But if you do it by inspection, it takes max 10 seconds, way less risk of making a mistake. For clarity, I do not find brackets challenging, if this is C3, which I think it probably is, inspection should be very doable.

Reply 8

philipd

12

Original post by RDKGames

Seriously guys...?

Just use substitution...

Why bother? Takes way more steps than just inspecting it, its not like its a challenging integration.

Original post by RDKGames

Seriously guys...?

Just use substitution...

I was under the assumption that this was a C1 question (and hence the OP would only know how to integrate term-by-term), but I could be wrong in that assumption.

Original post by philipd

Why bother? Takes way more steps than just inspecting it, its not like its a challenging integration.

Not everyone is good at inspection at A-Level. Susbtitution would be the usual go-to rather than expansion or inspection...

Original post by philipd

But if you do it by inspection, it takes max 10 seconds, way less risk of making a mistake. For clarity, I do not find brackets challenging, if this is C3, which I think it probably is, inspection should be very doable.

As the OP is asking this question, I doubt that it's beyond C1.

Reply 12

Notnek

21

Original post by RDKGames

Not everyone is good at inspection at A-Level. Susbtitution would be the usual go-to rather than expansion or inspection...

I know for Edexcel, most C4 students follow the official textbook and learn the reverse chain rule so are familiar with this process:

\displaystyle \int (ax+b)^n \ dx = \frac{1}{a(n+1)}(ax+b)^{n+1}+c

And the general rule for linear inner functions:

\displaystyle \int f'(ax+b) \ dx = \frac{1}{a}f(ax+b) + c

@Littleonezz Are you a AS or an A2 student?

Reply 13

3121

21

I would just reverse the chain rule…
1) + 1 to the power
2) Differentiate the inside and make it 1/(-----)
3) Then divide it by the power…

So the e.g: (3+5x)^3
1) (3+5x)^4
2) 1/5 (3+5x)^4
3) 1/5 divided by 4 = 1/20 so 1/20(3+5x)^4
4) +c!

But only do this once you're confident with substitution and how the chain rule works, otherwise stick to the chain rule and make your inside term U

Original post by notnek

I know for Edexcel, most C4 students follow the official textbook and learn the reverse chain rule so are familiar with this process:

\displaystyle \int (ax+b)^n \ dx = \frac{1}{a(n+1)}(ax+b)^{n+1}+c

And the general rule for linear inner functions:

\displaystyle \int f'(ax+b) \ dx = \frac{1}{a}f(ax+b) + c

@Littleonezz Are you a AS or an A2 student?

Hm.. for AQA I dont remember this being part of the book.

Also I forgot that they can ask this at AS where expansion would be needed (or binomial formula too) :smile:

(edited 7 years ago)

Reply 15

Notnek

21

Original post by RDKGames

Hm.. for AQA I dont remember this being part of the book.

Also I forgot that they can ask this at AS where expansion would be needed (or binomial formula too) :smile: