问个非常愚蠢的数学问题…………=_=

[*~Smartie_Coco~*]

what's the antiderivative of (x^3+1)/(x^2+3)
i'm very embarrassed to post this..cause it looks easy and i don't have a freaking clue how to do it........

 

[Sunnyboy]

sofa

 

[晨色]

最初由 *~Smartie_Coco~* 发布
what's the antiderivative of (x^3+1)/(x^2+3)
i'm very embarrassed to post this..cause it looks easy and i don't have a freaking clue how to do it........

3x^2/2x

 

[蓝离阵列]

x^2/2 + ArcTan[x/Sqrt[3]]/Sqrt[3] - (3*Log[3 + x^2])/2
dont think its that easy..

 

[mds]

=

 

[NAN_BO_ONE]

use long division,then do integral by parts.

 

[双鱼]

最初由 NAN_BO_ONE 发布
use long division,then do integral by parts.

呵呵

 

[*~Smartie_Coco~*]

我知道- (3*Log[3 + x^2])/2 和 x^2/2 是怎么来的……arctan 我就不会了
老师说要 intergration using substitution for 1/(x^2+3)....能不能详细地说明一下
谢谢大家了^__^

 

[*~Smartie_Coco~*]

我得出来的arctan 是:arctan(x/sqrt[3])/[3*sqrt(3)]

 

[uknowhat]

做代换u=x/sqrt(3)的时候, 你忘了du=d[x/sqrt(3)]=dx/sqrt(3)
==>dx=sqrt(3)du
唉

 

[uknowhat]

粗心呀

 

[卧虎藏龙]

up

 

[*~Smartie_Coco~*]

哦，明白了 那么说，应该是 arctan(x/sqrt[3])/[sqrt(3)/3]？？？？？？？？

 

[游樂場]

你读那科也有数学啊？

 

[easterngod]

正在复习partial integration中....郁闷