{(1-x^2/1+x^2)^1/2}xdx这个不定积分咋算啊?

来源：学生作业帮助网编辑：六六作业网时间：2024/12/21 15:29:49

{(1-x^2/1+x^2)^1/2}*x*dx这个不定积分咋算啊?{(1-x^2/1+x^2)^1/2}*x*dx这个不定积分咋算啊?{(1-x^2/1+x^2)^1/2}*x*dx这个不定积分咋算

{(1-x^2/1+x^2)^1/2}*x*dx这个不定积分咋算啊?
{(1-x^2/1+x^2)^1/2}*x*dx这个不定积分咋算啊?

{(1-x^2/1+x^2)^1/2}*x*dx这个不定积分咋算啊?
令:(1-x^2)/(1+x^2)^1/2 =t ; x^2= (1-t^2)/(1+t^2)
∫(1-x^2)/(1+x^2)^1/2 *x*dx
=1/2∫(1-x^2)/(1+x^2)^1/2 *dx^2
=1/2∫t d[(1-t^2)/(1+t^2)]
=1/2*t*(1-t^2)/(1+t^2) - 1/2∫(1-t^2)/(1+t^2)dt
=1/2*t*(1-t^2)/(1+t^2) - 1/2∫(2-(1+t^2))/(1+t^2)dt
=1/2*t*(1-t^2)/(1+t^2) - ∫1/(1+t^2)dt +1/2∫1dt
=1/2*t*(1-t^2)/(1+t^2) - arctant+1/2t +C
=1/2*(1-x^2)/(1+x^2)^1/2*(1-t^2)/(1+t^2)-arctan(1-x^2)/(1+x^2)^1/2 +1/2(1-x^2)/(1+x^2)^1/2 +C

看图,这类积分少见吧

*-----------------------------------------------*| 6 4 X | 8 X X | X X 5 || X X X | X X X | X 7 8 || X X X | X X X | X X X ||---------------+---------------+--------------- || X X X | X X X | 5 1 X || X X X | X 6 X | X X X || 8 X X | 3 5 X | 2 X X || 填九宫格帮帮忙.x x 6 x x 7 x x 98 x x x 3 x 1 x x 9 x x 6 x 5 x 3 x x x 3 x x x x 1 8x x x 9 x 1 x x x2 1 x x x x 6 x x x 6 x 7 x 3 x x 1 x x 9 x 2 x x x 47 x x 8 x x 5 x x 七年级下册政治复习提纲(山东人民出版社)第五单元是青春的脚步青春的气息别弄错了啊!格式：X X X X X X X X X 1、X X X X X X X X X X.2、X X X X X X X X X.3、X X X X X X X X X X X. 分解因式----（X*X-X)(X*X-X-2)+1 】x(x+1)+x^2(x-1) 1/(1-x)+1/(1+x)+2/(1+x*x)+4/(1+x*x*x*x)+8/(1-x*x*x*x*x*x*x*x)怎么做 x-1/x-2 {2X+1}+{X} (x^2-1)/x x^2-1/x 2X+|X+1| ｜x-1｜+｜x-2｜ (x+1)/(x+2) /X+1/+/X+2/ 2x/(1-x) |X+2|+|X-1| 2x-1 (x |x-2|+|x-1|