AP EAMCET · Maths · Indefinite Integration
If \(\int \frac{\cos 4 x+1}{\cot x-\tan x} d x=k \cos 4 x+c\), then \(k\) is
- A \(-\frac{1}{2}\)
- B \(-\frac{1}{4}\)
- C \(-\frac{1}{8}\)
- D -1
Answer & Solution
Correct Answer
(C) \(-\frac{1}{8}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \int \frac{\cos 4 x+1}{\cot x-\tan x} d x \\ & =\int \frac{2 \cos ^2 2 x}{\cos ^2 x-\sin ^2 x} \times \sin x \cos x d x \\ & =\int \frac{\cos ^2 2 x}{\cos 2 x} \sin 2 x d x=\int \sin 2 x \cos 2 x d x \\ & =\frac{1}{2} \int \sin 4 x d x=-\frac{1}{8} \cos 4 x+c…
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