Warning: Use of undefined constant title - assumed 'title' (this will throw an Error in a future version of PHP) in /home/www/wwwroot/izhixiu.com/www/mzxroot/caches/caches_template/ifcom2017/content/show_question.php on line 15
积分∫(2r)/{(x^2+r^2)^(3/2)}dr求完全具体步骤!∫(

题目

积分∫(2r)/{(x^2+r^2)^(3/2)} dr
求完全具体步骤!
∫(2r)/{(x^2+r^2)^(3/2)} dr
=∫(x^2+r^2)^(-3/2) dr^2
为啥?

数学2021-04-12 13:46

优质解答

∫(2r)/{(x^2+r^2)^(3/2)} dr
=∫(x^2+r^2)^(-3/2) dr^2
=∫(x^2+r^2)^(-3/2) d(x^2+r^2)
=(x^2+r^2)^(-3/2+1)/(-3/2+1)+C
=-2(x^2+r^2)^(-1/2)+C
=-2/√(x^2+r^2)+C

延伸阅读