∫(dx)/(1 + tan x) equals:
∫(dx)/(1 + tan x) equals:
- A. x/2 + (1/2)ln|cos x + sin x| + C
- B. x/2 + ln|cos x + sin x| + C
- C. ln|1+tan x| + C
- D. x + ln|cos x + sin x| + C
Answer: A) x/2 + (1/2)ln|cos x + sin x| + C
Explanation: 1/(1+tan x) = cos x/(sin x+cos x) = (1/2)[(sin x+cos x)+(cos x−sin x)]/(sin x+cos x) = 1/2 + (1/2)(cos x−sin x)/(sin x+cos x). Integral = x/2 + (1/2)ln|sin x+cos x| + C.
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