CUET · MATHS · PYQ PAPER 2023
\(\int \log _e x d x\) is equal to:
- A \(x\left(\log _e x\right)+x+C\)
- B \(x\left(\log _e x\right)-x+C\)
- C \(x-x\left(\log _e x\right)+C\)
- D \(-x-x\left(\log _e x\right)+C\)
Answer & Solution
Correct Answer
(B) \(x\left(\log _e x\right)-x+C\)
Step-by-step Solution
Detailed explanation
\(\int \log _e x d x = \int \log _e x \cdot 1 d x\) Let \(u = \log _e x, d v = 1 d x\). Then \(d u = \frac{1}{x} d x, v = x\). \(\int u d v = u v - \int v d u\) \(\int \log _e x d x = x \log _e x - \int x \left(\frac{1}{x}\right) d x\)…
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