Question

Первообразные функции f(x). F(x)=3tgx F(x)=5ctgx F(x)=3/cos в квадрате x F(x)=-5/sin в квадрате x

Answer 1

                         f(x) = F'(x)

F(x)=3tgx                                f(x) = 3/cos²x

F(x)=5ctgx                              f(x) = -5/sin²x

F(x)=3/cos²x = 3·(cosx)²         f(x) = 3·(-2)·(cosx)⁻³·(-sinx) = 6sinx/cos³x

F(x)=-5/sin²x  = -5·(sinx)⁻²      f(x) = -5·(-2)·(sinx)⁻³·cosx = 10cosx/sin³x