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Evaluate the integrals.$$\int \frac{1}{x^{2} \sqrt{9-x^{2}}} d x$$

$-\frac{\sqrt{9-x^{2}}}{9 x}+c$

Calculus 1 / AB

Calculus 2 / BC

Chapter 6

Integration Techniques

Section 3

Trigonometric Techniques of Integration

Integrals

Integration

Missouri State University

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

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Okay, so for this question will be using tricks up. So let's look at what's inside or square root. So this is in the form. The square root of nine years. X Squared nine is the perfect word. That's three detract, too. So we can let's in this case XP equal to, um three sign of data. Okay. And I was holding for triangle. That's X over three. Did you go to China? Better. So Data has ah, high part news of three and the next turn on the opposite side of And then our, um, close eye inside that squared three minus X squared or three squared minus X squared is grateful for that. So this is actually 99 sex. What? Okay, so this is equal to integral of one over exclaimed, That's three square jawed. It's nine fine square debate up. And then we have, um this portion here is co sign of it. So actually, we can rewrite this as a square root of nine. Minus X is three son of a dust, we get nine sine squared of beta, and then this is the data which is equal to the integral of was over nine fine squared Vega and then we could factor out of line. That's the 293 times three. And then we have the square root of one minus sine squared, not equal to co sign square DaVita. Okay, so I give this in a girl, uh, 1/27 sine squared of data and then co sign of data. Okay. And we also note that's well, yeah, that's equal to three. Co sign of data data, so we need to build it in. This is three co sign Beta three. Cool sign of data and Rico sign. They don't notice tricking counts of this three hair. So we're actually left for the line, and then we can count. So its coast on a vato and we're left with, um, in a girl of 1/9 1 over sign. That's cool. Seacon Square data They don't and in a group that, um, sing that equal to negative coach engines. Fatal debate. What actually happened? Let's see. Overnight. And we said data is equal to a coach engine of the better. That's, um, went over, son. Actually, with you at this as when it's cool. Sign of data over Final Beta, and then we have nine here. Let's see sickos. Angelita. That's this over this accidents. We committed this as negative square roots of nine minus X squared over three and then sign of data. That's X over three. Okay, so we're left with the negative square roots of nine minus X squared over nine x and in policy.

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