Question

интеграл (sin x/5 sin π/10 - cos x/5 cos π/10) dx​
интеграл (1-2cos²3x) dx

Answer 1

Ответ:

$1)\ \ \int \Big(sin\dfrac{x}{5}\cdot sin\dfrac{\pi}{10}-cos\dfrac{x}{5}\cdot cos\dfrac{\pi}{10}\Big)\, dx=-\int cos\Big(\dfrac{x}{5}+\dfrac{\pi}{10}\Big)\, dx=\\\\\\=-5\cdot sin\Big(\dfrac{x}{5}+\dfrac{\pi}{10}\Big)+C\\\\\\2)\ \ \int (1-2cos^23x)\, dx=-\int cos6x\, dx=-\dfrac{1}{6}\cdot sin6x+C\\\\\\\star \ \ cos(\alpha +\beta )=cos\alpha \cdot cos\beta -sin\alpha \cdot sin\beta \ \ \star \\\\\star \ \ cos2\alpha =2cos^22\alpha -1\ \ \star$