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Integrate each of the given functions.$$\int \frac{d r}{r \ln r}$$

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 2

The Basic Logarithmic Form

Integrals

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Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

03:19

Use substitution to find e…

01:09

04:51

Evaluate the integrals usi…

03:31

01:18

Evaluate the integrals.

02:55

Evaluate the integral.…

00:37

Find the indefinite integr…

01:58

01:22

04:08

So when we're going to find this indefinite ineffable using the substitution, the first thing you want to do is kind of think about Well, what's the thing that's really making this difficult to integrate? So if I want to integrate our times e to the negative r squared with respect are you might kind of see how this e to the negative are square is giving us issues So you might just first make the guests that you is equal to he to the negative are square And then we can go ahead and take the derivative of this with respect to our to find our gave you We'LL get you over e r is equal to so taking the door But it will be to the negative are squared will be changeable because remember, we have parentheses right here So this is actually the composition with each X So we'll end up with first just e to the negative r squared since the derivative of X urgency to necks So that doesn't change And then we have to multiply by the derivative of the inside functions ddr of negative are square and this here will be eats his negative are squared times negative to R. This is You are So you might notice that this looks very similar to what we already have. But the only difference is we're being multiplied by this negative too. So what I'm going to do is I'm going to divide over by negative too. Bye bye, dear. So doing that gives us d'You over Negative too is equal to on i'LL move the r out front So ar e to the r spirit d r And now this here is exactly what we have here. So let's go ahead and re vipers has the integral Oh, so I'll plug in d'You over Negative too. You over mobile too. And now we can cool the negative one half out negative one have integral of one do you? And remember when we integrate a constant will just end up with the variable Negative one half you lost See? And now we can go ahead and take our view It's here plug it in on it Do so in negative from half heed the negative are square What? And this year will be our indefinitely

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