Question

How do you find the antiderivative of `2/z^2`?

Answer 1

Represent the fraction as a negative exponent and use the reverse power rule.

Explanation:

`2/z^2` can be rewritten as `2z^-2`
So our integral becomes:
`int 2z^-2 dz`
we can now pull out the `2` from the integral as it is a constant.
`2int z^-2 dz`
The reverse power rule states `int x^n dx = x^(n+1)/(n+1) + c`
Thus `2int z^-2 dz = 2*[z^(-2+1)/(-2+1)] = 2*[z^-1/-1] = 2*[-1/z]`
Simplifying this we get: `-2/z + c`
We add a `+c` at the end because the integral is indefinite.