Question

Найдите первообразную функцию для f(x)=48sinx*sin7x

Answer 1

из тригонометрии знаем:
sina * sinb = 1/2 (cos(a - b) - cos(a + b)) =>
sin7x * sinx = 1/2(cos6x - cos8x) =>

48sinx*sin7x = 24(cos6x - cos8x)$intlimits {24(cos6x - cos8x)} , dx = 24intlimits {cos6x - cos8x} , dx = =24 intlimits {cos6x} , dx - 24 intlimits{cos8x} , dx = =24(-sin6x/6 - (-sin8x/8)) = 3sin8x - 4sin6x$