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In this problem, we are practicing an integration technique called the u substitution.
00:06
And this is a really helpful technique to solve integrals because what we do is we technically substitute the hard part of our integral to make our integral into something that we recognize, that we can solve easily.
00:22
And that's why we use u substitution.
00:24
So that's what we're going to be doing in this problem.
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So let's just review the integral that we're starting.
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With.
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We have the indefinite integral, meaning we don't have limits to plug in.
00:36
We have the indefinite integral, dx over 5 minus 3x.
00:41
Well, if we weren't using u substitution, or maybe you solve the integral for the first time, that looks pretty hard.
00:48
Maybe we don't know how to solve it.
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So we're going to use u substitution.
00:52
We're going to let u equal 5 minus 3x.
00:55
So we would take the derivative du equals negative 3 dx.
01:00
So we're going to let u equal 5 minus 3 dx...