lunes, 5 de agosto de 2019

funcions inverses hiperboliques


d_{x}[arcsinh[n](x)]=(n^{n+1}+x^{(n+1)})^{(-1)(n+1)}
d_{x}[arcsinh[n](x)]=(1/n)·(1+(x/n)^{(n+1)})^{(-1)(n+1)}
d_{x}[arcsinh[n](sinh[n](x))]=cosh[n](x)·(1/n)·(1+(sinh[n](x)/n)^{(n+1)})^{(-1)(n+1)}=1


d_{x}[arccosh[n](x)]=((-1)n^{n+1}+x^{(n+1)})^{(-1)(n+1)}
d_{x}[arccosh[n](x)]=(1/n)·((-1)+(x/n)^{(n+1)})^{(-1)(n+1)}
d_{x}[arccosh[n](cosh[n](x))]=sinh[n](x)·(1/n)·((-1)+(cosh[n](x)/n)^{(n+1)})^{(-1)(n+1)}=1


int[( sinh[n](x) )^{m}]d[x] =( 1/(m+1) )( sinh[n](x) )^{m+1} [o(x)o] ( sinh[n](x) )^{[o(x)o](-1)}
int[( cosh[n](x) )^{m}]d[x] =( 1/(m+1) )( cosh[n](x) )^{m+1} [o(x)o] ( cosh[n](x) )^{[o(x)o](-1)}

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