937 (2) dlfg jali tan X dx = tan(2x)Select one:O1 X- cot x + C 2b 1 X= cot( Zx) + € 2C. 1 X - tan X+c 2d_ 1 X 2 tan(2 x)+ c...

$\int[1 /(\tan x+\cot x+\sec x+\operatorname{cosec} x)] d x=\ldots$ (a) $(1 / 2)(\cos x-\sin x)+(x / 2)$ (b) $(1 / 2)(\sin x-\cos x)-(x / 2)$ (c) $(1 / 2)(\sin x+\cos x)+(x / 2)$ (d) $(1 / 2)(\sin x-\cos x)-(x / 2)$

So section six dot too Looking at problem number 73 it's a multiple choice, but you really can't do the multiple choice until you figure out what the answer to this integral is. Um so let's just take a look and ah, and work through this. So the integral change it x t x. Okay, So in order to do this, I need to see something that's like a a function and it's derivative. One of the keys here is when you see tangent. If I could write this as a sign of X over the coastline of axe, then I see what I'm looking for. I see a function and it's derivative. So if I could let you equal the co sign of X, then d'you is equal to minus do you, as you go to minus sign of X dx so I could rewrite this original derivative as what minus sign of x d. X over co sign of X, Put a negative in front of that. And so now what we have is negative the integral of one over you, do you, which is negative log of natural lateral log of the absolute value view plus a constant of integration. Okay. Use it with a co sign. XO, this is minus natural log co. Sign of X plus, a constant of integration. Okay. And then if you look at your choices that come up with this is choice D in your list of Walter Choices, okay?

We have our number 39. What we need to enter occurred. Uh Science codex cause correctly X. We have to find the value. So let us right, this is 11 as science. We're explorers cause Parex by science called explorers because corrects DX. So if you separate it out it will be science Quebec's by science square X caused quite ex place caused quite ex by science squad X. And cause square X and Dx. So this is science correct. Science camps will get cancelled out and caused the accident causes quarterbacks will get cancelled out. So what you say is one by cost Kerekes. That is six square X. Dx place because sick quite ex deal the integration of sake expert X. Is always 10 X and minus casillas cortex cortex leslie. So they should be the answer. Option number B is the correct one. Thank you.

Yeah.

Hi I'm gonna solve this. So what we can do here beyond one over to see annex plus three cortex. Hold it was a joint number two nanometer by all spirits. So we get it as uh seconds correct? Be it or we have whether we do 10 x plus three Falls directly integrate this substitution here you know equals two 10 X plus three or beyond except equals B. He here he was just did it was too you can correct. Did so yes we have Got here now it's going to be uh get 1/2. So secret strategy I can be DP or we have The spear was coming out to be 1/2 times. Here's the 1 82 +12 plus one will be negative 1/2. Then these do 10 x plus three plastic the on board here so negative one over to the next dose please. Option C. Thank you.