You are Here: Home >< Maths

# integration watch

1. i dont understand this method to work out ∫x/x^2+1

solution: 1/2 ∫ 2x/ x^2+1 dx = 1/2 In|x^2 + 1| + c.

Do I need to know this method for AQA C3 or should I just use integration by substitution.

In addition, can someone help me prove ∫cot x = In|sin x| + c
2. (Original post by man111111)
i dont understand this method to work out ∫x/x^2+1

solution: 1/2 ∫ 2x/ x^2+1 dx = 1/2 In|x^2 + 1| + c.

Do I need to know this method for AQA C3 or should I just use integration by substitution.

In addition, can someone help me prove ∫cot x = In|sin x| + c
Yes substitution is fine but you need to know what to substitute because you might not be given it for a question like this.

Do do it their way, consider the derivative of . This is

This means that

So then if you adjust the constant you end up with

3. (Original post by man111111)
i dont understand this method to work out ∫x/x^2+1

solution: 1/2 ∫ 2x/ x^2+1 dx = 1/2 In|x^2 + 1| + c.

Do I need to know this method for AQA C3 or should I just use integration by substitution.

In addition, can someone help me prove ∫cot x = In|sin x| + c
It is a handy trick to know, but not a ‘must’ for C3.
All they did was mult the numerator by 2 and place a half outside (this does not change the integral since 2 and 1/2 would cancel) and the 2x on the numerator is precisely the derivative of the denominator hence you can just interate straight to natural log as shown.

For cot, note that cot=cos/sin where the numerator is the derivative of the denominator. Hence natural log
4. (Original post by RDKGames)
It is a handy trick to know, but not a ‘must’ for C3.
All they did was mult the numerator by 2 and place a half outside (this does not change the integral since 2 and 1/2 would cancel) and the 2x on the numerator is precisely the derivative of the denominator hence you can just interate straight to natural log as shown.

For cot, note that cot=cos/sin where the numerator is the derivative of the denominator. Hence natural log
ok thank you
5. (Original post by Notnek)
Yes substitution is fine but you need to know what to substitute because you might not be given it for a question like this.

Do do it their way, consider the derivative of . This is

This means that

So then if you adjust the constant you end up with

thanks

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: March 1, 2018
Today on TSR

### He lied about his age

Thought he was 19... really he's 14

### University open days

Wed, 25 Jul '18
2. University of Buckingham
Wed, 25 Jul '18
3. Bournemouth University
Wed, 1 Aug '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams