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Find the most general antiderivative of the function. (Check your answers by differentiation.)$f(x) = \sqrt[3]{x^2} + x\sqrt{x}$

$\frac{3 x^{5 / 3}}{5}+\frac{2 x^{5 / 2}}{5}+C$

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Heather Z.

Oregon State University

Caleb E.

Baylor University

Michael J.

Idaho State University

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Video Transcript

S o B. Have Savannah was generated through the function after backs, so we have affected calls. Thie Q boot of X squared plus X time to square X. So let's go ahead and rewrite this function in terms of acronym s So this is going to become EXT. T to third plus X times. Ah, next to the one half And thieves too. Khun B simplified. You can actually add the one plus one half is going to give us. So we have exited itude there and in plus X to the three half. Now we take the injured girl of X to third. It's actually have dee eggs and then this is going to be equal to reapply the expert and we're also going to act Teo Teo third class one all of their to third plus one And it is going to plus extra three, huh? Close one and over three half plus one And then on the next it'LL come out to be X to the five thirty over five third plus X to the five half over five, and it's a plus C and then you take the reciprocal, so that's going to come. Three. Act five third plus two, thanks to the five and plus Constant, and that is your answer

Heather Z.

Oregon State University

Caleb E.

Baylor University

Michael J.

Idaho State University

Lectures

Join Bootcamp