Задача 35935 dx/3x^(2)-5...

vk173500291

2019-04-16 18:28:06

dx/3x^(2)-5

sova

2019-04-16 18:56:48

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Табличный интеграл

∫ dx/(x^2-a^2)=(1/(2a))ln|(x-a)/(x+a)|+C


3x^2-5=3*(x^2-(5/3))

∫ dx/(3x^2-5)=(1/3)∫ dx/(x^2-(5/3))=

=a^2=5/3; a=sqrt(5/3)=

=(1/(2sqrt(5/3)))ln|(x-sqrt(5/3))/(x+sqrt(5/3))|+C=

=(sqrt(3)/2sqrt(5))ln|(sqrt(3)x-sqrt(5))/(sqrt(3)x+sqrt(5))|+C