How do you integrate the function 1/x^2 dx?

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To integrate the function 1/x2, we can follow these steps:

  1. Rewrite the integrand in a more convenient form. We can express 1/x2 as x-2.

  2. Now, we set up the integral:

    ∫ x-2 dx

  3. We can apply the power rule of integration, which states:

    ∫ xn dx = &frac{xn+1}{n+1} + C, for n ≠ -1

  4. In our case, n = -2

    So, we have: &frac{x-1}{-1} + C = -x-1 + C

  5. Finally, rewriting the expression in terms of the original variables gives us:

    -&frac{1}{x} + C

Thus, the integral of 1/x2 dx is:

-&frac{1}{x} + C

where C is the constant of integration.

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