设 x = 3tant,则 dx = 3(sect)^2*dt∫dx/(x^2 +9)=∫3(sect)^2*dt/[9(tant)^2 + 9]=1/3*∫(sect)^2*dt/(sect)^2=1/3*∫dt=1/3*t + C=1/3*arctan(x/3) + C