∫x^3/(9+x^2)dx=?后面步骤是∫xdx-9/2∫d（9+x^2)/(9+x^2)问下怎么出来的.?_数学解答

∫x^3/(9+x^2)dx=?
后面步骤是
∫xdx-9/2∫d（9+x^2)/(9+x^2)
问下怎么出来的.?

人气：301 ℃　时间：2020-04-20 15:54:42

解答

∫x^3/(9+x^2)dx=∫[x-9x/(9+x^2)]dx=∫xdx-9/2∫1/(9+x^2)dx^2=∫xdx-9/2∫1/(9+x^2)d(9+x^2)=1/2x^2-9/2ln(9+x^2)+c