Question

How do you solve this question?

Answer 1

`\large \boxed{\sf \ \ \ 2x-ln(1-x) \ \ \ }`

Explanation:

Hello,

for any real x different from 1

`(3-2x)/(1-x)=(2-2x+1)/(1-x)\\\\=(2(1-x)+1)/(1-x)\\\\=2(1-x)/(1-x)+(1)/(1-x)\\\\=2+(1)/(1-x)`

if f(x)=2x

f'(x)=2

if g(x)=-ln(1-x)

`g'(x)=(-1*-1)/(1-x)=(1)/(1-x)`

So antiderivative of

`(3-2x)/(1-x)=2+(1)/(1-x)`

Is

2x-ln(1-x)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you