JEE Mains · Maths · STD 12 - 7.1 indefinite integral
The integral \(\int\left(\frac{x}{x \sin x+\cos x}\right)^{2} d x\) is equal to (where \(C\) is a constant of integration)
- A \(\sec x+\frac{x \tan x}{x \sin x+\cos x}+C\)
- B \(\sec x-\frac{x \tan x}{x \sin x+\cos x}+C\)
- C \(\tan x+\frac{x \sec x}{x \sin x+\cos x}+C\)
- D \(\tan x-\frac{x \sec x}{x \sin x+\cos x}+C\)
Answer & Solution
Correct Answer
(D) \(\tan x-\frac{x \sec x}{x \sin x+\cos x}+C\)
Step-by-step Solution
Detailed explanation
\(\int\left(\frac{x}{x \sin x+\cos x}\right)^{2} d x=\int\left(\frac{x}{\cos x}\right) \cdot \frac{x \cos x d x}{(x \sin x+\cos x)^{2}}\) \(=\frac{x}{\cos x}\left(-\frac{1}{x \sin x+\cos x}\right)\)…
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