gwzhenen-coment

I smoket-banat a white gwzhen-cigar,

of the gwzhenen-packatch of white tobaco.

I smoket-banat a black gwzhen-cigar,

of the gwzhenen-packatch of black tobaco.

d_{x}[ int[ g(y) ] d[x] ] = d_{y}[ int[ g(y)·d_{y}[x] ]d[y] ]·d_{x}[y] = g(y)

F(x) = int[0-->f(x)][ g(x) ] d[x] = G(f(x))+(-1)·G(0)

d_{x}[F(x)] = g(f(x))·d_{x}[f(x)]

Si [Ec][ f(c) = 0 ] ==> F(c) = 0

F(x) = int[0-->f(x)][1] d[x] = f(x)

d_{x}[F(x)] = ( f(x) )^{0}·d_{x}[f(x)]

F(x) = int[0-->f(x)][ g(x) ] d[x] = ( f(x) ) [o(x)o] G(f(x))

d_{x}[F(x)] = ( f(x) )^{0}·g(f(x))·d_{x}[f(x)]

F(x) = int[0-->f(x)][ g(x) ] d[x] = ( f(x) ) [o(x)o] G(f(x))

H(x) = int[0-->f(x)][ x^{n}·g(x) ] d[x] = (1/(n+1))·( f(x) )^{n+1} [o(x)o] G(f(x))

d_{x}[F(x)] = ( f(x) )^{0}·g(f(x))·d_{x}[f(x)]

d_{x}[H(x)] = ( f(x) )^{n}·g(f(x))·d_{x}[f(x)]

Si [Ec][ f(c) = 1 ] ==> d_{x}[F(c)] = d_{x}[H(c)]

int[ e^{( ax^{2}+bx+c )^{n}} ] d[x] = ...

... (1/n)·e^{( ax^{2}+bx+c )^{n}} [o(x)o] ( 1/((-n)+2) )·( ax^{2}+bx+c )^{(-n)+2} [o(x)o] ...

... ln(2ax+b) [o(x)o] (1/(2a))·x

int[ e^{( ax^{2}+bx+c )} ] d[x] = ...

... e^{( ax^{2}+bx+c )} [o(x)o] ln(2ax+b) [o(x)o] (1/(2a))·x

int[ e^{( ax^{2}+bx+c )^{2}} ] d[x] = ...

... (1/2)·e^{( ax^{2}+bx+c )^{2}} [o(x)o] ln( ax^{2}+bx+c ) [o(x)o] ...

... ln(2ax+b) [o(x)o] (1/(2a))·x

int[ ln( ( ax^{2}+bx+c )^{n} ) ] d[x] = ...

... (1/n)·( ln( ( ax^{2}+bx+c )^{n} )·( ax^{2}+bx+c )^{n}+(-1)·( ax^{2}+bx+c )^{n} ) ...

... [o(x)o] ...

... ( 1/((-n)+2) )·( ax^{2}+bx+c )^{(-n)+2} [o(x)o] ...

... ln(2ax+b) [o(x)o] (1/(2a))·x

3x =[3]= 9 <==> 3x = 3k+9 <==> x = k+3

3n·x =[3]= 9 <==> 3n·x = 3k+9 <==> x = ( (k+3)/n ) <==> ( k = pn+(-3) & x = p )

(qn)·x =[q]= q^{2} <==> qn·x = qk+q^{2} <==> x = ( (k+q)/n ) <==> ...

... ( k = pn+(-q) & x = p )

congruencia racional:

3x =[3]= 12 <==> 3x = 3k+12 <==> x = k+4

qx =[q]= p <==> qx = qk+p <==> x = k+(p/q)

ax =[m]= b <==> ax = mk+b <==> x = (m/a)·k+(b/a)