[艾志康]基础积分常用公式[持续更新]

$1.\int{\frac{1}{\sqrt{x^2±a^2}}}dx=ln|x+\sqrt{x^2+a^2}|+C(a>0)$
$1.5.特别地, \int{\frac{1}{\sqrt{x(x+a)}}}dx=ln(\sqrt{x}+\sqrt{x+a})+C(a>0)$
$2.\int{tan^2(x)}dx=tanx-x+C$
$3.\int{\frac{1}{x^2+a^2}}dx=\frac{arctan{(\frac{x}{a})}}{a}+C$
$4.\int{\frac{1}{cos(x)+1}}dx=tan(\frac{x}{2})+C$
$4.5.\int{\frac{1}{cos(x)-1}}dx=cot(\frac{x}{2})+C$
$5.\int{sec(x)}dx=ln|tan(x)+sec(x)|+C$
$5.5.\int{csc(x)}dx=ln|csc(x)-cot(x)|+C$
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仅供参考
last_update: 2019.8.31