integrate-each-of-the-given-functions-int_13-frac3-x38-x210-x2xx13-d-x-2

Question

Integrate each of the given functions.
$$\int_{1}^{3} \frac{3 x^{3}+8 x^{2}+10 x+2}{x(x+1)^{3}} d x$$

Vikash Ranjan · Accepted Answer

in the problem we have been given integration one and three three x cubed plus eight x square Plus 10 x plus two bon X into X plus one to the power three dicks. This is equal to Dress in 1, 2 3, one upon x plus one Plus three upon x plus one whole square plus to opponents dicks. No, this is regionals. Ellen marks plus one plus three into x minus one. So the X plus one to the power -2 upon -2 plus twice. Ellen mod X one and three. So this is equal to Ellen Marred X-plus one minus three upon two into one upon X plus one. Well it&#x27;s quite mhm Plus to Ellen marks one and 3, the limits putting the limits we have the answer. S Ellen 4 -3 upon 32 Plus to Ellen Model three minus Ellen this is Ellen mod two Plus three upon 8. So further this equals to 3.17162. So this is the answer.

Matt Just · Answer

I don&#x27;t know. We have the definite integral zero two four of minus X to the three halves plus x to the one half d x. I could start by finding an anti derivative. So we have so this minus Khun stay are here. And then the entire derivative is so we add one to the exponents We get X to the five hands over five hands plus x to the three halves over three. House evaluated from zero to four. Okay. And so four to the five halves We&#x27;LL take the square root and then take the fifth power. So it&#x27;s two to the fifth, which he be thirty two over five halves plus okay. Squared two cubes of eight over three halves and then minus this evaluated your over that Syria. Okay, so, uh, this is minus can multiply by their sim prickles of both the numerator is get doubles at sixty for over five plus sixteen over three and so we need to get a common denominator. I mean, we could leave it like this, but if we do get the common denominator of fifteen, you should get negative. Six fifty six. Divided by fifteen is the final answer

Xiaomeng Zhang · Answer

So those one dressy coast through my nose three times acts to power off, Serie over to and miners into grow off access to the power off house. Okay, so for our 1st 1 that a cow shoe True over five times, actually. Power are 5/2 40 and my noticed us to over three times acts to the power off. 3/2, full zero. So for the 1st 1 that they go to six. So our five I&#x27;m too through the power off five that is 32. And for those one, we have to over three times, two to the power off street so we can see that he has to six times or be too. And that&#x27;s why he goes to 16/3. So we&#x27;re have the answer. You kill two minor 65 6/15

Aishwarya Krishnakumar · Answer

problem. 13 were asked to find this definite in and to do this problem, since it&#x27;s has, since it has a fraction and a function inside of the function where we&#x27;re gonna use U substitution and let you equal three X Plus two and we choose this for you because it&#x27;s a function inside of a square. So if you find the derivative of both sides, you get three d ETS. And this comes out handy because we have a three D X in our originally kitchen so we can go ahead and write this. But before doing that, we have to notice that we have bounds and in the bounds these air expounds We have changed them too. Why bound? And to do that, we just plug it into this equation who, 33 times before plus two to find the upper bound and to find the lower bound we would do three times one plus two. So the upper round is 14 and the lower bound is five. And now we can do the U substitution so would be won over you squared times the u. So this equals you to the minus one over. Now get a one. And you would evaluate this from I to 14. So that just means you have to plug in 14 in replacement of you and then minus Have to plug in five in replacement of you. And this gives us one over 14 minus one word. Negative five. Is this nine over 70?

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

Problem

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

Problem 10 Easy Difficulty

Integrate each of the given functions.
$$\int_{1}^{3} \frac{3 x^{3}+8 x^{2}+10 x+2}{x(x+1)^{3}} d x$$

Answer

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Basic Technical Mathematics with Calculus

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

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus