Integrate c4 help

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 :smile:

Scroll to see replies

Reply 1

Notnek

Original post by Econowizard

Hi, please post everything you've tried.

Reply 2

black1blade

Are you sure you wrote out those substitution equations out right?

Reply 3

black1blade

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.

Reply 4

WiseLeo

Original post by Notnek

Hi, please post everything you've tried.

u=e^x, u=2tanv . Sorry my bad its late 😋😁

(edited 6 years ago)

Reply 5

WiseLeo

Original post by black1blade

Are you sure you wrote out those substitution equations out right?

u=tanv and u=e^x sorry my bad

Reply 6

RDKGames

Study Forum Helper

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?

Reply 7

WiseLeo

Original post by Notnek

Hi, please post everything you've tried.

Here. Genuinely dont know what im doing :/

Reply 8

WiseLeo

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 :smile:

(edited 6 years ago)

Reply 9

RDKGames

Study Forum Helper

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.

Reply 10

WiseLeo

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?

Reply 11

RDKGames

Study Forum Helper

Original post by Econowizard

No. You'd end up integrating 1/2.

Also 1/f(x) does not integrate to ln(f(x)/f'(x))

Reply 12

WiseLeo

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 :smile:

Reply 13

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.

Reply 14

WiseLeo

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.

Reply 15

black1blade

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?

Reply 16

WiseLeo

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

Reply 17

black1blade

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.

Reply 18

WiseLeo

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 :smile:

what about you?

Reply 19

black1blade

Original post by Econowizard

Yep . Trying to make life easy :smile:

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.