AP EAMCET · Maths · Indefinite Integration
If \(\int \frac{d x}{e^x+4 e^{-x}} d x=f(x)+c\), then \(f(x)\) is
- A \(2 \operatorname{Tan}^{-1}\left(2 e^x\right)\)
- B \(\frac{1}{2} \operatorname{Tan}^{-1}\left(\frac{e^x}{2}\right)\)
- C \(2 \operatorname{Tan}^{-1}\left(\frac{e^x}{2}\right)\)
- D \(\frac{1}{2} \operatorname{Tan}^{-1}\left(2 e^x\right)\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{2} \operatorname{Tan}^{-1}\left(\frac{e^x}{2}\right)\)
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Detailed explanation
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