Q111 / 180 · KCET 2025 · Mathematics

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
    $\log \left|\frac{x+2}{x+1}\right|+c$
  • Correct answer
    D
    $\log \left|\frac{x+1}{x+2}\right|+c$

Solution

$\begin{aligned} \int \frac{\mathrm{dx}}{(\mathrm{x}+1)(\mathrm{x}+2)} & =\int \frac{(\mathrm{x}+2)-(\mathrm{x}+1)}{(\mathrm{x}+1)(\mathrm{x}+2)} \mathrm{dx} \\ & =\int \frac{1}{x+1} d x-\int \frac{1}{x+2} d x\end{aligned}$ $=\log \left|\frac{x+1}{x+2}\right|+c$

Hence, the correct answer is option: 'D'.

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