Help with Calculus

[Maleficus]

I drew a picture (im no artist i just threw it together in paint) of the problem worked out according to my teacher. I cannot figure out where the 36 came from (circled in red) and where did the X^3 go also?

Calc

I'm sure its real easy and I am just being dumb but any help would be appreciated. Thanks

All you defenders of the derivative etc, etc, can come out and play now

 

[Random Variable]

let u =1+9x^4
therefore du =(36x^3)dx
du/36= x^3dx

2pi/36 *Integral u^(1/2)du
(2pi/36)*(2/3) *u^(3/2)
pi/27 * (1+9x^4)^(3/2) + C

 

[Random Variable]

You have to perform a substitution. In this case the substitution is for what's inside the square root,1+9x^4. So let 1+9x^4 equal u, which means that du = (36x^3)dx. If you then divide both sides of the equation by 36, you can cancel out the x^3 in the original integral. And you are left with 2pi/36*Integral u^(1/2)du, which equals (2pi/36)*(2/3)*u^(3/2). And then after reducing and plugging in 1+9x^4 for u, you have pi/27*(1+9x^4)^(3/2) + C.