WBJEE · Maths · Indefinite Integration
\(\int \frac{d x}{x(x+1)}\) equals
where \(c\) is an arbitrary constant.
- A \(\ln \left|\frac{x+1}{x}\right|+c\)
- B \(\ln \left|\frac{x}{x+1}\right|+c\)
- C \(\ln \left|\frac{x-1}{x}\right|+c\)
- D \(\ln \left|\frac{x-1}{x+1}\right|+c\)
Answer & Solution
Correct Answer
(B) \(\ln \left|\frac{x}{x+1}\right|+c\)
Step-by-step Solution
Detailed explanation
\[ \text { Hints : } \int \frac{d x}{x(x+1)}=\int\left(\frac{1}{x}-\frac{1}{x+1}\right) d x=\int \frac{d x}{x}-\int \frac{d x}{x+1}=\ln |x|-\ln |x+1|+C=\ln \left|\frac{x}{x+1}\right|+C \]
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