integrals de imatge

y = e^{x} 

d[y] = e^{x}·d[x]

int[0-->x]-[ e^{x} ] d[x] = int[0-->x]-[ y(x) ] d[x] = ...

... int[0-->x]-[ (y/y) ] d[y] = y(x)+(-1)·y(0) = e^{x}+(-1)

y = ax+b 

d[y] = a·d[x]

int[0-->x]-[ ax+b ] d[x] = int[0-->x]-[ y(x) ] d[x] = int[0-->x]-[ (y/a) ] d[y] = ...

... (1/2a)( y(x) )^{2}+(-1)·(1/2a)( y(0) )^{2} = ...

... (1/2a)( ax+b )^{2}+(-1)·(b^{2}/2a) = (1/2)·x^{2}+bx 

y = (1/x) 

d[y] = (-1)·(1/x^{2})·d[x]

int[1-->x]-[ (1/x) ] d[x] = int[1-->x]-[ y(x) ] d[x] = ...

... int[1-->x]-[ (-1)·(y/y^{2}) ] d[y] = int[1-->x]-[ (-1)·(1/y) ] d[y] = ...

... (-1)·ln(y(x))+ln(y(1)) = ln(x)