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Numerade Educator



Problem 14 Easy Difficulty

Find the most general antiderivative of the function.
(Check your answers by differentiation.)

$ f(t) = \dfrac{3t^4 - t^3 + 6t^2}{t^4} $


$3 t-\ln 1+1-6 t^{-1}+C$


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Video Transcript

I saw something has to find the most general anti derivative of the function after t oo Street to the fourth managed thank you while sixty squared over teeth report. So this may look like a complicated function, but luckily we have a very simple denominator. And now this decision is just a fact of simple fraction and sometimes is overlooked. So you can actually hear you. We can ask you break this up so you can do three to thirteen, fourth over tea for minus Team Cube. You know that, uh, over teacher afford plus sixty squared over two meters a fourth and now we can begin the simplifies. A teaching fourth of it is the fourth wall that just cancel And I can just three, two Cuba teeth to fourth. We do you subtract it, Toby T minus one more shirt just the same as one over tea and then to square two, then discovers us six over t squared. And now we can take the We did the interval of this, but I'm going to rewrite it in terms of the exponents of three to the minus teas or minus one half. I mean to the minus one and plus six T minus two. And now it could take the interval of this D key. And this is a lot easier game compared to death. Well, I'm just bring it over. So I was going to give a three t and then teasing minus one is going to the natural log of absolute knowledge of tea and minus two plus one. Well, that's negative. One and then over negative one. Well, that's just gonna minus six, Uh, T to the minus one and then this pussy, and this is our answer.