S(1/x+2/x^+2)dx

Answer 1

To find the integral of (1/x + 2/x^2) dx, we need to split the terms into separate integrals:

∫(1/x + 2/x^2) dx = ∫(1/x) dx + ∫(2/x^2) dx

Now, let's find the antiderivative for each term:

∫(1/x) dx = ln|x| + C

∫(2/x^2) dx = -2/x + C

Therefore, the original integral simplifies to:

∫(1/x + 2/x^2) dx = ln|x| - 2/x + C

So, the final answer is ln|x| - 2/x + C, where C is the constant of integration.