What is the intergral of (1/u)(1/(1+u))

[camboguy]

Homework Statement

what is the intergral of (1/u)(1/(1+u))

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

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 I am 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)

 

[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!

 

[lurflurf]

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