AQA C3 integral

Hi basically I rote learn most formulae in maths and it works for me.

I basically want to ask anyone who does this specification if integrals or differential in these forms EVER come up because I don't really recall ever doing Qs where I've had to apply this?

Should I learn it?

Thanks

Hi basically I rote learn most formulae in maths and it works for me.

I basically want to ask anyone who does this specification if integrals or differential in these forms EVER come up because I don't really recall ever doing Qs where I've had to apply this?

Should I learn it?

Thanks

Hi basically I rote learn most formulae in maths and it works for me.

I basically want to ask anyone who does this specification if integrals or differential in these forms EVER come up because I don't really recall ever doing Qs where I've had to apply this?

Should I learn it?

Thanks

@SeanFM

The second formula given (with the integral of e^f(x)) is false: for example, if you try to find the integral of e^(x^2) using it, you get the answer (e^(x^2))/(2x), but differentiate that back and you find that it doesn't work. In fact, whilst the derivative formula d/dx(e^(f(x))) = f'(x)*e^(f(x)) is always true, by the Chain Rule, the integral one is only true if f(x) is linear, i.e. of the form ax+b where a and b are constants. The idea that the chain rule can universally be used backwards is a common mistake among students; when people refer to the "reverse chain rule", what they really mean is that they are integrating by substitution, but doing the algebra in their head as it's fairly simply, so that they can just write down the result. If in doubt, by the way, always show working rather than trying to be fancy and do it in your head, as you will then be able to get marks for method even if you make a slip, whereas if you just write down a wrong answer with no working, you will score 0 marks.

That's just the chain rule (and reverse chain rule), substituting u=f(x). It definitely comes up in AQA C3 and I imagine it also comes up in every other exam board at A2 as well

I wouldn't bother trying to memorise specific formulas like that, in favour of just memorising the main differentiation/integration tricks

i thought these came up in like every paper o.o

You'd have better luck posting in maths I have asked for this to be moved there.

I'm not sure about AQA, but they come up in Edexcel and A2 integration (C4). If you see the chain rule anywhere (in differentiation) then this is just the reverse chain rule, so if you see one you can probably expect to see the other - but best to consult with past papers!

Do note what the other used has said about the formula in the textbook being incorrect. You haven't seem to have acknowledged that.