∫x^3/(9+x^2)dx

来源：学生作业帮编辑：神马作文网作业帮分类：数学作业时间：2024/11/10 11:46:09

∫x^3/(9+x^2)dx

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

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