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

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

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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chrissy93b | Student, Undergraduate | (Level 1) eNoter

Posted on

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!

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