Question

integration of [x³ - x² + x - 1]/(x - 1) . dx

Answer 1

you can see your answer

Answer 2

HELLO DEAR,

the anti derivatives of [x³ - x² + x - 1]/(x - 1) is a function of x whose derivative is [x³ - x² + x - 1]/(x - 1)

now,
$\bold{\int{\frac{x^3 - x^2 + x - 1}{x - 1}}\,dx}$

$\bold{\Rightarrow \int{\frac{x^2(x - 1) + (x - 1)}{x - 1}}\,dx}$

$\bold{\Rightarrow \int{x^2 + 1}\,dx}$

$\bold{\Rightarrow \int{x^2}\,dx + \int{1}\,dx}$

$\bold{\Rightarrow x^3/3 + x + C}$
where, c is the arbitrary constant


HENCE, the Anti derivatives of [x³ - x² + x - 1]/(x - 1) is (x³/3 + x) + C.

I HOPE ITS HELP YOU DEAR,
THANKS