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