Question

помогите срочно надо очень 3 и 5

Answer 1

3) 

$displaystyle int { frac{dx}{ sqrt{2-x^2}} }= int{ frac{dx}{ sqrt{ frac{1}{2}(1- frac{x^2}{2})}}}= int{ frac{ sqrt{2} dx}{ sqrt{1-( frac{x}{ sqrt{2}})^2}}}= sqrt{2}arccos( frac{x}{ sqrt{2}})+C$

5)

$displaystyle int { frac{2x^3-5x+8}{3x^2}}= int{ frac{2}{3} x}dx- int { frac{5}{3x}} , dx+ int{ frac{8}{3x^2}}, dx =\= frac{2}{3} frac{x^2}{2}- frac{5}{3}ln|x|+ frac{8}{3}( -frac{1}{x})+C= frac{x^2}{3}- frac{5}{3}ln|x|- frac{8}{3x}+C$