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Numerade Educator

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Problem 44 Easy Difficulty

Use a computer algebra system to evaluate the integral. Compare the answer with the result of using tables. If the answers are not the same, show that they are equivalent.

$ \displaystyle \int \frac{1}{\sqrt{1 + \sqrt[3]{x}}}\ dx $

Answer

$\frac{6}{5}(1+\sqrt[3]{x})^{5 / 2}-4(1+\sqrt[3]{x})^{3 / 2}+6(1+\sqrt[3]{x})^{1 / 2}+C$

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Video Transcript

All right, This question wants us to use technology to find this anti derivative and then compare that to our tabular answer and make sure that they match So plugging this into a computer algebra system, this is very anti derivative. But then if we plug into a table, we get this. So these are the same answers you can see by inspection here. But the only difference is writing rational exponents in the computer algebra version. So just re rating the CS version. We get 6/5 times X to the 1/3 is just cube root of X minus four Again X to the 1/3 is Cuban X, and then only had to do was just expand this out and rewrite our rational exponents as cube roots. And now this answer completely matches what we're given in the tape. 6/5 negative. Four and six are coefficients here and 6/5 negative. Four and six are coefficients there. And of course, the order inside here doesn't matter, because addition is competitive