∫x^3/(9+x^2)dx

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/14 08:35:52

∫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

∫x^3/9+X^2 dx. ∫x^3/(9+x^2)dx ∫2^x*3^x/(9^x-4^x) dx x-9/[(根号)x]+3 dx ∫ x+1/[(根号)x] dx ∫ [（3-x^2）]^2 dx ∫(2^x)/((2^x)+3)dx ∫(1-x)^2/x^3 dx ∫(x-1)^2/x^3 dx ∫x^3/1+x^2 dx ∫(X^3)/(1+X^2)dx ∫X^2 e^-X^3 dx. ∫(2^x+3^x)²dx ∫[(x^2-x+6)/(x^3+3x)]dx