Question

(4) $\int (-3\sin x - \cos x)dx$

Explanation:

Step1: Use integral sum - difference rule

$$\int(-3\sin x-\cos x)dx=\int(-3\sin x)dx-\int\cos xdx$$

Step2: Use integral constant - multiple rule

$$\int(-3\sin x)dx-\int\cos xdx=- 3\int\sin xdx-\int\cos xdx$$

Step3: Use basic integral formulas

Recall that $\int\sin xdx=-\cos x + C_1$ and $\int\cos xdx=\sin x + C_2$.
So, $-3\int\sin xdx-\int\cos xdx=-3(-\cos x)-\sin x + C$.

Answer:

$3\cos x-\sin x + C$