Question

∫(3x-1)／(x^2+9)dx每一步都要详细

Answer 1

原式=∫3x/(x²+9) dx-∫1/(x²+9) dx=3/2*∫d(x²+9)/(x²+9)-∫1/9*1/(x²/9+1) dx=3/2*ln(x²+9)-1/3*∫1/[(x/3)²+1] d(x/3)=3/2*ln(x²+9)-1/3*arctan(x/3)+C