Question

Помогите пожалуйста решить интегралы

Answer 1

Объяснение:

1) -4cosx + C

2) (sin(7x+3))/7 +C

3) -2cosx - 3sinx + C

4) (sin(5x-1))/5 + C

Вспомним формулы:

∫sin x dx = -cosx

∫cos x dx = sinx

$\displaystyle1) \int4 \sin x \: dx = 4 \int \sin x \: dx = - 4 \cos x + C$

$\displaystyle 2) \int \cos(7x + 3) \: dx = \bigg[d(7x + 3) = 7 \: dx \bigg] = \\ \\ = \frac{1}{7} \int \cos(7x + 3) \: d(7x + 3) = \frac{ \sin(7x + 3)}{7} + C$

$\displaystyle 3) \int(2 \sin x - 3 \cos x) \: dx = 2 \int \sin x \: dx - \\\\ - 3 \int \cos x \: dx = - 2 \cos x - 3 \sin x + C$

$\displaystyle 4) \int \cos(5x - 1) \: dx = \bigg [ d(5x - 1) = 5 \: dx\bigg] = \\ \\ = \frac{1}{5} \int \cos(5x - 1) \: d(5x - 1) = \frac{ \sin(5x - 1)}{5} + C$