Let `f:[1,oo]` be a differentiable function such that `f(1)=2.` If `6int_1^xf(t)dt=3xf(x)-x^3` for all `xgeq1,` then the value of `f(2)` is

Explanation

To solve the problem step by step, we will follow the instructions given in the video transcript, while ensuring clarity in each step.

### Step-by-Step Solution

1. **Given Equation**: We start with the equation provided in the problem:
\[ 6 \int_1^x f(t) \, dt = 3x f(x) - x^3 \]
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