# 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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