WEBVTT
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Let's start by making the substitution here, let's take
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you to be tangent ot then do you? C
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can't square d t so this integral becomes D you
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over u squared three u plus two. Okay,
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and let's go ahead and factor mhm. And now
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we'll do partial fraction Shit. Let's go ahead and
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multiply both sides by this denominator here on the left
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and we get one equals a you plus one BU
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plus two and we can rewrite this. And by
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comparing coefficients, we see that a plus b has
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to be zero to be plus a has to be
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one. So we get a is minus one B
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as well. Let's go ahead and plug these in
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over here. And then we'll integrate this instead of
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integrating that. So plug again are constants. Yeah
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, And then there you can do a use sub
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here, for example, you can do and then
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here you can do you plus one, in any
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case, are integral becomes and that constant c and
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then finally recall that we defined you to be tangent
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of T. So we should go back here and
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plug this in. So this and there's our final
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answer