Question

Integrate sqrt(1+sqrt(x))/x

Answer 1

\[\huge \int \frac{\sqrt{1 + \sqrt x}}x\]
right?

Answer 2

yep

Answer 3

have you tried substitution?

Answer 4

I'm not sure what the best sub. option would be. I believe I've faced a similar problem, I just can't recall.....

Answer 5

let a = \(\sqrt x\)

square both sides\[a^2 = x\]
derive both sides
\[2ada = dx\]

so your integral will become \[\huge \int \frac{\sqrt{1 - a}}{a^2} (2ada)\]

Answer 6

try sqrt(1 + sqrt(x)) = y ... better.