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Okay and dot Okay and from this one we will take -5. No problem because we have to make it x minus a.
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Okay, so three common factor and it will be X plus five by three. Okay, so integration we are taking from left hand side, so it will be two X plus nine in the numerator divided by we will take three. So we will eliminate this three and this minus five. Okay, so in the standard form there is coefficient of x is one and here is also one. Okay, so we will Right this integrated into the standard form. Okay, we have to write this integration into the standard form and we have to find out the value of concerns that are A, B, C and D. And in the form integration of C X plus D, divided by x minus A and x minus B. Okay And discussion what is given that given is integration of two X plus nine divided by three X plus five. So it's going to be 14 last night over to, right, so it's going to be 17. Right? So it's gonna be so this one this one and this one canceled Hell's This one is four plus 2, 14. And Mina tell plus, so four plus six is 10 and then minus 9/4. So it's gonna be 9/4 Last night over 4, 9 over to plus 16. Right? So uh so after simplification then you will get the final answer and the final answer is uh yeah so it's a bunch of calculation. And do you do the same thing for the neck integral? So you get this minus negative three over to all of that's where minus three times negative 3/2. Right? So it's negative four square last three times negative four. And then you minus and because minus with a minus sign is a blast. Right? You're fucking And what you've got is negative three over to all of that square minus three times negative 3/2. Sorry About it from negative for 2 -1.5 plus the inter row of So this is gonna be at square last three X deep out from negative 3/2 22. And now we just need to integrate these it's going to be and so this is negative X squared plus three X -3. So it's gonna be negative oh two X plus three and this is two X plus three. Right? So from here less than negative 3/2. And then you need you just need to fill in the blank for the negative park. So in the second section is from -3 over 222. And now you divide this into roll into two sections. So that means speaker than negative 3/2 and then equal to negative of two, experts three whenever acts strictly less than negative 3/2. Equal to two experts three whenever to act plus three is positive. Um What is it? So you divide it by? So first I need to remind you the formula for absolute value, absolute value of two X plus three. And so it's going to be two blasts form with just six right Now for the 2nd 1 we need to in the rate from negative to negative 4 to 2 of the asshole value of two X. Right? So it is 4 -16 and then plus three times 6 is 18. First we need to simplify it and now it's going to be two square minus negative for all the best square and then plus three times two minus of negative four. So it's going to be X square from two negative four. The 2nd 1 is three Time ex about it from 2 2 -4. Right? So for the first term it's going to be two times X squared over two. And then you plus three you put it outside of the intro is gonna be negative three. First you need to compute the interview of two time X. This question covers topics relating to integration. Thus are integral evaluates to A X plus B over two X squared plus C over three X cubed plus D. The anti derivative is by the power on each term X plus B over two X squared plus C over three X cubed. So our first thing to do is to find capital Fx for A plus B. And our integration formula to account for any such costing. It arises because of the inverse formula Foundation. Remember that capital Fx is the anti derivative of lower case F X. To better understand this formula in order to utilize it to solve this problem. In order to solve, we must have that indefinite integration. This question is challenging our understanding of the topics of anti differentiation and integration. In this problem, we wish to find the indefinite integral.