The greatest integer less than | Maths |JEE ADVANCED 2022

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The greatest integer less than or equal to $$ \int_1^2 \log _2\left(x^3+1\right) d x+\int_1^{\log _2 9}\left(2^x-1\right)^{\frac{1}{3}} d x $$ is $\_\_\_\_$ .

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