Question

Найдите общий вид первообразной для функции f(x)=(5x-3)^3+3sin(2x-П/6)

Answer 1

$f(x)=(5x-3)^3+3sin(2x-fracpi6);\ F(x)=int{left{(5x-3)^3+3sin(2x-frac{pi}{6})right}}dx=\ =int{(5x-3)^3}dx+3int{sin(2x-fracpi6)}dx=\ =frac{1}{5}int{(5x-3)^3}d(5x-3)dx+frac32int{sin(2x-fracpi6)}d(2x-fracpi6)=\ =frac15cdotfrac{(5x-3)^4}{4}-frac32cdotcos(2x-fracpi6)+C=\ =frac1{20}(5x-3)^4-frac32cos(2x-fracpi6)+C$