JEE Mains · Maths · STD 12 - 7.1 indefinite integral
If \(\int {\frac{{dx}}{{{{\cos }^3}\,x\sqrt {2\,\sin \,2x} }} = {{(\tan \,\,x)}^A} + C{{(\tan \,\,x)}^B} + k,} \) where \(k\) is a constant of integration, then \(A+ B + C\) equals
- A \(\frac {16}{5}\)
- B \(\frac {27}{10}\)
- C \(\frac {7}{10}\)
- D \(\frac {21}{5}\)
Answer & Solution
Correct Answer
(A) \(\frac {16}{5}\)
Step-by-step Solution
Detailed explanation
\(\int \frac{d x}{\cos ^{3} x \sqrt{4 \sin x \cos x}}\) \(=\int \frac{d x}{2 \cos ^{4} x \sqrt{\tan x}}\) \({\rm{ Let }}\tan x = {t^2}\) \( \Rightarrow {\sec ^2}x = 1 + {t^4}\) \(\sec ^{2} x d x=2 t d t\) \( = \int {\frac{{{{\sec }^4}xdx}}{{2\sqrt {\tan x} }}} \)…
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