Question

СРОЧНО НУЖНА ПОМОЩЬ!

Answer 1

$int frac{10-2x}{sqrt{3x+1}-4}dx =[, t^2=3x+1,; x=frac{1}{3}(t^2-1),; dx=frac{2t}{3}dt,t=sqrt{3x+1}]=\\=int frac{10-frac{2}{3}t^2+frac{2}{3}}{t-4} cdot frac{2t}{3}, dt=frac{2}{3}cdot int frac{ (frac{32}{3}-frac{2}{3} t^2 )cdot t}{t-4} dt= -frac{2}{3} cdot frac{2}{3} cdot int frac{(t^2-16)cdot t}{t-4} dt=\\=-frac{4}{9}cdot int frac{(t-4)(t+4)t}{t-4} dt=- frac{4}{9} int (t^2+4t)dt= -frac{4}{9} cdot ( frac{t^3}{3}+4cdot frac{t^2}{2} )+C=$

$=- frac{4}{9}cdot (frac{sqrt{(3x+1)^3}}{3} +2sqr(3x+1))+C=- frac{4}{9} cdot (frac{1}{3}cdot sqrt{(3x+1)^3}+6x+2)+C$