find the most general antiderivative or indefinite integral. ∫(- 10 sec²x) dx
find the most general antiderivative or indefinite integral. ∫(- 10 sec²x) dx
Answer
Explanation:
Step1: Recall integral rule
We know that $\int\sec^{2}x dx=\tan x + C$. Also, by the constant - multiple rule of integration $\int kf(x)dx = k\int f(x)dx$, where $k=- 10$ and $f(x)=\sec^{2}x$.
Step2: Apply the rules
$\int(-10\sec^{2}x)dx=-10\int\sec^{2}x dx$. Since $\int\sec^{2}x dx=\tan x + C$, then $-10\int\sec^{2}x dx=-10\tan x + C$.
Answer:
$-10\tan x + C$