Stamfunktion til f(x)??

Du skal bruge substitution ved integration. Substituer x².

du kan også bruge delvis/partiel-integration

      substitution:
                          sæt
                                           u = x²   og dermed   (1/2)du = xdx
                          hvoraf             

                                           ∫ x·ln(x²)dx = ∫ ln(x²)·xdx = ∫ ln(u)·(1/2)du = (1/2)·∫ ln(u)du =

                                                  (1/2)·(u·ln(u) - u) + k = (1/2)·u·(ln(u) -1) + k =

                                                  (1/2)·x²·(ln(x²) - 1) + k

      partiel integration:
                                           ∫ x·ln(x²)dx = (1/2)x²·ln(x²) - ∫ (1/2)x²·x^-2·2xdx =

                                                  (1/2)x²·ln(x²) - ∫ x dx = (1/2)x²·ln(x²) - (1/2)x² + k =

                                                  (1/2)·x²·(ln(x²) - 1) + k