5

Point)dx VSx+CSee Example 1 page 400 for a similar problem....

Question

Point)dx VSx+CSee Example 1 page 400 for a similar problem.

point) dx VSx +C See Example 1 page 400 for a similar problem.



Answers

Use the shortcut formulas (see page 970 and Exercises 49-52) to calculate the given integral. $$ \int(x-1)^{-1} d x $$

In this question it is us to integrate a function that is one divided by five X -1. So you can see that first of all it can be written as in what? So five X -1. Now we apply the shortcut formula and the formula is integration of n words of X plus B is given by one by island Modelers X. Let's be Now in this formula we put the value of the N. B. is five in our question BA -1. So put this values here So you can see that we get here five X -1 inward Its integration and that is one divided by five Land Modelers five X -1 Plus C. So this is dance that we got here, that is one bite fight. I learned models five X -1. Let's see. Okay thank you.

In this fusion that given integral is that is integral you to deport eggs sack of it to deport X. Dx. So this integral is given. And now in the community is saying that we have to solve this human integral. So let's start answering this fusion so far so fast. I will apply a method that is called substitution method. So according to this method I will assume that each of the power X. Is equal to you. Mhm. Sure. After taking differentiation on both sides, it will be written as that is need to dip our X. D. X. Is equal to D. You. No I'm giving numbering to both the steps. So I can say that this is a step number one and this is a step number two. Now next step is by using this step number one and number two the given integral will be written as that is integral to the power X. Sack of it. To the poor X. Dx is equal to. Yeah integral into the port X. And dx will be replaced by the U. By step number two. And sec into the power shake off to the power X. Will be written is by using the shape number one. I can see that sack you. No next step is we have to take integration of sec you about you. So we know the result will be written as after taking integration. The result is that there is Ellen. Ellen off absolute value of thank you plus 10. You sorry? Yes can you then plus C. So Mhm did she say he's old which get after taking integration of sake you about you? No next step is replace the you by using the state number one. So I can say that it will be written as that is given integral that is integral to the politics back into the power, sick of it into the body X. Will be equal to Internet studies. Ellen off Ellen absolute value of sec. You will be witness. That is by using Step number one. I can say that U. Is equal to E. To the power X. So it means here I will write sick of it to deport X. Plus. Then you will be witnessed by using Eastern number one. I can see the turn off into the vortex, then plus C. So this is the answer for given integral. Thank you.

In this question. It is us to integrate a function with the help of shortcut formula. And that function is forest to the power minus two X. So I'm going to write the formula of shortcut. And that formula is integration of serious to the power X plus B is given by one by a L. And more. Let's see serious to the power exp let's be let's Mhm. The daily kos turned here Now I am going to put the values of c. That is four, here is -2 and B is zero. After substituting these values, we can see here get four leads to the power minus two X plus zero. Its integration That is one x -2. I learned over four and four raised to the power minus two X plus zero plus C. Now you can see that further. It can also be written as porters to be about minus two X. Divided by minus two into Ireland four. Let's see. So this is the final answer of this question here. Okay, thank you.

First we use that non division, So x squared over X -1. Your calls max square miners, X Plus X -1. Plus one Over acts -1 and the SD cole's acts plus while Plus one over acts wearing as well. So the integral vehicles tax plus one class while over parents miners what? And we need to find it's the anti derivative, a half X squared plus tax. And for this term it's anti directives. Just log The Absolute Value of X -1. And then we should add a council member.


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