is there a solution for integration of x^-1 ? if so, how? if not, why?

Expert Answers info

sciencesolve eNotes educator | Certified Educator

calendarEducator since 2011

write5,349 answers

starTop subjects are Math, Science, and Business

You need to find if there exists `intx^(-1) dx` , hence, you should use the following formula that help you to solve the integral, such that:

`int 1/x dx = ln |x| + c`

You should convert the negative power `x^(-1)`  into a fraction, using the following identity, such that:

`x^(-a) = 1/(x^a)`

Reasoning by analogy, yields:

`x^(-1) = 1/x`

You need to evaluate the integral of the function `x^(-1) ` such that:

`int x^(-1) dx = int 1/x dx = ln |x| + c`

Hence, evaluating the integral of the function `x^(-1)`  yields `int x^(-1) dx = ln |x| + c.`

check Approved by eNotes Editorial

chrissy93b | Student

If you're talking about an indefinite integral, then yes. The solution would be ln(x)+C, C being an unknown constant. X^-1 is the same thing as 1/x, so when you integrate that the antiderivative of 1/x would be ln(x). I'm fairly certain this is right, hope this helps!

check Approved by eNotes Editorial

Unlock This Answer Now