WEBVTT
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Let's use integration by parts for this one. Let's
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go ahead and take you to be the Numerator Explorer
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plus one inside the radical. Then do you go
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ahead and use the chain rule here from Kokkalis and
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then simplify should get this for do you and then
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we're left over with DV equals less right as X
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to the minus two and this gives us that the
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so here you have to integrate to use the power
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rule. Negative one over X. Yeah, so
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they're recalled the formula UV minus integral video. So
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let's go ahead and plug in Are you and being
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and let's not forget the limits here. This is
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a definite our world's on our problem. We will
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still be using these limits here. So we have
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you times be that will give us That's a negative
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in front of the radical oops over X And then
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we plug in one and then route three. So
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that's are you. Times be there this term over
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here and then now will do the subtraction And then
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we have this term over here, so we have
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negative and then we have inner girl and then V
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and then we have, do you as well.
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So let's go ahead and write that. So VD
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you that gives us negative one over X and then
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X over square root, X squared plus one.
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And here we see that we can cancel these minuses
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that gives us a plus. And then we could
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cancel those exes as well. And we just have
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the integral of one over this square. Next plus
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one, you can use a trick. So for
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this one, go ahead and take X to be
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tan data to evaluate the tricks up there. And
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let's not forget our limits. One blue three still
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, just as the original problem. So here I
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go, after using that tricks up and then for
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all so we could plug in these limits into this
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expression. So plug in room three first and then
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because of this minus sign here, we add that's
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plugging in one right there and then after in aerating
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this thing, using the tricks of and then going
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back in terms of X, this's our anti derivative
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. And then we still have the same end points
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after sense for back in X. So it's going
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a lot Next page here. The last thing to
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do is this toe plug in thes two values for
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X into this expression here, and that's a threat
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. And so, after simplifying we have room to
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that's from the root to over one square before is
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too. So that's negative to O. R.
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Room three and then natural Log to plus through three
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and then minus natural log one plus square or two
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. And we do not need absolute value here because
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these terms are both positive and that's a finalist.