KCET · Maths · Indefinite Integration
The value of \(\int \frac{d x}{(x+1)(x+2)}\) is
- A \(\log \left|\frac{x-1}{x+2}\right|+c\)
- B \(\log \left|\frac{x-1}{x-2}\right|+c\)
- C \(\log \left|\frac{x+2}{x+1}\right|+c\)
- D \(\log \left|\frac{x+1}{x+2}\right|+c\)
Answer & Solution
Correct Answer
(D) \(\log \left|\frac{x+1}{x+2}\right|+c\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \int \frac{\mathrm{dx}}{(\mathrm{x}+1)(\mathrm{x}+2)} & =\int \frac{(\mathrm{x}+2)-(\mathrm{x}+1)}{(\mathrm{x}+1)(\mathrm{x}+2)} \mathrm{dx} \\ & =\int \frac{1}{x+1} d x-\int \frac{1}{x+2} d x\end{aligned}\)
\(=\log \left|\frac{x+1}{x+2}\right|+c\)
\(=\log \left|\frac{x+1}{x+2}\right|+c\)
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