Задача 26893 интеграл 1/(5-x^(2/3))...

u8526164121

28.04.2018

интеграл 1/(5-x^(2/3))

SOVA

28.04.2018

∫ dx/(5–x^(2/3))

Замена переменной
x^(2/3)= t^2
x^2=t^6
x=t^3
dx=3t^2dt


∫ dx/(5–x^(2/3)) = ∫ 3t^2dt/(5-t^2)=

=-3 ∫ ((5-t^2)-5)dt/(5-t^2)=

= - 3 ∫ dt+15 ∫ dt/(5-t^2) = - 3t -
- (15/2sqrt(5))ln|(t-sqrt(5))/(t+sqrt(5))| + C, t=∛x