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Let f:[1,oo] be a differentiable fun...

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

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`6 int_1^x f(t)dx= 3xf(x)-x^3`
differentiate wrt x``
`6f(x) = 3f(x) + 3xf'(x) - 3x^2`
`cancel(3)f(x) = cancel(3)xf'(x) - cancel(3)x^2`
`y = x(dy/dx) - x^2`
`ydx-xdy= -x^2dx`
now`(xdy-ydx)/x^2=dx`
`=> intd(y/x) = intdx`
...
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