# Q13  Find the following integrals intergration of  $\int \frac{x^3 - x^2 + x -1 }{x-1 } dx$

D Divya Prakash Singh

Given integral $\int \frac{x^3 - x^2 + x -1 }{x-1 } dx$

It can be written as

$= \int \frac{x^2(x-1)+(x+1)}{(x-1)} dx$

Taking $(x-1)$ common out

$= \int \frac{(x-1)(x^2+1)}{(x-1)} dx$

Now, cancelling out the term $(x-1)$ from both numerator and denominator.

$= \int (x^2+1)dx$

Splitting the terms inside the brackets

$=\int x^2dx + \int 1dx$

$= \frac{x^3}{3}+x+c$

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