∫(1 + tan x)/(1 − tan x) dx equals:
∫(1 + tan x)/(1 − tan x) dx equals:
- A. −ln|cos x − sin x| + C
- B. ln|sec x| + C
- C. ln|cos x + sin x| + C
- D. tan(x + π/4) + C
Answer: A) −ln|cos x − sin x| + C
Explanation: (1+tan x)/(1−tan x) = tan(x + π/4). But also note that it can be written as (cos x + sin x)/(cos x − sin x). Numerator is derivative of negative denominator. Integral = −ln|cos x − sin x| + C.
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