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# C4 help: Integrate 2sec^2xtanx

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1. Doing C4 trig, any idea how you would you integrate this? Thanks!
2. use the identity sin^2x+cos^2x=1 to find an expression for sec^2x, tan^2x and 1, substitute in for sec^2x
3. (Original post by alevelstresss)
use the identity sin^2x+cos^2x=1 to find an expression for sec^2x, tan^2x and 1, substitute in for sec^2x
Thanks
So you get 2(1+tan^2x) tanx?
Then 2+ 2tan^2x tanx??

Is this right, if so where from there?
4. i would make it 2sec^2x + 2sec^tanx and then integrate seperately
5. (Original post by delta-T)
Doing C4 trig, any idea how you would you integrate this? Thanks!
Alternative, much simpler method - think about what the derivative of tanx is and how that is relevant.
6. The answer is (Tanx)^2 + c
7. yeah it is actually just tan^2x, as its where you have f(x)f'(x)
8. Consider derivative of (tanx)^2 .
9. (Original post by alevelstresss)
yeah it is actually just tan^2x, as its where you have f(x)f'(x)
(Original post by Rafoleeno)
The answer is (Tanx)^2 + c

Apparently it's sec^2x??
10. (Original post by delta-T)

Apparently it's sec^2x??
crap yeah sorry my heads messed up

its because with sec^2x you differentiate as 2secx times the derivative of sec x which is sec x tan x

so d(sec^2x)/dx is 2secxsecxtanx or 2sec^2xtanx

sorry haha
11. (Original post by alevelstresss)
crap yeah sorry my heads messed up

its because with sec^2x you differentiate as 2secx times the derivative of sec x which is sec x tan x

so d(sec^2x)/dx is 2secxsecxtanx or 2sec^2xtanx

sorry haha
Can it not be tans^2x though? If not why not?
12. (Original post by delta-T)
Doing C4 trig, any idea how you would you integrate this? Thanks!
Set u=tanx and use integration by substitution. This comes up a lot in FP3 papers
13. (Original post by bartbarrow)
Set u=tanx and use integration by substitution. This comes up a lot in FP3 papers
At FP3 level you should really be doing a question like this by recognition.

C4 students should too but some aren't taught it well so have to resort to substitution.
14. (Original post by notnek)
At FP3 level you should really be doing a question like this by recognition.

C4 students should too but some aren't taught it well so have to resort to substitution.
Yes, I sat my FP3 paper about a month ago and you start to recognise them so you can do it by inspection, but if you aren't at that point yet one of the best ways to prove it is to use a substitution.
15. (Original post by alevelstresss)
crap yeah sorry my heads messed up

its because with sec^2x you differentiate as 2secx times the derivative of sec x which is sec x tan x

so d(sec^2x)/dx is 2secxsecxtanx or 2sec^2xtanx

sorry haha
Ok I get that, but how would you know that if you didn't know he answer was sec^2x?
That's what I don't get
16. (Original post by Rafoleeno)
Can it not be tans^2x though? If not why not?
It can be tan^2 x. Differentiating it: Bring the two down then differential of tan= sec^2 x therefore it will be 2tanxsec^2x
17. (Original post by Ventsi21)
It can be tan^2 x. Differentiating it: Bring the two down then differential of tan= sec^2 x therefore it will be 2tanxsec^2x
But why is the answer sec^2x even though it's tan^2x=sec^2x
18. (Original post by Rafoleeno)
But why is the answer sec^2x even though it's tan^2x=sec^2x
No idea
19. (Original post by Ventsi21)
No idea
(Original post by Rafoleeno)
But why is the answer sec^2x even though it's tan^2x=sec^2x
I've been wondering this myself, and think that it could be that you take '1' from the c term in tan^2x + c to give tan^2x + 1 + b (some other constant) which gives sec^2x + b and for whatever reason, this is more useful but...
20. (Original post by delta-T)

Apparently it's sec^2x??
Either sec^2(x) or tan^2(x) would be correct here, as SeanFM has explained.

Constants of integration are not needed when using integration by parts so either is fine.

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