Solving Fermi-Dirac Integral: Step-by-Step Guide

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arneet
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i am completely lost. there is an integral in my textbook in fermi dirac statistics whose result is written directly and am not able to understand . it is
∫⌽(u) du /exp.((u-uf)/kt) + 1 from 0 to ∞
expanded by tayor's series to give

∫⌽(u) du (from 0 to uf) +∏²/6 (kT)² [⌽'(u)] |at u=uf + 7∏⁴/360 (kT)⁴ [⌽''(u)] |at u=uf +...

where uf is such that function of u is zero for u greater than uf.
please reply as soon as possible. thanks.
 
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please reply. the answer on expansion by taylor series should be
 

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