integrate-each-of-the-given-functions-int-frac8-xex2-d-x-3

Question

Integrate each of the given functions.
$$\int \frac{8 x}{e^{x^{2}}} d x$$

Tyler Moulton · Accepted Answer

mhm. We want to evaluate the following integral which is the indefinite integral of X over E. To the X squared dx. So this question is testing our knowledge of methods of integration. We&#x27;ve already learned about the power rule and long rhythmic integration. So this question is testing a finally found knowledge of exponential integration which states that the integral of E d u d u E D plus C. So use whatever raised the power of E. Since E X squared in the denominator we must have that you is negative X squared. So do you is negative two X. Dx as well. Therefore are eight X dx has an extra power of negative four. Or rather an extra constant or multiple factor of negative for which we carry over to our final solution. Thus we have that are integral is negative for integral. E. To the U. D. You plugging in for the exponential integration formula. We have negative for each of the negative X square plus. See the concept of integration.

Sid Wan · Answer

number eight We won&#x27;t fight ll active. Integral to CSC square eight ACS Tio with U equals a thie course. Aid the ax. So this guy equals an active into grow too. C s u square t you doing about eight? Two or eight? He was ninety one. Forcing Divorcee sees where you do You know this one by the form in there we got collective coat hand. You see that? The one force more by there. So cool one course code hands eight acs use of still back kowtow Look, cause I

Alex Johnson · Answer

in this problem, we&#x27;re gonna find the anti drug of two X to the seventh Coast end of next to the eighth, and we use a U substitution by letting you equal X titty eighth and d&#x27;you, which would equal eight X to the seventh DX. And we don&#x27;t have an eight representative in the original. And so we compare it to what we do have, which is going to be two X to the seventh. And so, through division of four, we can get the equivalent two X to the seventh DX that we&#x27;re searching for. Okay, Our new integral then would be 1/4 the integral of co sign of you, D you and the anti derivative is 1/4 sign of you plus C. And we can convert this back to be in terms of X. So it&#x27;s 1/4 sign of X to the eighth plus C

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

Linh Vu · Answer

indiscretion when you defend Indefinite integral on the job Age of the banks Minus ain&#x27;t go side. Thanks T X Yeah, The first term here. The number to stay the same and exponential way status them. Even when we do the relative their phone We have h of X here Now the for a second term the number 18 stay the same. And for the course I&#x27;m the X and we trying to sigh expiry with two We get regular cosa. Thanks Exactly This one They&#x27;re farmers. Uganda eight sigh. Thanks. And don&#x27;t forget to bless a constancy and the end.

Problem

Integrate each of the given functions. $$\int_{1}…

Problem 10 Easy Difficulty

Integrate each of the given functions.
$$\int \frac{8 x}{e^{x^{2}}} d x$$

Answer

$-\frac{4}{c^{x^{2}}}+C$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Heather Z.

Caleb E.

Kristen K.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

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$-\frac{4}{c^{x^{2}}}+C$

Basic Technical Mathematics with Calculus

Heather Z.

Caleb E.

Kristen K.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

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

Heather Z.

Caleb E.

Kristen K.

Michael J.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus