求不定积分∫(x+3)/(x^2+9) dx需要过程～～

令x = 3tant,则x²+9 = 9sec²t, dx = 3sec²tdt
∫(x+3)/(x²+9) dx
=∫3(1+tant)/9sec²t 3sec²tdt
=∫(1+tant)dt
=t - ln|cost| + C
=arctan(x/3) - ln√[9/(9+x²)] + C

∫(x+3)/(x^2+9) dx
＝∫(x^3+3x^2+9x+27)dx
=1/4x^4+x^3+9/2x^2+27x+C

∫d(x^2+9)/(x^2+9)/2+∫3 dx/(x^2+9) dx