For α, β, γ, δ N, if ∫((x/e)²ˣ+(e/x)²ˣ) log e x d x=1/(α)(x/e)^(β x)-1/(γ)(e/x)^(δ x)+C, where e=Σ n=0 ^(∞) 1/(n !) and C is constant of integration, then α+2 β+3 γ-4 δ is equal to:

Integral Calculus: JEE Main 2023 Mathematics question

JEE Main 2023 · 10 Apr, Evening shift · Q4055

JEE Main 202310 Apr, Evening shiftMathematicsHardIntegral Calculus369× since 2002

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_\limits{n=0}^{\infty} \frac{1}{n !}

and

\mathrm{C}

is constant of integration, then

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

is equal to :

JEE Main 2023 Integral Calculus Question with Solution (10 Apr Evening shift, Q4055) | JEE Arc