> 数学 >
求定积分∫【5/0】{x^3/(x^2+1)}dx
人气:320 ℃ 时间:2020-04-09 04:32:12
解答
∫{x^3/(x^2+1)}dx
=(1/2)∫x^2/(x^2+1)d(x^2)
=(1/2)∫[1-1/(x^2+1)]d(x^2)
=(1/2)∫d(x^2)-(1/2)∫1/(x^2+1)d(x^2)
=x^2/2-(1/2)ln(1+x^2)+C
上限5、下限0代入:
原式=12.5-0.5ln26
推荐
猜你喜欢
© 2024 79432.Com All Rights Reserved.
电脑版|手机版