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Question

Evaluate the integrals. Some integrals do not require integration by parts.
$$
\int\left(1+2 x^{2}\right) e^{x^{2}} d x
$$

Ruirui Liu · Accepted Answer

transport mission. No, I won&#x27;t us so we can know Separate. They&#x27;ve seen mission two parts. The first part of your abs, he asks, perhaps in the wood. Um, use the integration by parts. Created the first meeting here. He wasn&#x27;t? No, we can&#x27;t axe. Yeah, Myers Axe. So there&#x27;s q r e que us interviewing. These can&#x27;t be lost too. So these term in these terms get cancer. No So looking. Get they in questionable arsenal or it&#x27;s actually eggs.

Robert Daugherty · Answer

okay, Section eight dot to problem number 54. So we&#x27;re dealing with integral is that require substitution tze and require integration by parts So I haven&#x27;t indefinite integral exit of the X over X plus one square. So in order to make this one happen, let&#x27;s let you equal X e to the X then do you It&#x27;s going to be equal to I&#x27;ve got to use the product rule. So that&#x27;s going to be the derivative of X, which is one times e to the x plus x times the derivative eating the access just e to the X. So this is just e to the X, um X plus one the ex. Okay. And then we&#x27;ll let Devi equal to, um will say X plus one to the minus two d x. So you integrate that and you end up with negative X plus one to the negative one. So negative one over X plus one. So this inter goal turns into U V. So that&#x27;s going to be negative. X you to the ex over X plus one Um, minus the integral of VD. You, Sophie, look at those turns already have a minus that that&#x27;s gonna be a plus. So the inner role, it of the X Times X plus one over X plus one DX. There is a very nice cancellation right there. What&#x27;s the integral eat of the X? That&#x27;s just eat of the ex. So this turns into negative X eat of the X over X plus one plus either the X plus constant of integration. Okay, and you can factor out an E to the X here. When you do that, you can have this turns into so e to the X and you&#x27;ll be left with one one minus X over X plus one plus c. Okay, so this would be a really good answer or just factoring out the E to the X.

Vikash Ranjan · Answer

I saw the divinities. It&#x27;s beautiful. Necks into one over our X plus one for the Squire. This is their denies exploded. Boris. Inefficient off X plus one for the far right. Gibbs, My division off. It&#x27;s beautiful. Russ, it isn&#x27;t. It&#x27;s plus one to the bar minus school. The abs? Yes. So we have that. I am. He was the bar X minus starting. This is Indu. It&#x27;s plus one to the bar, minus one over. And miners position off. Inference plus tips. I know. It&#x27;s plus one to the bar minus one over on this one. Ideas get as my steps Bar X in here. This place went to the bar minus one minus delusional. Why not get Boris minus X it on my steps. So this is excellent in one of our X plus one in the end. So if if that this now further division is becomes minus that bar bets about it plus one last delusional inference lastex parts for it&#x27;s less blood in the eggs. This is a huge alas, my sex. You perhaps over X placement, plus additional you perhaps one plus x for one ex these back after this park. So this is gonna minus X for X Poor, explicit one plus, perhaps left. See? So we have sex plus four x plus parents. Sore explosive. It&#x27;s canceled his bar. Plessy. So we have. The final answer is equal inference over X plus one. Let&#x27;s see.

Robert Daugherty · Answer

so Section eight dot to number 34 Indefinite integral one over X natural log of X squared. So it&#x27;s a combination of substitution tze and integration by parts and integration is like a puzzle. So you&#x27;ve gotto get comfortable doing this. What I wouldn&#x27;t really want to look for if I can cease an expression in the Inter Gran and it&#x27;s derivative, that&#x27;s gonna simplify. When I look at this, I know that the derivative of the natural log of X is one over X. So I&#x27;m seeing a function and it&#x27;s derivative. So let&#x27;s try that. Let&#x27;s let ah, you equal to the natural log of X Then d&#x27;you is going to be one over x dx. Okay, so what it means here is I see one over X d. X. So this, in a role, just turns into the integral one over x d x. That&#x27;s d&#x27;you one over the natural log of X square. That&#x27;s just one over you squared. So this is the integral of you to the negative, too, do you? That&#x27;s just a polynomial. Integration doesn&#x27;t get any easier than that. So that&#x27;s you to the minus one over minus one plus C and we know that you is equal to, um, the natural log of X. So this just turns into, um, negative one over the natural log of X plus, a constant of integration. Okay. And that is it.

Vikash Ranjan · Answer

D&#x27;oh! It&#x27;s no. One. So you wouldn&#x27;t in asking What d There&#x27;s one over x. The people&#x27;s didi on off. Really? So this is equal in the long bar minus film. Edie, this is given ass. Do the bottom off minus one of our minus one. Let&#x27;s see, this is equal to minus one over X then.

Ruirui Liu · Answer

Okay. Last local. They said axe psych. It&#x27;s here X and the u. It is changing in, you know. You know you miss Thank you faces long then you loss. Thank you. We stick. You were spent X needs.

Problem

Evaluate the integrals. Some integrals do not req…

Problem 53 Easy Difficulty

Evaluate the integrals. Some integrals do not require integration by parts.
$$
\int\left(1+2 x^{2}\right) e^{x^{2}} d x
$$

Answer

$\int\left(1+2 x^{2}\right) e^{x^{2}} d x=x e^{x^{2}}+C$

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$\int\left(1+2 x^{2}\right) e^{x^{2}} d x=x e^{x^{2}}+C$

Thomas Calculus

Anna Marie V.

Kayleah T.

Michael J.

Joseph L.

Integration Review - Intro

Definite vs Indefinite

George B. Thomas Jr.Thomas Calculus

Anna Marie V.

Kayleah T.

Michael J.

Joseph L.

George B. Thomas Jr.

Thomas Calculus