∫(arctanx)/(x^2(x^2+1))dxletx=tanadx = (seca)^2da∫(arctanx)/(x^2(x^2+1))dx= ∫ [a/(tana)^2] da=-∫ ad(cota+a)= -a(cota+a) + ∫ (cota+a)da= -a(cota+a) + ln|sina| + a^2/2 + C=-arctanx( 1/x + arctanx) ...