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Indefinite Integrals question

2021 · 25 Feb · Shift 2 · Q27

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JEE Main
Mathematics
Indefinite Integrals
2021 · 25 Feb · Shift 2 · Q27

Indefinite Integrals question

2021 · 25 Feb · Shift 2 · Q27

JEE MainMathematicsIndefinite IntegralsMCQ+4 / −1

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)

A
${\log _e}\sqrt {{x^2} + 5x - 7} + c$
B
$4{\log _e}|{x^2} + 5x - 7| + c$
C
${1 \over 4}{\log _e}|{x^2} + 5x - 7| + c$
D
${\log _e}|{x^2} + 5x - 7| + c$

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