exponencial més unitat

e^{[x]}=e^{x}+1
[x]=ln( e^{x}+1 )


e^{x+[(-x)]}=e^{[x]}
e^{x}·(1+e^{(-x)})=e^{x}+1


e^{y}+e^{x}=e^{x}·e^{[y+(-x)]}
e^{x}+e^{y}=e^{y}·e^{[x+(-y)]}


ln(y+x)=ln(x)+[ ln(y)+(-1)ln(x) ]=ln(x)+ln( (y/x)+1 )
ln(x+y)=ln(y)+[ ln(x)+(-1)ln(y) ]=ln(y)+ln( (x/y)+1 )



[0]=ln(2)


e^{[x]}e^{[y]}=e^{x+y}+1+e^{x}+e^{y}
e^{[x]}e^{[y]}=e^{[x+y]}+e^{x}+e^{y}
e^{[x]}e^{[y]}=e^{[x+y]}+e^{x}(1+e^{y+(-x)})
e^{[x]}e^{[y]}=e^{[x+y]}+e^{x}e^{[y+(-x)]}
e^{[x]}e^{[y]}=e^{[x+y]}+e^{x+[y+(-x)]}
e^{[x]}e^{[y]}=e^{[x+y]}(1+e^{x+[y+(-x)]+(-1)[x+y]})
e^{[x]}e^{[y]}=e^{[x+y]}e^{[ x+[y+(-x)]+(-1)[x+y] ]}


[x]+[y]=[x+y]+[ x+[y+(-x)]+(-1)[x+y] ]
[x]+[y]=[y+x]+[ y+[x+(-y)]+(-1)[y+x] ]


[x]+ln(2)=[x]+[ x+[(-x)]+(-1)[x] ]
[x]+ln(2)=[x]+[ [x]+(-1)[x] ] & [ MP e^{x+[(-x)]}=e^{[x]} ]
ln(2)+[y]=[y]+[ y+[(-y)]+(-1)[y] ]
ln(2)+[y]=[y]+[ [y]+(-1)[y] ] & [ MP e^{y+[(-y)]}=e^{[y]} ]


d_{x}[ [x] ]=(1/e^{[x]})·d_{x}[e^{[x]}]
int[e^{[x]}]d[ [x] ]=e^{x}+1


d_{x}[ [f(x)] ]=(1/e^{[f(x)]})·d_{f(x)}[e^{[f(x)]}]·d_{x}[f(x)]
int[e^{[f(x)]}]d[ [f(x)] ]=e^{f(x)}+1