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Use Integration By Parts to integrate:xe?xdxA) x(2x2)-e+c 1 C) 21 re ~2e 2 +0 2B) 2xezx ~el +C D) Lxezx Lel*+C 2 4...

Question

Use Integration By Parts to integrate:xe?xdxA) x(2x2)-e+c 1 C) 21 re ~2e 2 +0 2B) 2xezx ~el +C D) Lxezx Lel*+C 2 4

Use Integration By Parts to integrate: xe?xdx A) x(2x2)-e+c 1 C) 21 re ~2e 2 +0 2 B) 2xezx ~el +C D) Lxezx Lel*+C 2 4



Answers

Integrate the given functions. $$\int \frac{4 x d x}{\left(1+x^{2}\right)^{2}}$$

Mhm. In the given question we need to find a definite integral using a substitution. So we make artists and musical to express to definitely think about sex. We have to use it for two years. From the first question we get when X is equal to zero, Beautiful too X-plus two until people to to And when X is equal to say that huge call to nine. So the integration becomes risen from 2-9. Do you buy you? Did you go to natural hydrating of you? Some 2- nine. We've got to call other tellers nine. My last night from al. Already moved to Which can return this natural. But by the most nine x 2. So this was the final answer.

All right. So for the first stuff in this integral, I'm going to make it a little bit easier to work with. I know that this detox own since it's being multiplied, it is fair to write it like this. Uh, but I would rather to make things a little easier for us. I would Watari write it off to the side like this because it looks a little bit more familiar, but it still means the exact same thing. So then the next thing I wanted you is I want to write one over to Lex as something that's easier to work with. So I want to write this in turns of exponents, rather than as a fraction. So this can be separated. Sorry. Don't want to forget that internal simple. I'm going to separate the 1/2 and the one over X. So, really, this can be written as 1/2 times flying over X. Yes. And then since I'm multiplying by a constant, I can just bring that out front. It's that becomes one. How times integral one over X years. So this is something that you might want to try to remember. There's a proof for it. But one rule you might want to remember is that the integral of one over X is just Ellen of X. So we get 1/2 times Ellen of X. We always wanna put X inside of absolute values. Because, love, Ellen, we can't plug in negative numbers. Um, so we have 1/2 gallon of X, and then since this is an indefinite in general, we don't want to forget a plus C. So this is our answer.

We're going far, but where we have the inter go on the use sinew Do you ever get the gorgeous I knew? Why must you go sign new press A constancy in here We have a question off. Uh, thanks. Side Teoh X t x. So everybody knew you, could you That your thanks And then you culture patootie x So, I mean, it's not just the exit, could you Did you are what? You and this accident a contender. You on with you. And now this is no way you could you could, you know, before we can remind us in the car in terms of, you know, funny, funny matures will be that you would you say you, Dean, you on do so that you cancel out? Yeah. Then we get Echo June into grow on the new sign You d you on my formal again? Incredulous. I knew when I asked you because you plus a constant C because you recruited your ex. So we have a side You. Thanks, Linus. Do thanks. Ghost site. You expensive Constance

In the problem we have integration to ice of XDX upon this is 4 -3 eggs Squire. So for solving this, let us assume this four minus three X Squire equals P. That is minus three into two ice of X. Dx. That is equal to D. P. And further it is twice of X. Dx become minus one upon three D p. So further the integration become minus one upon three. Integrated integral dP upon P which is equal to minus one upon three Ln mod P plus C. This is equal to minus one upon three Ln model four minus three X Squire plus C. So this is the final answer to the problem.


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