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Numerade Educator

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Problem 11 Easy Difficulty

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

$ f(x) = 3\sqrt{x} - 2\sqrt[3]{x} $

Answer

$2 x^{3 / 2}-\frac{3 x^{4 / 3}}{2}+C$

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Video Transcript

Okay, so we've been asked to find e jet move journal, Anti derivative of the function and the functions after Mexico. Story would X managed to our time to the Cube of X, Uh, before everyone. I'm just going to write down the how to express a square in terms of exponent in terms, in case you didn't know. So this is for General. So? So if you have any experimento or expert and the form ext to this group to the power em over end, you can rewrite this the end route of eggs to the empower. So with that guideline, we could ask you go ahead and rewrite FX. The aftereffects will be real enough. Three x to the one have minus two X to the one third. Now we take the integral of aftereffects DX. So the internal, um, has he let me just write the integral three act to the one have minus two ax one third and in a de eggs and now it's going to be now we applied. The experimentalist owes me one half plus one over one half plus one minus two act to the one third plus one over one third it was fun. So then this gives us three X to the three half associates to the next page. So three x to the three. Half over to third. Now over three have said sorry on then. This is going to be minus Ah, two acts to the fourth, third over for third. And then when you have a fraction at the bottom ah, you take the reciprocal of its and multiply it. So it's going to become two times three extra three half this is over three. It's in the minus three point to extend for third and Plus, even though he doesn't see you three and three cancels this, give this to accident. We have. And then this simplifies to sixth fourth, except for third. And you could ask me rewrite six fourth, um, as ah as we have. And then you push it plus Carson and then you are done