What is the general antiderivative of 4/x ?

Question

4 ln |x| + c

ln |x| + c

(1/4) ln |x| + c

(1/2) ln |x| + c

Answer 1

4ln!x!+C

Answer 2

It is 4 ln|x| + c as said in other answers but I'll tell you why:

Consider 4/x as 4 times 1/x, so 4 is just a constant that can be separated outside of the anti-derivative if 1/x.

In general for the anti-derivative of 1/x is ln|x| + c, so apply the constant after this operation to get the answer. True, 4 x c = 4c, but just reset the constant. (A constant times a constant is still a constant).

A little overkill here, but I'm writing as if I were speaking in a lecture hall.

Answer 3

4 ln |x| + c

You can factor out the 4, leaving you with

4 S 1/x

The antiderivative of 1/x is ln |x| + c1; multiply that by the 4 you have factored out leaves you with 4ln|x| + c2 - or generalize, 4ln|x| + c