 So initially it looks double over x is t square by t in 1 plus t to the power 2. Are you getting this? So t and t will get there which means 1 plus 1 by t square dt is equal to dk. So it is 2 dk by k square per person. So the answer will be 2 times 1 by root 2 tan inverse k by root 2 k. So the answer is root 2 tan inverse k itself is t minus 1 by t and t itself is root tan x. So root tan x minus 1 by root tan x. You can present an answer in this form also tan inverse tan x minus 1 by root. Next question is integrate xx plus sign to the power 6x since childhood is done. How many pairs of disjoint sets you can make from it? How many pairs of disjoint sets can you make from that set? And that's all it also. Which term? So 1 by minus 3 sin square x plus square x. Let's discuss this. So I will get sin square x cos square x. This term again this will become minus 3 sin square cos square. So far so good. Which is nothing but dx by 1 minus 3 sin square x cos square x. t to the power 4x. 1 plus tan square x. C square square which is 1 plus tan square square. When you substitute tan x as t, then sin square x dx will be observed as 1 plus t square by 1 plus t to the power 2 whole square minus 3 t square. Correct? We become 1 plus t square dt by t to the power 4 minus t square plus 1. Correct? What do you do next? Correct? So you will get 1 plus 1 by t square square minus 1. Then what do you do is 1 by t. So basically 1 plus 1 by t square dt will become dk. So the entire t square plus 1 by x cortex. Yes 1 by tan x can be done as cortex. That means 2. How many pairs of disjoint sets can you make from A? So how many x and y are mutually solute. What is joint? Disjoint. Meaning. What is joint? Okay. Sir, correct. Any choices? Either to go 10 would be the number of pairs you can make. Except for one such case. They are all same. When both all sets. When every other you answer because none intersection null is also null. Yeah. Okay. But I want a pair of two factors. You will say 1 into 36, 2 into 18, 18 into 2, 36 into 1. So if I ask you how many we need this and they got this. Option of the element is not here. It can be. You can have case position and give you two cases. So I subtracted that one case. This case from if I want two factors. 2, 3, 4, 5, 6, 7, 8, 9 minus 1 by 2 plus 1. Because originally they are these 5 ways only. This is just a repetition of this. This is just a repetition of this. This is just a repetition of this. In the same way 3 to the power n is this. Subtract the one. That one.