integrate-each-function-by-using-the-table-in-appendix-d-int-frac3-x-d-x25-x-2

Question

Integrate each function by using the table in Appendix $D$.
$$\int \frac{3 x d x}{2+5 x}$$

Vipender Yadav · Accepted Answer

So here on this problem here to evaluate an indefinite Androgel which is integration three X. B X Divide by two Plus 5 x. And to evaluate this integral we have to use the formula which is given in the appendix D. Now this integration can also be written us this three I can take outside the integration because it&#x27;s a constant. So integration three empting outside ex d. Ex Divide by two Plus 5 x. Now if you compare it with the formula which is integration you do you divide by A plus B. U. So it is equal to one over B square pains, A plus B. U minus a natural log A plus B. Now if you compare this one with this formula we can say that here you is equal to X And do you is equals two DX And is equal to two And B is equal to five. So the this is the answer for this integration would be This tree would remain as it is. So three integration X dx divide by two Plus 5 Fix. So it would be called to three as it is divide will be square. So be we have a five so it would be 25 times A. We have to Plus B. We have five. So five you we have ex plus A is to natural log two Plus 5 x plus C. Where C is the concept of integration because it will come because it&#x27;s an indefinite integral. So this is a required answer for the given problem. I hope you have understood the problem. Thank you.

Amy Jiang · Answer

Okay, so we plug our phone integral into our calculator. We see that to be a silver for 15. A loan of actually value of X over three X minus five and in, plus seat.

Andrija Isakov · Answer

we&#x27;ll be finding the integral of 10 to the power of five up. Three X Using an integration to so in the integration table, we should be able to find a formula with 10 to the power of and oh, a ton sex and our formula is one over a time zone minus one 10 to the power of and minus one of X minus the integral of 10 to the power of and minus two of the X dear, that&#x27;s the formula. And so as a next step, we can simplify. Simplify this part That&#x27;s one of 12 and this is an integral we confined in our integration table. 10 to the power of three of three x are tens of power of three of ex like a constant times X. That formula is 1/2 turns the constant 10 squared of yeah, in their constant terms there wolf 1/3 of the natural longer than of the absolute value of coastline of our constant, which is a three in this case, has X. And of course we want to add a constant of integration. Therefore, when we simplify, this gives us what could be a final answer 1 12 10 to the power of 43 x minus 16 10 square t three x minus 1/3 loan of absolute value of coast of three X plus the constant of integration. You can also rewrite 10 in terms of C can&#x27;t and coast. You can write us coast of, uh, seeking to the power of negative one and take up the exponents negative one, since this is a longer of them. But this is also this could also be a final form.

Andrija Isakov · Answer

and this question will be finding the value of this integral using an integration table. The only for males will be needing are this one for the integral of one over some quadratic function and this one which is the integral of X over some quadratic function. Okay, so let&#x27;s ah right this out so that we can use the formula. If we call Q of X X squared plus two exposed to being Mr Nominator here, then our integral is the integral of X over Q of explosives three times the integral of one over Cuba. And since Q of X is a quadratic function, we can use these to integral formulas. Okay, so now let&#x27;s proceed. So our X over q x in the integral becomes by this formula 1/2 long of the quadratic function. Let us be over to a the integral of one over a quadratic function here, the same quadratic function as before. So that is our formula there. And also we remember to add the 3/3 times the integral of one over Q x. So this is what our expression becomes and notice these two are like terms so that we can add them to get to the integral of one over Q X and notice also, since we have to use ah, absolute values for this natural lager of them, or the Q X to make sure that the argument of the longer them is positive if we look more closely, our particular quadratic function experts was to expose to is always positive, so we actually don&#x27;t need to use the absolute value. Barnes. It&#x27;s just long of q X And now let&#x27;s simplify this using our first formula. So if we take a close look to the formula, we would find. Or we should find that this part evaluates to two over the square root of eight minus four are kind of two explodes to over the exact same value as here. See, these two are the same, so no would just be, too. And then, with Thea Constant of integration added onto the end, let&#x27;s see. So what is that? What is the final expression? Sorry, I made a mistake here. There was a type of this to should also be multiplied in there so that we get 1/2 long of experiments to expose to plus two arc. 10 of experts. One, we&#x27;ll see the constant took integration. That is the value this integral here

Linh Vu · Answer

the question We called a formula for the power. You have it into form the expert and the act. Don&#x27;t get me, could you, expert? And this one over. And this one plus c. And now in the question we&#x27;ve given in to go on the five x plus geometry X about five g x. You noticed them? We can register a on the ground. Here is the five X Plus 2/3 and then expert minus five the X and it&#x27;ll continue to pound one. And by the associative launder in the girl, we can get the constant outside and we can distribute in the code to the X the X plus Georgia three in the car on the Expo minus five X. And from here for the first term here, we should get X square on with ju for this one. You got Eagle June the X power with this one to the power of a rebound minus far on the minus. Far blesses. See, it wasn&#x27;t if I&#x27;m gonna go to find out of Joe X square, then minus one out of six expel for Let&#x27;s see, Just needs to the answer

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.

Problem

Integrate each function by using the table in App…

Problem 9 Easy Difficulty

Integrate each function by using the table in Appendix $D$.
$$\int \frac{3 x d x}{2+5 x}$$

Answer

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Basic Technical Mathematics with Calculus