c4 help

so ive been looking at exam solutions videos and he doesnt explain much about integration by recognition.

i was wondering if for the c4 edexcel exam you need to know integration by recognition (in the c4 spec i havent seen anything to do with integration by recognition)

I was stuck on a question which is in the book which wanted me to integrate secxtanx, I tried using by parts but couldnt do it.

Hi. You will be expected to spot a standard derivative, hence to be able to integrate it.

Here, d/dx (sec x) = secxtanx, so integrating secxtanx gives secx.

I'd recommend strongly the learning/familiarization of the derivatives so that even if they are disguised, you can still spot them, e.g integrate 10tanxsecx.

There is another trick you can do here...

secxtanx
=(1/cosx) x (sinx/cosx)
=sinx / cos²x
=sinx(cosx)^-2

This can be made to fit the pattern f'(x)[f(x)]ⁿ by writing as -(-sinx(cosx)^-2, the derivative of cosx being -sinx. Integrating this gives f(x)ⁿ⁺¹.

Applying this to sinx(cosx)^-2 gives (cosx)^-1, which is secx