find-antiderivatives-of-the-given-functions-fx12-x56-x-3

Question

Find antiderivatives of the given functions.
$$f(x)=12 x^{5}+6 x$$

Tyler Moulton · Accepted Answer

we want to find the anti derivative of the function of X is equal to £12 extra, fifth plus six X. This is testing our knowledge of anti differentiation as a precursor to the topic of integration as such. We need to be able to solve so remember that the anti derivative is just the inverse derivative. So if we understand derivative rules such as rules one through three here, we should understand how to take an anti eroded for this problem. Fx We only need to use the power rule since the power rule states are derivative that G D X X is a is a, the X ray of the minus one. It holds that the anti derivative actually A is by the inverse one over a plus one times actually a plus one. Thus we can solve. So the anti capital F X is 12 times 16 X six plus six times one half X squared. This is using one over a plus one times actually a plus one on each term individually. Thus we obtain final solution. Anti derivative capital fx is to actually six plus three X squared

Linh Vu · Answer

it is quitting were given a function f thanks. They go ju six X minus five. And did you find the entire derivative camp toe f X For the first time here, we use a formal off other power expert and the accidentally go to the expert and this one over amorous on the aggressive constancy their fund for the constant six. We&#x27;re staying the same except will be expanding one. Therefore, expect you on with you. Put a constant 500 units touched the X next to it and at the end of get your blazer constancy in which only if I get ego. June 3 Banks grab minus five x plus C. Now what? You&#x27;ll find a value. See here we know none. The answer. It could you five. When the observing Nico everything it touches there also eager to five. Therefore, eventually we get the F X in with equal June the three x graham and his five angst. That&#x27;s five

Linh Vu · Answer

in this question. We&#x27;re leaving the function f X go you 68 about three thanks. And we need to find the untidy reviewing a function and accounts down six to stay the same for this one. We know that they were trying to able three x River Day. We get included age about three ANC&#x27;s on but a general win it two times three this number three reading 12 different. We wanted everything by one out of three. No phone we have entirely rebuilt the most in Could you one of the three times? Table three. Thanks. Let&#x27;s see. It was even if I get included a Jew. Eva three experts see And to find out value, say here, you know after their own echo to five and everyone is doing some unit two plus C now for the same in CO. 203 and the and weeks again that untimely ripped UMA Zenkoji that you able three x plus three

Vikash Ranjan · Answer

think of intensities effects because, well, you tomorrow X minus five x to the part off minus school. And I&#x27;ve been that everything off a fence this is integration. Off affects DX egos. In addition, off 12 in bar X minus five x to the power of minus two, dear, this is equal Do 12 about off X minus five. My last one. It&#x27;s the power off minus one plus c. This is equal. Do well, you know Bart off X plus five upon x last. See, this is the answer.

Amrita Bhasin · Answer

The first thing we know is that we can break up the integral so pulling out, too, because it&#x27;s a constant we have two Integral of Axe Jackson pulling out the sex because it&#x27;s a constant co sign. Axe DX The supplies to two x squared, divided by two with six sign x Plus e, which simplifies to simply X squared plus six sign x plus e Now, this point me no see is a constant. You know, the half of pious pi squared plus two. So given this weaken set pi squared plus two equals pi squared plus six sign pie plus C Giving us C equals pi squared plus two minus pi squared So pious cripples two mice Passport Just to cause the pie Sports cancel out So our final equation after vax equals X squared plus six sine x plus two

Linh Vu · Answer

in this question. Where did you find the anti derivative? Off the X plus X pound, Five plus expo minus five T x. Yeah, we didn&#x27;t do one by one. Now follow first ex hand antennae reviewing the X equal to the X going on with, you know, for the next one for the Expo five, which would get equal to the X power six, almost six. And the last one here began it. We could, you know, plus on now. Ex power minus far off, minus four. Plus a constant. See there the way we can do this under being were blind of formula if you have an experiment and and then it will find anti nearly of them. The expert and the they were Eagle Jundallah X Well, and this one over and rest one Presser, constancy.

Problem

Find antiderivatives of the given functions. $$f(…

Problem 16 Easy Difficulty

Find antiderivatives of the given functions.
$$f(x)=12 x^{5}+6 x$$

Answer

$F(x)=2 x^{6}+3 x^{2}$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Anna Marie V.

Heather Z.

Kayleah T.

Caleb E.

Precalculus Review - Intro

Functions on the Real Line - Overview

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$F(x)=2 x^{6}+3 x^{2}$

Basic Technical Mathematics with Calculus

Anna Marie V.

Heather Z.

Kayleah T.

Caleb E.

Precalculus Review - Intro

Functions on the Real Line - Overview

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

Anna Marie V.

Heather Z.

Kayleah T.

Caleb E.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus