Question

Integral of sqrt(ln(9-x))/(sqrt(ln(9-x))+sqrt(ln(x+3)))?

Answer 1

no idea at all

Answer 2

Try a reduction using U-substitution and then compare with integration tables...

Answer 3

So far I have tried u-sub for
u=9-x, du=-dx
u=x+3, du=dx
u=ln(9-x), du=-1/(9-x)dx
u=ln(x+3), du=1/(x+3)dx
u=sqrt(u=ln(9-x)), du=-1/2(9-x)sqrt(ln(9-x))dx
u=sqrt(u=ln(x+3)), du=1/2(x+3)sqrt(ln(x+3))dx
u=sqrt(ln(9-x))+sqrt(ln(x+3)), du=...messy

So far no matches. We have only done basic integration formulas so far in my calc class, but I had a look at the tables and can't see any matches there either. Any ideas?

I found a hint that says to use change of variables x=6-t to rewrite as \[1-(\sqrt{\ln(x+3)}/(\sqrt{\ln(9-x)}+\sqrt{\ln(x+3)}))\]
but I have no idea how to make that happen!