Integral of 1/x

How to solve the given integral by using the integral of 1/x: formula, 1 example, and its solution.

Formula

Formula

Recall that
the derivative of ln |x| is
1/x.

And integral and derivative
are the opposite operations.

So the integral of 1/x is
ln |x| + C.

For an indefinite integral,
there should be +C.

Example

Example

Solution

Divide each term of the numerator
by the denominator x.

x2/x = x
-x/x = -1
+1/x = +1/x

The integral of x is [1/2]x2.

Integral of a Polynomial

The integral of -1 is -x.

The integral of +1/x is +ln |x|.

The given integral is an indefinite integral.
So write +C.

So [1/2]x2 - x + ln |x| + C is the answer.