Find the indefinite integral of x – 3/x^2

To find the indefinite integral of the given function, we will break it down into two separate integrals:

∫ (x – 3/x^2) dx = ∫ x dx – ∫ (3/x^2) dx

Taking the integral of x with respect to x gives us:

∫ x dx = (1/2)x^2 + C1

Next, let’s find the integral of 3/x^2 with respect to x. We can rewrite this as:

∫ 3x^(-2) dx

Using the power rule of integration, the integral of x^(-n) with respect to x is x^(-n+1)/(1-n), except when n = 1. Thus, we have:

∫ 3x^(-2) dx = 3(x^(-2+1))/(1-2) + C2 

              = -3x^(-1) + C2 

              = -3/x + C2

Combining the two integrals, we get:

∫ (x – 3/x^2) dx = (1/2)x^2 – 3/x + C

Therefore, the indefinite integral of x – 3/x^2 is (1/2)x^2 – 3/x + C, where C is the constant of integration.

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