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Problem 13 Easy Difficulty

Use the Table of Integrals on Reference Pages 6-10 to evaluate the integral.

$ \displaystyle \int \frac{\arctan \sqrt{x}}{\sqrt{x}}\ dx $

Answer

$2 \sqrt{x} \arctan \sqrt{x}-\ln (1+x)+C$

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Video Transcript

Okay, This question wants us to calculate this integral using the tape. So what we should do is find a way to get this into a form that we know the integral of. So let's make the obvious U substitution. Oh, squared of X because that's the only choice we really have for use up. So that means that do you is equal to one over to root ex d X, but we only have one over rude ex So two d u is equal to one over two rejects. Sorry, just just one DX. So now we have two times the integral of tan in verse. Have you? Do you? And we know the anti derivative of that from the table. So it's you 10 and verse you minus 1/2 the natural log both one plus U squared plus C, and this simplifies to two squared of X Times 10 and verse of spirit of X minus two times 1/2 which is one times the natural log of one plus U squared, which is Route X squared. So ex plus C

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