JEE Mains · Maths · STD 12 - 7.1 indefinite integral
\(\text { If } \int \frac{2 e^{x}+3 e^{-x}}{4 e^{x}+7 e^{-x}} d x=\frac{1}{14}\left(u x+v \log _{c}\left(4 e^{x}+7 e^{-x}\right)\right)+C\) where \(\mathrm{C}\) is a constant of integration, then \(\mathrm{u}+\mathrm{v}\) is equal to .... .
- A \(5\)
- B \(6\)
- C \(7\)
- D \(8\)
Answer & Solution
Correct Answer
(C) \(7\)
Step-by-step Solution
Detailed explanation
\(\int \frac{2 e^{x}}{4 e^{x}+7 e^{-x}} d x+3 \int \frac{e^{-x}}{4 e^{x}+7 e^{-x}} d x\) \(=\int \frac{2 e^{2 x}}{4 e^{2 x}+7} d x+3 \int \frac{e^{-2 x}}{4+7 e^{-2 x}} d x\) Let \(\quad 4 e^{2 x}+7=T \quad\) Let \(\quad 4+7 e^{-2 x}=t\)…
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