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삼각함수적분표,trigonometric_integrals

삼각함수 적분 ¶

삼각함수_적분표
{

$\int\sin x\,dx$	$\int\csc x\,dx$
$\int\cos x\,dx$	$\int\sec x\,dx$
$\int\tan x\,dx$	$\int\cot x\,dx$

는 각각 다음과 같다.

$-\cos x+C$	$-\ln\|\csc x+\cot x\|+C$
$\sin x+C$	$\ln\|\sec x+\tan x\|+C$
$-\ln\|\cos x\|+C$ $(=\ln\|\sec x\|+C)$	$\ln\|\sin x\|+C$

}

역삼각함수 적분 ¶

역삼각함수_적분표
{

$\int\sin^{-1} x\,dx=x\sin^{-1}x+\sqrt{1-x^2}+C$	$\int\csc^{-1}x\,dx=x\csc^{-1}x+\ln\left(\|x\|+\sqrt{x^2-1}\right)+C=x\csc^{-1}x+\cosh^{-1}\|x\|+C$ CHK
$\int\cos^{-1} x\,dx=x\cos^{-1}x-\sqrt{1-x^2}+C$	$\int\sec^{-1}x\,dx=x\sec^{-1}x-\cos^{-1}\|x\|+C$ CHK
$\int\tan^{-1} x\,dx=x\tan^{-1}x-\frac{\ln(x^2+1)}{2}+C$	$\int\cot^{-1}x\,dx=x\cot^{-1}x+\frac{\ln(x^2+1)}{2}+C$

Twins:

List_of_integrals_of_inverse_trigonometric_functions
}

쌍곡선함수 적분 ¶

쌍곡선함수_적분표
{

$\int\sinh x\,dx=\cosh x+C$	$\int\operatorname{csch} x\,dx=$
$\int\cosh x\,dx=\sinh x+C$	$\int\operatorname{sech} x\,dx=$
$\int\tanh x\,dx=$	$\int\coth x\,dx=$

쌍곡선함수.적분
}

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last modified 2020-08-25 15:24:58