find the most general antiderivative or indefinite integral. ∫(6 sec x tan x - 5 sec²x) dx

Explanation:

Step1: Use integral sum - difference rule

$\int(6\sec x\tan x - 5\sec^{2}x)dx=\int6\sec x\tan xdx-\int5\sec^{2}x dx$

Step2: Use constant - multiple rule of integration

$=6\int\sec x\tan xdx - 5\int\sec^{2}x dx$

Step3: Recall antiderivative formulas

We know that $\int\sec x\tan xdx=\sec x + C_1$ and $\int\sec^{2}x dx=\tan x + C_2$. So, $6\int\sec x\tan xdx - 5\int\sec^{2}x dx=6\sec x-5\tan x + C$ (where $C = 6C_1-5C_2$ is an arbitrary constant)

Answer:

$6\sec x - 5\tan x+C$