삼각함수적분표,trigonometric_integrals

삼각함수, 역삼각함수, 쌍곡함수, 역쌍곡함수 적분 표,table
  • 적분상수 생략

$\displaystyle f(x)$ $\displaystyle \int f(x)dx$ 자주 나오는 다른 표현 증명
$\displaystyle \sin x$ $\displaystyle -\cos x$ sin_x_적분_증명
$\displaystyle \cos x$ $\displaystyle \sin x$ cos_x_적분_증명
$\displaystyle \tan x$ $\displaystyle \ln|\sec x|$ $\displaystyle -\ln|\cos x|$ tan_x_적분_증명
$\displaystyle \csc x$ $\displaystyle \ln|\csc x-\cot x|$ $\displaystyle -\ln|\csc x+\cot x|$ csc_x_적분_증명
$\displaystyle \sec x$ $\displaystyle \ln|\sec x+\tan x|$ sec_x_적분_증명
$\displaystyle \cot x$ $\displaystyle \ln|\sin x|$ $\displaystyle -\ln|\csc x|$ cot_x_적분_증명
$\displaystyle \sin^{-1}x$
$\displaystyle \cos^{-1}x$
$\displaystyle \tan^{-1}x$
$\displaystyle \csc^{-1}x$
$\displaystyle \sec^{-1}x$
$\displaystyle \cot^{-1}x$
$\displaystyle \sinh x$ $\displaystyle \cosh x$
$\displaystyle \cosh x$ $\displaystyle \sinh x$
$\displaystyle \tanh x$ $\displaystyle \ln(\cosh x)$ 이하 네개 wpko에서 왔음,CHK
$\displaystyle \operatorname{csch} x$ $\displaystyle \ln\left|\tanh\frac{x}{2}\right|$
$\displaystyle \operatorname{sech} x$ $\displaystyle \tan^{-1}(\sinh x)$
$\displaystyle \coth x$ $\displaystyle \ln|\sinh x|$
$\displaystyle \sinh^{-1} x$ $\displaystyle x\sinh^{-1}x-\sqrt{x^2+1}$ arcsinh_x_적분_증명
$\displaystyle \cosh^{-1} x$ $\displaystyle x\cosh^{-1}x-\sqrt{x^2-1}$ arccosh_x_적분_증명
$\displaystyle \tanh^{-1} x$ $\displaystyle x\tanh^{-1}x+\frac12\ln(1-x^2)+C$ arctanh_x_적분_증명
$\displaystyle \operatorname{csch}^{-1} x$
$\displaystyle \operatorname{sech}^{-1} x$
$\displaystyle \coth^{-1} x$

$\displaystyle \sec^2x $$\displaystyle \tan x$
$\displaystyle \csc^2x $$\displaystyle -\cot x$
$\displaystyle \sec x\tan x$ $\displaystyle \sec x$
$\displaystyle \csc x\cot x$ $\displaystyle -\csc x$