Answer to Question #171678 in Calculus for Mandy

Question #171678

Evaluate:

  1. &Integral 3 (x2 -4x + 4x – 2) dx
1
Expert's answer
2021-03-16T08:44:11-0400

(x²4x+4x2)dx=(x²4x+4x²)dx=x² dx4x dx+41x² dx=x³34(x²2)+4(1x)+c=\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 =


13x32x24x1+c\dfrac{1}3 x^3 - 2x^2 - 4x^{-1}+c

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