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Integrate each of the given functions.$$\int \frac{\sqrt{1-x^{2}}}{x^{2}} d x$$

$-\frac{\sqrt{1-x^{2}}}{x}-\sin ^{-1} x+C$

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 8

Integration by Trigonometric Substitution

Integrals

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

01:58

Evaluate each integral.

01:23

Evaluate each definite int…

03:04

Evaluate the integrals.

02:38

05:54

Use integration by parts t…

04:50

01:24

Evaluate the following int…

01:21

01:09

01:17

Evaluate the indicated int…

So hello everyone today we're going to solve the integral of route one man in fact square the whole upon x squared dx. So for this we need to use integration by parts um the integration by parts formula is utV is UV minus video. So from this um functions integral we need to choose you and me to choose devi so for this integral we're going to take us route one minus X square and D V as one more X square. So do you um after differentiating this, you get um minus X over route of one minus x square, you need to use the chain rule in this to find the differentiation and hopefully you know what to do that and for this you need to integrate it. Now integral of this can be written as x rays to minus two. And he said you just had one and then minus two plus one and you get your answer as a minus one over x. Now you have all the variables at hand. So what you need to do is just plug it into the formula UV a root of one minus x square minus x. Yeah. My uh minus root of one minutes expire over X minus integral of video which is management or X into the U. Which is minus X. Or wrote off one minus x square. This excess cancel out these minus signs, cancel out and you end up getting minus one minus x square over X minus integral off one over root of one month's X square. Now, if you remember. Um Mhm going through the textbook, the formula for integral of are exciting. I mean this integral of one over route one man effect square can be written as arc sign X. So um it's one of the tricky geometric identities of integration. Um You can prove it by integration but I'm not going to do so in this video because that's not the question. Uh It's one of the formulas given in the text book and you can just learn them. Um And so this is the formula 1/1 minus X square Isaac Clarke Synnex. So what you just had to do in this question that you had to identify the integral as a sign and more sex. So Arcs and can read it to know signing, signing more sex. So straighten over here. So our X sign or sign in or sex. So you just have to identify this. Uh and you would get the answer. So um your final answer should be minus route of one man inside square over X furnace arc sine our sign and Merce, X plus C. Hi, this is not a definite integral. You will have to write the constant plus C. And that is your final answer. So I hope you understand uh, this identification um, was the main part of this problem. You have to identify this integral, and you can get to know more about these integral ah, intervals in your textbook as there might be a table in there, strict no metric integral identities. So, yeah, uh thanks for watching guys.

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