integrate-each-of-the-given-functions-int-fracsin-2-xcos-3-x-d-x-2

Question

Integrate each of the given functions.
$$\int \frac{\sin 2 x}{\cos ^{3} x} d x$$

Sid Wan · Accepted Answer

Okay. Lumber six with newt. Toe calculates integral to axe Kasai. Ax squared DX Sorry. We cannot orders prerogative of ex squares. Toe substitution do equals at square. Ah, the U equals two ax Teo. So he comes to you. That guy equals cause I you to you. Not this one. If you checked the four Miller is going to be fine. You pussy And you can substitute back sine x square, Plus it does it.

Pagadala Kishore Reddy · Answer

look it. So we&#x27;re going toe. We You&#x27;re really hurting, though. And do the laugh. Thank you, Bix Koszics DX. We know that the baby well say next equals Koszics. So we evaluated this integral bye U substitution matter. So the next thing is lead you equals say nix No d&#x27;you equals that every radio outside next is car six and that very creative off excuse the ex. So degree love saying que Bix car six d x equals sign. Is you so saying cube is you Q and Koszics VX. He&#x27;s do you and we know that in do the love export in B X equals export and plus one by n plus one plus c so integral a few q b u equals you forward here in the street So three plus one by three plus one Let&#x27;s see that equals you. Powerful way cool Let&#x27;s see requires we know that you is say nix Saint ex playing board for ticks before bless seat so integral off sine que bix koszics DX equals same power for ticks before. Let&#x27;s see. Thank you

Vipender Yadav · Answer

here in this problem we have evaluate danger girl Isaac leads to sign square X assign cubic not DX on We have to use the substitution mattered so we can write ST Squid Aches Dart Hussein Que picks as saints critics James cuisines Critics time school say nix on we can write designs critics as one minus signs quicks So saints critics here I am writing one minus sine squared x on there and Harry Disco Sane X So rain jiggle becomes same squid ICS one minus science critics times cosine x dx Now I&#x27;m substituting you as signings So will get Do you is equal to you&#x27;re saying next DX So then trickle becomes you square one minus you square do you so it will be equals two in jiggle you square minus you the power four dot do you So will it comes out to be as you cube Divide by three minus u to the power Fife Divide by five plus c where c is a constant off and constant off integration now always substituting the really of you. So you was signed x so to become Sign que Bix divide by three minus Sign to the power five Fix divide by five. Bless, See So this is the and so for the given in drug

Amit Srivastava · Answer

we have going to great Sank you. What was you? Ex beatniks? We can dry signed you Science kinetics or scared? It&#x27;s sign Knicks The X No, we can write signed skeptics is one minus more spirits. Course care. It&#x27;s sign. Mix be. It&#x27;s course X is equal, only appreciating. We get minus seven it. Site Sign Knicks Deitz 80 Be to become signings. The It&#x27;s ISS minus big I easy to do. Indicate one minus. He&#x27;s good. A scared minus b. It become a four brightness. He scared the A only invigorating. We care a five upon five minus take you upon Cube. Let&#x27;s see. Would be value. Who&#x27;s five x upon fight a goes you, Becks a street? Let&#x27;s see. Is it?

Geena Pullo · Answer

I think I said this question will be solving for the integral of the sign of X cubed times coast of X squared DX. So the first thing we have to do is rewrite are integral as the integral of these sign of X squared times, sign of acts, times the coasts of X squared DX. And from here, we&#x27;re going to do is when you use a trick function. So function that states that sign of X squared plus the coasts of X squared. It&#x27;s equal to one Andi. So we&#x27;re going to have that. The sign of X squared is equal to one minus the coasts x squared. And so we&#x27;re gonna plug this in for our sign of X squared. So now we&#x27;re going to have the integral of one minus e coasts of X squared times the sign of X times the coast of X squared the X on. So from here we&#x27;re going to just distribute our sign of X. So we&#x27;re gonna have sign of X minus the sign of X both X squared times The coasts of X squared T X on from here we&#x27;re going to do is we&#x27;re going to distribute our coasts of expert. And so we&#x27;re going to have a sign of X time Seacoast of X squared minus the sign of acts times the coasts of X to the fourth D X. And now from here, we&#x27;re going to split this into two different integral. We&#x27;re gonna have the integral of sine of x times, coast of X squared minus the integral of sine of I&#x27;m sorry for God R D X here, minus the integral of the sign of acts times the coast of X to the fourth d X. From here we&#x27;re gonna do a U substitution and both they&#x27;re gonna have the same the substitution. So we&#x27;re going to say that, are you? It is equal to the coasts of acts that are protected derivative. Both sides for D. U is equal to negative sign of Act D X. And from here, we&#x27;re going to divide both sides by negative time. Ex, we&#x27;re gonna have d&#x27;you over Negative sign of X is equal to X on now from fear substitute in. So we have the integral and so we&#x27;re gonna substitute in for our, um we have the integral of the sign of acts were going to substitute in for our coast of acts. So we&#x27;re gonna have you do squared and I we&#x27;re and we&#x27;re going to substitute in for r d x r D you over negative sine x They were going toe have you over negative side Acts on this is gonna be minus are integral of the site of acts. And again, we&#x27;re going to substitute in Are you for coast of X? So we&#x27;re going to have you to the fourth. Right? Um and now we&#x27;re going to institute in for our D of X are deep you over negative sign of X. And from here we can do is we&#x27;re going to across out are signed of exes on we can take out our negatives. So we&#x27;re gonna have, um, time integral of you square d u plus the integral of you to the fourth d you. And from here we&#x27;re going to use the equation that states that the integral of X to the n is equal to X to the n plus one over and plus one. And this is when you is equal to acts. And so we&#x27;re going tohave negative times. So you do you the integral of that is going to be new. And this is what see on then, plus, the integral of you to the fourth is going to be you to the fifth over five and also plus c on so we can simplify this negative cubed over three plus you to fit over five plus. See, you only need one c. And now we&#x27;re going to plug in for Are you and are you is equal to the coast of X. So we&#x27;re going to have you equal to the coasts. Um X and so we&#x27;re going to have a negative Khost huge X over three plus the coasts, the fifth of X over five plus, see.

Problem

Integrate each of the given functions. $$\int \fr…

Problem 31 Easy Difficulty

Integrate each of the given functions.
$$\int \frac{\sin 2 x}{\cos ^{3} x} d x$$

Answer

$2 \sec x+C$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Grace H.

Catherine R.

Kristen K.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

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$2 \sec x+C$

Basic Technical Mathematics with Calculus

Grace H.

Catherine R.

Kristen K.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

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

Grace H.

Catherine R.

Kristen K.

Michael J.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus