Integrate c4 help

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WiseLeo
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#1
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#1
Going in yr 13 trying to learn c3/c4 in advance. Stuck on c4 chpt 2 a bit help on this qs would be appreciated.

Find the integral of 1/(e^x+4e^(-x)) usong sub x=e^x and v=2tanv

Thanks in advance
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Notnek
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#2
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(Original post by Econowizard)
Going in yr 13 trying to learn c3/c4 in advance. Stuck on c4 chpt 2 a bit help on this qs would be appreciated.

Find the integral of 1/(e^x+4e^(-x)) usong sub x=e^x and v=2tanv

Thanks in advance
Hi, please post everything you've tried.
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black1blade
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Are you sure you wrote out those substitution equations out right?
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black1blade
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Yeah it's meant to be u=e^x then u=2tanv. You do the first substitution and then the second one and it works out quite nicely.
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WiseLeo
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#5
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(Original post by Notnek)
Hi, please post everything you've tried.
u=e^x, u=2tanv . Sorry my bad its late 😋😁
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WiseLeo
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#6
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(Original post by black1blade)
Are you sure you wrote out those substitution equations out right?
u=tanv and u=e^x sorry my bad
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RDKGames
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(Original post by Econowizard)
u=e^x, u=2tanv . Sorry my bad its late 😋😁
Okay, so basically just let e^x=2\tan(v). Also note that the inside of the integral is the same as \frac{e^x}{(e^{x})^2+4}.

What's the issue?
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WiseLeo
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(Original post by Notnek)
Hi, please post everything you've tried.
Here. Genuinely dont know what im doing :/
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WiseLeo
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#9
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(Original post by RDKGames)
Okay, so basically just let e^x=2\tan(v). Also note that the inside of the integral is the same as \frac{e^x}{(e^{x})^2+4}.

What's the issue?
The issues is ive never done these types of questions before and i genuinely have no clue how to go about doing it *to clarify thos isnt homework im doing this to get a headstart on the year im not looking just for the answer i have wolfram for that*
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RDKGames
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#10
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(Original post by Econowizard)

Here. Genuinely dont know what im doing :/
It's fine up until you decide to do integration by parts for some reason. So at \displaystyle \int \frac{1}{u^2+4} .du use u=2\tan(v) substitution and see where that gets you.
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WiseLeo
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#11
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(Original post by RDKGames)
It's fine up until you decide to do integration by parts for some reason. So at \displaystyle \int \frac{1}{u^2+4} .du use u=2\tan(v) substitution and see where that gets you.
Thank you its getting late so cant finish rivht now but after subbing u=2tanv would i integrate using property integrate 1/f (x) =lnf (x)/f'(x), get a solution sub u back in for v amd x back in for u?
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RDKGames
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(Original post by Econowizard)
Thank you its getting late so cant finish rivht now but after subbing u=2tanv would i integrate using property integrate 1/f (x) =lnf (x)/f'(x), get a solution sub u back in for v amd x back in for u?
No. You'd end up integrating 1/2.

Also 1/f(x) does not integrate to ln(f(x)/f'(x))
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WiseLeo
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(Original post by RDKGames)
No. You'd end up integrating 1/2.

Also 1/f(x) does not integrate to ln(f(x)/f'(x))
Oh wait a second i think i got it! Thank you very much. Talking with you helped me click
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black1blade
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#14
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You're gonna breeze thru next year and find it so boring if you have an at all good memory of what you are doing atm.
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WiseLeo
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(Original post by black1blade)
You're gonna breeze thru next year and find it so boring if you have an at all good memory of what you are doing atm.
Thats the aim. Although i highly doubt ill breeze through further maths.
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black1blade
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(Original post by Econowizard)
Thats the aim. Although i highly doubt ill breeze through further maths.
So which modules did you do this year and which ones next?
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WiseLeo
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#17
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(Original post by black1blade)
So which modules did you do this year and which ones next?
Im going into yr 13. Ive just done fp1,m1 ,d1,c1,c2,s1. This year i do c3 c4 s2 m2 fp2 fp3
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black1blade
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(Original post by Econowizard)
Im going into yr 13. Ive just done fp1,m1 ,d1,c1,c2,s1. This year i do c3 c4 s2 m2 fp2 fp3
Getting ahead on c3 and 4 is probably a good idea then because you need c1-4 and fp1 for fp2 and 3.
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WiseLeo
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(Original post by black1blade)
Getting ahead on c3 and 4 is probably a good idea then because you need c1-4 and fp1 for fp2 and 3.
Yep . Trying to make life easy what about you?
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black1blade
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(Original post by Econowizard)
Yep . Trying to make life easy what about you?
I did c1-2 and s1 in year 11 then c3-4 and m1 this year. Doing fp1-3, m2,s2,d1 next year. I've gotta say that I like the way my school has arranged it but it's only possible if you get put in fast track based on year 8 in year 9 which is a bit of a flaw in the system. I definitely think doing maths then further maths is ideal but understand it's not possible for some places because timetabling.
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