∫(3x-1)/(x^2+9)dx每一步都要详细

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∫(3x-1)/(x^2+9)dx每一步都要详细
∫(3x-1)/(x^2+9)dx每一步都要详细

∫(3x-1)/(x^2+9)dx每一步都要详细
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