Question

integration of [x²(1 - 1/x²)].dx

Answer 1

$\mathbb{I}=\bf{\int{x^2(1-\frac{1}{x^2})}\,dx}$

$=\bf{\int{(x^2 - \frac{x^2}{x^2})}\,dx}$

$=\bf{\int{x^2}\,dx-\int{dx}}$

$=\bf{\frac{x^{2+1}}{2+1}-x+C}$

$=\bf{\frac{x^3}{3}-x+C}$

hence, I = x³/3 - x + C

Answer 2

HELLO DEAR,

given function is∫ x²/(1 - 1/x²).dx

⇒∫(x² - 1).dx

⇒∫x².dx - ∫1.dx

⇒x³/3 - x + c

where, c is arbitrary constant.

HENCE, the integration of x²/(1 - 1/x²) is (x³/3 - x)

I HOPE ITS HELP YOU DEAR,
THANKS