Question

How do you solve this question?

Answer 1

Answer:

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

Step-by-step explanation:

Hello,

for any real x different from 1

$\dfrac{3-2x}{1-x}=\dfrac{2-2x+1}{1-x}\\\\=\dfrac{2(1-x)+1}{1-x}\\\\=2\dfrac{1-x}{1-x}+\dfrac{1}{1-x}\\\\=2+\dfrac{1}{1-x}$

if f(x)=2x

   f'(x)=2

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

   $g'(x)=\dfrac{-1*-1}{1-x}=\dfrac{1}{1-x}$

So antiderivative of

$\dfrac{3-2x}{1-x}=2+\dfrac{1}{1-x}$

Is

2x-ln(1-x)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you