Найти неопределенный интеграл:∫( 2/(√x)+5x√x-4∛x)dx ∫〖(x^2-3)/(2(1+x^2)) dx〗

Question

Найти неопределенный интеграл:

∫( 2/(√x)+5x√x-4∛x)dx

∫〖(x^2-3)/(2(1+x^2)) dx〗

Answer 1

1) Int (2x^(-1/2) + 5x^(3/2) - 4x^(1/3)) dx =
= 2x^(1/2)/(1/2) + 5x^(5/2)/(5/2) - 4x^(4/3)/(4/3) + C = 4√x + 2x^2*√x - 3x*∛x + C
2) Int (x^2 - 3)/(2(1+x^2)) dx = 1/2*Int x^2/(1+x^2) dx - 3/2*Int 1/(1+x^2) dx =
= 1/2*Int (1+x^2-1)/(1+x^2) dx - 3/2*arctg x = 1/2*Int (1 - 1/(1+x^2)) dx - 3/2*arctg x =
= 1/2*(x - arctg x) - 3/2*arctg x + C = x/2 - 2arctg x + C