Fungsi Hiperbolik dan Inversinya


Dari Wikipedia Indonesia, artikel bebas.

 

Fungsi hiperbolik

int sinh x , dx = cosh x + C
int cosh x , dx = sinh x + C
int tanh x , dx = ln| cosh x | + C
int mbox{csch},x , dx = lnleft| tanh {x over2}right| + C
int mbox{sech},x , dx = arctan(sinh x) + C
int coth x , dx = ln| sinh x | + C

Fungsi Invers Hiperbolik

 

int operatorname{arsinh} x , dx  = x operatorname{arsinh} x - sqrt{x^2+1} + C
int operatorname{arcosh} x , dx  = x operatorname{arcosh} x - sqrt{x^2-1} + C
int operatorname{artanh} x , dx  = x operatorname{artanh} x + frac{1}{2}log{(1-x^2)} + C
int operatorname{arcsch},x , dx = x operatorname{arcsch} x+ log{left[xleft(sqrt{1+frac{1}{x^2}} + 1right)right]} + C
int operatorname{arsech},x , dx = x operatorname{arsech} x- arctan{left(frac{x}{x-1}sqrt{frac{1-x}{1+x}}right)} + C
int operatorname{arcoth} ,x , dx = x operatorname{arcoth} x+ frac{1}{2}log{(x^2-1)} + C

 

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