Posted by Erica on .
Use substitution to evaluate the indefinite integral:
The integral of [ (sq. root (1 + ln x)) ((ln x)/x) dx]
Im confused on what i should substitute u and du for.
Thank you so much!!

Calc 
Steve,
Let u = 1+ln x
so,
du = 1/x dx
ln x = u1
So, we have
u^1/2 * (u1) du
= u^3/2  u^1/2 du
Integrate that to get
2/5 u^5/2  2/3 u^3/2
=
2/5 (1 + ln x)^5/2  2/3 (1+ln x)^3/2
Check your work by taking the derivative. Trust me  it comes out right.