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GUJCET · Maths · Integrals
\(\int \frac{e^{2025+x} - e^{2025-x}}{e^{2026+x} + e^{2026-x}} \cdot dx = \underline{\hspace{1cm}} + C\)
- A \(\log|e^x + e^{-x}|\)
- B \(e\log|e^x + e^{-x}|\)
- C \(\frac{1}{e} \log|e^x + e^{-x}|\)
- D \(-\frac{1}{e} \log \left|e^x+e^{-x}\right|\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{e} \log|e^x + e^{-x}|\)
Step-by-step Solution
Detailed explanation
\(\int \frac{e^{2025}(e^x - e^{-x})}{e^{2026}(e^x + e^{-x})} \cdot dx\) \( = \frac{1}{e} \int \frac{e^x - e^{-x}}{e^x + e^{-x}} \cdot dx \)
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