もっと自己紹介
特に書くことがないです…
以下Cは積分定数
∫logxdx
=∫(x)′logxdx
=xlogx-∫dx
=xlogx-x+C
∫xlogxdx
=∫(x²/2)′logxdx
= x²logx/2-∫x/2dx
= x²logx/2-x²/4+C
∫1/sinxdx
=∫sinx/(1-cos²x)dx
=(1/2)∫{sinx/(1-cosx)+sinx/(1+cosx)}dx
=(1/2)(log|1-cosx|-log|1+cosx|)+C
=(1/2)(log|(1-cosx)/(1+cosx)|)+C
∫1/cosxdx
=∫cosx/(1-sin²x)dx
=(1/2)∫{cosx/(1-sinx)+cosx/(1+sinx)}dx
=(1/2)(-log|1-sinx|+log|1+sinx|)+C
=(1/2)log|(1+sinx)/(1-sinx)|+C
