Integrate (x^3 + 4x)/sqrt(x^2-4) dx

[anderma8]

I'm trying to integrate the following: int (x^3 + 4x)/sqrt(x^2-4) dx

I let u= x^2-4
so du/2 = xdx

granted, the above also gives me x^2=u+4 so, this gives me:

1/2 int u+8 u^-1/2 du

but the professor has:

1/2 int [u^1/2+8 u^-1/2] du

Did I miss the first u^1/2 somewhere? where did it come from?

 

[anderma8]

Never mind... I found my answer:

(u+8)u^-1/2= u^1/2 + 8u^-1/2


Sorry about that! I forgot the parenthesis!