How do I find the integral of ∫ 1/ [(1-sin(x))(1+sin(x))] with respect to dx

I'm just at home all day rummaging through the review exercises and the failed amount of work my teacher didn't bother to set me, hence why Im asking so many questions because I have noone else to help me

Remember your trig identities and difference of two squares: (1-sin x)(1+sin x) = 1 - sin^2 x = cos^2 x

So you're integrating 1/cos^2 x = sec^2 x.

Do you know how to integrate this?

Oh okay thank you x

You seem to be replying to all my posts like this and ignoring any questions in it that I ask. Do you actually understand what's going on? There's no point in doing all the work unless you actually understand what's happening...

Yes, I do understand what is going on sorry that I am not clarifying. It is just I am doing an immense amount of work whilst replying to these posts and Im trying to get it all done. Im really stressed out because my teacher has failed to set us the amount of work needed and these review exercises are very hard. I spent 8 hours straight doing maths last saturday and I still only manage to get through minimal amount of exercises, sorry I really don't mean to be rude and I really really appreciate your help, thank you so much. x

To amplify Zacken's comment: you've posted a lot of "how do I integrate this?" posts over the last couple of days, and looking at them, there's been a fairly common theme of "you can rearrange this into something you can integrate, if you only put in a little thought".

How long are you spending on these problems before asking for help? And are you familiar with all the trig identities in the formula booklet? Are you actively looking at ways you can use trig identities to simply the things you want to integrate?

I've said before, that one of the reasons people find C4/trig integration hard is because they don't "really" know the trig identities - they can get through a question that explicitly tells them "use a trig identity to...", but when they have an integration problem with sin 2x cos 2x, they don't immediately see "oh, I can reduce that to a single trig function using a double angle identity". It looks like an area you definitely need to work on.

Oh okay, I will spend a little longer looking at it. I do admit sometimes, I just look at it and go OMGG i have no idea, but then other times, I have actually repeated the question 10+ times and I am genuinely really stuck

To repeat Zacken's concerns: I asked 3 questions about how you approach these questions, and you've answered none of them.

How do I approach them? Okay, so if I see a question that I'm unfamiliar with I will rummage through my book to find examples and if I do find examples, I'm like great! and then I apply the example solution to the question. Or, if I find a question hard, I will repeat it 2-7 times until I get the answer right, but after the 7th time I will just cry and leave it. But if I see a question that I'm totally unfamiliar with and there are no examplesin the book I will post it here. I mean, this book has no solutions, so I would ultimately just google the solution to help me and save annoying people online but its this Edexcel GCE essential for maths A2 book which is massive.

I'm not trying to be obnoxious here, but did you actually read the post where I asked the questions?

Because you still haven't answered any of them!

It's not so much "it's frustrating when it feels I'm being ignored" (although it is frustrating), but what I actually find very telling is that even your responses to people's questions about what you're doing show you're not actually thinking about what's being asked, but just rushing off to provide an answer that is actually completely missing the point.

For what it's worth, what you've just said about your approach sounds very messed up. As Zacken said, it looks like your goal is "'solve' as many exercises as possible", which is kind of pointless if you're rushing through them without actually learning anything.

Oh okay, sorry, I will reply to your posts from now on

I would also like to point out that you have officially scared an 18 year old girl from posting questions on the internet 👀👀👀 goodbye !!

I would also like to point out that you have officially scared an 18 year old girl from posting questions on the internet 👀👀👀 goodbye !!