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GUJCET · Maths · Integrals
\(\int \frac{x}{(x-1)(x-2)} d x=\) __________ \(+C\).
- A \(\log \left|\frac{(x-1)^2}{x-2}\right|\)
- B \(\log \left|\frac{(x-2)^2}{x-1}\right|\)
- C \(\log \left|\left(\frac{x-1}{x-2}\right)^2\right|\)
- D \(\log |(x-1)(x-2)|\)
Answer & Solution
Correct Answer
(B) \(\log \left|\frac{(x-2)^2}{x-1}\right|\)
Step-by-step Solution
Detailed explanation
Let \(\frac{x}{(x-1)(x-2)} = \frac{A}{x-1} + \frac{B}{x-2}\) \(x = A(x-2) + B(x-1)\)
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