integrate-each-of-the-given-expressions-int-frac3-x2-4x2-d-x-3

Question

Integrate each of the given expressions.
$$\int \frac{3 x^{2}-4}{x^{2}} d x$$

Dwijendra Rao · Accepted Answer

Yeah. Hello friends. We have to integrate of this given Express and that is integration of three X squared minus four upon x squared dx. Yeah. Mhm. So this will be a quest to three X squared up on x squared minus of four upon excess square of dx. So this will be caused to three of indication of one. The X- of 4 to Depart -2 of TX. So now the integration of one will be x minus of four indication of x minus two. Extra department store will be extra developments two plus one upon managed to plus one. Okay so this will be cost 23 x- of four x to the power of yeah minus okay one ball minus one. Mhm. Mhm. So answer will be three x -4 Upon my husband will be plus four. Okay Into one upon X. Sorry conscience will be there because it is indefinite integral. So this will be like this. Okay So final answer is three x. place four upon X plus constancy. So this is the as I hope you understood. Thank you.

Bobby Barnes · Answer

So if we want to find the anti derivative of this expression here, first thing we might want to look for is what most complicated portion of this function is that might so lead to something that if we take the derivative little kind of cancel out. So mine first thought is that X squared plus three is the most difficult thing here. And if I take the derivative of this, I end up with two eggs, which kind of looks like negative for ex. So you may say, Well, let you equal X squared plus running. Taking the derivative of this with respect to X gives you ideas Max physical to two hooks and then solving for what? Yeah, So now solving for d X, I want to multiply over by t X divided by six and one that will do over to ATS is equal to DX. So now let&#x27;s go ahead and do our substitution. Sze so negative or axe Well oh, so in the denominator will have are you and then DX becomes you over to so first noticed how thanks here and x there, counselor and the negative for over to give negative to remove the negative too. And I end up with just the integral of one of you. Did you so negative to now? Remember that he anti derivative of one over you is the natural log of the absolute hell you of you watch some constant C. Now we can go ahead and take what we&#x27;ve been partners for you, which is X squared plus one and plugged him and doing that, we have negative to natural law of the absolute value of X squared plus three kwasi and then X squared Plus three is always better than zero. So this here isn&#x27;t an issue, So I could go ahead and drop the absolute values and get natural log of exploited plus me pussy This year will be our indefinite.

Amy Jiang · Answer

Okay, So let&#x27;s ever noticing that we haven&#x27;t x squared in our denominator an ex inter numerator. And we know that the derivative of X squared is in terms of X. So why don&#x27;t we let u equal x squared plus three. And in our Djerba tive, that&#x27;s equal to two x d? Well, we have negative for here. And four is we can bring out of the two. I didn&#x27;t have to x the X like, are you? So it&#x27;s here at this. That&#x27;s two and a girl of do you over you. Okay, so that gives me negative to Ellen, you pussy. And I&#x27;m replacing, aren&#x27;t you? Well, yet x squared plus three and then plus seat.

Amy Jiang · Answer

because what start very letting you equal to X. Because three and I always take the derivative of that. So that gives us, um, Do you eat a culture too? The X So it was here that we have before she lets break that up into two times two. So we bring out one of the twos and have a two inside. So we see that, um and Bill, we have to the ex unethical to do you and then this inside two X Plus three. That&#x27;s equal to you. So we&#x27;re placing our extra for used. We get the following we get you to the power of four times to you and then we can take the Serono. So that&#x27;s two times you two par five over five plus See another. Let&#x27;s put back in or you Are you is two x plus three and that&#x27;s did a part of five over five plus C

Matt Just · Answer

All right. Here. We have a definite intergroup from two to three of the function. Three axe to the minus. Third minus five. Next to the minus fourth. The ex. All right, so we&#x27;LL start by finding an anti derivatives. Too bad these just powers of backs. So we have three fix to the minus. Second over, minus two minus five X to the minus, third over minus three. And in this function, evaluated from two to three. Okay, so not so bad. As he said, This is negative three house, and then this excellent Maya second, I could just evaluate at three and then subtract it. Evaluated at minus two. So that&#x27;s just one nine minus one fourth and then minus minus of plus five thirds and then x the minus thirty. Evaluated at three into take the difference of one over twenty seven. Minus one over eight. Okay. And reaching simplify. This could be it. Um, so when we do that, we get eyes over eighty one where you can just look at the calculator. Either way,

Xiaomeng Zhang · Answer

Yeah. So for this one, dressy comes to three times in key Grow off acts of the power off my nursery. My nose five times in Q grow off. Acts to the power off Renders full before the Force one. Does he coastal three times. Minus half axle power off my nose too. My nose. Five times my nose One, sir. Times oxidant. My power off my industry. So ministry over two times one nice miners. One force minor class five over. Three times 20 siwa. One were 20. So I would minus 1/8. So VSE breath echoes through my nose. 16 Last 3/8 class 0 5/81 My nose 24. Last five. Yes, it&#x27;s true. You kill too by over 24 then minus 5/24. Last 5/81. We all have our solutions. I over 81

Problem

Integrate each of the given expressions. $$\int \…

Problem 18 Easy Difficulty

Integrate each of the given expressions.
$$\int \frac{3 x^{2}-4}{x^{2}} d x$$

Answer

$3 x+\frac{4}{x}+C$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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$3 x+\frac{4}{x}+C$

Basic Technical Mathematics with Calculus

Catherine R.

Caleb E.

Kristen K.

Samuel H.

Precalculus Review - Intro

Functions on the Real Line - Overview

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

Catherine R.

Caleb E.

Kristen K.

Samuel H.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus