integrate 1/x^2 — step-by-step solution

Let's integrate:

\int(\frac{1}{x^{2}})dx

For the math expression:

\frac{1}{x^{2}}

, we know the derivative formula:

{(a^{n})}^{'} = n a^{(n - 1)}

, so we try differentiating with ^(m+1)

Let's differentiate:

{(x^{(- 2 + 1)})}^{'}

{(x^{-1})}^{'}

Apply the differentiation rule:

{(f^{n})}^{'} = n \cdot {(f)}^{'} \cdot f^{(n - 1)}

with f =

x

-1 \cdot x^{-2}

- x^{-2}

\frac{1}{- x^{2}}

- \frac{1}{x^{2}}

The computed derivative matches the original math expression up to a constant factor. Therefore, the integral is:

-1 \cdot \frac{1}{x}

- \frac{1}{x}

Indefinite integrals are defined up to an additive constant C, so this yields:

- \frac{1}{x} + C

▷Answer: $- \frac{1}{x} + C$ , where C is a constant