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all right uh let's look at the homework 5.1 uh problem number six all right so let's uh solve this initial value problem all right so uh in order to find the original function uh f of x uh we need to find an anti-derivative so uh f of x is equal to right anti-derivative of x squared minus nine over x squared uh with respect to x right uh you know to evaluate this integral we need to uh simplify the integrand so uh let's do that all right first i'm going to split this into uh two um smaller fraction right x squared over x squared and then uh minus 9 over x squared right so this is going to be equal to all right so you have an integral right first one is very easy x squared divided by x squared is going to be 1 right then minus right 9 right instead of writing as a fraction uh since x squared is on the bottom so we can actually turn it into x to the negative 2 power right which is the sam