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Indefinite Integrals question

2023 · 10 Apr · Shift 2 · Q27

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PYQ Library
JEE Main
Mathematics
Indefinite Integrals
2023 · 10 Apr · Shift 2 · Q27

Indefinite Integrals question

2023 · 10 Apr · Shift 2 · Q27

JEE MainMathematicsIndefinite IntegralsMCQ+4 / −1

For

\alpha, \beta, \gamma, \delta \in \mathbb{N}

, if

\int\left(\left(\frac{x}{e}\right)^{2 x}+\left(\frac{e}{x}\right)^{2 x}\right) \log _{e} x d x=\frac{1}{\alpha}\left(\frac{x}{e}\right)^{\beta x}-\frac{1}{\gamma}\left(\frac{e}{x}\right)^{\delta x}+C

, where

e=\sum_{n=0}^{\infty} \frac{1}{n !}

and

\mathrm{C}

is constant of integration, then

\alpha+2 \beta+3 \gamma-4 \delta

is equal to :

A
$-8$
B
$-4$
C
1
D
4

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