Question

Find the most general antiderivative f(x) given the function below. f(x)=tan(x)(4cos(x) 8sec(x))

A. f(x) = tan(x) (4cos(x) - 8sec(x)) + C
B. f(x) = tan(x) (4cos(x) + 8sec(x)) + C
C. f(x) = tan(x) (4cos(x) - 8sec(x)) - C
D. f(x) = tan(x) (4cos(x) + 8sec(x)) - C

Answer 1

The most general antiderivative of the given function is f(x) = -ln|cos(x)|(4sin(x) - 8sec(x)) + C. So, the correct answer is A. f(x) = tan(x)(4cos(x) - 8sec(x)) + C.

Step-by-step explanation:

To find the most general antiderivative of the function f(x) = tan(x)(4cos(x) - 8sec(x)), we can use the formula for the integral of a product of functions. The antiderivative of tan(x) is -ln|cos(x)| and the antiderivative of cos(x) is sin(x). Therefore, the antiderivative of the product is:

f(x) = -ln|cos(x)|(4sin(x) - 8sec(x)) + C

So, the correct answer is A. f(x) = tan(x)(4cos(x) - 8sec(x)) + C.