find the most general antiderivative or indefinite integral. ∫(-10 sec²x) dx ∫(-10 sec²x) dx = □

Explanation:

Step1: Recall integral rule

We know that $\int\sec^{2}x dx=\tan x + C$. Also, for a constant $k$, $\int kf(x)dx = k\int f(x)dx$.

Step2: Apply the rules

Here $k=- 10$ and $f(x)=\sec^{2}x$. So $\int(-10\sec^{2}x)dx=-10\int\sec^{2}x dx$. Since $\int\sec^{2}x dx=\tan x + C$, then $-10\int\sec^{2}x dx=-10\tan x + C$.

Answer:

$-10\tan x + C$