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.30,1960.
[2]:KIT 数学ナビゲーション:積分 1/sinx

Remarks

・LaTeX: \\\int_{a}^{b}\frac{1}{\sin x}dx=\frac{1}{2}\log\left (\frac{1-\cos x}{1+\cos x} \right )+C\\=\frac{1}{2}\log\left ( \frac{\sin^{2}\frac{x}{2}}{\cos^{2}\frac{x}{2}}\right )+C\\=\frac{1}{2}\left [ 2\log\left ( \sin\frac{x}{2} \right )-2\log\left ( \cos\frac{x}{2} \right ) \right ]+C\\=\log\left ( \sin\frac{x}{2} \right )-\log\left ( \cos\frac{x}{2} \right ) \right+C
・Making above Equation Image is powered by CODECOGS

History

・2010/04/28:Upload.