Calculation of Indefinite Integral.

Keyword

Physics Formulas,Indefinite Integral,Transcendental Function.

Reference

[1]:オーム社編:『機械工学公式集』,オーム社,pp.32,1960.
[2]:Branch Cuts and Principal Values:UNIX at SLAC

Remarks

・LaTeX: \\\int_{a}^{b}\tan ^{-1}xdx=x\tan^{-1}x-\frac{1}{2}\ln\left ( 1+x^{2} \right )+C\\\\\tan^{-1}x\\=\left ( \ln\left ( 1+ix \right ) -\ln\left ( 1-ix \right )\right )/\left ( 2i \right )\\=\frac{i}{2}\left ( \ln\left ( 1-ix \right ) -\ln\left ( 1+ix \right )\right )
・Making above Equation Image is powered by CODECOGS

History

・2010/06/08:Upload.