原式=∫(x^3+9x-9x)dx/(x^2+9)
=∫xdx-9∫xdx/(x^2+9)
=x^2/2-(9/2)∫d(x^2+9)/(x^2+9)
=x^2/2-(9/2)ln(x^2+9)+C.
x^3/x^2+9的不定积分
原式=∫(x^3+9x-9x)dx/(x^2+9)
=∫xdx-9∫xdx/(x^2+9)
=x^2/2-(9/2)∫d(x^2+9)/(x^2+9)
=x^2/2-(9/2)ln(x^2+9)+C.