username1631419
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the bear
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#2
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you can times out the brackets then integrate the terms.
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philipd
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#3
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(Original post by Littleonezz)
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Try adding one to the index and then differentiating them to see where you end up. Adjust them from there.
Sort of by inspection.
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_gcx
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(Original post by Littleonezz)
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Expand (should be a simple task as the exponents are only 2 and 3), and integrate each term. Don't forget the arbitrary constant, C at the end of your antiderivative.

Edit, as others have pointed out, if you're at A2, use the substitution u=3+4x. (I was under the impression this was a C1 question, however I just checked the OPs post history and they seem to be an A2 student)
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philipd
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(Original post by the bear)
you can times out the brackets then integrate the terms.
That's wayyyy harder than needed.
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the bear
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(Original post by philipd)
That's wayyyy harder than needed.
it's only hard if you find brackets challenging.
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RDKGames
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Seriously guys...?


(Original post by Littleonezz)
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Just use substitution...
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philipd
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(Original post by the bear)
it's only hard if you find brackets challenging.
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.
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philipd
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(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.
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_gcx
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(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.
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RDKGames
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(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...
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_gcx
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(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.
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Sir Cumference
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(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?
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3121
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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
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RDKGames
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(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)
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Sir Cumference
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(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)
I'm always a bit uneasy about it being taught before substitution but Edexcel exams often have integrands of the type f(ax+b) so it's useful to be able to integrate them quickly.
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username2769500
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#17
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(Original post by the bear)
you can times out the brackets then integrate the terms.
This. In Edexcel it will tell you when to use the reverse of the chain rule.
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