Hello, can someoneu help me with Integration of function f(x) = sqrt(ln(x)) or (ln(x))^(1/2) ...

Hello, can someoneu help me with Integration of function f(x) = sqrt(ln(x)) or (ln(x))^(1/2) ...

 

Hmmm tricky one ...

 

The only thing I can think of is to substitue the ln x such that x = e^v, which leads to int: v^2.e^v and finish off by using integration by parts.

 

Don't take my word for it though. I ain't tried it.

 

EDIT: should've read v^1/2.e^v but still not sure of this route.

mathematica spit out -1/2PiEr[sqrt[ln(X)]]+xsqrt[ln[x]] but i have no idea how you would get it...probably write an infinte series for it then intergrate it and try to realte them to some function

Error functions usually aren't good in results; usually it means that the function you're trying to integrate won't give a definite answer.

you can use the generic fomula for natural logarithm integration

LN(a•x)^p dx ⇒ x•LN(a•x)^1/2 - p• int LN(a•x)^-1/2 dx

 

that is the standard answer but as dave said it won't give you a definite answer.