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AP EAMCET · Maths · Indefinite Integration

\(\int \frac{x-1}{(x-2)(x-3)} d x\) is equal to

  1. A \(2 \log |x-3|+\log |x-2|+c\)
  2. B \(\log |x-3|-\log |x-2|+c\)
  3. C \(\log |x-3|-\log |x+2|+c\)
  4. D \(\log \left|\frac{(x-3)^2}{x-2}\right|+c\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\log \left|\frac{(x-3)^2}{x-2}\right|+c\)

Step-by-step Solution

Detailed explanation

Let \(I=\int \frac{x-1}{(x-2)(x-3)} d x\) \(\begin{aligned} & I=\int\left(\frac{2}{x-3}-\frac{1}{x-2}\right) d x \\ & I=\int \frac{2}{x-3} d x-\int \frac{d x}{x-2}\end{aligned}\)…