COMEDK · Maths · 28. Indefinite Integration
If \(\int \dfrac{1}{\sqrt{\sin ^3 x \cos x}} d x=\dfrac{k}{\sqrt{\tan x}}+c\) then the value of \(k\) is
- A \(-2\)
- B \(-1\)
- C 1
- D 2
Answer & Solution
Correct Answer
(A) \(-2\)
Step-by-step Solution
Detailed explanation
Let \(I = \int \dfrac{1}{\sqrt{\sin^{3} x \cos x}} dx\). Rewrite the integrand as \(I = \int \dfrac{1}{\sqrt{\sin^{2} x \cdot \sin x \cos x}} dx = \int \dfrac{1}{\sin x \sqrt{\sin x \cos x}} dx\). Divide the numerator and denominator by \(\cos^{2} x\) inside the square root or…
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