AP EAMCET · Maths · Indefinite Integration
\(\int \frac{\cos x+x \sin x}{x(x+\cos x)} d x=\)
- A \(\log \left|x^2+x \cos x\right|+c\)
- B \(\log \left|\frac{x}{x+\cos x}\right|+c\)
- C \(\log \left|\frac{\cos x}{x+\cos x}\right|+c\)
- D \(\log \left|\frac{1}{x+\cos x}\right|-\log x+c\)
Answer & Solution
Correct Answer
(B) \(\log \left|\frac{x}{x+\cos x}\right|+c\)
Step-by-step Solution
Detailed explanation
\(I=\int \frac{\cos x+x \sin x}{x(x+\cos x)} d x\) \(=\int \frac{\cos x}{x(x+\cos x)} d x+\int \frac{\sin x}{(x+\cos x)} d x\) \(=\int\left\{\frac{1}{x}-\frac{1}{x+\cos x}\right\} d x+\int \frac{\sin x}{x+\cos x} d x\)…
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