反双曲函数积分表

以下是部份反雙曲函數的積分表

$\int\mathrm{asinh}\frac{x}{\complement}\mathrm{d}x=x\mathrm{asinh}\frac{x}{\complement}-\sqrt{x^2+\complement^2}$

$\int\mathrm{acosh}\frac{x}{\complement}\mathrm{d}x=x\mathrm{arcosh}\frac{x}{\complement}-\sqrt{(x-\complement)(x+\complement)}$

$\int\mathrm{atanh}\frac{x}{\complement}\mathrm{d}x=x\mathrm{atanh}\frac{x}{\complement}+\frac{\complement\ln|(-x+\complement)(x+\complement)|}{2}\qquad(|x|<|\complement|)$

$\int\mathrm{acoth}\frac{x}{\complement}\mathrm{d}x=x\mathrm{acoth}\frac{x}{\complement}+\frac{\complement\ln|(x-\complement)(x+\complement)|}{2}\qquad(|x|<|\complement|)$

$\int\mathrm{asech}\frac{x}{\complement}\mathrm{d}x=x\mathrm{asech}\frac{x}{\complement}-\complement\mathrm{atan}\frac{x\sqrt{\dfrac{-x+\complement}{x+\complement}}}{x-\complement}\qquad[x\in(0,\complement)]$

$\int\mathrm{acosech}\frac{x}{\complement}\mathrm{d}x=x\mathrm{acosech}\frac{x}{\complement}+\complement\ln\left|\frac{x+\sqrt{x^2+\complement^2}}{\complement}\right|\qquad[x\in(0,\complement)]$