What is the result of the integral ∫ (2/x^3) dx?

To solve the integral ∫ (2/x^3) dx, we start by rewriting the integrand in a more convenient form. The expression 2/x^3 can be rewritten as 2x^(-3). Thus, we are tasked with integrating 2x^(-3).

When integrating a function of the form x^n, we use the rule:

∫ x^n dx = (x^(n+1))/(n+1) + C, where n ≠ -1.

In this case, n = -3. According to the rule, we calculate n + 1, which results in -3 + 1 = -2. Now we apply the rule:

∫ 2x^(-3) dx = 2 * (x^(-2)/(-2)) + C.

This simplifies to:

= 2 * (-1/2) * x^(-2) + C

= -x^(-2) + C

= -1/x^2 + C.

This outcome matches the correct result provided in the first choice, which states -1/x^2 + C. Thus, the integration yields the expression that correctly represents the area under the curve described by the given