integrate-each-of-the-given-expressions-int-frac8-d-v032-v3-3

Question

Integrate each of the given expressions.
$$\int \frac{8 d V}{(0.3+2 V)^{3}}$$

Dwijendra Rao · Accepted Answer

Hello Friends we have to integrate of this given expression that is interior send off eight of devi upon .3 Place to be. Yeah. Who the power off 3? Yeah. Okay. Mhm. So we will substitute .3 plus. Do we buy so by differentiating it with respect we we can get two of Devi question did he? So we can write it eight of the we will because to four of duty so weekend right four of duty upon. Mhm 2 to the power of three so mhm. Yeah. Okay this is the substitution so further we can active foreign news T to the power of monastery duty so we can I did four. Okay key to the bottom minus three plus one upon minus three plus one plus constant see so this will be cause to four upon managed to Do you do the power of -2 plus c. So this will because to manage to that&#x27;s right mm. So in the place of tv can right .3 Place to be Yes 13 place To be to the power of -2 plus constant c. Okay, so we can write it managed to upon 0.3 plus gooey holy squared plus constancy. So this is the answer. I hope you understood. Thank you.

Aishwarya Krishnakumar · Answer

So for this problem, we&#x27;re asked to use substitution to find the integral. So we&#x27;re gonna let you equal whatever&#x27;s inside of function. So this, since it&#x27;s the power of eight, So you equals three x squared plus one. Do you would be six x t x. You can move the six to the other side would be. Do you over six equals x t X. Now you can see that we have a next e X in the given in a girl. So that makes it easy. So we can just rewrite this as eight to the you Power times do you over six and you can move the Constance to the front. That would be one over six times theater Girl of eight to the u D. U. And this gives us 1/6 eight to the U over Ellen of eight pussy. And now we just have to plug in three x squared plus one into you. So eight to the power of three eggs squared, plus one over six Ellen of eight. See, then this would be the answer

Amy Jiang · Answer

Okay, So what&#x27;s that? By letting you equal you going? What&#x27;s to the power of eight? Sort of three X squared, plus one. And then we have that d you that you could 26 packs D x. Okay, so we&#x27;ll divide by six on the side, so we get X dx. Okay. I know what&#x27;s replaced what we have. So we have a 1/6 in your girl, eight to the power of you, and then do you Okay? So what&#x27;s the inner role of eight part of you? Well, that&#x27;s equal to I hate to part of you over Ellen of our inside, which is eight. And then plus, give me 1/6 01 of eight and then eight to the power of you. But you is three x squared, plus one. Okay, so we get the following

Matt Just · Answer

Okay, So another definite integral from negative to the negative one of this function. Negative to over tea plus three e to the zero point three team Dean. So anti derivative. So? Well, just remember that. Um okay, so, So anti derivative of one of her t is log absolute value of tea, since it&#x27;s going to be negative too. Log Absolutely. T plus. Okay, well, this is going to be three eating a zero point three t, but I might have to divide by this constant factor. I just think when you take the derivative, you multiplied by zero point three by the chain roll you were just going to divide. So I have three divided by zero point three. Me too. The zero point three t evaluated from negative to donate one. Okay. So again, we can just actually evaluate each one of these turns at the end points and take the difference. So and you have two times log to minus log one and notice that I&#x27;m applying the absolute value to negative one and and negative, too, and actually ended their records. So long. Absolute value of one minus long. Absolute values too. Plus Okay, three overs your point three. That&#x27;s one over&#x27;s your point. One or one over one tenth. Let&#x27;s just ten. And then we have into the minus zero point three. Brian&#x27;s A to the minus, sirrah point six. Okay? And so that&#x27;s good. I mean, one thing we can do. Okay, Log of one zero. So this is just to sow the negatives. Cancel natural, too. Plus ten times this difference. At this point, we can probably just plug this end and what we get Approximately three point three zero six.

Xiaomeng Zhang · Answer

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Xiaomeng Zhang · Answer

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Problem

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

Problem 32 Easy Difficulty

Integrate each of the given expressions.
$$\int \frac{8 d V}{(0.3+2 V)^{3}}$$

Answer

$-\frac{1}{4(0.3+2 V)^{2}}+C$

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$-\frac{1}{4(0.3+2 V)^{2}}+C$

Basic Technical Mathematics with Calculus

Grace H.

Anna Marie V.

Caleb E.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

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

Grace H.

Anna Marie V.

Caleb E.

Michael J.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus