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hello everyone in this video were going to be solving for f of x would you call this a differential equation or an integral equation whatever you want to call this we have the integral of f of x times f prime of x dx and its equal to x and f of 1 is equal to 4 were supposed to solve for f of x so this is an integral were going to be solving this integral without knowing what f of x is actually our goal is to find what f of x is okay so for this integral since this integrand i guess thats what its called right this integrand contains a function and its derivative together were going to use u substitution okay so lets start by saying let u equal f of x this implies d u equals f prime times dx great so now when we do the replacements and obviously this is an indefinite integral so were going to be using constant c here were going to get the integral of u times d u okay now as you know this is an easy integral this is equal to u squared over 2 plus c awesome now we can go ahead