The integral ∫ (e^(3 log e 2x) + 5e^(2 log e 2x))/(e^(4 log e x) + 5e^(3 log e x) - 7e^(2 log e x)) dx, x > 0, is equal to: (where c is a constant of integration)

(A) log e √(x² + 5x - 7) + c

(C) 1/4 log e |x² + 5x - 7| + c

Integral Calculus: JEE Main 2021 Mathematics question

JEE Main 2021 · 25 Feb, Evening shift · Q4030

JEE Main 202125 Feb, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

The integral

\int {{{{e^{3{{\log }_e}2x}} + 5{e^{2{{\log }_e}2x}}} \over {{e^{4{{\log }_e}x}} + 5{e^{3{{\log }_e}x}} - 7{e^{2{{\log }_e}x}}}}} dx

, x > 0, is equal to : (where c is a constant of integration)

JEE Main 2021 · 25 Feb, Evening shift · Q4030

JEE Main 202125 Feb, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

The integral

\int {{{{e^{3{{\log }_e}2x}} + 5{e^{2{{\log }_e}2x}}} \over {{e^{4{{\log }_e}x}} + 5{e^{3{{\log }_e}x}} - 7{e^{2{{\log }_e}x}}}}} dx

, x > 0, is equal to : (where c is a constant of integration)