∫x^3⼀(9+x^2)dx

2024-12-19 05:49:38
推荐回答(3个)
回答1:

∫x^3/(9+x^2)dx
=∫[x(x^2+9)-9x]/(9+x^2)dx
=1/2x^2-9∫x/(9+x^2)dx
=1/2x^2-4.5ln(9+x^2) +C

回答2:

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

回答3:

∫x^3dx/(9+x^2)
=(1/2)∫x^2dx^2/(9+x^2)
=(1/2)∫dx^2-(9/2)∫d(x^2+9)(9+x^2)
=(1/2)x^2-(9/2)ln(9+x^2)+C