# Integrate #(1-x)/(1+x)^2#?

##### 2 Answers

#### Explanation:

This is done by using partial fractions.

Let

and comparing coefficients on both sides, we get

Hence,

=

=

Seperate numerators

lets call these terms as,

,

Now we will evaluate

this is a simple integration,

Integration of

now,

as

NOW as per above,

L=

L=

Ahh,L is solved now :)!

Now lets deal with M,

we will solve M with Substitution,

now,lets take

**{Why not x=t???? Because taking x=t will not do any thing good to
M as M will show as #t/(1+t)^2# see nothing happened , so (1+x)=t}**

Now as

(1+x)=t

diffrentiating,

Now,

M=

Seperating denominator as we did initially,

M=

M=(

**Integration of #1/x#=ln(x)**

To integrate M,

M=

M=

M=

Now to write the answer in tems of x

so,1+x=t

M=

Add

L-M

YOu got the answer,