If int_1^e [log_e x] dx = m/n log_e ( (e^2)/c ), where m and n are coprime natural numbers, then m^2 + n^2 - 5 is equal to

If int_1^e [log_e x] dx = m/n log_e ( (e^2)/c ), where m… — JEE Main 2023 Mathematics PYQ

JEE Main 2023 · 25 Jan · Shift 2 · numerical answer

\int_1^e [\log_e x] \, dx = \frac{m}{n} \log_e \left( \frac{e^2}{c} \right)

, where

m

and

n

are coprime natural numbers, then

m^2 + n^2 - 5

is equal to

Show answer

Answer: 20

[JEE Main 2023 · 25 Jan · Shift 2]

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