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Question

The functions $y=e^{x^{3}}$ and $y=x^{3} e^{x^{3}}$ do not have elementary anti-
derivatives, but $y=\left(1+3 x^{3}\right) e^{x^{3}}$ does.
Evaluate
$$\int\left(1+3 x^{3}\right) e^{x^{3}} d x$$

Ruirui Liu · Accepted Answer

look at this won&#x27;t cause separate out first. Next. And I wouldn&#x27;t be using the place in my heart for this tax lives. This is Max. You cannot do that thes term into these. Chairman. Get canceled. So we got we wish.

J Hardin · Answer

So here we are to evaluate this following in the girl. Let&#x27;s just start off by rewriting it. So I&#x27;m just distributing the even X square. Now here, let me rewrite this as X times and then two ex either the X Square plus and then one times either that square. Now notice that if I called this f And if I called this G here then we have f prime equals one and we have g prime is two x e to the x square. So we cf prime here and then we see ji prime here. So we noticed that this is coming from the product rule. So the right hand side is what we have right now in this intolerant and so we&#x27;LL go ahead and write this in this form here someone in our f NRG. So that&#x27;s her f and then RG is either the X Square and then we also have, of course, when he prime out there and then we use the fundamentals they remove Kokkalis, which allows us to cancel out the derivative with Ian a girl here as long as we go ahead and and that constant of integration c at the variant. And that&#x27;s your final answer

Robert Daugherty · Answer

section 3.6 problem 35. We&#x27;re dealing with derivatives that involve the use of the chain role. And you see this first term, not only will it be, change will also be the product rule, So why prime going to be equal to use treat? It is a product. The derivative of X is one So times e to the minus X plus X now the derivative of E to the minus sex That&#x27;s gonna be e to the minus. X times the derivative of minus X which is minus one. And this move onto this next term the derivatives gonna B e to the X cube times The derivative of X cubed, which is three x squared Oculus has done, is just now combining like terms. So why prime is equal to e to the minus x minus x e to the minus X was three x squared you to the X Cubed. It looks like the only further simplification is I can factor out of e to the minus x here. So why prime is e to the minus X and then one minus X plus three x squared you to the X cubed and that&#x27;s our final answer

Amy Jiang · Answer

Okay, So before, with your conservative, let&#x27;s start by splitting up this up into two, fracturing. So it to over three you two x plus 3/3 sets. You didn&#x27;t think of X and I. Let&#x27;s take the derivative. So why five? That&#x27;s equal to 2/3 years, since the derivative of eases is itself. I know we have, um, good of Evita, Partly direct. So that&#x27;s equal to itself. And in times derivative of our inside, which is negative one. So we just have a negative here. So this is our solution.

Linh Vu · Answer

function. Why you go to expert tree Deveney Bigotry less expert to given you But you plus teaching about Tom And thanks on. And we need to fight in the first and secondary video record up. It would have the banks bell and they reverted, which you can echo Jew and Thames Expo minus on. And, uh, expert I am on this one, and you will have each of the x d rive until we get it. Could you Each of the AKs on and we have agent about minus. Thanks, dearie. With you begin. And could u minus agent a minus x using those formula hell, we will be about you find And the first day rivet your now my Bram Nico ju three. Thanks Grant of anybody tree sending him would be do thank you very very to. And this one here we can do this formula and then we get echo to the minus age The Manus X on we consume. You find this and then we get trinkets and will treat you with that. You to have the X grabbed us X minus agent minus Thanks. And then it isn&#x27;t will be the white Graham by the wind number Bram, We do one most limited. We have a Jew acts for this one for additional Ghenda Best one doesn&#x27;t have about one here. And fathers when you have a minus and age of the age of the Manus X again this wonderful, we have the minus 80 minus X. So I&#x27;m really going to wind up a prime equity that you experts one that&#x27;s each of the Manus X Well, the answer for the world about crime.

Amy Jiang · Answer

Okay, so we want to find the falling interval by using use up, and we&#x27;re given our new value were given that use people to accept our three. So it&#x27;s fine to you. That&#x27;s three X squared The nurse here that we have X squared. Yeah, let&#x27;s move. This three will divide by preamble sites where we get to you over three. Okay, but I gives us integral of X squared the X that&#x27;s d U over three, and it f of X cube, which is you. Now let&#x27;s find our Our endpoints is well, when acceptable to to U is equal to two per three, which is eight. And when accident which one? You is equal to two or actually wanted Barbary and it&#x27;s equal to one. So we have from 1 to 8. Okay, I know it&#x27;s, um pull out this 1/3. You get the interval from one two Aides of f applied at you and into you

Problem

Use the substitution $u=\tan x$ to evaluate the i…

Problem 51 Easy Difficulty

The functions $y=e^{x^{3}}$ and $y=x^{3} e^{x^{3}}$ do not have elementary anti-
derivatives, but $y=\left(1+3 x^{3}\right) e^{x^{3}}$ does.
Evaluate
$$\int\left(1+3 x^{3}\right) e^{x^{3}} d x$$

Answer

$x e^{x^{3}}+C$

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$x e^{x^{3}}+C$

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Michael J.

George B. Thomas Jr.

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