求 ∫ [(x^3)/(x^2-1)^(1/2)]dx,

来源：学生作业帮助网编辑：作业帮时间：2024/05/04 16:28:33

求 ∫ [(x^3)/(x^2-1)^(1/2)]dx,
求 ∫ [(x^3)/(x^2-1)^(1/2)]dx,

求 ∫ [(x^3)/(x^2-1)^(1/2)]dx,
设u=(x^2-1)^(1/2),则
x^2=u^2+1
dx^2=d(u^2+1)=2udu
∫[(x^3)/(x^2-1)^(1/2)]dx=∫[(x^2)/[2(x^2-1)^(1/2)]]dx^2
=∫[(u^2+1)/(2u)]*2udu
=∫(u^2+1)du
=u^3/3+u
=u(u^2+3)/3
=(x^2-1)^(1/2)(x^2+2)/3

(2x-1)dx刚好就是d(x^2-x+3)
所以结果就是ln（x^2-x+3）

求不定积分∫(x^2-3x)/(x+1)dx x(x+1)+(x+2)+(x+3)+(x+4)+(x+5) = 27求x |x^2-4x+3|+|x+1|>8 求x 求x/(x+1)(x+2)(x+3)的不定积分求x/(x-1)(x-2)(x-3)积分设f(x)=x㏑(1+x^2),x≥0.(x^2+2x-3)e^(-x),x＜0,求∫f(x)dx 求一个数独答案X X X 9 X X X 8 2 X 6 3 X X 1 4 X 99 X 8 X X X X X XX X X 6 7 X 3 X XX 4 6 X 5 X 2 9 XX X 7 X 2 3 X X XX X X X X X 7 X 17 X 4 3 X X 6 2 X6 3 X X X 7 X X X 一个“整式的乘法”的问题请先阅读下列解题过程,再仿做下面的问题.已知X*X + X - 1=0,求X*X*X + 2*X*X + 3的值.解X*X*X + 2X*X +3=X*X*X +X*X -X +X*X +X +3=X{X*X +X -1} +X*X +X -1 +4=0+0+4=4+ x + X*X + X*X*X=0.+ X*X + X*X*X (x+1)(x-1)+2x(x+2)=3(x的平方+1),求X. 已知x^-x-1=0,求x^4+x^3-x^2-4x+3 已知x*x-3x+1=0求√(x*x+1/x-2)=? y=(2x*x-2x+3)/(x*x-x+1),求值域? 求|x-1|+|x-2|+|x-3|+|x-4|+|x-5|+...+|x-2007|的最小值 /x-1/+/x-2/+/x-3/x-4/+/x-5/ +/x-6/求最小值求不定积分∫(2x∧2+x+1)/(x+3)(x-1)∧2dx 求积分∫(2x^4+x^3+x-1)/(x^3-1)dx 求∫ x^4-3x^2+5x-1 / x^3dx的不定积分? 求不定积分∫( x/2 - 1/x + 3/x^3 + 4/x^4)dx,