Задача 32129 ...

mnuzhnaya

2018-12-19 14:01:00

∫ x^(4) / x^(2) - 1 dx

sova

2018-12-19 14:03:51

★

∫ x^4dx /( x^2 – 1)=∫ (x^4-1+1)dx /( x^2 – 1)=

=∫ (x^4-1)dx /( x^2 – 1)+ ∫ (1dx /( x^2 – 1))=

= ∫ (x^2+1)dx)+ ∫ (1dx /( x^2 – 1))=

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