Question

ПОМОГИТЕ!НАЙДИТЕ ИНТЕГРАЛ!

Answer 1

$int frac{dx}{1-sqrt[3]{2-x}} =[, t=sqrt[3]{2-x},t^3=2-x,; x=2-t^3,; dx=-3t^2dt, ]=\\=int frac{-3t^2, dt}{1-t} =-3int (-t-1+frac{1}{1-t})dt=3frac{t^2}{2}+3t+3int frac{dt}{t-1}=\\=frac{3}{2}t^2+3t+3ln|t-1|+C=\\=frac{3}{2}sqrt[3]{(2-x)^2}+3sqrt[3]{2-x}+3ln|sqrt[3]{2-x}-1|+C$