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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 = \ln\left| \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[x\left(\sqrt{1+\frac{1}{x^2}} + 1\right)\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