Question

Найдите интегралы.
Заранее спасибо

Answer 1

$\ int {x^3over sqrt[3]{2x^4+1}}{mathrm{d}x}=[u=2x^4+1, {mathrm{d}x}={{mathrm{d}u}over8x^3}]={1 over 8}int {{mathrm{d}u}over sqrt[3]{u}}={3over 16}{sqrt[3]{u^2}}+C={3over 16}{sqrt[3]{(2x^4+1)^2}}+C\\ int {x{mathrm{d}x}over sqrt[3]{(3x^2-1)^2}}=[u=3x^2-1, {mathrm{d}x}={{mathrm{d}u}over 6x}]={1over6}int{{mathrm{d}x}oversqrt[3]{u^2}}={1over2}sqrt[3]{u}+C={1over2}sqrt[3]{3x^2-1}+C$