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Evaluate 4e IntegrolXz dx -3ki...

Question

Evaluate 4e IntegrolXz dx -3ki

Evaluate 4e Integrol Xz dx -3ki



Answers

Find value. $XZ$

So let's evaluate this integral again. There are radicals in the denominator. The denominator has radicals for truth. Five par Sorry expire five before on export three by four But the denominators are four and four. So it's five by four and three by four. So what is the Elysium Off denominators? It's for only So our substitution. The par four is suitable. So when existing power for what will be expired five by four it's deep are four whole power five before it is deep our fight and what will be expired three by four It's deep. Are four whole party before it is too cute. And what is the X? Dx is four p cubed et So our integral becomes So I call this is I. So it will be integration of DX, which is 40 Cube. Did he divided by its power five a four. A power file minus four times expired three way for which is take you. But if you can observe, I can take take you comin So it is four times integration off DT divided by I mean I'm canceling take you so basically take you divided by take you been to t square minus four. This is what I get a break in cancer take you so it is deeply divided by the square minus four. Okay, interestingly, I'll keep for inside. Only so four d d. Divided by what is three square minus four. It's the minus two into deep list, too. Now see the magic. What will I do is the new burrito four. I'll write something like this. D plus two minus off T minus two. Is it for Off goes? Yes, because he gets canceled and to minus off minus two is four. But why? Why I'm writing like this. I can split this into two parts. So it is Indication off people is too divided by D minus two in tow. T plus two minus. D minus two. Divided by T minus two into t plus two d d. This is what I get. I can cancel d plus two here. I can cancel t minus two here, so I'll get two simple integrates d d by T minus two minus integration off DT by deep list, too. Now what is integration off? D D by D minus toe. Ln more T minus two And what is integration of one by T plus two. Is Ellen more deepest? Took by standard indications. But what's your tea if xsd par for what is your D for two topics? So let's substitute So the finance it will be a lot more food. Truth affects minus two minus Ellen More for truth off X plus two and we should I the constant off integration see?

The question is immigration off due to the power off minus four upon five minus Get to the power off to a born three plus jaded about off five upon food Indu deejay This gives us due to the power off one upon five This is one here and find here Mine as due to the ballot off five upon three So five here on DDE See here Blast did about off nine by full So nine year and for you last series constant off integration This equals do fine due to the power off one of on five minus three a bun five Digital power off five A bone three class for a bon Sonny This is for a bomb Nile jaded a power off nine by four plus See this system and so but

So we got eat to the three minus four x dx here. So let's start using substitution. So you is three minus four x and do you over DX his minus four. So do you. Over Negative four is equal to DX. So moving on from there, Or get in a girl of e to the u times do you over Negative for this means we can just factor out negatives for so that's minus 1/4 into girl a fee to the you Do you integral off each of the U is just going to be e to the U So this will become minus 1/4 he to the u plus c. However, we're not done. We need to plug in three minus four X into you. So this becomes 1/4 each of the three minus four x plus c negative here and this is your final answer.

7.1 Problem number 10 We need to integrate e to the three monies for X dx. One of the key things here is just that that e to the three. That's just a constant. So it may help to just think of this is this is e cubed e to the minus four x dx OK, e cubed is just the constant. So this is e cubed times an integral e to the minus for X dx And how do I integrate this? This is going to be e cubed and then e to the minus four extra integrated to get e to the minus four x but you have to divide by negative four plus a constant of integration. So this is just negative 1/4 e cube you to the minus four x plus a constant. Or you could put this back together and just rewrite it as negative 1/4 e to the three minus for X plus constant of integration. Either those is the equivalent answer


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