C4 integration.....help!

Hi,
This may be a simple question but I just can't understand it.

I'm trying to integrate 2x/(1+x)

The answer is apparently 2 - 2/(1+x)

Please could someone tell me how would you get this and what rule would you use etc

Thank you in advance!

Hi,
This may be a simple question but I just can't understand it.

I'm trying to integrate 2x/(1+x)

The answer is apparently 2 - 2/(1+x)

Please could someone tell me how would you get this and what rule would you use etc

Thank you in advance!

Can't you do this by substitution, using the same order rule?

You can use long division to split your fraction into $A + \dfrac{B}{1+x}$

A much neater approach is to rewrite the numerator as $2x = 2x+2-2 = 2(1+x)-2$ hence you have $\dfrac{2(1+x)-2}{1+x}$ which you can split into two fractions and hence obtain the answer.


Furthermore, that is not the answer for integrating it. That there is simply long division applied. It still needs to be integrated.

The second way @RDKGames explained is beautiful. But I'm not sure if you'd get the full method marks in the exam

It's valid algebra so there's no reason why marks wouldn't be awarded. Exams will never favour one method over another as long as they are all mathematically valid.

Yeah, I understand that. But, I used that method too lol (for a different module) and my teacher just destroyed me. But, it was for partial fractions rather than an integration question involving the need to split into partial fractions. It was worth 3 marks and I done it using that method in like one line and I got 1 mark lmao.

What teachers do is very different to what is/isn't allowed in an exam. Teachers often get set in their ways and don't like methods that they're not used to even though they are valid and maybe even quicker. Teachers that do this are poor teachers in my opinion unless they have a valid reason for rejecting a certain method e.g. because it's slower.

The worst example I've seen of this is a teacher giving a student 12% in a C1 coordinate geometry test because they didn't use the y-y1=m(x-x1) formula even though all their answers were correct, which was better than every other student in the class. The student lost all their confidence because of this test and I was not happy (an understatement).

The worst example I've seen of this is a teacher giving a student 12% in a C1 coordinate geometry test because they didn't use the y-y1=m(x-x1) formula even though all their answers were correct, which was better than every other student in the class. The student lost all their confidence because of this test and I was not happy (an understatement).

That's crazy! A lot of my students prefer to use y = mx + c whenyou've found the gradient as you are just translating the line up or down to go through the specific point you're given - in many ways this shows greater understanding than just blindly using 'that formula'.

Yes I'm also fine with either method.

I could see the teacher's reasoning for wanting all of the students to follow the same method but giving the best student in the class 12% was ridiculous and irresponsible. The parents immediate response was to come down very hard on the student, especially since this was at one of the best schools in the country. In the end the student just thought it was easier to never go against the teacher's methods to avoid it happening again.

blindly applying a technique is not what mathematics is about imho.

Yeah, I understand that. But, I used that method too lol (for a different module) and my teacher just destroyed me. But, it was for partial fractions rather than an integration question involving the need to split into partial fractions. It was worth 3 marks and I done it using that method in like one line and I got 1 mark lmao.