MHT CET · Maths · Indefinite Integration
\(\int \frac{\mathrm{e}^{2030 \log x}-\mathrm{e}^{2029 \log x}}{\mathrm{e}^{2028 \log x}-\mathrm{e}^{2027 \log x}} \mathrm{~d} x=\ldots\).
- A \(\frac{x^2}{2}+c\), where \(c\) is the constant of integration
- B \(x+c\), where \(c\) is the constant of integration
- C \(\frac{x^3}{3}+c\), where \(c\) is the constant of integration
- D \(\frac{x}{3}+c, \quad\) where \(c\) is the constant of integration
Answer & Solution
Correct Answer
(C) \(\frac{x^3}{3}+c\), where \(c\) is the constant of integration
Step-by-step Solution
Detailed explanation
\( \frac{\mathrm{e}^{2030 \log x}-\mathrm{e}^{2029 \log x}}{\mathrm{e}^{2028 \log x}-\mathrm{e}^{2027 \log x}} = \frac{x^{2030}-x^{2029}}{x^{2028}-x^{2027}} \) \( = \frac{x^{2029}(x-1)}{x^{2027}(x-1)} = x^2 \)
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