Question

Неопределенный интеграл

Answer 1

1

$\Large \displaystyle \int {(2x - 3)^7} \, dx = \frac{1}{2} \int {(2x - 3)^7} \, d(2x - 3) = \frac{(2x - 3)^8}{16} + C$

2

$\Large \displaystyle \int {e^{7x}} \, dx = \frac{1}{7}\int {e^{7x}} \, d(7x) = \frac{e^{7x}}{7} + C$

3

$\Large \displaystyle \int {\sin x \cos^6 x} \, dx = -\int {\cos^6 x} \, d(\cos x) = -\frac{\cos^7 x}{7} + C$