WEBVTT
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and this problem. We are practicing an integration technique
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called the U substitution. And this is a really
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helpful technique to solve. Integral is because what we
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do is we technically substitute the hard part of our
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integral to make our integral into something that we recognize
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that we can solve easily. And that's how we
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use U substitution. So that's what we're going to
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be doing in this problem. So let's just review
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the integral that we're starting with. We have the
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indefinite and the girl meeting. We don't have limits
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to plug in. We have the indefinite integral DX
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over five minus three x. Well, if we
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weren't using use substitution. Or maybe you solve the
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integral for the first time, that looks pretty hard
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. Maybe we don't know how to solve it.
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So we're going to use U substitution. We're going
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to let u equal five minus three x So we
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would take the derivative d u equals negative three d
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x so we can rearrange that and thio finding something
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that we know we have in our integral, which
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is d x so d x equal negative do you
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over three So we can rearrange are integral using the
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variable. You we would get negative 1/3 times the
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integral one over you and that looks like something that
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we can anti derive. That's a function that we
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know that we can solve. So we would get
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negative 1/3 times the natural log of the absolute value
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of U plus C remember sees that constant that we
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have to add on to an indefinite integral. So
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then we have to plug in our substitution for you
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. We can't just make this substitution and call it
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a day. We have to plug in that substitution
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back into our essentially our anti derivative to in order
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to get the correct answer. So we started with
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the integral DX over five minus three x. So
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once we plug you back in, you would get
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that Our solution is negative 1/3 times the natural log
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of the absolute value of five minus three x plus
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c. So I hope with this problem helped you
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understand how we can use u substitution to solve an
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indefinite integral on. I hope that it makes sense
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why we use U substitution in the first place.