Mathematics · 2021
JEE Main · 27 August 2021, Shift 2 · Q84
If ∫ (2 e^x+3 e^-x)/(4 e^x+7 e^-x) d x=1/14( u x+ v log_e (4 e^x+7 e^-x))+ C, where C is a constant of integration, then u + v is equal to \ \ \ \.
If $\displaystyle \int \frac{2 \mathrm{e}^x+3 \mathrm{e}^{-x}}{4 \mathrm{e}^x+7 \mathrm{e}^{-x}} \mathrm{~d} x=\frac{1}{14}\left(\mathrm{u} x+\mathrm{v} \log _{\mathrm{e}}\left(4 \mathrm{e}^x+7 \mathrm{e}^{-x}\right)\right)+\mathrm{C}$, where C is a constant of integration, then $\displaystyle \mathrm{u}+\mathrm{v}$ is equal to \_\_\_\_.
Official answer
7
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JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.