# How do you integrate #x( (x^2) +1 )^ (1/2)#?

##### 1 Answer

Aug 19, 2017

#### Explanation:

#intx(x^2+1)^(1/2)dx#

Let

We already have

#=1/2intunderbrace((x^2+1)^(1/2))_(u^(1/2))overbrace((2xcolor(white).dx))^(du)#

#=1/2intu^(1/2)du#

#=1/2u^(3/2)/(3/2)#

#=1/3u^(3/2)#

#=1/3(x^2+1)^(3/2)+C#