coroneos 100 intergrations! (1 Viewer)

[~*MeLy*~]

Hey hey, i was choosing a few of the intergratoins in the 100 set out in the coronious book, and i came across one which i just couldnt do, maybe im not seeing the trick, i dont know

i am geussing its done by parts but ?? i dont know

its number 40. page 180

the inergral of :

(3x+2)dx
------3---
x(x+1)

(in words)
(3x+2)dx all over x times (x+1) to the power of 3

 

[:: ck ::]

this one isnt too tricky - just use substitution and partial fractions

let u = x+1
x = u-1
du=dx

u end up with integral(3u-1) / [ (u-1)(u³) ] du

use partial fractions

u end up with integral (2/(u-1)) + (-2u^2-2u+1)/(u³) du

then u get 2ln|u-1| -2ln|u| + 2/u -1/(2u²) + C

so answer is 2ln|x| -2ln|1+x| + 2/(1+x) - (1/2)(1+x)² + C

 

[George W. Bush]

or just use partial factions straight up..

 

[:: ck ::]

yeh u could do that

using substitution seems nicer for me... i dont like working with messy stuff

 

[George W. Bush]

ehh, i suppose you don't have to write that -1 every line..

 

[:: ck ::]

yeh my writings bad...

since its messy i cant read.. then i get screwed over

 

[redslert]

partial fractions more complicated

subsitution is more straight forward and less mistakes

 

[George W. Bush]

what substitution are you using? im pretty sure you're going to end up using partial.

 

[:: ck ::]

yeh u have to use partial.. no other way u can do it i think

 

[arielbelle]

hey guys, i heard coroneous' 4U books are really useful but don't know which one you are talking about, is it the ext 2 supplement? could somebody post the full name of whatever book they use or like, thanks.

 

[:: ck ::]

i have the old one... its blue and white... typewriting font..

 

[arielbelle]

what's the title of your book ryan? there might be a newly revised edition now. anyone else got any?

 

[:: ck ::]

"Revised 4 Unit Course ... A higher School Certificate ... Course in Mathematics Years 11 and 12"

my frnd gave it to me.. was his sisters old textbook from ages ago...

its really really really old i dont think u can get it at bookstores... u have to buy it directly from the man himself

 

[arielbelle]

what's the title of the book that the 100 integrations come from? the 4u supplement doesn't have that.