integrate-each-of-the-given-expressions-intleftx7-3-x5right-d-x-2

Question

Integrate each of the given expressions.
$$\int\left(x^{7}-3 x^{5}\right) d x$$

Dwijendra Rao · Accepted Answer

elephants. We have to integrate this given expression integration age Actually power 7- off three extra departed five and D. X. Okay so we can write it X to the power seven minus of three. After the Power 70 x- of three actually about five dx. So this will be cause to extradite about seven plus one upon seven plus one minus of three X to devour five plus one upon five plus one. This is 20 years and of extra depart five. This question to see. Okay so X to the power eight upon eight minus of three upon six X. To the Power six. Let&#x27;s see. So this will be cause to actually power eight upon it minus after the public sex upon to let&#x27;s constraints see so this is that okay answer. Yeah I hope you understood. Thank

Aishwarya Krishnakumar · Answer

problem if I were asked to solve this Negro and too soft This we&#x27;re going to use U substitution and substitute the thing that&#x27;s inside the parentheses. In this case, we would look you equal seven X plus five and then we take the derivative off both sides. So do you Clothes the derivative of the side would just be seven d x. So next we just have to substitute the you into our initial in a girl. So we have 28 over you to the five. And this is because of our U substitution times. Do you, However, do you is seven d x? We only have a DX here. And because of that, we have to include a seven No weaken, take out the Constance. So if you simplify this, we get four. And since fourth, the constant you can take it out. And by that I mean that it has no you. Since we&#x27;re differentiating, it would respect to you, it would be one over you to the fifth power, do you? And now we just take the integral of this. So this is this is basically you to the negative fifth. So it&#x27;s the same thing, and that makes it easier because we just add one as usual. So you to the minus four in the times won over minus four. Don&#x27;t forget the pussy since you&#x27;re integrating. And if you simplify it, these to cancel out it would be negative won over you to the four. I&#x27;m just moving it to the denominator plus c. And whenever you have these type of problems, you cannot leave the answer with a U. So you have to plug in. You&#x27;re U substitution back into the equation. To get the final answer, it would be negative one over seven x plus five to the fourth power plus C.

Kathryn Novak · Answer

Okay, So we&#x27;re going to use our property that the in a row from A to B plus the inner roll from Fetus E. It&#x27;s gonna equal in a row from A to Z. So what we&#x27;re given is the interval from 7 to 3, plus the integral of three at night and all of these air of f of x, the X and just not rewriting that. So if you notice in our property you have ah upper bound to be here and you have the lower bound feet. Those numbers are the same. They&#x27;re the same here in the way we have everything set up. So we&#x27;re going to be left with an inner roll from 7 to 9 of the vets the ex

Matt Just · Answer

the area of the definite in a girl. Negative. Two two three of the function Negative. X squared minus three X plus five. The ex. Okay, so we need first and anti derivative of dysfunction. So that should be negative. X cubed over three minus three. How&#x27;s X squared? Plus five x And then evaluate this from negatives too. Two, three. Okay. And so we get negative. Twenty seven over three Witches like you didn&#x27;t know. Minus three halves. Time&#x27;s nines and minus seven over too. Plus fifteen and then minus. I mean a plug in negative, too. So that&#x27;s going to give us now, say negative negatives. That&#x27;s plus eight over three minus. Uh, this will be for so they don&#x27;t just make that six and then minus can. Okay, so minus nine plus fifteen is going to give us. So negative. Nine plus fifteen, six minus twenty seven over to. And then over here. Minus six minus ten. That&#x27;s minus sixteen. Minus negative. Sixteen plus eight thirds. Okay. And sixes. Twelve over Tuesday. Twelve minus twenty seven is nineteen, fifteen over, too. And then minus two sixteen is forty eight over three. So this is kind of mean minus forty over three. Okay, We got to get a common denominators. Negative system over two plus forty over three is the same thing is negative. Forty five out, plus Eddie Oliver six, which is thirty five over six.

Xiaomeng Zhang · Answer

So does one dressy clothes who mine us into you grow off axe choir three times into grow off axe, you know? So the constant. So we can say for integral Rothwax choir, that is X two hour Alstory over three. And for acts that as AC Squire over to and for those constant that is five comes axe. So that&#x27;s why we can see E co two Costa Rica powerhouse Ray that as 20 Simon So nine minus run a tooth of power off Serie that US eight. So plasters 8/3. Then this 13 times return power to ni over two and also through the power of to so miners to in for adults worry L C. Five times three minus minus. True, that lost to So for the 1st 1 That&#x27;s one he chose whose trio that is 27 last a So that is 35/3 friends for those one of three times five over True. So that is 15/2. Yeah, And for those one, we can&#x27;t see, fraud comes fried. That is 25 So calculated. Now we can see in their sakes and thus woman 70 And this one is minus 45 and that&#x27;s one this plus but one from T. So those one dress Eco&#x27;s who 35/6?

Aishwarya Krishnakumar · Answer

for problem 19 were out to u substitution to find this indefinite integral. So we&#x27;re gonna let you equal the denominator. U equals X to the four plus for X squared plus seven. Now we take the derivative of both sides, maybe four x cubed eight. Thanks D x, and you can simplify this by taking out a two X. Actually, you could take it a four x my bad B X squared close to detox and then you can divide both sides by four. It would be do you over four equals x times X squared clothes two times d x So now as you can see this, if you foil it, this would be right a year x cubed plus two x, which is the same thing as a the numerator of the original equation. So that makes it easy when we rewrite this interval. So it beat the integral of won over you because of this. And instead of the three X, we would have do you over four and you can move the constant the front would be won over four, which was the constant and then the integral of you to the negative first power and in a girl of one of her you is out and of the absolute value off you. And don&#x27;t forget the plus C, and you cannot have a you in the answer. So we&#x27;re gonna plug in this You So, Helen, uh, next to the floor waas four x squared plus seven post C and this is the answer.

Problem

Integrate each of the given expressions. $$\int(3…

Problem 13 Easy Difficulty

Integrate each of the given expressions.
$$\int\left(x^{7}-3 x^{5}\right) d x$$

Answer

$\frac{1}{8} x^{8}-\frac{1}{2} x^{6}+C$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Grace H.

Kayleah T.

Caleb E.

Samuel H.

Precalculus Review - Intro

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$\frac{1}{8} x^{8}-\frac{1}{2} x^{6}+C$

Basic Technical Mathematics with Calculus

Grace H.

Kayleah T.

Caleb E.

Samuel H.

Precalculus Review - Intro

Functions on the Real Line - Overview

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

Grace H.

Kayleah T.

Caleb E.

Samuel H.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus