The integral $\int \frac{{e}^{3lo{g}_{e}2x}+5{e}^{2lo{g}_{e}2x}}{{e}^{4{\log }_{e}x}+5{e}^{3{\log }_{e}x}-7{e}^{2{\log }_{e}x}}dx,x0$ is equal to: (where c is a constant of integration) [JEE Main 2021, 25 Feb (Shift 2)]

Question

The integral $\int \frac{{e}^{3lo{g}_{e}2x}+5{e}^{2lo{g}_{e}2x}}{{e}^{4{\log }_{e}x}+5{e}^{3{\log }_{e}x}-7{e}^{2{\log }_{e}x}}dx,x>0$ is equal to: (where c is a constant of integration) [JEE Main 2021, 25 Feb (Shift 2)]

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The integral \(\int \frac{{e}^{3lo{g}_{e}2x}+5{e}^{2lo{g}_{e}2x}}{{e}^{4{\log }_{e}x}+5{e}^{3{\log }_{e}x}-7{e}^{2{\log …

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