Question

谁是th分之一的积分?th指双曲正切函数

Answer 1

∫ 1/ th(x) dx = ∫ coth(x) dx = ln|sinh(x)| +C

附：双曲函数导数表及积分表

(sinh(x))'=cosh(x)

(cosh(x))'=sinh(x)

(tanh(x))'=sech^2(x)

(coth(x))'=-csch^2(x)

(sech(x))'=-sech(x)tanh(x)

(csch(x))'=-csch(x)coth(x)

(arcsinh(x))'=1/sqrt(x^2+1)

(arccosh(x))'=1/sqrt(x^2-1) (x>1)

(arctanh(x))'=1/(1-x^2) (|x|