Integrate sqrt(ln(x))

[Guest Julo]

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

[The Rebel]

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.

[bishnu]

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

[Dave]

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.

[kingjewel1]

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.