One of the reasons explains why you can get two apprently different answers.

Your answer should be 2 ln

|x/2 + 1

| + C.

Your friends answer should be 2 ln

|x+2

| + K.

C and K are arbitrary constants of integration. Your teacher will have told you many many times not to forget including it.

**Note:** 2 ln |x/2 + 1| + C = 2 ln |1/2 (x + 2)| + C = 2 ln (1/2) + 2 ln|x+2| + C = 2 ln|x + 2| + K where K = C + 2ln(1/2).