Indefinite integral

Let f a function, it is said that F is a primitive of f if F’ = f.


NOTE: if F is a primitive of fF + k (k Є R) is a primitive of f.


The indefinite integral of f is the set of primitives of f:

Example: 1) ∫cosx dx = sinx + k; k Є R



  2) ∫3sinxdx =3 ∫sinxdx = -3cosx + k    k Є R

  3) ∫(ex+3)dx = ex + 3x + k      k Є R



Exercise. Solve:

a) ∫3x2 dx =

b) ∫2sinx·cosx dx =





Solutions: a) x3 + k; b) sin2x + k

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