Решите \(\int{\sqrt[8]{1-2x^5}x^4dx}\)

Решение

\(\int{\sqrt[8]{1-2x^5}x^4dx}=[t=1-2x^5]=\int{-\frac{1}{10} \cdot \sqrt[8]{t}dt}=-\frac{1}{10}\int{\sqrt[8]{t}dt}=-\frac{1}{10} \cdot \frac{8t\sqrt[8]{t}}{9}=-\frac{1}{10} \cdot \frac{8(1-2x^5)\sqrt[8]{1-2x^5}}{9}=-\frac{4(1-2x^5)^{\frac{9}{8}}}{45}\)+С

Ответ: \(-\frac{4(1-2x^5)^{\frac{9}{8}}}{45}\)+С.