Let f be a function f : R → R , f ( x ) = 4 x 3 + 1

Question

Let f be a function   f  :      R    →      R  ,   f  (  x  )  =  4      x    3    +  1

metodikkf6z · Accepted Answer

∫          1              x        ln  ⁡  (  4      t    3    +  1  )      d    t  ≥      ∫          1              x        ln  ⁡  (  4      t    3    )      d    t  =      ∫          1              x        ln  ⁡  (  4  )  +  ln  ⁡  (      t    3    )      d    t  ≥      ∫          1              x        ln  ⁡  (  4  )      d    t  =  (  ln  ⁡  4  )  (  x  −  1  )

limunom623 · Accepted Answer

You can figure out how fast the integral converges to infinity with the estimates

\int_{1}^{x} \log 4 t^{3} d t \leq \int_{1}^{x} \log (4 t^{3} + 1) d t \leq \int_{1}^{x} \log 5 t^{3} d t

and

\int_{1}^{x} \log (a x^{3}) d t = \log a \cdot (x - 1) + 3 (x \log x - x + 1)

Let f be a function f:RR -> RR, f(x)=4x^3+1

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