WEBVTT
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Okay. This question wants us to integrate this function
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using a table. But the issue is that this
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doesn't look like any of the forms we know.
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So we're gonna have to put it into that for
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so a lot of square root expressions have a use
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squared in the room. So let's pick you squared
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equal the exit fourth. And this implies that you
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Cols X squared or squared of you is equal Dax
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. So from there we confined that d x is
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equal to one over to root you. Do you
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00:00:53.340 --> 00:00:58.820 A:middle L:90%
? So now we can plug everything back in so
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we have the integral of X is squared of you
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Times x to the fourth That's you squared. We're
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leaving the two alone divided by to root you do
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you? Because we have to have that factor.
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And now we see we get a nice cancellation,
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doesn't root use and we're left with 1/2 times the
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integral of square root of two plus u squared.
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Do you? And this is something that we know
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the answer based on our table. We see that
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this is you over too. Time squared of two
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plus u squared, plus the natural law of you
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plus square root of you squared plus two plus c
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, of course. And no, all we gotta
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do is back. Substitute everything in So this is
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equal to well, you is equal to X squared
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. So we get distributing X squared over four times
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the square root of X to the fourth plus two
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because you squared is extra fourth plus 1/2 times the
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natural log of X squared plus the square root of
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two. Sorry for consistency will write it this way
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, plus C and this will be our final answer
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making sure we substituted back in properly.