Question

integration of x - 1/x​

Answer 1

Answer:

x=1

x=-1..…

................

Answer 2

Answer:

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Step-by-step explanation:

∫x/(1−x)dx

Now solving:

I=-∫x/(x−1)dx

Substitute u=x−1 ⟶ dx=du

I=-∫((u+1)/u)du

Expand:

=∫((1/u)+1)du

Apply linearity:

=∫(1/u)du+∫1du

Now solving:

I’=∫(1/u)du

This is a standard integral:

I'=ln(u)+C'

Now solving:

I''=∫1du

Apply constant rule:

I''=u+C''

Plug in solved integrals:

∫1udu+∫1du

I=-(ln(u)+u+C'+C'')

Undo substitution u=x−1:

I=-(x+ln(x−1)−1+C)

Here C=C'+C''

I=−x−ln(x−1)+1

The problem is solved.

I=−x−ln(|x−1|)+1+C

Rewrite/simplify:

I=−x−ln(|x−1|)+C

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