本文给出基本积分表和常用积分表。
基本积分表
$$ begin{array}{c} int x^{a} mathrm{~d} x=frac{1}{a 1} x^{a 1} C quad(a in R, a neq-1)\ int frac{1}{x} mathrm{~d} x=ln |x| C\ int cos x mathrm{~d} x=sin x C\ int sin x mathrm{~d} x=-cos x C\ int tan x mathrm{~d} x=-ln |cos x| C\ int cot x mathrm{~d} x=ln |sin x| C\ int frac{1}{cos ^{2} x} mathrm{~d} x=tan x C \ int frac{1}{1 x^{2}} mathrm{~d} x=arctan x C \ int mathrm{e}^{x} mathrm{~d} x=mathrm{e}^{x} C\ int x mathrm{e}^{x} mathrm{~d} x=mathrm{e}^{x}(x-1) C \ int a^{x} mathrm{~d} x=frac{1}{ln a} a^{x} C end{array} $$
常用积分表
$$ begin{array}{l}int sin ^{2} x mathrm{~d} x=frac{1}{2}(x-sin x cos x) C \ int cos ^{2} x mathrm{~d} x=frac{1}{2}(x sin x cos x) C \ int sec x mathrm{~d} x=ln |tan x sec x| C\ int ln x mathrm{~d} x=x ln x-x C \ int sqrt{a^{2}-x^{2}} mathrm{~d} x=frac{1}{2}left(x sqrt{a^{2}-x^{2}} a^{2} arcsin frac{x}{a}right) C \ int frac{1}{sqrt{1-x^{2}}} mathrm{~d} x=arcsin (x) C \ int frac{1}{sqrt{1 x^{2}}} mathrm{~d} x=ln left(x sqrt{1 x^{2}}right) C=sinh ^{-1} x C end{array} $$
定积分
参考资料
- https://wuli.wiki/changed/ITable.html#eq13
