Figure it out

Calculus Level 4

\(f\left( x \right) ={ \int _{ 0 }^{ \infty }{ \frac { t\cdot dt }{ { \left( t+1 \right) }^{ x } } } } \)

If \(f\left( x \right)\) is defined when \(x>2\), which of the following is equivalent to \(f\left( x \right)\)?


This problem is original.
Picture credits: Bi-crystal by Richard Bartz, Wikipedia
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