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GUJCET · Maths · Integrals
If \(\int \frac{3 e^x-5 e^{-x}}{4 e^x+5 e^{-x}} d x=p x+q \cdot \log \left|4 e^x+5 e^{-x}\right|+ C\), then
- A \(p=1 / 8, q=-7 / 8\)
- B \(p=1 / 8, q=7 / 8\)
- C \(p=-1 / 8, q=-7 / 8\)
- D \(p=-1 / 8, q=7 / 8\)
Answer & Solution
Correct Answer
(D) \(p=-1 / 8, q=7 / 8\)
Step-by-step Solution
Detailed explanation
\(N = A(4 e^x+5 e^{-x}) + B(4 e^x-5 e^{-x})\) \(3 e^x-5 e^{-x} = (4A+4B)e^x + (5A-5B)e^{-x}\)
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