Integral of sqrt(1+ln x)/(x*ln x), this is driving me nuts.

[DrummingAtom]

Homework Statement

Integral of sqrt(1+ln x)/(x*ln x)

Homework Equations

The Attempt at a Solution

I've tried substitutions and they seem to lead to nowhere. I need help getting started on this one. Thanks

 

[DrummingAtom]

Oooppss. I got it now, I had to double substitute.

 

[Dick]

Did you try u^2=log(x)+1? So log(x)=u^2-1.

 

[fzero]

Did you try y = ln x? That should give something that you can probably integrate by using hyperbolic functions.

 

[Apphysicist]

Oooppss. I got it now, I had to double substitute.

But...why?

u=lnx, du=1/x

thus sqrt(u)du/u= u^(-1/2)du...easy power rule, and that's only one sub...

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Edit: Thank you DrummingAtom for showing me an error, the likes I have made many a time.

 

[DrummingAtom]

But...why?

u=lnx, du=1/x

thus sqrt(u)du/u= u^(-1/2)du...easy power rule, and that's only one sub...

But where does the 1 go? The answer would then be 2sqrt(ln x) which doesn't equal the original function.

 

[Apphysicist]

But where does the 1 go? The answer would then be 2sqrt(ln x) which doesn't equal the original function.

Well you see, that would just be me neglecting the one to make it an easy question. xD

My bad.

 

[DrummingAtom]

=) no worries. This problem gave me about 1.5 hours of sloppy algebra and confusion. I love Sunday nights.