∫{x^2/[(x-3)(x+2)^2]}dx

来源：学生作业帮编辑：搜搜考试网作业帮分类：数学作业时间：2024/04/29 11:48:35

$∫{x^2/[(x-3)(x+2)^2]}dx$

x^2/[(x-3)(x+2)^2=(9/25)[1/(x-3)]+(16/25)[1/(x+2)]-(20/25)[1/(x+2)^2].
原式=(9/25)∫1/(x-3)dx+(16/25)∫1/(x+2)dx-(4/5)∫1/(x+2)^2dx
=(9/25)ln|x-3|+(16/25)ln|x+2|+(4/5)[1/(x+2)]+C.

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