WEBVTT
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let's use integration. My parts here, let's just
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take you to be the entire intolerant. So most
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of our work here will be and finding and then
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simplifying to you So here will get the derivative of
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the log and then we'Ll also apply the chain rule
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here. So on the time we'LL have the multiplied
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by the derivative of this term here in the denominator
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So that'LL be one plus And then after simplifying right
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when we differentiate the radical, we get this So
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here for our next let's just go ahead and get
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a common denominator up there in the numerator. So
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multiply it top and bottom of won by the radical
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So that will be our numerator. And then we
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still have our denominator. And here before we simplify
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anything noticed that these two terms in the parentheses are
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exactly the same. So we could cancel them and
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we left over with one over X squared minus one
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d X. So all that work was just to
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find our do you And then, since we chose
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you to be the entire Interbrand we're left over with
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, DV equals DX, so V equals X.
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So the next part here will be to replace the
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original integral with the formula from integration. My parts
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. So let's go on to the next page and
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rewrite this formula here using our choice is of you
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, Andy. And here we see that we'LL need
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to you as well. So we'LL need just her
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So going on to the next page we still have
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you the inner grove e t u And then let's
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plug in our Eun Bi's Finally. So we get
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extra times the natural log and then minus in a
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girl And then we'LL have a X over tyrannical.
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So we just have one more integral to evaluate.
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But this animal is simpler than the original, and
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we could just do another substitution here. Let's take
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X squared minus one dw over, too. No
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x t x so that in a girl just becomes
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one half and then we just have w to the
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negative one half a t w. So after cancelling
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that one half with the two that you get from
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the power rule so we just get X squared minus
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one to the one half. So finally, let's
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just rewrite this UV term so x times log again
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. And then don't forget the minus here in between
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minus. We just evaluated this inaugural over here using
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the use of it became this radical. And since
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we've evaluated all the intervals, let's go ahead and
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add that Sian and that's your final answer.