evaluate-the-indefinite-integral-int-5t-sin-left5tright-d-t

Question

Evaluate the indefinite integral.
$$\int 5^{t} \sin \left(5^{t}\right) d t$$

Vikash Ranjan · Accepted Answer

Division five hour de sign happened about a duty said Hey, just starting June 30. Ellen, Fire duty equal inducing on. We have DT disease. Well, five for the body. And this equals in division Jalen in The sign did Is it over? June? Ellen, find that deserved there we have a deficient. It is gonna born Ellen. Final condition, Sanjay Disease. It is equally one of home. Kill in fight minus cost you classy disease. And then finally, do God forbid about these. Bless. See, this is down, sir.

Amrita Bhasin · Answer

We know that you knew this fact, T which means that Gene you is five to the tee times natural over five DT. Which means we have won over natural over five times taking the role. You have negative co sign you plus C which plugging end because we don&#x27;t want you. In our final answer, we have a negative co sign property divided by natural over five plus e.

Margaret Keymakh · Answer

five teaching. It&#x27;s all gonna be applying the river&#x27;s Carol ominous indefinite ads. After so by the river&#x27;s car, it&#x27;ll be I want to be exploded. Five. So provide to their you get five t before did I by Ford really on then Similarly here, we&#x27;re gonna add one to be accidents that&#x27;s gonna give us two. Then in second on, let me divide by Negative too. So plus T to the neck and second over, too on B plus c so we can rewrite this. Bring you down? Yeah, five to you before Before what? Over to cheese word? Let&#x27;s see of And this is the final be definite.

Vipender Yadav · Answer

heavy of evaluate the integral due to the power Fife deride by under route t Square place to not ditty. Now here I&#x27;m substituting under route the square blessed to as way. So if our division both aside will get one divide by two under group D squared plus two on Harry Get to be the 12 will cancel out on is equal to the way So we&#x27;re left with G divide by under route D squared less too is equals to delay. No, we could write this in Dragila&#x27;s d squared hold square and the emptying out state. So, Doctor ah t d y under route thescore place to observe carefully. This is nothing but do I system now? We&#x27;re to calculate T Square. Initially, we assume it Underpay square plus two vehicles to buy From here we can say that if I squaring waterside you get t Square plus two equals to white square from her P square would be equals two y squared minus two. Now we conceptual level is here on the integral become Why square minus two Hold square and there is nothing What do you weigh now again? You will read this expression this enough. The function and they tickle becomes Why did a powerful bless four minus four way dot de i And this will be good shoe. Why did the bottom five divided by five plus four way minus hair? It would be wise Square should be there on Dhere, We get vie it forwarded about three divided by a tree. Bless. See where Caesar contravene relation that we have include because the integral is indefinite integral are simply there to plug really off Why? So it will be quilts to why we assumed as under root two square plus two to the power Fife Divide by five plus four Wife is a T square plus two minus four. Why is the school blessed to cube? Divide by three Blessed See So this is the answer for the intruder Due to the far Fife divide by underfoot T square Blessed to not ditty I hope you have the problem. Thank you

Gregory Higby · Answer

right. The theme in this problem is that if you are asked to take a to the T. Power D. T. So the location of your expense important, uh The anti griddle is one divided by the natural log of T. Um times A. To the T. Power. And it&#x27;s just undoing the chamber and you do need to remember plus your constant. So the key in this problem then is to get your problem to look like that uh to the T. One plus five to the T. Power DT. So what we need to do is because there&#x27;s a multiplication right here, we need to distribute that in there before trying anything. And a rule here is that because we have to the T. Power. So there&#x27;s T. Number of twos and there&#x27;s T. Number of fives. That should be the same as two times 52 times five tee times. So it&#x27;s the same thing as 10 to the T. Power. I hope my explanation made sense why that&#x27;s true because now we can just use this rule up here. Uh put a boxer on that, that&#x27;s what we&#x27;re using. Um And it&#x27;s going to be won over natural log of two times, two to the T. Power, plus one over natural log of 10 times 10 to the T. Power. And don&#x27;t forget about plus C. You can verify that this is correct because the derivative of this will get us back to here, which we already know is equal to that, so we have the correct answer.

Linh Vu · Answer

it was to find a indefinite integral armed with a thesis Krampus five day plus one. Did they record down the indefinite integral on the power form. And we could get a table and one on endless one. Plus a constant C is in this formula. And then we get for the first time again included at the poetry over three for the second term, the five we stayed the same. And do you hear the repairman? Wonderful. We have a table too long with you. And for the last one, the constant rich image touched the tea next to it s a constancy here.

Problem

Evaluate the indefinite integral. $$\int \frac{d…

Problem 29 Easy Difficulty

Evaluate the indefinite integral.
$$\int 5^{t} \sin \left(5^{t}\right) d t$$

Answer

$-\cos \left(5^{t}\right) / \ln (5)+C$

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$-\cos \left(5^{t}\right) / \ln (5)+C$

Essential Calculus Early Transcendentals

Anna Marie V.

Heather Z.

Kayleah T.

Samuel H.

Integration Review - Intro

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James StewartEssential Calculus Early Transcendentals

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Kayleah T.

Samuel H.

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