∫arctan(2x) dx
Poniamo:
g'(x)=1 e f(x)= arctan(2x)
∫arctan(2x) dx =x (arctang(2x))-∫x [x/(1+4x^2)] (2) dx =x (arctang(2x))-1/4 ∫8x/(4x^2+1) dx=
=x (arctang(2x))-1/4 ln(4x^2+1) + c
§arctg(2x)= xarctg(2x) - § x(2/(1+4x^2)= // - 1/4 § 8x/(4x^2 +1)= // - log(4x^2+1)=
= xarctg(2x) - log(4x^2+1)/4 +c
Bravo Bruno :D