Question

Нужно написать концовку

Answer 1

$int frac{sqrt{x^2-4}}{x^3} dx=[, x=frac{2}{cost},; dx=frac{2sint}{cos^2t}dt,; x^2-4=frac{4}{cos^2t}-4=4tg^2t,\\cost=frac{2}{x}; ,; t=arccosfrac{2}{x}, ]=int frac{sqrt{4tg^2t}}{frac{8}{cos^3t}}cdot frac{2sint}{cos^2t}dt=int frac{2frac{sint}{cost}cdot 2sint}{frac{8}{cost}} dt=\\=frac{1}{2}int sin^2t, dt=frac{1}{2}int frac{1}{2}(1-cos2t)dt=frac{1}{4}(t-frac{1}{2}sin2t)+C=\\=frac{1}{4}(arccos frac{2}{x}-frac{1}{2}sin(2arccosfrac{2}{x}))+C=$

$=frac{1}{4}arccosfrac{2}{x}-frac{1}{8}cdot frac{4}{x}sqrt{x^2-4}+C$