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AP EAMCET · Maths · Indefinite Integration

If \(\int \frac{3}{2 \cos ^3 x \sqrt{2 \sin 2 x}} d x=\frac{3}{2}(\tan x)^B+\frac{1}{10}(\tan x)^A+c\) then \(\mathrm{A}=\)

  1. A \(\frac{1}{2}\)
  2. B \(1\)
  3. C \(5\)
  4. D \(\frac{5}{2}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{5}{2}\)

Step-by-step Solution

Detailed explanation

\(\frac{3}{2 \cos ^3 x \sqrt{2 \sin 2 x}}=\frac{3}{2 \cos ^3 x \sqrt{\frac{4 \tan x}{1+\tan ^2 x}}}\) \(I=\int \frac{3 \sec ^4 x}{4 \sqrt{\tan x}} d x=\int \frac{3}{4} \frac{\left(1+\tan ^2 x\right)}{\sqrt{\tan x}} \sec ^2 x d x\)…