Home > Calculus > Integrals of Rational Functions

How do you find the integral of #1/(2x) dx #?

Answer 1

Scarlett Allison

It is#int1/(2x)dx=1/2*lnx+c#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Ezra Adams

To find the integral of ( \frac{1}{2x} ) with respect to ( x ), you can use the integral rule for logarithmic functions. The integral of ( \frac{1}{x} ) is ( \ln|x| ), so by applying this rule:

[ \int \frac{1}{2x} , dx = \frac{1}{2} \int \frac{1}{x} , dx ]

[ = \frac{1}{2} \ln|x| + C ]

Where ( C ) is the constant of integration. Therefore, the integral of ( \frac{1}{2x} ) with respect to ( x ) is ( \frac{1}{2} \ln|x| + C ).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.