Intergral help

1. Dec 8, 2008

camboguy

1. The problem statement, all variables and given/known data
what is the intergral of (1/u)(1/(1+u))

its more complicated but i did u du sub to make it more viewable.

3. The attempt at a solution

kinda stuck but i think i get the idea.
i have to take the anti derivative of (1/u) then the anti derivative of (1/(1+u)) and then multiply them.. i think.. i know the anti derivative of (1/u) but what is the anti derivative of (1/(1+u)) iv been looking every where my book, online, nothing except something about partial diffraction. final tomorrow.. and im kinda stuck on this part.

the full problem is find the intergral of dx/ [([squroot(1+squrootX)] * [squroot(1+squroot(1+squrootX))]]
i did u du for (1+squrootX)

Last edited: Dec 8, 2008
2. Dec 8, 2008

Pere Callahan

$$\frac{1}{u(1+u)}=\frac{1}{u}-\frac{1}{1+u}$$
then do the integral term by term. yes, this is called partial fraction decomposition. And be aware, the anti-derivative of a product is NOT the product of the anti-derivatives of each factor!!

3. Dec 8, 2008

lurflurf

(1/u)(1/(1+u))=1/[u(1+u)]=[(1+u)-u]/[u(1+u)]=1/u-1/(1+u)