Who's up to the challenge? 14

Calculus Level 4

\(f,g\) are real functions that are integrable on \([0,1]\). If \[\displaystyle\int_0^1 |f(x)|^7 \, dx = 1\] and \[\displaystyle\int_0^1 |g(x)|^7 \, dx = 16384,\] find the maximum value of \[\displaystyle\int_0^1 |f(x)+g(x)|^7 \, dx.\]


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