Hyperbolic Functions


1.        d(sinh u) = cosh u du

2.        d(cosh u) = sinh u du

3.        d(tanh u) = sech2 u du

4.        d(coth u) = - csch2 u du

5.        d(sech u) = - sech u tanh u du

6.        d(csch u) = - csch u tanh u du

1.        sinh u du = cosh u + C

2.         cosh u du = sinh u + C

3.         sech2 u du = tanh u + C

4.         csch2 u du = - coth u + C

5.         sech u tanh u du = - sech u + C

6.         csch u coth u du = - csch u + C

1.        d(arcsinh u) =       du           
                                     (1 + u2)

2.        d(arccosh u) =       du                                
                                       (u2 - 1)

3.        d(arctanh u) =        du                                |u|  <  1
                                        1  -   u2

4.        d(arccoth u) =          du                              |u|  >  1
                                         1  -  u2

5.        d(arcsech u) =      -    du                          
                                         u  (1 - u2)

6.        d(arccsch u) =       -    du           
                                    |u| (1 + u2)

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