If ∫ (2eˣ + 3e⁻ˣ)/(4eˣ + 7e⁻ˣ)dx = 1/14(ux + v log e (4eˣ + 7e⁻ˣ)) + C, where C is a constant of integration, then u + v is equal to _ _ _ _ _ _ _.

Integral Calculus: JEE Main 2021 Mathematics question

JEE Main 2021 · 27 Aug, Evening shift · Q38

JEE Main 202127 Aug, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

\int {{{2{e^x} + 3{e^{ - x}}} \over {4{e^x} + 7{e^{ - x}}}}dx = {1 \over {14}}(ux + v{{\log }_e}(4{e^x} + 7{e^{ - x}})) + C}

, where C is a constant of integration, then u + v is equal to _____________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2021 Integral Calculus Question with Answer (27 Aug Evening shift, Q38) | JEE Arc

JEE Main 2021 · 27 Aug, Evening shift · Q38

JEE Main 202127 Aug, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

\int {{{2{e^x} + 3{e^{ - x}}} \over {4{e^x} + 7{e^{ - x}}}}dx = {1 \over {14}}(ux + v{{\log }_e}(4{e^x} + 7{e^{ - x}})) + C}

, where C is a constant of integration, then u + v is equal to _____________.

Your answerType your answer. Integers and decimals are accepted.