 Sine to the power of 6x, sine square x cos square x. Now apart from this, anybody? Sine square x plus equation of cos square x minus x cos square x. Okay, first of all, numerator 1 by AB minus 3. So, this is A cubed plus B. Is this understood so far? Cos x squared. Are we aware of it? What is it? What is the answer? 2 sine x plus x plus c. 2 sine x plus x plus c. So, ultimately you are integrating 2 cos x plus 1 integration with 2 sine x plus x. This is proven by the limit of Sine square x minus Sine square x minus Sine square x. So, second one, heart and soul of integration. Almost 70 to 80 percent of the problem. Now why do we use substitution in solving integration problem? Because we don't have enough rules. So, we mostly have functions. We need to use some substitutions in order to, except for here and there are some, but if a part of a function is running in terms of that variable, we don't have integration of times. But I don't get to the name of, which is minus sine into dt, which means sine x into dx, which implies you can substitute not, right? Minus as i mod x. So, in a similar way, times integral 1 by t dt will be minus 1 ln mod t plus c. Now, you can't because t is something which you introduce into the problem. So, replace it back by n cos x inverse plus c, which is ln mod ckx. So, this is a very small example, correct? So, please, I think the other way. In a similar way, that means cos x will be, which implies, so this entire x will become sin x plus c. Now, when ckx, there will be some problem because ckx requires a special treatment. So, in case of ckx, what do we do? You would get the del, do you see that? So, this facilitates us to substitute ckx plus tan x times, you get ckx tan x plus c square x is dt by dx. Take the dx on the left, would be dt and this term would, you must be thinking every time, which is ln ckx plus tan x mod plus c. Now, many times in the answer at the back of the book, you would realize that some different function is given in the answer. For example, it is just that they have simplified identities to write ckx plus tan x as tan x by 2 plus y by 4. I will quickly show you how it comes. So, ckx plus tan x, you can write it as sin square x by 2. One of them will get tan square minus y, 1 plus tan x by 2 by 1. This is clearly the formula of tan. So, you have to bring it to that form, which the option is demanding from you. In case of body exams, multiple answers of ckx minus tan x plus ckx plus tan x. Do I need to tell you, in a similar way, in a very similar title integrate for ckx. And before that, please append your point integral of c. This one, see, into ckx minus tan. So, you will also ckx minus tan x. So, this term I can write one by this. So, this was ln of ckx plus tan x. Again, coincidentally, kx minus cot x. The answer written is ln and can also be minus ln for ckx plus cot x, as what Aditi told. This is also a formula. You can go see, but now we have x times x plus x. It would have become nearly impossible to solve that problem. We must test the steps, specific types of integrals, which will only come through practice, plus ckx. So, put back your x and this is your answer. And still, I used to come across as a requirement. It will happen with another type. Let's give you an example of xsx. Put it towards xsx. Minus ln, you can write it as 1. Minus 2. Yeah, you can write it as 1. Then I will simplify to this. 1 minus t squared, minus 2 minus t squared, minus 1 minus... This problem can be 87. So, such a simple example...