Задача 48471 ...

sova

2020-04-27 10:23:35

★

так как (1-x^5)`=-5x^4dx, то

d(1-x^5)=-5x^4dx, значит

[m] \int ^{1}_{0} \frac{x^4}{\sqrt[3]{1-x^5}}dx=

-\frac{1}{5}\int ^{1}_{0} \frac{(-5x^4)}{\sqrt[3]{1-x^5}}dx=-\frac{1}{5}\int ^{1}_{0}(1-x^5)^{-\frac{1}{3}} d(1-x^5)=[/m]

формула ∫ u^( α )du

[m]=\frac{(1-x^5)^{-\frac{1}{3}+1}}{-\frac{1}{3}+1}|^{1}_{0}=[/m]

[m]=\frac{3}{2}(1-x^5)^{\frac{2}{3}}|^{1}_{0}=0-\frac{3}{2}=-1,5[/m]