grup producte integral

definició
f_{1}(x) [o(x)o] ...(n)... [o(x)o] f_{n}(x) = ∫ [ d_{x}[f_{1}(x)]·...·d_{x}[f_{n}(x)] ] d[x]
d_{x}[ f_{1}(x) [o(x)o] ...(n)... [o(x)o] f_{n}(x) ] = d_{x}[f_{1}(x)]·...·d_{x}[f_{n}(x)]


∫ [ (1/d_{x}[f(x)]) ] d[x] = ( f(x) )^{[o(x)o](-1)}


( f(x) [o(x)o] g(x) ) [o(x)o] h(x) = f(x) [o(x)o] ( g(x) [o(x)o] h(x) )
∫ [ ( d_{x}[f(x)]·d_{x}[g(x)] )·d_{x}[h(x)] ] d[x] = ∫ [ d_{x}[f(x)]·( d_{x}[g(x)]·d_{x}[h(x)] ) ] d[x]
f(x) [o(x)o] ( f(x) )^{[o(x)o](-1)} = x
∫ [ d_{x}[f(x)]·( 1/d_{x}[f(x)] ) ] d[x]=x
f(x) [o(x)o] x = f(x)


( f(x)  )^{[o(x)o]n} = ∫ [ d_{x}[f(x)]^{n} ] d[x]


( e^{x} )^{[o(x)o](-1)} = (-1)e^{-x}
( x^{n} )^{[o(x)o](-1)} = (1/n)·(1/((-n)+2))·x^{(-n)+2}
( bx )^{[o(x)o](-1)} = (1/b)·x
( ax^{2}+bx )^{[o(x)o](-1)} = (1/2a)·ln(2ax+b)
( ax^{3}+bx^{2}+cx )^{[o(x)o](-1)} = ( ln(3ax^{2}+2bx+c) [o(x)o] (1/6a)·ln(6ax+2b) )
( ax^{4}+bx^{3}+cx^{2}+dx )^{[o(x)o](-1)} =...
... ( ln(4ax^{3}+3bx^{2}+2cx+d) [o(x)o] ln(12ax^{2}+6bx+2c) [o(x)o] (1/24a)·ln(24ax+6b) )