Maths C4 - Integration... Help???

I think I used to but I don't anymore sorry. You can always use Wolfram Alpha to check your answers or you could ask here.

@Philip-flop

Thanks so much for that.



@Philip-flop I forgot to say that this is a list of integrals where the method isn't given to you. Since for substitution questions the substitutions will always be given to you in C4, there are no substitution integrals in this list (well none that require substitution).

Thanks so much for that.



@Philip-flop I forgot to say that this is a list of integrals where the method isn't given to you. Since for substitution questions the substitutions will always be given to you in C4, there are no substitution integrals in this list (well none that require substitution).

That awkward moment when your answer to the first integral was worked out by using Substitution I'm having a lot of trouble recognising what type of integration to use

Maybe that $\cos(x^2)$ integral was supposed to be $\cos(\sqrt{x})$?? In which case solving it would require a nice mix of two different methods.

No it was meant to be $\cos(x^2)$ to make sure that students don't try to use some kind of reverse chain rule.

The first one can be done simply by expanding the brackets. Always look for the simplest method first

Oh I see! I never would have known to do that!

There are a few in there that are C1 integrals but they're mixed in with C4 integrals, which is why students often forget the easy methods.

Ok so all of the integrals can be worked out without the need of having to use Substitution? So Integration by Parts is still in there etc?

I ask because I'm thinking of using it on...

$\int 2x(x^2-3)^4 dx$

Ok so all of the integrals can be worked out without the need of having to use Substitution? So Integration by Parts is still in there etc?

I ask because I'm thinking of using it on...

$\int 2x(x^2-3)^4 dx$

This one is much easier than you think. No int by parts needed.
How does the 2x relate to the thing inside the brackets?

You can certainly use substitution, but you can use inspection for that one.

EDIT: I managed to get it but only by looking at the general formula for these types. I would have had to resort to Substitution if I was given this in a real exam!

Oh yeah it's in the format $\int f'(x) [f(x)]^n dx$

But these ones I'm still not use to doing

That's fine, as long as you solve it and don't take up too much time...

When looking at an integral that one there should be the first or second thing you look for. Once you get more familiar with all the methods the easiest way to do integration is looking and seeing if you can do the easiest stuff first. Start with "can I just expand it or something", then this thing:


and so on. You can usually attempt a substitution for most if all else fails, but if you're like me and are a bit at the whole C4 shabang it's generally an awful idea unless the question specifically gives you a substitution to use.

Can someone explain how I'm meant to start this?...
$\int cos(3x-2)sin^2(3x-2) dx$