give-the-proper-trigonometric-substitution-and-find-the-transformed-integral-but-do-not-integrate-17

Question

Give the proper trigonometric substitution and find the transformed integral, but do not integrate.
$$\int \frac{d x}{x \sqrt{x^{2}-1}}$$

Rukhmani Jain · Accepted Answer

in this question that given integration is noted by I hear Okay and it is one divided by X into square root texas where minus one it is told that we have created in simplest form for that we have to see that which form is that here is the form of square root taxes square minus a square. And for this form we know that the proper substitution is I can say that actually it was two a sect later. Okay. And in this case at the place of we have one here so I&#x27;m going to make your substitution actually it was two seconds later. Okay now it&#x27;s derivative shows that the X can be replaced by sect theater 10 theater data. So make these replacements in the question so we see what we get here. We have in the numerator of one and X is replaced by a spectator and then square root of six square theater minus one. And the X is replaced by a spectator 10 to to data. You can cancel out the sector to OK cancel out and you can see that in the denominator we apply their identity which says that second squared to minus one is chinese square data And multiplied by 10 to the theatre. Okay. Further square out of china square to can be original simply wanna born commentator And we can now cancel out both of these 10 theater and then we have the simplest form of this integration here. That is the integration of digital. Okay this was only asked here it is not told that we have to make the integrations. Okay so this is the integration and you can also right here one also if you want. Okay and we can see that to achieve this work I had done here is I had taken the substitution of facts by sector it Okay thank

Pagadala Kishore Reddy · Answer

Okay, So way are going Retaliating, Bigelow DX by Texas. Way into or not one minus by using them at our economic substitution. Here we have excess quail underwrote off one minus Texas create. So let X equals saying dude up. That in place be ex ese cost. Do you go? Did you tell? No letters later. Praying? Yeah, we see. Yeah. Scientist A equals thanks. So babies makes and is he is one and v Z equals under Rudolph one minus excess grief So costed a equals on the photo One witness extra square So big love dx way nexus Squaring to one minor Sex is great Close, you *** lover d x v x Ys cost you get beat, you dog Bye. Excess queer excess Berries transferred Tita into on the road up on minus x A squid is cost a little dark for man in Texas Quickies, you know, cost you okay? They&#x27;re equals love cost. It&#x27;ll cost you targets. Cancel the teeter Wait ST square meter. That equals because he can square it up. Did you go integral love forsaken Square meter duty calls minus card data. Let&#x27;s see. We&#x27;re equals minus from their triangle. Argued I quarrels. Unnatural, Daph. One minus x er square. Bye mix. Plus so integral hour. Be expert X squared and do on the road off on minus X squared equals minus one minus X is collateral top one, minus extra square by X plus c thank you.

Amy Jiang · Answer

Okay, so we&#x27;re doing the integral of X squared DX over square root of one minus X squared. OK, so we&#x27;re gonna draw a triangle. You know, that&#x27;s this part is square roots of one when it&#x27;s explained beside his ex. And this is one. Okay, so let&#x27;s let x equal to sign of data, and then we have d X. It&#x27;s good to co sign of data data, and we know that co sign is Jason. Over. Hi, Pontius. So you know that CO sign of data is equal to the square root of one minus X. Quite OK, because we know that we can plug it into our previous form. We have sign squared it up. The X is gonna be co sign data date up over Gore. Roots of one. My sex word. That&#x27;s cool. So innovative. But it&#x27;s cancels. We&#x27;re left with the underworld side squared. Data get up. Now. Let&#x27;s use our trick function. This is equal to one minus coast side to their to data. Okay, that&#x27;s the sequel to date. Over to minus. Sign to date up over two plus. See. Okay, we know that science to data that&#x27;s equal to to sign data was laid up over two seats. Okay, so we have data over to minus sign of data outside of data. See, he said, that&#x27;s executed science of better. So sine inverse of X is equal to data. You get sine inverse of X over to find a sign of data saying it&#x27;s X close on the square root of one minus X squared plus C.

Amy Jiang · Answer

They say that the integral of this group of one plus x squared the ex all over excellence draw out triangle. We&#x27;re gonna have the square root of one plus x squared of hip hop news and won an X over here. No, it&#x27;s like tangents Get up equal to X based on our Rangel right sign over coastline is equal to tend it if they don&#x27;t. So when we take the derivative, be acceptable to seek it It&#x27;s where you know, you know, we&#x27;re also gonna need to find something of the form this group of one plus x squared But that&#x27;s this seeking it later, right? It&#x27;s the party&#x27;s over colon. Our hypothesis over adjacent that gives me this square root of one plus x ray. Okay, so looks, rewrites or enema. We have this group of one plus x squared that&#x27;s you could seek in data and we have the axe which is seeking squared data. You get off and that it is all over X, which is tangents of that get. But we know that seeking square they don&#x27;t is equal to one plus tangent. We&#x27;re here. You can&#x27;t know it&#x27;s distributed in are seeking to So we get begins a bit up for retention of Ada. Plus can Jin&#x27;s squared data you can get up, you know, over changing. You can&#x27;t look in cancer. One of our champions. This is one. Yeah. So he gets in a row of Sikkim. PETA over 10 to is there that&#x27;s equal to see thinking is one over. Co sign. This is over. A sign of the coastlines of get Well. Speaking of data plus tangents of data, seeking of data. This cracks, you can date up us. Get data. It&#x27;s great. Yeah. Okay. You know? Yeah. So what should we do from here? Well, we know that in a local seeking their that&#x27;s equal to ln of those sequence data minus tangents of data. And we also know that the integral of seeking of data, apples, tangent of data it&#x27;s equal to you, seeking of data. Now all we have to do is pledging what we know. So we have that cool. Seeking a beta is whatever signed. So that&#x27;s I thought youse over exit. We get Ellen, I want you over opposite, which is X. And then we have minus tangents of data. He&#x27;s attending a there is this extra? That&#x27;s what it takes. And and we have plus secretly beta. What a secret of it all always can. Speaking of, there was this square roots of one plus x squared. See? Yeah. And this is our solution.

Pagadala Kishore Reddy · Answer

look it. So we are going to be You&#x27;re really hurting the integral off the ex baby X squared Bento under hold off X squared plus one He had We have excess creer into underwrote half X squared plus one. So let X equals Dan Tito not in place d X equals sneak him squared feta day Tito No, Let us Brian dang triangle you be See here X equals down Tita. So hey, B e quarters x and BC quotes one and is equal. I&#x27;m not one plus extra square. So from the triangle c computer equals extra square plus one No Bigelow the ex way excess square into when little topics were scared Plus one quarters integral off B x dxc clothes sequence work detail The take off base Next was clear. Extra square t Cornell&#x27;s stance Quit butto. I do. And the roads are x squared. Plus one equals seeking Tito which is equal door. Bigelow C Can Tita di Tito by dance quickly not equality. Diggle off. If you simplify, you will get Kosik Dita in true car Peter defeat us equals two Integral. Of course, he can take a card theater. The theater equals minus because he can&#x27;t Rita. Let&#x27;s see which is equal. Do minus because he can theater from that triangle. ABC, of course, he can get I equals a little golf X squared plus one bye makes flood. So you take the law be explained excess square in tow on that off excess. Create less. One equals miners on that. Rudolph. It&#x27;s a squared plus one by X plus c Thank you, no.

Amy Jiang · Answer

Well, here&#x27;s what we have in the girl Back squared over square root of one plus X squared X. Let&#x27;s drop out or try and go. We have these two as positive. So we&#x27;re that are popping. Uses square one plus x squared. I mean, we&#x27;re gonna have a one in X over here. No, let&#x27;s let our X equal tangents of data and the X is equal to sequence square. They don&#x27;t. We also need to find this portion over here. That&#x27;s the sequel to second. They don&#x27;t miss on our graph. Right? Um, seek it is Hi, Panis. Over adjacent. So that skirt of one plus X squared over one? No, it&#x27;s plugged in. What We know. Yeah, the integral of X squared. That&#x27;s tangents. Squirt a little bird Get down and And the ex is seeking squared data. Okay, We could cancel one of our secrets. So we&#x27;re left with in a row of attendants where they don&#x27;t You get it. You did it and we don&#x27;t attendant score data that&#x27;s equal to Deacon&#x27;s squared data minus one times. Get data. No, it&#x27;s distribute that we get secrets to use the data mining to get better. You better. Okay, now let&#x27;s integrate this. We are not seeking Cuba. Data is equal to 1/2 seasons of data engines to dig up, plus 1/2 of Ellen sequence of beta tangents of Buddha and the integral of sequins. Evita in just ln of sequins, you know, change in there is the office. See? No need to just plugging. What Deacon Evita intention of there is. He said speaking of data is discovered of one plus x squared. That&#x27;s one hat skirt, bit of wonderful sex. Quaid. It&#x27;s changing a Vera. It&#x27;s it&#x27;s X. That same sex us 1/2 Elin of I believe this is minus X. You have one. It&#x27;s over here. Get Owen, Huh? Mm. Actually, we can combine these two. This one and this one over here. So we&#x27;re left with. This is minus. We have 1/2 minus one. So we get negative. Helen, we read it out your negative island of seeking, but you square it with one plus x squared. Upstanding was his X plus c for a solution. Make it 1/2. That is because one or would have minus one is 1/2. Yeah,

Problem

Give the proper trigonometric substitution and fi…

Problem 7 Easy Difficulty

Give the proper trigonometric substitution and find the transformed integral, but do not integrate.
$$\int \frac{d x}{x \sqrt{x^{2}-1}}$$

Answer

$x=\sec \theta, \quad \int d \theta$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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$x=\sec \theta, \quad \int d \theta$

Basic Technical Mathematics with Calculus

Anna Marie V.

Heather Z.

Caleb E.

Samuel H.

Precalculus Review - Intro

Functions on the Real Line - Overview

Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Anna Marie V.

Heather Z.

Caleb E.

Samuel H.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus