is there a solution for integration of x^-1 ?

if so, how?

if not, why?

Expert Answers

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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.`

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