Question

How do you evaluate this integral using integration by parts ?
∫In(x)^1/2

Answer 1

to clarify is that (ln(x))^(1/2) or ln(x^(1/2))?

Answer 2

i think its
\[\int\limits \ln (\sqrt{x}) dx\]because there is no closed form for
\[\int\limits \sqrt{\ln x} dx\]

Answer 3

@mukushla yeah thats the question

Answer 4

how would you solve it ?

Answer 5

better to write it in the form\[\int\limits \ln (\sqrt{x}) dx=\frac{1}{2} \int\limits \ln x dx\]

now for integration by parts let \(u=\ln x\) and \(dv=dx\)

Answer 6

oh Yeaahh I got the rest . thanks alot :)

Answer 7

very well........:)