Question

Evaluate:

1. &Integral ³ (x² -4x + 4x ^{– 2}) dx

Answer 1

$\int(x² - 4x + 4x^{-2}) dx =\\ \int(x² -4x + \dfrac{4}{x²}) dx = \\ \int x²\ dx - 4\int x \ dx+4 \int \dfrac{1}{x²}\ dx =\\ \dfrac{x³}3 - 4(\dfrac{x²}2) + 4(-\dfrac1x)+c =$

$\dfrac{1}3 x^3 - 2x^2 - 4x^{-1}+c$