WEBVTT
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let's use integration by parts, possibly with the techniques
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of the section. We may have to do partial
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fractions after immigration My parts well issues. This is
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our starting point here and maybe easiest to just go
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ahead and take you to be our camp. We
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know the derivative of that one over X squared plus
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one D x devi is X tx So then the
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expert over too. So you think in aggression my
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parts recall that this is UV minus in roll video
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. So for you, times v ex cleared over
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two times are tan and then minus in a girl
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And then we have VD you. Let's go ahead
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and pull that one half are the rules. Now
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before we try partial fraction to composition if it's even
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necessary First we should do long division here because the
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numerator has degree That's equal. So the denominator Saagar
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decide to do that and we have a remainder of
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minus one. This means we can rewrite this all
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. So here we have our quotient which was one
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and there are remainder was minus one. So we
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have minus one over X squared plus one. Now
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we know from basically going backwards from to you to
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you, We know that the integral of one over
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X squared plus one is our ten. So otherwise
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, if you have forgotten that factor didn't see this
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up here, you could go ahead and do it
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shrinks up if you had to. And that will
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give you the anti derivative. So now let's evaluate
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X squared over to our ten and then we have
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minus one half and then x minus Ark ten of
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X. We've just evaluated the integral. So don't
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forget to add that constant of Integration City. And
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then the last step is maybe we can go ahead
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and just distribute this net negative one half. So
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I'll go to the next page to write that X
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squared over to ten in verse of X. This
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was our UV term, and then the general gave
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us this and that's your final answer